The Economics of Protecting Tiger PopulationsLinking Household Behavior to Poachingand Prey DepletionRichard Damania Randy Stringer K Ullas Karanthand Brad Stith

ABSTRACT The tiger (Panthera tigris) is classi- ed as endangered and populations continue todecline This paper presents a formal economicanalysis of the two most imminent threats to thesurvival of wild tigers poaching tigers and hunt-ing their prey A model is developed to examineinteractions between tigers and farm householdsliving in and around tiger habitats The analysisextends the existing literature on tiger demogra-phy incorporating predator-prey interactionsand exploring the sensitivity of tiger populationsto key economic parameters The analysis aims tocontribute to policy debates on how best to pro-tect one of the worldrsquos most endangered wild cats(JEL Q22)

I INTRODUCTION

The earthrsquos remaining wild tiger (Pan-thera tigris) populations continue to shrinkand fragment under ever increasing human-related pressures Over time human activi-ties have reduced tiger habitats by more than90 As a consequence tigers now live inonly a small fraction of the potential habitatRecent estimates suggest that wild tigers in-habit less than 5 of the 15 million km2 offorest habitat available (Karanth 2001) Atpresent more tigers exist in captivity than inthe wild (Nowell and Jackson 1996)

The evidence to date indicates that wild ti-ger populations continue to decline despitesubstantial conservation efforts by interna-tional agencies local conservation groupsand governments (Seidensticker Christieand Jackson 1999) The IUCN identi es ti-gers in all the range countries as endangeredand the signatories to CITES have placed a

Land Economics May 2003 79 (2) 198ndash216ISSN 0023-7939 E-ISSN 1543-8325atilde 2003 by the Board of Regents of theUniversity of Wisconsin System

ban on all international trade in live tigersand tiger parts

Tigers need extensive areas to hunt andbreed thus protecting wild populations andsustaining their habitats present wildlifemanagers with a set of complex and dauntingtasks For instance tigers are large-bodiedobligate carnivores and readily come intocon ict with humans by killing livestockand occasionally people Tiger numbers aresensitive to the depletion of their prey causedby local hunting (Karanth and Stith 1999)The role tigers play as top predators is vitalto regulating and perpetuating ecologicalprocesses and systems (Sunquist Karanthand Sunquist 1999 Terborgh 1999) If eitherpredator or prey numbers decline entire eco-logical communities may become unstablewith more and more species being graduallylost

A further dif culty for conservation ef-forts is that wild tigers occur only in Asiawhere the high incidence of rural povertylarge numbers of livestock and high levels ofhuman population density and growth speedforest degradation Unlike much of Africaand Latin America the vast majority of for-

The authors are respectively senior lecturer Schoolof Economics Centre for International Economic Stud-ies University of Adelaide deputy director Centre forInternational Economic Studies School of EconomicsUniversity of Adelaide conservation scientist WildlifeConservation Society India Program and research sci-entist US Geological Survey Florida Caribbean Sci-ence Center Sirenia Project

The authors gratefully appreciate the assistance andsuggestions from Kym Anderson Edward Barbier Er-win Bulte Anthony Cheshire Jon D Harford JohnHatch Peter Jackson Suraj Saigal and two anonymousreferees Information provided by the Wildlife Trust ofIndia is gratefully acknowledged The authors alsothank Parvin Mahmoudi for research assistance

79(2) Damania et al The Economics of Protecting Tiger Populations 199

ests in Asia have already been converted toother land uses In countries like India forestboundaries appear to have stabilized and themajor conservation management problem ismost often related to how communities useforest resources within protected areas andpublic forests (Wells1992 Ghimire 1994Nepal and Weber 1995 Studsrod and Wegge1995 Gunatilake 1998 Gunatilake andChakravorty 2000 Kumar et al 2000 Leleet al 2000)

The proximate causes for the persistentdecline of wild tiger populations are manyPressures vary regionally and change overtime The numerous forces threatening the ti-gerrsquos survival include poaching prey deple-tion and habitat fragmentation due to landclearing livestock grazing weed infesta-tions fuelwood and fodder extraction smug-gling for the illegal timber trade and intru-sive infrastructure (World Bank 1996Siedensticker Christie and Jackson 1999)What the relative contributions of theseforces are to declining tiger populations andhow they interact are less well understoodTiger poaching which is driven by the de-mand for tiger products in the traditional Ori-ental medicine trade and prey depletioncaused by local hunting are considered to bethe most imminent threats to survival of thespecies in the short run In the early 1990swildlife authorities observed a dramatic esca-lation in the scale of poaching as tigers werekilled to satisfy the burgeoning demand fortiger bones and organs for traditional Orien-tal medicine (Meacham 1997)

The demographic consequences of de-clining tiger populations through poachingand prey depletion have been examined inprevious research (Kenney et al 1995 Kar-anth and Stith 1999) However no formalstudies have examined the fundamental eco-nomic causes driving wild tigers to extinc-tion This paper argues that a clearer under-standing of how biological factors interactwith economic forces is crucial for guidingpolicy choices aimed at sustaining viablehabitats and reversing the decline in wild ti-ger populations The work presented hererepresents a rst attempt to integrate eco-nomic incentives into a predator-prey modelof tiger ecology

The paper is organized as follows Section2 provides a brief description of the back-ground to the problem Section 3 outlines thebasic model describing the behavior of sub-sistence farmers and their interaction with ti-gers and their prey Section 4 presents astage-based demographic model of tiger pop-ulation growth dynamics Section 5 outlinesthe simulation results of alternative scenar-ios Section 6 concludes the paper

II BACKGROUND

The tiger once had a wide distributionstretching across Asia from Bali through In-dia to the Russian Far East and West AsiaHunting and habitat erosion have extermi-nated tigers through much of their previousrange Most reserves are isolated from eachother and contain less than 30 animals (Sie-densticker Christie and Jackson 1999) Ti-gers feed predominately on large ungulates(hoofed mammals such as deer pigs andwild cattle) They cannot survive if a habitatdoes not support suf cient densities of largeungulates To meet its basic nutritionalneeds an average tiger requires a minimumof 3000 kg of meat (or about 50 ungulates)per annum to survive (Sunquist Karanth andSunquist 1999) A tigress raising three cubsmay need twice that amount Like other bigcats tigers can crop only 10 of the avail-able prey biomass suggesting that approxi-mately 500 ungulates are required to supportone tiger in the wild (Karanth 2001)

Tigers require vast forest areas of reason-able quality in which to roam hunt andbreed Tiger densities vary across regions Inrelatively prey-rich forests such as IndiarsquosKanha Kaziranga and Nagarahole NationalParks densities can exceed 10ndash15 tigers per100 km2 (Karanth and Nichols 1998) In con-trast in areas where prey is less abundant andmore widely dispersed like the Russian FarEast tiger densities are considerably lowerless than 1ndash2 tigers per 100 km2 The centralmessage emerging from the biological stud-ies is that where prey is plentiful tigers sur-vive and may even endure limited poachingpressures

Conserving wild tiger populations re-quires protecting the quality of their habitat

200 Land Economics May 2003

as well as their prey base The forests thattigers and their prey inhabit provide a widerange of economic social and environmen-tal bene ts to people These bene ts contrib-ute greatly to human welfare but they arevalued differently by different people anddifferent groups Local national and interna-tional interests in tigers and their habitatsalso differ greatly across landscapes To gov-ernment policymakers tiger habitats are of-ten seen only for their ability to generateincome employment revenue and foreignexchange when converted to agriculture tim-ber mines or other development-oriented ac-tivities To a small proportion of the humansliving in and around the forests killing tigersfor their body parts yields a substantiallygreater income than live tigers roaming freeMany small-scale agricultural producersview tigers and their prey as pests that dam-age their livestock and crops

Various studies document the crop dam-age caused by large ungulates (Sekhar 1988World Bank 1996) Little quantitative infor-mation is available about two of the most im-minent threats to the survival of wild tigersthe poaching of tigers and poaching of theirprey Recent investigations suggest that thetrade in tiger parts is controlled by organizedcriminal groups involved in a host of otherillegal activities In contrast tiger poachingis undertaken by locals who have an intimateknowledge of the forests The evidence sug-gests that the illegal traders capture the bulkof the pro ts while poachers are paid lowprices for each tiger killed (Nowell 2000WPSI 2001)1

National governments tend to in uencecontrol over the choice of forest bene tsWhen traditional rights and access shift inways that adversely impact local communi-ties households may have little incentive touse natural resources and in particular pro-tect animals in a sustainable way (Barbier1992 Panayotou 1993 Gunatilake 19941998 Tisdell 1995 Shyamsundar andKramer 1996) For this reason providinggreater access and use of tiger habitats is of-ten argued as the appropriate response tomeet conservation objectives (Saberwal1996 Kothari Suri and Singh 1995)

India possesses the largest number of wild

tigers of any of the range states and has hada relatively successful history of tiger protec-tion (Nowell and Jackson 1996 Karanth2001) Its response to declining tiger popula-tions focuses on establishing special pro-tected reserves and on law enforcement2Although the appropriateness of policy mea-sures needed to halt or reverse declining tigerpopulations is still contested the overallmanagement approach has recently shiftedtowards a participatory style known as JointForest Management (JFM) at times drivenby external donor encouragement The extentto which JFM is adopted varies by state inIndia In most cases households living in ornear forests utilize timber and non timberforests resources for subsistence cash andwage incomes (drsquoSilva and Nagnath 2002)Through sharing products responsibilitiesand decision-making authority JFM ap-proaches seek to provide local communitieswith incentives to protect the forest resourcesthat provide their income base and futurewelfare

Some argue that JFM should also be ex-tended to reserves aimed at protecting wild-life (Kothari Suri and Singh 1995) Otherstudies raise important concerns about theappropriateness of JFM-style conservationand protection efforts (Gunatilake 1998Karanth and Stith 1999) For instance Bar-rett and Arcese (1995 1998) question the as-sumptions linking local communities andsustainable forest resource use across diversegeographic conditions and economic situa-tions Simpson (1995) suggests the need forgreater experimentation with direct-paymentfor conservation efforts rather than fundinguntested participatory projects based on rais-ing the value of forest products in ways thatmay fail to deliver improved conservationoutcomes This view nds support in Gunati-lakersquos (1998) analysis of Sri Lanka whichprovides evidence that policies aimed at re-ducing dependency on forest based resources

1 For instance Nowellrsquos (2000) study of the trade intiger parts suggests that the retail value of an adult maletiger varies from $15000ndash $20000 while the WildlifeProtection Society of India reports cases where poach-ers in the eld are paid $15ndash$20

2 The Indian Government introduced the Project Ti-ger program in 1973

79(2) Damania et al The Economics of Protecting Tiger Populations 201

can be a much more effective way to protectforests than policies aimed at using forest re-sources The issues concerning participatorymanagement addressed in these studies raiseimportant questions about the appropriate-ness of the widespread promotion of JFM inIndia for protecting tigers

The model and simulations presented hereexamine how the tigerrsquos biological needs in-teract with economics incentives facinghouseholds living in and around their habi-tats The analysis aims to contribute to thepolicy debate about how best to protect tigerpopulations

III THE MODEL

Most of Indiarsquos tiger habitats are in parksand protected areas that also support variousforms of land uses including agriculturelivestock grazing and fuelwood collection(Mishra 1997 Sekhar 1998) The intersper-sion of humans in and around these parksleads inevitably to con icts over resource use(Schultz and Skonhoft 1996) Two motivesfor local people hunting the tigerrsquos prey spe-cies are considered The rst is when thelarge ungulates cause damage to crops in ad-joining agricultural areas termed the lsquolsquonui-sance effectrsquorsquo by Marks (1984) The secondmotive arises from the incentive of subsis-tence producers to hunt ungulates as a sup-plementary food source On the other handthe incentive to hunt tigers is driven entirelyby the demand for tiger products

The context for this model is a wild tigerpopulation in an insular forest patch sur-rounded by agricultural landmdasha typical char-acteristic of tiger reserves on the Indian sub-continent We extend the most recent modelof tiger population dynamics developed byKaranth and Stith (1999) to include preda-tor-prey interactions The biological model isincorporated into a household productionmodel in which subsistence farmers hunt ti-gers and their prey

The model presented here is similar toBluffstonersquos (1995) analysis of fuelwood ex-traction by subsistence farmers in Nepal It ismore closely related to Barrett and Arcesersquos(1998) model of the hunting incentives forfarmers in an integrated conservation and de-

velopment project (ICDP) in Tanzania3 Thispaper extends this literature by incorporatingan economic model of poaching behaviorinto a multiple species predator-prey model

The Household Model

As noted earlier we consider a tiger re-serve that is surrounded by agricultural landThe production and consumption units arehouseholds engaged in four kinds of activi-ties agricultural production off-farm workhunting tigers and hunting herbivores (iethe tigerrsquos prey) Income from agriculturalproduction and off-farm work is used to pur-chase food and other commodities House-holds hunt prey animals as a supplementarysource of food and to protect crops fromdamage4 The incentive to poach tigers isdriven entirely by the illegal trade in tigerproducts that is controlled by criminal gangswho determine the price paid to farmers foreach tiger killed5 Since very little is knownabout the nature of such poaching we adoptfunctional forms with parsimonious data re-quirements There are N households in thearea surrounding the tiger reserve A Cobb-Douglas function is employed to representhousehold utility

U 5 aF log(F ) 1 azlog(Z) 1 axlog(hx) [1a]

3 Barrett and Arcesersquos (1998) work is of consider-able relevance for wildlife conservation policies Theauthors develop a bio-economic simulation model thatshows that ICDP programs may be time inconsistent ina stochastic environment

4 In contrast to conditions in Africa there appears tobe no substantial market for game meat on the Indiansubcontinentand limited demand for the hides of ungu-lates Thus we ignore the possibility that hunted preyare sold in open markets

5 Tigers that stray into agricultural lands and preyupon domestic livestock are often killed by farmersWhile this issue is clearly important we do not considersuch lsquolsquonuisancersquorsquo killing of tigers for two reasons Firstsuch kills appear to be concentrated on animals thatstray outside reserves while our attention is mainly fo-cused upon the condition of animals with home rangeswithin a reserve However the main reason we haveneglected this problem is that in the absence of suf -cient data there appears to be no obvious manner inwhich to parameterize the extent of nuisance killing inthe simulations presented in Section 5 This suggeststhat our results may underestimate the true impacts oftiger poaching

202 Land Economics May 2003

where F represents consumption of food Zconsumption of non-food items hx consump-tion of prey animals ai 0 (i 5 F Z x) arethe parameters of the utility function withaF 1 aZ 1 ax 5 1

Equation [1a] is maximized subject to theconstraints

wLo 1 pgG 1 (PT 2 qTWT)hT

5 pzZ 1 pFF 1 qxWxhx [1b]

G 5 kLbg(1 2 mX) [1c]

hx 5 dLxX [1d]

hT 5 LgT1T

R2e

[1e]

L 5 Lo 1 Lg 1 Lx 1 LT [1f]

where G is agricultural output X is the bio-mass of prey animals Lg is labor time de-voted to agriculture Lo is labor time devotedto off-farm work Lx is labor time spent hunt-ing prey animals LT is labor time on huntingtigers and pg pF pz PT are the prices of ag-ricultural produce food non-food commodi-ties and tigers respectively qi(i 5 T X) is theprobability of being convicted for poachingtigers (T) and their prey (X) and W i(i 5 TX) is the ne per unit harvest if convicted forpoaching tigers or their prey T is the numberof tigers and R the area of the reserve k xb g m d 0 are parameters

By equation [1a] household utility de-pends on the consumption of food (F ) othergoods (a non-food composite commodity[Z]) and the quantity of prey animalsconsumed (hx)

Equation [1b] is the household budgetconstraint Food and other goods are pur-chased at given prices pz and pF respectivelyThese purchases are nanced by (i) the saleof agricultural produce (G) which is sold ata price pg (ii) off farm labor (Lo) which isremunerated at a wage rate of w and (iii) ti-ger poaching (hT) The farmers receive anamount PT for each tiger killed which is de-termined by traders Since poaching is ille-gal it may result in conviction The expected

penalty for poaching tigers is qT WT whereqT is the probability of detection and convic-tion WT is the ne per tiger killed Thus theexpected payoffs from tiger poaching is de- ned by pT 5 (PT 2 qTWT) Finally sincepoaching prey is also illegal the householdmay incur an expected penalty qxWxhxwhere qx is the probability of detection andconviction Wx is the ne per prey animalpoached (hx)

Equation [1c] describes the agriculturalproduction function Following empiricalstudies on subsistence farming in India ag-ricultural production (G) is assumed to de-pend upon labor inputs (Lg) where b is theelasticity and ka constant (Deninger and Bis-wanger 1998 Saha 1994)6 The productionfunction also takes into account the damageto crops by the grazing and trampling of wildtiger prey This is given by (mX where X isthe biomass of prey animals and m is thedamage coef cient

Equation [1d] describes the prey harvestproduction function In the absence of dataon poaching of ungulate-prey in tiger habi-tats we adopt a functional form that hasbeen used in African studies of ungulatehunting (Kinyua van Kooten and Bulte2000) Thus the harvest of herbivores (hx) isa function of labor inputs (Lx) and the popu-lation of ungulate prey (X) with unit elastici-ties with respect to labor inputs and preypopulations

Equation [1e] is the tiger poaching pro-duction function There is no data availableon the nature of tiger poaching Hence anyfunctional form that is adopted is necessarilyconjectural Existing evidence suggests thattigers are usually killed by poisoning shoot-ing or setting traps and snares (WPSI 2001)techniques requiring only minimal invest-ment in capital equipment To economize onparameters we abstract from the need forcapital equipment and assume that the har-vest rate depends on the density of tigers and

6 The models used by Deninger and Biswanger(1999) and by Saha (1994) focus on agricultural house-holds While it is unclear how appropriate their models t the type of agriculture practiced in and around tigerhabitats in India the lack of better data limits our op-tions

79(2) Damania et al The Economics of Protecting Tiger Populations 203

the amount of search effort7 Tiger poachingis thus speci ed using a Cobb-Douglas func-tion with search effort and tiger densities asthe only arguments in the production func-tion The method by which the parameters onsearch effort (LT) and tiger density (TR) areestimated is described in the Data Appendix

Equation [1f ] is the time allocation con-straint which requires that labor time devotedto off-farm work (Lo) agriculture (Lg) andhunting tigers and their prey (LT Lx) mustequal the xed endowment of time (L) avail-able to the household Leisure is not includedas a choice variable as existing householdsurvey data in potential tiger habitats in Ne-pal suggest that opportunities for leisure con-sumption are limited in such poor ruralhouseholds (Bluffstone 1995)8

The utility maximization problem is basedon the notion that households take the timepath of exogenous variables such as thestock of herbivores (X) as given This re- ects the fact that there are assumed to bemany such households who have no propertyrights in wild animals Hence they have littleincentive to take account of the future conse-quences of their current actions Formallythis implies that households solve a static op-timisation problem Thus for notationalbrevity time symbols are suppressed in theabove equations9

Of particular interest in this context arethe solutions for poaching tigers and prey an-imals Solving the utility maximisation prob-lem in equations [1a]ndash[1f ] yields the follow-ing solution for the allocation of effortexpended on hunting tigers in each house-hold

LT 5 1gpTDe

w 21(12g)

[2a]

where pT 5 (PT 2 qTWT) is the net expectedpayoff from poaching a tiger D 5 TR is thedensity of tigers

Using [1e] the aggregate harvest of tigersis given by

HT NhT 5 N1gpTDe

w 2g12g

(D)e [2b]

The returns to off-farm work are exoge-nous and de ne the minimum payoffs to anyactivity that the household will accept Thusan increase in the wages paid for off-farmwork lowers poaching effort while an in-crease in the net expected payoffs frompoaching pT or an increase in the density oftigers D increases poaching effort

Labor time spent on hunting prey animalsis given by

Lc 5ax(w(L 2 Lg 2 LT) 1 pgG 1 pThT)

(w 1 qxWxdX)

[3a]

where

Lg 5 1 wbpgk(1 2 mX)2

1(b21)

[3b]

Substituting [3a] and [3b] in [1d] and aggre-gating over the N households gives the totallevel of prey animals hunted

Hx 5 NdLxX [3c]

The implicit price of hunting prey is againdetermined by the opportunity cost of timewhich is de ned by the off-farm wage rateThe hunted prey animals are consumedrather than sold hence an increase in thewage rate has con icting income and substi-tution effects on prey hunting levels (ie

7 Unlike many other species tigers are highly secre-tive animals inhabiting dense forests Therefore themain poaching constraint is likely to be the dif cultyinvolved in nding a tiger Field studies suggest that thelikelihood of an encounter depends on inter alia thedensity of tigers and the amount of search effort (Kar-anth and Nichols 2000)These key features are capturedin equation [1e]

8 Note also that since the analysis focuses on subsis-tence households with limited incomes we ignore thepossibility that households may hire labor In the ab-sence of adequate data we also ignore several othercomponents of agricultural household behavior includ-ing production and use of livestock (which may bepreyed upon by tigers) different types of farm outputconsumption of part of the farm output and the use ofother non-labor inputs (eg fertilizers)

9 It is perhaps worth noting that such myopic behav-iour has also been observed on communally held triballands where users own property rights to forest re-sources (Madhusudan and Karanth 1997)

204 Land Economics May 2003

paraHxparaw () 0) Speci cally the incomeeffect of higher wages increases the demandfor prey animals as a consumption goodwhile the substitution effect of higher off-farm wages raises the opportunity costs oftime devoted to hunting prey The net impactof higher off-farm wages therefore dependson the relative parameters of the model Incontrast an increase in the price of agricul-tural goods raises both income and the valueof crops damaged by prey This leads to in-creases in prey hunting levels (paraHxparapg 0)Similarly as expected a reduction in the ex-pected ne (qxWx) or an increase in the cropdamage coef cient (m) both lead to higherlevels of prey poaching (ie paraHxpara(qxWx) 0 paraHxparam 0)

This simple model of household behaviorignores a number of signi cant issues thatare of relevance in the context of wild animalpoaching in India10 For example anecdotalevidence suggests that corruption amongstforest of cials may be widespread in sometiger reserves in India (Breeden and Wright1996) This is perhaps a consequence of therelatively low wages that are paid to forestof cialsmdashoften in arrears In the absence ofdata on the incidence of corruption we donot explicitly deal with the modeling com-plications that arise when corruption ispervasive However it can be shown thatthe expected penalty for poaching in equa-tion [1b] is formally equivalent to the re-duced form payoff function that ariseswhen poachers bribe corrupt of cials11 Themodel also assumes that the probability ofconviction is xed In practice the proba-bility of a successful prosecution is likelyto depend on the level of expenditure bypoachers on their legal defense and the atti-tudes of local magistrates to wildlife pro-tection Moreover conviction rates andthe formal penalties for poaching may notcapture all the costs associated with beingdetected if caught poaching suggesting con-siderable uncertainty in the payoffs topoaching

IV TIGER BIOLOGY

The use of a single equation to model pop-ulation dynamics is often considered inap-

propriate for large predators that exhibitcomplex patterns of behaviour and face dif-ferent mortality rates over various stages intheir life cycle (see Burgman Ferson andAkcakaya 1993) Accordingly the existingliterature describes tiger population dy-namics using stage based stochastic demo-graphic models In this paper we follow thisconvention and extend the most recent modelof tiger demography by Karanth and Stith(1999) to incorporate predator-prey interac-tions

The Karanth-Stith model identi es tigersof both sexes in four distinct demographicstages cubs (younger than one year) juve-niles (one to two years) transients (tigersolder than two years in search of a homerange) and adults (breeding tigers with ahome range) In the absence of human pres-sures mortality rates at each stage of the lifecycle depend on intrinsic survival rateswhich incorporate deaths from natural fac-tors such as disease and intraspeci c compe-tition For expositional ease we begin bydescribing the dynamics of tiger populationswhen prey are plentiful and there is nopoaching

The number of cubs that survive in anyyear is determined by the birth rate of breed-ing females and the survival rate of cubs

Tct11 5 s cbTaf

t [4a]

where subscripts denote time periods Tct1 1 is

the number of surviving cubs in period t 11 s c is the survival rate of cubs b is the birth

10 We are grateful to a referee for suggesting theseissues

11 To see this suppose for simplicity that a fractionh of forest of cials are corruptible perhaps because ofthe low wages they receive The Indian forest serviceis a hierarchical organisation and the anecdotal accountsof corruption allege that bribery is most pervasiveamongst the lowestpaid of cials Let w be the probabil-ity that a poacher encounters a forest of cial Then cet-eris paribus the probability of being prosecuted isgiven by w(1 2 h) Furthermore if l is the probabilityof a successful conviction then q j 5 l jw j(1 2 h) ( j5 T X) is the total probability of being convicted forpoaching Damania (2002) assesses the complicationsthat arise in determining optimal environmental regula-tions under corruption We do not explore these impor-tant and complex issues in this paper

79(2) Damania et al The Economics of Protecting Tiger Populations 205

rate per breeding adult female and Taft is the

number of breeding adult females FollowingKaranth and Stith (1999) we assume anequal sex ratio at birth and mean litter size ofthree The birth rate b is treated as a Poissonvariable with a mean of three Randomnessis included in the model to capture demo-graphic stochasticity12

The surviving cubs move to the juvenilestage in the following period The number ofjuveniles who survive is

T jst11 5 s jsT cs

t (s 5 m f ) [4b]

where T jst1 1 is the number of surviving juve-

nile males (m) and females ( f ) in period t 11 s js(s 5 m f ) is the intrinsic survival rateof juvenile males (m) and females ( f )

At two years the surviving juveniles be-come transients Transients are de ned asadult tigers in search of home territories inwhich to hunt and breed If a vacant homerange is available a transient immediatelyoccupies the territory and is classi ed as abreeding adult Let Ks (s 5 m f ) denote themaximum number of territories available foradults of gender s 5 m f Let Tas

t be the num-ber of surviving adults of gender s 5 m fwith existing home ranges Then the numberof vacant territories available for the tran-sients to occupy is given by

V st11 5 Max(0 Ks 2 Tas

t )(s 5 m f ) [4c]

The number of transients in period (t 1 1) isde ned by (i) the number of transients whosurvive from the previous period (ii) juve-niles who progress to the transient stage (iii)minus the transients who nd home rangesand thus exit to the breeding adult stage

Ttst11 5 sts(s jsT js

t 1 Ttst ) 2 Vs

t11(s 5 m f ) [4d]

where Tt st1 1 is the number of surviving tran-

sients in period t 1 1 st s is the survival rateof transients of gender s 5 m f

Finally the number of breeding adults isgiven by the existing number of survivingadults and the new recruits to the category ofbreeding adult

T ast11 5 (s asTas

t 1 Vst11) [4e]

where s as is the survival rate of adults of gen-der s 5 m f The total population of non-cubtigers (T) is de ned to include the sum of ju-veniles transients and adults of both sexesThe model thus far assumes that prey areplentiful The only constraints on populationgrowth considered so far are the intrinsic sur-vival rates and the amount of territory avail-able to establish home ranges (ie Ks) Ifprey depletion lowers hunting success ratesit will lead to greater mortality of tigers Wetherefore extend the model to take account ofthe impact of prey availability on tiger popu-lation growth

Data on the intrinsic growth rates of indi-vidual prey species and the effects of browseand forage competition between species in ti-ger habitats is unavailable Hence we adopta simple approach and model the combinedbiomass of all prey species using a logisticequation of the form

Xt11 2 Xt 5 Xtr(1 2 XtX) 2 Hxt 2 Yt [5]

where Xt is the prey biomass at time t r is theintrinsic growth rate X is the prey carryingcapacity of the forest Hxt is the human har-vest of the prey biomass de ned in equation[3c] and Yt is the harvest of the prey by ti-gers which is described below

Field studies suggest that on average a ti-ger requires approximately 3000 kg of preyper year to survive (Sunquist Karanth andSunquist 1999) We therefore de ne the min-imum food intake of a tiger as M 5 3000kg Field observations also reveal that tigerssucceed in capturing between 10ndash20 ofthe available prey biomass in their homeranges (Schaller 1967 Sunquist 1981 John-singh 1983) In the presence of competingpredators such as wild dogs (Cuon alpinus)and leopards (Panthera pardus) a predationrate of 10 is deemed more appropriate(Karanth 2001) Thus the predation rate isde ned as r 5 010 It follows that the maxi-mum number of tigers that can be sustainedwith a prey base of Xt is rXtM Accord-

12 The random numbers were generated in Excel us-ing a random seed of 1 and mean of 3

206 Land Economics May 2003

ingly the prey biomass consumed by tigersis given by

Yt 5 MTt if rXt MTt

Yt 5 rXt otherwise [6a]

where Tt is the total number of tigers in pe-riod t M is the minimum food intake and ris the predation rate

Thus when prey are plentiful (ie rXt MTt) each tiger is able to meet its nutritionalneeds and successfully captures Mkg of preyper annum hence Yt 5 MTt On the otherhand if there is insuf cient prey to meet theneeds of the total population the level of pre-dation is at its maximum level Yt 5 rXt

A shortage of prey could have two effectson tiger survival prospects First prey deple-tion is likely to depress survival rates acrossall demographic stages Second a shortageof prey may also lower the carrying capacityof the habitat and thus lead to an expansionin the home ranges of breeding adult femalesIn the absence of data on the effects of preydepletion across demographic groups wefollow Karanth and Stith and assume thatprey depletion effects only (i) the carryingcapacity of the habitat and (ii) the survivalrates of cubs Thus under conditions of preydepletion the survival rates of cubs and thecarrying capacity are depressed by a preydepletion factor that is de ned as

h t11 5 51 if rXt 2 MTt $ 0

rXi

MTt

if rXt 2 MTt 0 [6b]

The cub survival rate (s c) and the carryingcapacity (Ks) are pre-multiplied by [6b]

It is acknowledged that the neglect of preydepletion effects on the survival rates acrossother demographic categories is unsatisfac-tory This approach can therefore be ex-pected to underestimate the true impact ofprey depletion if survival rates are depressedmore generally across all demographicstages However re nements of the modelmust await further research on this issue

Turning next to the effects of poachingPoachers target juveniles transients and

adults The number of tigers killed at eachstage is assumed to be proportional to the ex-isting distribution of tigers across the variousdemographic stages Let superscript i(i 5 jt a) denote demographic stages and recallthat superscript s 5 M F denotes genderDe ne k is

t as the proportion of male or femaletigers at demographic stage i(i 5 j t a) Thenthe numberofgenders tigers poachedatdemo-graphic stage i(i 5 j t a) is de ned as

HisTt11 5 HTtk is

t [6c]

where HTt is the total harvest of tigers as de-termined in equation [2b] k is

t 5 (T ist Tt) is

the proportion of gender s tigers at stagei(i 5 j t a) T is

t 5 number of gender s ti-gers at stage i and Tt is the total populationof tigers The number of tigers at each stageis thus lowered by the amount de ned inequation [6c]

V SIMULATION RESULTS

We now combine the economic models ofbehavior (equations [2b] and [3c]) and tigerpopulation growth (equations [4a]ndash[6c]) todetermine the time paths of lsquotiger stocksrsquo un-der alternative scenarios For given parame-ters the level of poaching emerges from theoptimising decisions of farmers and poach-ers This in turn affects tiger stock levelsModel parameters are varied to determinethe sensitivity of tiger population levels tochanges in economic circumstances

In the model labor is allocated across dif-ferent activities until the marginal returns areequalised The returns to off-farm work areexogenously xed and hence de ne the mini-mum payoffs to any activity that a householdwill accept The returns to agriculture varywith the price of agricultural commoditiesand the losses due to wildlife predation Thepayoffs to poaching also vary with wildlifestocks and the expected penalties for convic-tion It follows that changes in the returns toany one activity may induce a reallocation oflabor across other activities and thereforecould alter the level of poaching

The parameters for the basic tiger popula-tion model (equations [4a]ndash[4e]) are fromKaranth and Stith (1999) and are based on

79(2) Damania et al The Economics of Protecting Tiger Populations 207

eld research in India and Nepal Behavioraldata for subsistence farmers are drawn froma variety of sources13 The Data Appendixprovides details of the sources of informa-tion assumptions estimation methods andparameter values

The benchmark simulation draws on pa-rameter estimates based on the best availabledata for those regions with reasonablyhealthy tiger populations (eg the Kanha andBandipur Tiger Reserves in India) The habi-tat is assumed to comprise an area of approx-imately 1000 km2 with a prey carrying ca-pacity of 4500 kgkm214 It is supposed thatwhen prey are plentiful (rXt MTt) the un-disturbed habitat can sustain Kf 5 24 breed-ing adult females and Km 5 12 adult males(Karanth and Stith 1999 Kenney et al1995) In the base case farmers receive Rs1000 for each tiger killed face a ne of Rs25000 and a 2 probability of conviction(WPSI 2001)15 The off-farm wage rate is setat Rs 40 per day and the price of agriculturalproduce at Rs 85kg We begin by assuminga human population density of N 5 400households

It is important to distinguish between theecological effects and economic causes ofprey depletion from those of tiger poachingIn order to gain some understanding of theselinkages we begin by presenting simulationsfor the stylized case when only tiger poach-ing occurs We then assume that there is notiger poaching and consider the impact ofprey poaching on tiger populations Finallysimulations are presented for the completemodel where both tigers and their prey arehunted by subsistence farmers

Consider rst the effects of tiger poachingin isolation16 Curve A in Figure 1 shows thetiger population trajectory in a pristine habi-tat with no tiger poaching or prey depletionThe population achieves a stable equilibriumat 87 adult and juvenile tigers suggesting adensity of 9 tigers100 km2 This outcomeapproximates population levels in the frag-mented yet relatively healthy habitats foundin India and Nepal Curve B simulates the ef-fects of tiger poaching when the parametersare at the base case levels17 The tiger popula-tion declines to a stable 53 adult and juveniletigers with poachers harvesting 6 tigers per

year (approximately 11 percent of the popu-lation) Curve C simulates the effects of a50 increase in the price per tiger killed (Rs1500) The population falls substantially to27 tigers with 4 tigers harvested each year(approximately 12 of the population)

The simulation presented in Curve Dillus-trates the effects of an 80 increase in theprice paid to tiger poachers When the priceis increased to Rs 1800 the population de-clines to 19 tigers with 3 harvested each yearIn curve E when the poaching price is in-creased from Rs 1800 to Rs 1900 the tigerpopulation collapses within 50 years

This nding suggests that a relativelysmall increase in the payoffs to poaching(from Rs 1800 to Rs 1900) can drive a smallpopulation to extinction in a relatively shorttime period This is a signi cant resultwhich is consistent with Karanth and Stithrsquos(1999) simulations and related evidence thathunting of large felids can lead to sudden ex-tinction when it exceeds a certain thresholdlevel (Martin and de Meulanaer 1988 Bailey1993) The impact of poaching may thus bediscontinuous and prone to induce collapsesin populations This appears to be an exam-ple of the unstable equilibria frequently en-countered in discrete time predator-prey

13 Many of the tiger reserves are in tribal areas Itseems likely that behavior of tribal agriculturalistswould differ from those of other non-tribal agricultural-ists We have been compelled to use the only availabledata on agriculture which is based on non-tribal agri-culture There is clearly an urgent need for eldworkin and around tiger reserves to obtain more accurateinformation

14 The estimates of prey biomass in prime areas withtiger densities of between 10ndash12 per 100 km2 is derivedfrom data in Karanth and Nichols (2000) It is useful tonote that this estimate is also consistent with earlierstudies conducted using less advanced techniques Forinstance Johnsingh (1983) estimates a prey density of3382 kgkm2 in Bandipur reserve and a predation rateof 30 suggesting a possible carrying capacity of3382 (1 1 30) 5 4397 kgkm2

15 The assumption of a 2 conviction rate is a clearoverestimate of the true conviction probabilities ourbase case results thus underestimate the most likelyconsequence of poaching (WPSI 2001)

16 Formally this can be achieved by setting all thecoef cient of prey poaching to zero

17 In the base case farmers receive Rs 1000 for eachtiger killed face a ne of Rs 25000 and a 2 probabil-ity of conviction N is xed at 400 households

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

79(2) Damania et al The Economics of Protecting Tiger Populations 199

ests in Asia have already been converted toother land uses In countries like India forestboundaries appear to have stabilized and themajor conservation management problem ismost often related to how communities useforest resources within protected areas andpublic forests (Wells1992 Ghimire 1994Nepal and Weber 1995 Studsrod and Wegge1995 Gunatilake 1998 Gunatilake andChakravorty 2000 Kumar et al 2000 Leleet al 2000)

The proximate causes for the persistentdecline of wild tiger populations are manyPressures vary regionally and change overtime The numerous forces threatening the ti-gerrsquos survival include poaching prey deple-tion and habitat fragmentation due to landclearing livestock grazing weed infesta-tions fuelwood and fodder extraction smug-gling for the illegal timber trade and intru-sive infrastructure (World Bank 1996Siedensticker Christie and Jackson 1999)What the relative contributions of theseforces are to declining tiger populations andhow they interact are less well understoodTiger poaching which is driven by the de-mand for tiger products in the traditional Ori-ental medicine trade and prey depletioncaused by local hunting are considered to bethe most imminent threats to survival of thespecies in the short run In the early 1990swildlife authorities observed a dramatic esca-lation in the scale of poaching as tigers werekilled to satisfy the burgeoning demand fortiger bones and organs for traditional Orien-tal medicine (Meacham 1997)

The demographic consequences of de-clining tiger populations through poachingand prey depletion have been examined inprevious research (Kenney et al 1995 Kar-anth and Stith 1999) However no formalstudies have examined the fundamental eco-nomic causes driving wild tigers to extinc-tion This paper argues that a clearer under-standing of how biological factors interactwith economic forces is crucial for guidingpolicy choices aimed at sustaining viablehabitats and reversing the decline in wild ti-ger populations The work presented hererepresents a rst attempt to integrate eco-nomic incentives into a predator-prey modelof tiger ecology

The paper is organized as follows Section2 provides a brief description of the back-ground to the problem Section 3 outlines thebasic model describing the behavior of sub-sistence farmers and their interaction with ti-gers and their prey Section 4 presents astage-based demographic model of tiger pop-ulation growth dynamics Section 5 outlinesthe simulation results of alternative scenar-ios Section 6 concludes the paper

II BACKGROUND

The tiger once had a wide distributionstretching across Asia from Bali through In-dia to the Russian Far East and West AsiaHunting and habitat erosion have extermi-nated tigers through much of their previousrange Most reserves are isolated from eachother and contain less than 30 animals (Sie-densticker Christie and Jackson 1999) Ti-gers feed predominately on large ungulates(hoofed mammals such as deer pigs andwild cattle) They cannot survive if a habitatdoes not support suf cient densities of largeungulates To meet its basic nutritionalneeds an average tiger requires a minimumof 3000 kg of meat (or about 50 ungulates)per annum to survive (Sunquist Karanth andSunquist 1999) A tigress raising three cubsmay need twice that amount Like other bigcats tigers can crop only 10 of the avail-able prey biomass suggesting that approxi-mately 500 ungulates are required to supportone tiger in the wild (Karanth 2001)

Tigers require vast forest areas of reason-able quality in which to roam hunt andbreed Tiger densities vary across regions Inrelatively prey-rich forests such as IndiarsquosKanha Kaziranga and Nagarahole NationalParks densities can exceed 10ndash15 tigers per100 km2 (Karanth and Nichols 1998) In con-trast in areas where prey is less abundant andmore widely dispersed like the Russian FarEast tiger densities are considerably lowerless than 1ndash2 tigers per 100 km2 The centralmessage emerging from the biological stud-ies is that where prey is plentiful tigers sur-vive and may even endure limited poachingpressures

Conserving wild tiger populations re-quires protecting the quality of their habitat

200 Land Economics May 2003

as well as their prey base The forests thattigers and their prey inhabit provide a widerange of economic social and environmen-tal bene ts to people These bene ts contrib-ute greatly to human welfare but they arevalued differently by different people anddifferent groups Local national and interna-tional interests in tigers and their habitatsalso differ greatly across landscapes To gov-ernment policymakers tiger habitats are of-ten seen only for their ability to generateincome employment revenue and foreignexchange when converted to agriculture tim-ber mines or other development-oriented ac-tivities To a small proportion of the humansliving in and around the forests killing tigersfor their body parts yields a substantiallygreater income than live tigers roaming freeMany small-scale agricultural producersview tigers and their prey as pests that dam-age their livestock and crops

Various studies document the crop dam-age caused by large ungulates (Sekhar 1988World Bank 1996) Little quantitative infor-mation is available about two of the most im-minent threats to the survival of wild tigersthe poaching of tigers and poaching of theirprey Recent investigations suggest that thetrade in tiger parts is controlled by organizedcriminal groups involved in a host of otherillegal activities In contrast tiger poachingis undertaken by locals who have an intimateknowledge of the forests The evidence sug-gests that the illegal traders capture the bulkof the pro ts while poachers are paid lowprices for each tiger killed (Nowell 2000WPSI 2001)1

National governments tend to in uencecontrol over the choice of forest bene tsWhen traditional rights and access shift inways that adversely impact local communi-ties households may have little incentive touse natural resources and in particular pro-tect animals in a sustainable way (Barbier1992 Panayotou 1993 Gunatilake 19941998 Tisdell 1995 Shyamsundar andKramer 1996) For this reason providinggreater access and use of tiger habitats is of-ten argued as the appropriate response tomeet conservation objectives (Saberwal1996 Kothari Suri and Singh 1995)

India possesses the largest number of wild

tigers of any of the range states and has hada relatively successful history of tiger protec-tion (Nowell and Jackson 1996 Karanth2001) Its response to declining tiger popula-tions focuses on establishing special pro-tected reserves and on law enforcement2Although the appropriateness of policy mea-sures needed to halt or reverse declining tigerpopulations is still contested the overallmanagement approach has recently shiftedtowards a participatory style known as JointForest Management (JFM) at times drivenby external donor encouragement The extentto which JFM is adopted varies by state inIndia In most cases households living in ornear forests utilize timber and non timberforests resources for subsistence cash andwage incomes (drsquoSilva and Nagnath 2002)Through sharing products responsibilitiesand decision-making authority JFM ap-proaches seek to provide local communitieswith incentives to protect the forest resourcesthat provide their income base and futurewelfare

Some argue that JFM should also be ex-tended to reserves aimed at protecting wild-life (Kothari Suri and Singh 1995) Otherstudies raise important concerns about theappropriateness of JFM-style conservationand protection efforts (Gunatilake 1998Karanth and Stith 1999) For instance Bar-rett and Arcese (1995 1998) question the as-sumptions linking local communities andsustainable forest resource use across diversegeographic conditions and economic situa-tions Simpson (1995) suggests the need forgreater experimentation with direct-paymentfor conservation efforts rather than fundinguntested participatory projects based on rais-ing the value of forest products in ways thatmay fail to deliver improved conservationoutcomes This view nds support in Gunati-lakersquos (1998) analysis of Sri Lanka whichprovides evidence that policies aimed at re-ducing dependency on forest based resources

1 For instance Nowellrsquos (2000) study of the trade intiger parts suggests that the retail value of an adult maletiger varies from $15000ndash $20000 while the WildlifeProtection Society of India reports cases where poach-ers in the eld are paid $15ndash$20

2 The Indian Government introduced the Project Ti-ger program in 1973

79(2) Damania et al The Economics of Protecting Tiger Populations 201

can be a much more effective way to protectforests than policies aimed at using forest re-sources The issues concerning participatorymanagement addressed in these studies raiseimportant questions about the appropriate-ness of the widespread promotion of JFM inIndia for protecting tigers

The model and simulations presented hereexamine how the tigerrsquos biological needs in-teract with economics incentives facinghouseholds living in and around their habi-tats The analysis aims to contribute to thepolicy debate about how best to protect tigerpopulations

III THE MODEL

Most of Indiarsquos tiger habitats are in parksand protected areas that also support variousforms of land uses including agriculturelivestock grazing and fuelwood collection(Mishra 1997 Sekhar 1998) The intersper-sion of humans in and around these parksleads inevitably to con icts over resource use(Schultz and Skonhoft 1996) Two motivesfor local people hunting the tigerrsquos prey spe-cies are considered The rst is when thelarge ungulates cause damage to crops in ad-joining agricultural areas termed the lsquolsquonui-sance effectrsquorsquo by Marks (1984) The secondmotive arises from the incentive of subsis-tence producers to hunt ungulates as a sup-plementary food source On the other handthe incentive to hunt tigers is driven entirelyby the demand for tiger products

The context for this model is a wild tigerpopulation in an insular forest patch sur-rounded by agricultural landmdasha typical char-acteristic of tiger reserves on the Indian sub-continent We extend the most recent modelof tiger population dynamics developed byKaranth and Stith (1999) to include preda-tor-prey interactions The biological model isincorporated into a household productionmodel in which subsistence farmers hunt ti-gers and their prey

The model presented here is similar toBluffstonersquos (1995) analysis of fuelwood ex-traction by subsistence farmers in Nepal It ismore closely related to Barrett and Arcesersquos(1998) model of the hunting incentives forfarmers in an integrated conservation and de-

velopment project (ICDP) in Tanzania3 Thispaper extends this literature by incorporatingan economic model of poaching behaviorinto a multiple species predator-prey model

The Household Model

As noted earlier we consider a tiger re-serve that is surrounded by agricultural landThe production and consumption units arehouseholds engaged in four kinds of activi-ties agricultural production off-farm workhunting tigers and hunting herbivores (iethe tigerrsquos prey) Income from agriculturalproduction and off-farm work is used to pur-chase food and other commodities House-holds hunt prey animals as a supplementarysource of food and to protect crops fromdamage4 The incentive to poach tigers isdriven entirely by the illegal trade in tigerproducts that is controlled by criminal gangswho determine the price paid to farmers foreach tiger killed5 Since very little is knownabout the nature of such poaching we adoptfunctional forms with parsimonious data re-quirements There are N households in thearea surrounding the tiger reserve A Cobb-Douglas function is employed to representhousehold utility

U 5 aF log(F ) 1 azlog(Z) 1 axlog(hx) [1a]

3 Barrett and Arcesersquos (1998) work is of consider-able relevance for wildlife conservation policies Theauthors develop a bio-economic simulation model thatshows that ICDP programs may be time inconsistent ina stochastic environment

4 In contrast to conditions in Africa there appears tobe no substantial market for game meat on the Indiansubcontinentand limited demand for the hides of ungu-lates Thus we ignore the possibility that hunted preyare sold in open markets

5 Tigers that stray into agricultural lands and preyupon domestic livestock are often killed by farmersWhile this issue is clearly important we do not considersuch lsquolsquonuisancersquorsquo killing of tigers for two reasons Firstsuch kills appear to be concentrated on animals thatstray outside reserves while our attention is mainly fo-cused upon the condition of animals with home rangeswithin a reserve However the main reason we haveneglected this problem is that in the absence of suf -cient data there appears to be no obvious manner inwhich to parameterize the extent of nuisance killing inthe simulations presented in Section 5 This suggeststhat our results may underestimate the true impacts oftiger poaching

202 Land Economics May 2003

where F represents consumption of food Zconsumption of non-food items hx consump-tion of prey animals ai 0 (i 5 F Z x) arethe parameters of the utility function withaF 1 aZ 1 ax 5 1

Equation [1a] is maximized subject to theconstraints

wLo 1 pgG 1 (PT 2 qTWT)hT

5 pzZ 1 pFF 1 qxWxhx [1b]

G 5 kLbg(1 2 mX) [1c]

hx 5 dLxX [1d]

hT 5 LgT1T

R2e

[1e]

L 5 Lo 1 Lg 1 Lx 1 LT [1f]

where G is agricultural output X is the bio-mass of prey animals Lg is labor time de-voted to agriculture Lo is labor time devotedto off-farm work Lx is labor time spent hunt-ing prey animals LT is labor time on huntingtigers and pg pF pz PT are the prices of ag-ricultural produce food non-food commodi-ties and tigers respectively qi(i 5 T X) is theprobability of being convicted for poachingtigers (T) and their prey (X) and W i(i 5 TX) is the ne per unit harvest if convicted forpoaching tigers or their prey T is the numberof tigers and R the area of the reserve k xb g m d 0 are parameters

By equation [1a] household utility de-pends on the consumption of food (F ) othergoods (a non-food composite commodity[Z]) and the quantity of prey animalsconsumed (hx)

Equation [1b] is the household budgetconstraint Food and other goods are pur-chased at given prices pz and pF respectivelyThese purchases are nanced by (i) the saleof agricultural produce (G) which is sold ata price pg (ii) off farm labor (Lo) which isremunerated at a wage rate of w and (iii) ti-ger poaching (hT) The farmers receive anamount PT for each tiger killed which is de-termined by traders Since poaching is ille-gal it may result in conviction The expected

penalty for poaching tigers is qT WT whereqT is the probability of detection and convic-tion WT is the ne per tiger killed Thus theexpected payoffs from tiger poaching is de- ned by pT 5 (PT 2 qTWT) Finally sincepoaching prey is also illegal the householdmay incur an expected penalty qxWxhxwhere qx is the probability of detection andconviction Wx is the ne per prey animalpoached (hx)

Equation [1c] describes the agriculturalproduction function Following empiricalstudies on subsistence farming in India ag-ricultural production (G) is assumed to de-pend upon labor inputs (Lg) where b is theelasticity and ka constant (Deninger and Bis-wanger 1998 Saha 1994)6 The productionfunction also takes into account the damageto crops by the grazing and trampling of wildtiger prey This is given by (mX where X isthe biomass of prey animals and m is thedamage coef cient

Equation [1d] describes the prey harvestproduction function In the absence of dataon poaching of ungulate-prey in tiger habi-tats we adopt a functional form that hasbeen used in African studies of ungulatehunting (Kinyua van Kooten and Bulte2000) Thus the harvest of herbivores (hx) isa function of labor inputs (Lx) and the popu-lation of ungulate prey (X) with unit elastici-ties with respect to labor inputs and preypopulations

Equation [1e] is the tiger poaching pro-duction function There is no data availableon the nature of tiger poaching Hence anyfunctional form that is adopted is necessarilyconjectural Existing evidence suggests thattigers are usually killed by poisoning shoot-ing or setting traps and snares (WPSI 2001)techniques requiring only minimal invest-ment in capital equipment To economize onparameters we abstract from the need forcapital equipment and assume that the har-vest rate depends on the density of tigers and

6 The models used by Deninger and Biswanger(1999) and by Saha (1994) focus on agricultural house-holds While it is unclear how appropriate their models t the type of agriculture practiced in and around tigerhabitats in India the lack of better data limits our op-tions

79(2) Damania et al The Economics of Protecting Tiger Populations 203

the amount of search effort7 Tiger poachingis thus speci ed using a Cobb-Douglas func-tion with search effort and tiger densities asthe only arguments in the production func-tion The method by which the parameters onsearch effort (LT) and tiger density (TR) areestimated is described in the Data Appendix

Equation [1f ] is the time allocation con-straint which requires that labor time devotedto off-farm work (Lo) agriculture (Lg) andhunting tigers and their prey (LT Lx) mustequal the xed endowment of time (L) avail-able to the household Leisure is not includedas a choice variable as existing householdsurvey data in potential tiger habitats in Ne-pal suggest that opportunities for leisure con-sumption are limited in such poor ruralhouseholds (Bluffstone 1995)8

The utility maximization problem is basedon the notion that households take the timepath of exogenous variables such as thestock of herbivores (X) as given This re- ects the fact that there are assumed to bemany such households who have no propertyrights in wild animals Hence they have littleincentive to take account of the future conse-quences of their current actions Formallythis implies that households solve a static op-timisation problem Thus for notationalbrevity time symbols are suppressed in theabove equations9

Of particular interest in this context arethe solutions for poaching tigers and prey an-imals Solving the utility maximisation prob-lem in equations [1a]ndash[1f ] yields the follow-ing solution for the allocation of effortexpended on hunting tigers in each house-hold

LT 5 1gpTDe

w 21(12g)

[2a]

where pT 5 (PT 2 qTWT) is the net expectedpayoff from poaching a tiger D 5 TR is thedensity of tigers

Using [1e] the aggregate harvest of tigersis given by

HT NhT 5 N1gpTDe

w 2g12g

(D)e [2b]

The returns to off-farm work are exoge-nous and de ne the minimum payoffs to anyactivity that the household will accept Thusan increase in the wages paid for off-farmwork lowers poaching effort while an in-crease in the net expected payoffs frompoaching pT or an increase in the density oftigers D increases poaching effort

Labor time spent on hunting prey animalsis given by

Lc 5ax(w(L 2 Lg 2 LT) 1 pgG 1 pThT)

(w 1 qxWxdX)

[3a]

where

Lg 5 1 wbpgk(1 2 mX)2

1(b21)

[3b]

Substituting [3a] and [3b] in [1d] and aggre-gating over the N households gives the totallevel of prey animals hunted

Hx 5 NdLxX [3c]

The implicit price of hunting prey is againdetermined by the opportunity cost of timewhich is de ned by the off-farm wage rateThe hunted prey animals are consumedrather than sold hence an increase in thewage rate has con icting income and substi-tution effects on prey hunting levels (ie

7 Unlike many other species tigers are highly secre-tive animals inhabiting dense forests Therefore themain poaching constraint is likely to be the dif cultyinvolved in nding a tiger Field studies suggest that thelikelihood of an encounter depends on inter alia thedensity of tigers and the amount of search effort (Kar-anth and Nichols 2000)These key features are capturedin equation [1e]

8 Note also that since the analysis focuses on subsis-tence households with limited incomes we ignore thepossibility that households may hire labor In the ab-sence of adequate data we also ignore several othercomponents of agricultural household behavior includ-ing production and use of livestock (which may bepreyed upon by tigers) different types of farm outputconsumption of part of the farm output and the use ofother non-labor inputs (eg fertilizers)

9 It is perhaps worth noting that such myopic behav-iour has also been observed on communally held triballands where users own property rights to forest re-sources (Madhusudan and Karanth 1997)

204 Land Economics May 2003

paraHxparaw () 0) Speci cally the incomeeffect of higher wages increases the demandfor prey animals as a consumption goodwhile the substitution effect of higher off-farm wages raises the opportunity costs oftime devoted to hunting prey The net impactof higher off-farm wages therefore dependson the relative parameters of the model Incontrast an increase in the price of agricul-tural goods raises both income and the valueof crops damaged by prey This leads to in-creases in prey hunting levels (paraHxparapg 0)Similarly as expected a reduction in the ex-pected ne (qxWx) or an increase in the cropdamage coef cient (m) both lead to higherlevels of prey poaching (ie paraHxpara(qxWx) 0 paraHxparam 0)

This simple model of household behaviorignores a number of signi cant issues thatare of relevance in the context of wild animalpoaching in India10 For example anecdotalevidence suggests that corruption amongstforest of cials may be widespread in sometiger reserves in India (Breeden and Wright1996) This is perhaps a consequence of therelatively low wages that are paid to forestof cialsmdashoften in arrears In the absence ofdata on the incidence of corruption we donot explicitly deal with the modeling com-plications that arise when corruption ispervasive However it can be shown thatthe expected penalty for poaching in equa-tion [1b] is formally equivalent to the re-duced form payoff function that ariseswhen poachers bribe corrupt of cials11 Themodel also assumes that the probability ofconviction is xed In practice the proba-bility of a successful prosecution is likelyto depend on the level of expenditure bypoachers on their legal defense and the atti-tudes of local magistrates to wildlife pro-tection Moreover conviction rates andthe formal penalties for poaching may notcapture all the costs associated with beingdetected if caught poaching suggesting con-siderable uncertainty in the payoffs topoaching

IV TIGER BIOLOGY

The use of a single equation to model pop-ulation dynamics is often considered inap-

propriate for large predators that exhibitcomplex patterns of behaviour and face dif-ferent mortality rates over various stages intheir life cycle (see Burgman Ferson andAkcakaya 1993) Accordingly the existingliterature describes tiger population dy-namics using stage based stochastic demo-graphic models In this paper we follow thisconvention and extend the most recent modelof tiger demography by Karanth and Stith(1999) to incorporate predator-prey interac-tions

The Karanth-Stith model identi es tigersof both sexes in four distinct demographicstages cubs (younger than one year) juve-niles (one to two years) transients (tigersolder than two years in search of a homerange) and adults (breeding tigers with ahome range) In the absence of human pres-sures mortality rates at each stage of the lifecycle depend on intrinsic survival rateswhich incorporate deaths from natural fac-tors such as disease and intraspeci c compe-tition For expositional ease we begin bydescribing the dynamics of tiger populationswhen prey are plentiful and there is nopoaching

The number of cubs that survive in anyyear is determined by the birth rate of breed-ing females and the survival rate of cubs

Tct11 5 s cbTaf

t [4a]

where subscripts denote time periods Tct1 1 is

the number of surviving cubs in period t 11 s c is the survival rate of cubs b is the birth

10 We are grateful to a referee for suggesting theseissues

11 To see this suppose for simplicity that a fractionh of forest of cials are corruptible perhaps because ofthe low wages they receive The Indian forest serviceis a hierarchical organisation and the anecdotal accountsof corruption allege that bribery is most pervasiveamongst the lowestpaid of cials Let w be the probabil-ity that a poacher encounters a forest of cial Then cet-eris paribus the probability of being prosecuted isgiven by w(1 2 h) Furthermore if l is the probabilityof a successful conviction then q j 5 l jw j(1 2 h) ( j5 T X) is the total probability of being convicted forpoaching Damania (2002) assesses the complicationsthat arise in determining optimal environmental regula-tions under corruption We do not explore these impor-tant and complex issues in this paper

79(2) Damania et al The Economics of Protecting Tiger Populations 205

rate per breeding adult female and Taft is the

number of breeding adult females FollowingKaranth and Stith (1999) we assume anequal sex ratio at birth and mean litter size ofthree The birth rate b is treated as a Poissonvariable with a mean of three Randomnessis included in the model to capture demo-graphic stochasticity12

The surviving cubs move to the juvenilestage in the following period The number ofjuveniles who survive is

T jst11 5 s jsT cs

t (s 5 m f ) [4b]

where T jst1 1 is the number of surviving juve-

nile males (m) and females ( f ) in period t 11 s js(s 5 m f ) is the intrinsic survival rateof juvenile males (m) and females ( f )

At two years the surviving juveniles be-come transients Transients are de ned asadult tigers in search of home territories inwhich to hunt and breed If a vacant homerange is available a transient immediatelyoccupies the territory and is classi ed as abreeding adult Let Ks (s 5 m f ) denote themaximum number of territories available foradults of gender s 5 m f Let Tas

t be the num-ber of surviving adults of gender s 5 m fwith existing home ranges Then the numberof vacant territories available for the tran-sients to occupy is given by

V st11 5 Max(0 Ks 2 Tas

t )(s 5 m f ) [4c]

The number of transients in period (t 1 1) isde ned by (i) the number of transients whosurvive from the previous period (ii) juve-niles who progress to the transient stage (iii)minus the transients who nd home rangesand thus exit to the breeding adult stage

Ttst11 5 sts(s jsT js

t 1 Ttst ) 2 Vs

t11(s 5 m f ) [4d]

where Tt st1 1 is the number of surviving tran-

sients in period t 1 1 st s is the survival rateof transients of gender s 5 m f

Finally the number of breeding adults isgiven by the existing number of survivingadults and the new recruits to the category ofbreeding adult

T ast11 5 (s asTas

t 1 Vst11) [4e]

where s as is the survival rate of adults of gen-der s 5 m f The total population of non-cubtigers (T) is de ned to include the sum of ju-veniles transients and adults of both sexesThe model thus far assumes that prey areplentiful The only constraints on populationgrowth considered so far are the intrinsic sur-vival rates and the amount of territory avail-able to establish home ranges (ie Ks) Ifprey depletion lowers hunting success ratesit will lead to greater mortality of tigers Wetherefore extend the model to take account ofthe impact of prey availability on tiger popu-lation growth

Data on the intrinsic growth rates of indi-vidual prey species and the effects of browseand forage competition between species in ti-ger habitats is unavailable Hence we adopta simple approach and model the combinedbiomass of all prey species using a logisticequation of the form

Xt11 2 Xt 5 Xtr(1 2 XtX) 2 Hxt 2 Yt [5]

where Xt is the prey biomass at time t r is theintrinsic growth rate X is the prey carryingcapacity of the forest Hxt is the human har-vest of the prey biomass de ned in equation[3c] and Yt is the harvest of the prey by ti-gers which is described below

Field studies suggest that on average a ti-ger requires approximately 3000 kg of preyper year to survive (Sunquist Karanth andSunquist 1999) We therefore de ne the min-imum food intake of a tiger as M 5 3000kg Field observations also reveal that tigerssucceed in capturing between 10ndash20 ofthe available prey biomass in their homeranges (Schaller 1967 Sunquist 1981 John-singh 1983) In the presence of competingpredators such as wild dogs (Cuon alpinus)and leopards (Panthera pardus) a predationrate of 10 is deemed more appropriate(Karanth 2001) Thus the predation rate isde ned as r 5 010 It follows that the maxi-mum number of tigers that can be sustainedwith a prey base of Xt is rXtM Accord-

12 The random numbers were generated in Excel us-ing a random seed of 1 and mean of 3

206 Land Economics May 2003

ingly the prey biomass consumed by tigersis given by

Yt 5 MTt if rXt MTt

Yt 5 rXt otherwise [6a]

where Tt is the total number of tigers in pe-riod t M is the minimum food intake and ris the predation rate

Thus when prey are plentiful (ie rXt MTt) each tiger is able to meet its nutritionalneeds and successfully captures Mkg of preyper annum hence Yt 5 MTt On the otherhand if there is insuf cient prey to meet theneeds of the total population the level of pre-dation is at its maximum level Yt 5 rXt

A shortage of prey could have two effectson tiger survival prospects First prey deple-tion is likely to depress survival rates acrossall demographic stages Second a shortageof prey may also lower the carrying capacityof the habitat and thus lead to an expansionin the home ranges of breeding adult femalesIn the absence of data on the effects of preydepletion across demographic groups wefollow Karanth and Stith and assume thatprey depletion effects only (i) the carryingcapacity of the habitat and (ii) the survivalrates of cubs Thus under conditions of preydepletion the survival rates of cubs and thecarrying capacity are depressed by a preydepletion factor that is de ned as

h t11 5 51 if rXt 2 MTt $ 0

rXi

MTt

if rXt 2 MTt 0 [6b]

The cub survival rate (s c) and the carryingcapacity (Ks) are pre-multiplied by [6b]

It is acknowledged that the neglect of preydepletion effects on the survival rates acrossother demographic categories is unsatisfac-tory This approach can therefore be ex-pected to underestimate the true impact ofprey depletion if survival rates are depressedmore generally across all demographicstages However re nements of the modelmust await further research on this issue

Turning next to the effects of poachingPoachers target juveniles transients and

adults The number of tigers killed at eachstage is assumed to be proportional to the ex-isting distribution of tigers across the variousdemographic stages Let superscript i(i 5 jt a) denote demographic stages and recallthat superscript s 5 M F denotes genderDe ne k is

t as the proportion of male or femaletigers at demographic stage i(i 5 j t a) Thenthe numberofgenders tigers poachedatdemo-graphic stage i(i 5 j t a) is de ned as

HisTt11 5 HTtk is

t [6c]

where HTt is the total harvest of tigers as de-termined in equation [2b] k is

t 5 (T ist Tt) is

the proportion of gender s tigers at stagei(i 5 j t a) T is

t 5 number of gender s ti-gers at stage i and Tt is the total populationof tigers The number of tigers at each stageis thus lowered by the amount de ned inequation [6c]

V SIMULATION RESULTS

We now combine the economic models ofbehavior (equations [2b] and [3c]) and tigerpopulation growth (equations [4a]ndash[6c]) todetermine the time paths of lsquotiger stocksrsquo un-der alternative scenarios For given parame-ters the level of poaching emerges from theoptimising decisions of farmers and poach-ers This in turn affects tiger stock levelsModel parameters are varied to determinethe sensitivity of tiger population levels tochanges in economic circumstances

In the model labor is allocated across dif-ferent activities until the marginal returns areequalised The returns to off-farm work areexogenously xed and hence de ne the mini-mum payoffs to any activity that a householdwill accept The returns to agriculture varywith the price of agricultural commoditiesand the losses due to wildlife predation Thepayoffs to poaching also vary with wildlifestocks and the expected penalties for convic-tion It follows that changes in the returns toany one activity may induce a reallocation oflabor across other activities and thereforecould alter the level of poaching

The parameters for the basic tiger popula-tion model (equations [4a]ndash[4e]) are fromKaranth and Stith (1999) and are based on

79(2) Damania et al The Economics of Protecting Tiger Populations 207

eld research in India and Nepal Behavioraldata for subsistence farmers are drawn froma variety of sources13 The Data Appendixprovides details of the sources of informa-tion assumptions estimation methods andparameter values

The benchmark simulation draws on pa-rameter estimates based on the best availabledata for those regions with reasonablyhealthy tiger populations (eg the Kanha andBandipur Tiger Reserves in India) The habi-tat is assumed to comprise an area of approx-imately 1000 km2 with a prey carrying ca-pacity of 4500 kgkm214 It is supposed thatwhen prey are plentiful (rXt MTt) the un-disturbed habitat can sustain Kf 5 24 breed-ing adult females and Km 5 12 adult males(Karanth and Stith 1999 Kenney et al1995) In the base case farmers receive Rs1000 for each tiger killed face a ne of Rs25000 and a 2 probability of conviction(WPSI 2001)15 The off-farm wage rate is setat Rs 40 per day and the price of agriculturalproduce at Rs 85kg We begin by assuminga human population density of N 5 400households

It is important to distinguish between theecological effects and economic causes ofprey depletion from those of tiger poachingIn order to gain some understanding of theselinkages we begin by presenting simulationsfor the stylized case when only tiger poach-ing occurs We then assume that there is notiger poaching and consider the impact ofprey poaching on tiger populations Finallysimulations are presented for the completemodel where both tigers and their prey arehunted by subsistence farmers

Consider rst the effects of tiger poachingin isolation16 Curve A in Figure 1 shows thetiger population trajectory in a pristine habi-tat with no tiger poaching or prey depletionThe population achieves a stable equilibriumat 87 adult and juvenile tigers suggesting adensity of 9 tigers100 km2 This outcomeapproximates population levels in the frag-mented yet relatively healthy habitats foundin India and Nepal Curve B simulates the ef-fects of tiger poaching when the parametersare at the base case levels17 The tiger popula-tion declines to a stable 53 adult and juveniletigers with poachers harvesting 6 tigers per

year (approximately 11 percent of the popu-lation) Curve C simulates the effects of a50 increase in the price per tiger killed (Rs1500) The population falls substantially to27 tigers with 4 tigers harvested each year(approximately 12 of the population)

The simulation presented in Curve Dillus-trates the effects of an 80 increase in theprice paid to tiger poachers When the priceis increased to Rs 1800 the population de-clines to 19 tigers with 3 harvested each yearIn curve E when the poaching price is in-creased from Rs 1800 to Rs 1900 the tigerpopulation collapses within 50 years

This nding suggests that a relativelysmall increase in the payoffs to poaching(from Rs 1800 to Rs 1900) can drive a smallpopulation to extinction in a relatively shorttime period This is a signi cant resultwhich is consistent with Karanth and Stithrsquos(1999) simulations and related evidence thathunting of large felids can lead to sudden ex-tinction when it exceeds a certain thresholdlevel (Martin and de Meulanaer 1988 Bailey1993) The impact of poaching may thus bediscontinuous and prone to induce collapsesin populations This appears to be an exam-ple of the unstable equilibria frequently en-countered in discrete time predator-prey

13 Many of the tiger reserves are in tribal areas Itseems likely that behavior of tribal agriculturalistswould differ from those of other non-tribal agricultural-ists We have been compelled to use the only availabledata on agriculture which is based on non-tribal agri-culture There is clearly an urgent need for eldworkin and around tiger reserves to obtain more accurateinformation

14 The estimates of prey biomass in prime areas withtiger densities of between 10ndash12 per 100 km2 is derivedfrom data in Karanth and Nichols (2000) It is useful tonote that this estimate is also consistent with earlierstudies conducted using less advanced techniques Forinstance Johnsingh (1983) estimates a prey density of3382 kgkm2 in Bandipur reserve and a predation rateof 30 suggesting a possible carrying capacity of3382 (1 1 30) 5 4397 kgkm2

15 The assumption of a 2 conviction rate is a clearoverestimate of the true conviction probabilities ourbase case results thus underestimate the most likelyconsequence of poaching (WPSI 2001)

16 Formally this can be achieved by setting all thecoef cient of prey poaching to zero

17 In the base case farmers receive Rs 1000 for eachtiger killed face a ne of Rs 25000 and a 2 probabil-ity of conviction N is xed at 400 households

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

200 Land Economics May 2003

as well as their prey base The forests thattigers and their prey inhabit provide a widerange of economic social and environmen-tal bene ts to people These bene ts contrib-ute greatly to human welfare but they arevalued differently by different people anddifferent groups Local national and interna-tional interests in tigers and their habitatsalso differ greatly across landscapes To gov-ernment policymakers tiger habitats are of-ten seen only for their ability to generateincome employment revenue and foreignexchange when converted to agriculture tim-ber mines or other development-oriented ac-tivities To a small proportion of the humansliving in and around the forests killing tigersfor their body parts yields a substantiallygreater income than live tigers roaming freeMany small-scale agricultural producersview tigers and their prey as pests that dam-age their livestock and crops

Various studies document the crop dam-age caused by large ungulates (Sekhar 1988World Bank 1996) Little quantitative infor-mation is available about two of the most im-minent threats to the survival of wild tigersthe poaching of tigers and poaching of theirprey Recent investigations suggest that thetrade in tiger parts is controlled by organizedcriminal groups involved in a host of otherillegal activities In contrast tiger poachingis undertaken by locals who have an intimateknowledge of the forests The evidence sug-gests that the illegal traders capture the bulkof the pro ts while poachers are paid lowprices for each tiger killed (Nowell 2000WPSI 2001)1

National governments tend to in uencecontrol over the choice of forest bene tsWhen traditional rights and access shift inways that adversely impact local communi-ties households may have little incentive touse natural resources and in particular pro-tect animals in a sustainable way (Barbier1992 Panayotou 1993 Gunatilake 19941998 Tisdell 1995 Shyamsundar andKramer 1996) For this reason providinggreater access and use of tiger habitats is of-ten argued as the appropriate response tomeet conservation objectives (Saberwal1996 Kothari Suri and Singh 1995)

India possesses the largest number of wild

tigers of any of the range states and has hada relatively successful history of tiger protec-tion (Nowell and Jackson 1996 Karanth2001) Its response to declining tiger popula-tions focuses on establishing special pro-tected reserves and on law enforcement2Although the appropriateness of policy mea-sures needed to halt or reverse declining tigerpopulations is still contested the overallmanagement approach has recently shiftedtowards a participatory style known as JointForest Management (JFM) at times drivenby external donor encouragement The extentto which JFM is adopted varies by state inIndia In most cases households living in ornear forests utilize timber and non timberforests resources for subsistence cash andwage incomes (drsquoSilva and Nagnath 2002)Through sharing products responsibilitiesand decision-making authority JFM ap-proaches seek to provide local communitieswith incentives to protect the forest resourcesthat provide their income base and futurewelfare

Some argue that JFM should also be ex-tended to reserves aimed at protecting wild-life (Kothari Suri and Singh 1995) Otherstudies raise important concerns about theappropriateness of JFM-style conservationand protection efforts (Gunatilake 1998Karanth and Stith 1999) For instance Bar-rett and Arcese (1995 1998) question the as-sumptions linking local communities andsustainable forest resource use across diversegeographic conditions and economic situa-tions Simpson (1995) suggests the need forgreater experimentation with direct-paymentfor conservation efforts rather than fundinguntested participatory projects based on rais-ing the value of forest products in ways thatmay fail to deliver improved conservationoutcomes This view nds support in Gunati-lakersquos (1998) analysis of Sri Lanka whichprovides evidence that policies aimed at re-ducing dependency on forest based resources

1 For instance Nowellrsquos (2000) study of the trade intiger parts suggests that the retail value of an adult maletiger varies from $15000ndash $20000 while the WildlifeProtection Society of India reports cases where poach-ers in the eld are paid $15ndash$20

2 The Indian Government introduced the Project Ti-ger program in 1973

79(2) Damania et al The Economics of Protecting Tiger Populations 201

can be a much more effective way to protectforests than policies aimed at using forest re-sources The issues concerning participatorymanagement addressed in these studies raiseimportant questions about the appropriate-ness of the widespread promotion of JFM inIndia for protecting tigers

The model and simulations presented hereexamine how the tigerrsquos biological needs in-teract with economics incentives facinghouseholds living in and around their habi-tats The analysis aims to contribute to thepolicy debate about how best to protect tigerpopulations

III THE MODEL

Most of Indiarsquos tiger habitats are in parksand protected areas that also support variousforms of land uses including agriculturelivestock grazing and fuelwood collection(Mishra 1997 Sekhar 1998) The intersper-sion of humans in and around these parksleads inevitably to con icts over resource use(Schultz and Skonhoft 1996) Two motivesfor local people hunting the tigerrsquos prey spe-cies are considered The rst is when thelarge ungulates cause damage to crops in ad-joining agricultural areas termed the lsquolsquonui-sance effectrsquorsquo by Marks (1984) The secondmotive arises from the incentive of subsis-tence producers to hunt ungulates as a sup-plementary food source On the other handthe incentive to hunt tigers is driven entirelyby the demand for tiger products

The context for this model is a wild tigerpopulation in an insular forest patch sur-rounded by agricultural landmdasha typical char-acteristic of tiger reserves on the Indian sub-continent We extend the most recent modelof tiger population dynamics developed byKaranth and Stith (1999) to include preda-tor-prey interactions The biological model isincorporated into a household productionmodel in which subsistence farmers hunt ti-gers and their prey

The model presented here is similar toBluffstonersquos (1995) analysis of fuelwood ex-traction by subsistence farmers in Nepal It ismore closely related to Barrett and Arcesersquos(1998) model of the hunting incentives forfarmers in an integrated conservation and de-

velopment project (ICDP) in Tanzania3 Thispaper extends this literature by incorporatingan economic model of poaching behaviorinto a multiple species predator-prey model

The Household Model

As noted earlier we consider a tiger re-serve that is surrounded by agricultural landThe production and consumption units arehouseholds engaged in four kinds of activi-ties agricultural production off-farm workhunting tigers and hunting herbivores (iethe tigerrsquos prey) Income from agriculturalproduction and off-farm work is used to pur-chase food and other commodities House-holds hunt prey animals as a supplementarysource of food and to protect crops fromdamage4 The incentive to poach tigers isdriven entirely by the illegal trade in tigerproducts that is controlled by criminal gangswho determine the price paid to farmers foreach tiger killed5 Since very little is knownabout the nature of such poaching we adoptfunctional forms with parsimonious data re-quirements There are N households in thearea surrounding the tiger reserve A Cobb-Douglas function is employed to representhousehold utility

U 5 aF log(F ) 1 azlog(Z) 1 axlog(hx) [1a]

3 Barrett and Arcesersquos (1998) work is of consider-able relevance for wildlife conservation policies Theauthors develop a bio-economic simulation model thatshows that ICDP programs may be time inconsistent ina stochastic environment

4 In contrast to conditions in Africa there appears tobe no substantial market for game meat on the Indiansubcontinentand limited demand for the hides of ungu-lates Thus we ignore the possibility that hunted preyare sold in open markets

5 Tigers that stray into agricultural lands and preyupon domestic livestock are often killed by farmersWhile this issue is clearly important we do not considersuch lsquolsquonuisancersquorsquo killing of tigers for two reasons Firstsuch kills appear to be concentrated on animals thatstray outside reserves while our attention is mainly fo-cused upon the condition of animals with home rangeswithin a reserve However the main reason we haveneglected this problem is that in the absence of suf -cient data there appears to be no obvious manner inwhich to parameterize the extent of nuisance killing inthe simulations presented in Section 5 This suggeststhat our results may underestimate the true impacts oftiger poaching

202 Land Economics May 2003

where F represents consumption of food Zconsumption of non-food items hx consump-tion of prey animals ai 0 (i 5 F Z x) arethe parameters of the utility function withaF 1 aZ 1 ax 5 1

Equation [1a] is maximized subject to theconstraints

wLo 1 pgG 1 (PT 2 qTWT)hT

5 pzZ 1 pFF 1 qxWxhx [1b]

G 5 kLbg(1 2 mX) [1c]

hx 5 dLxX [1d]

hT 5 LgT1T

R2e

[1e]

L 5 Lo 1 Lg 1 Lx 1 LT [1f]

where G is agricultural output X is the bio-mass of prey animals Lg is labor time de-voted to agriculture Lo is labor time devotedto off-farm work Lx is labor time spent hunt-ing prey animals LT is labor time on huntingtigers and pg pF pz PT are the prices of ag-ricultural produce food non-food commodi-ties and tigers respectively qi(i 5 T X) is theprobability of being convicted for poachingtigers (T) and their prey (X) and W i(i 5 TX) is the ne per unit harvest if convicted forpoaching tigers or their prey T is the numberof tigers and R the area of the reserve k xb g m d 0 are parameters

By equation [1a] household utility de-pends on the consumption of food (F ) othergoods (a non-food composite commodity[Z]) and the quantity of prey animalsconsumed (hx)

Equation [1b] is the household budgetconstraint Food and other goods are pur-chased at given prices pz and pF respectivelyThese purchases are nanced by (i) the saleof agricultural produce (G) which is sold ata price pg (ii) off farm labor (Lo) which isremunerated at a wage rate of w and (iii) ti-ger poaching (hT) The farmers receive anamount PT for each tiger killed which is de-termined by traders Since poaching is ille-gal it may result in conviction The expected

penalty for poaching tigers is qT WT whereqT is the probability of detection and convic-tion WT is the ne per tiger killed Thus theexpected payoffs from tiger poaching is de- ned by pT 5 (PT 2 qTWT) Finally sincepoaching prey is also illegal the householdmay incur an expected penalty qxWxhxwhere qx is the probability of detection andconviction Wx is the ne per prey animalpoached (hx)

Equation [1c] describes the agriculturalproduction function Following empiricalstudies on subsistence farming in India ag-ricultural production (G) is assumed to de-pend upon labor inputs (Lg) where b is theelasticity and ka constant (Deninger and Bis-wanger 1998 Saha 1994)6 The productionfunction also takes into account the damageto crops by the grazing and trampling of wildtiger prey This is given by (mX where X isthe biomass of prey animals and m is thedamage coef cient

Equation [1d] describes the prey harvestproduction function In the absence of dataon poaching of ungulate-prey in tiger habi-tats we adopt a functional form that hasbeen used in African studies of ungulatehunting (Kinyua van Kooten and Bulte2000) Thus the harvest of herbivores (hx) isa function of labor inputs (Lx) and the popu-lation of ungulate prey (X) with unit elastici-ties with respect to labor inputs and preypopulations

Equation [1e] is the tiger poaching pro-duction function There is no data availableon the nature of tiger poaching Hence anyfunctional form that is adopted is necessarilyconjectural Existing evidence suggests thattigers are usually killed by poisoning shoot-ing or setting traps and snares (WPSI 2001)techniques requiring only minimal invest-ment in capital equipment To economize onparameters we abstract from the need forcapital equipment and assume that the har-vest rate depends on the density of tigers and

6 The models used by Deninger and Biswanger(1999) and by Saha (1994) focus on agricultural house-holds While it is unclear how appropriate their models t the type of agriculture practiced in and around tigerhabitats in India the lack of better data limits our op-tions

79(2) Damania et al The Economics of Protecting Tiger Populations 203

the amount of search effort7 Tiger poachingis thus speci ed using a Cobb-Douglas func-tion with search effort and tiger densities asthe only arguments in the production func-tion The method by which the parameters onsearch effort (LT) and tiger density (TR) areestimated is described in the Data Appendix

Equation [1f ] is the time allocation con-straint which requires that labor time devotedto off-farm work (Lo) agriculture (Lg) andhunting tigers and their prey (LT Lx) mustequal the xed endowment of time (L) avail-able to the household Leisure is not includedas a choice variable as existing householdsurvey data in potential tiger habitats in Ne-pal suggest that opportunities for leisure con-sumption are limited in such poor ruralhouseholds (Bluffstone 1995)8

The utility maximization problem is basedon the notion that households take the timepath of exogenous variables such as thestock of herbivores (X) as given This re- ects the fact that there are assumed to bemany such households who have no propertyrights in wild animals Hence they have littleincentive to take account of the future conse-quences of their current actions Formallythis implies that households solve a static op-timisation problem Thus for notationalbrevity time symbols are suppressed in theabove equations9

Of particular interest in this context arethe solutions for poaching tigers and prey an-imals Solving the utility maximisation prob-lem in equations [1a]ndash[1f ] yields the follow-ing solution for the allocation of effortexpended on hunting tigers in each house-hold

LT 5 1gpTDe

w 21(12g)

[2a]

where pT 5 (PT 2 qTWT) is the net expectedpayoff from poaching a tiger D 5 TR is thedensity of tigers

Using [1e] the aggregate harvest of tigersis given by

HT NhT 5 N1gpTDe

w 2g12g

(D)e [2b]

The returns to off-farm work are exoge-nous and de ne the minimum payoffs to anyactivity that the household will accept Thusan increase in the wages paid for off-farmwork lowers poaching effort while an in-crease in the net expected payoffs frompoaching pT or an increase in the density oftigers D increases poaching effort

Labor time spent on hunting prey animalsis given by

Lc 5ax(w(L 2 Lg 2 LT) 1 pgG 1 pThT)

(w 1 qxWxdX)

[3a]

where

Lg 5 1 wbpgk(1 2 mX)2

1(b21)

[3b]

Substituting [3a] and [3b] in [1d] and aggre-gating over the N households gives the totallevel of prey animals hunted

Hx 5 NdLxX [3c]

The implicit price of hunting prey is againdetermined by the opportunity cost of timewhich is de ned by the off-farm wage rateThe hunted prey animals are consumedrather than sold hence an increase in thewage rate has con icting income and substi-tution effects on prey hunting levels (ie

7 Unlike many other species tigers are highly secre-tive animals inhabiting dense forests Therefore themain poaching constraint is likely to be the dif cultyinvolved in nding a tiger Field studies suggest that thelikelihood of an encounter depends on inter alia thedensity of tigers and the amount of search effort (Kar-anth and Nichols 2000)These key features are capturedin equation [1e]

8 Note also that since the analysis focuses on subsis-tence households with limited incomes we ignore thepossibility that households may hire labor In the ab-sence of adequate data we also ignore several othercomponents of agricultural household behavior includ-ing production and use of livestock (which may bepreyed upon by tigers) different types of farm outputconsumption of part of the farm output and the use ofother non-labor inputs (eg fertilizers)

9 It is perhaps worth noting that such myopic behav-iour has also been observed on communally held triballands where users own property rights to forest re-sources (Madhusudan and Karanth 1997)

204 Land Economics May 2003

paraHxparaw () 0) Speci cally the incomeeffect of higher wages increases the demandfor prey animals as a consumption goodwhile the substitution effect of higher off-farm wages raises the opportunity costs oftime devoted to hunting prey The net impactof higher off-farm wages therefore dependson the relative parameters of the model Incontrast an increase in the price of agricul-tural goods raises both income and the valueof crops damaged by prey This leads to in-creases in prey hunting levels (paraHxparapg 0)Similarly as expected a reduction in the ex-pected ne (qxWx) or an increase in the cropdamage coef cient (m) both lead to higherlevels of prey poaching (ie paraHxpara(qxWx) 0 paraHxparam 0)

This simple model of household behaviorignores a number of signi cant issues thatare of relevance in the context of wild animalpoaching in India10 For example anecdotalevidence suggests that corruption amongstforest of cials may be widespread in sometiger reserves in India (Breeden and Wright1996) This is perhaps a consequence of therelatively low wages that are paid to forestof cialsmdashoften in arrears In the absence ofdata on the incidence of corruption we donot explicitly deal with the modeling com-plications that arise when corruption ispervasive However it can be shown thatthe expected penalty for poaching in equa-tion [1b] is formally equivalent to the re-duced form payoff function that ariseswhen poachers bribe corrupt of cials11 Themodel also assumes that the probability ofconviction is xed In practice the proba-bility of a successful prosecution is likelyto depend on the level of expenditure bypoachers on their legal defense and the atti-tudes of local magistrates to wildlife pro-tection Moreover conviction rates andthe formal penalties for poaching may notcapture all the costs associated with beingdetected if caught poaching suggesting con-siderable uncertainty in the payoffs topoaching

IV TIGER BIOLOGY

The use of a single equation to model pop-ulation dynamics is often considered inap-

propriate for large predators that exhibitcomplex patterns of behaviour and face dif-ferent mortality rates over various stages intheir life cycle (see Burgman Ferson andAkcakaya 1993) Accordingly the existingliterature describes tiger population dy-namics using stage based stochastic demo-graphic models In this paper we follow thisconvention and extend the most recent modelof tiger demography by Karanth and Stith(1999) to incorporate predator-prey interac-tions

The Karanth-Stith model identi es tigersof both sexes in four distinct demographicstages cubs (younger than one year) juve-niles (one to two years) transients (tigersolder than two years in search of a homerange) and adults (breeding tigers with ahome range) In the absence of human pres-sures mortality rates at each stage of the lifecycle depend on intrinsic survival rateswhich incorporate deaths from natural fac-tors such as disease and intraspeci c compe-tition For expositional ease we begin bydescribing the dynamics of tiger populationswhen prey are plentiful and there is nopoaching

The number of cubs that survive in anyyear is determined by the birth rate of breed-ing females and the survival rate of cubs

Tct11 5 s cbTaf

t [4a]

where subscripts denote time periods Tct1 1 is

the number of surviving cubs in period t 11 s c is the survival rate of cubs b is the birth

10 We are grateful to a referee for suggesting theseissues

11 To see this suppose for simplicity that a fractionh of forest of cials are corruptible perhaps because ofthe low wages they receive The Indian forest serviceis a hierarchical organisation and the anecdotal accountsof corruption allege that bribery is most pervasiveamongst the lowestpaid of cials Let w be the probabil-ity that a poacher encounters a forest of cial Then cet-eris paribus the probability of being prosecuted isgiven by w(1 2 h) Furthermore if l is the probabilityof a successful conviction then q j 5 l jw j(1 2 h) ( j5 T X) is the total probability of being convicted forpoaching Damania (2002) assesses the complicationsthat arise in determining optimal environmental regula-tions under corruption We do not explore these impor-tant and complex issues in this paper

79(2) Damania et al The Economics of Protecting Tiger Populations 205

rate per breeding adult female and Taft is the

number of breeding adult females FollowingKaranth and Stith (1999) we assume anequal sex ratio at birth and mean litter size ofthree The birth rate b is treated as a Poissonvariable with a mean of three Randomnessis included in the model to capture demo-graphic stochasticity12

The surviving cubs move to the juvenilestage in the following period The number ofjuveniles who survive is

T jst11 5 s jsT cs

t (s 5 m f ) [4b]

where T jst1 1 is the number of surviving juve-

nile males (m) and females ( f ) in period t 11 s js(s 5 m f ) is the intrinsic survival rateof juvenile males (m) and females ( f )

At two years the surviving juveniles be-come transients Transients are de ned asadult tigers in search of home territories inwhich to hunt and breed If a vacant homerange is available a transient immediatelyoccupies the territory and is classi ed as abreeding adult Let Ks (s 5 m f ) denote themaximum number of territories available foradults of gender s 5 m f Let Tas

t be the num-ber of surviving adults of gender s 5 m fwith existing home ranges Then the numberof vacant territories available for the tran-sients to occupy is given by

V st11 5 Max(0 Ks 2 Tas

t )(s 5 m f ) [4c]

The number of transients in period (t 1 1) isde ned by (i) the number of transients whosurvive from the previous period (ii) juve-niles who progress to the transient stage (iii)minus the transients who nd home rangesand thus exit to the breeding adult stage

Ttst11 5 sts(s jsT js

t 1 Ttst ) 2 Vs

t11(s 5 m f ) [4d]

where Tt st1 1 is the number of surviving tran-

sients in period t 1 1 st s is the survival rateof transients of gender s 5 m f

Finally the number of breeding adults isgiven by the existing number of survivingadults and the new recruits to the category ofbreeding adult

T ast11 5 (s asTas

t 1 Vst11) [4e]

where s as is the survival rate of adults of gen-der s 5 m f The total population of non-cubtigers (T) is de ned to include the sum of ju-veniles transients and adults of both sexesThe model thus far assumes that prey areplentiful The only constraints on populationgrowth considered so far are the intrinsic sur-vival rates and the amount of territory avail-able to establish home ranges (ie Ks) Ifprey depletion lowers hunting success ratesit will lead to greater mortality of tigers Wetherefore extend the model to take account ofthe impact of prey availability on tiger popu-lation growth

Data on the intrinsic growth rates of indi-vidual prey species and the effects of browseand forage competition between species in ti-ger habitats is unavailable Hence we adopta simple approach and model the combinedbiomass of all prey species using a logisticequation of the form

Xt11 2 Xt 5 Xtr(1 2 XtX) 2 Hxt 2 Yt [5]

where Xt is the prey biomass at time t r is theintrinsic growth rate X is the prey carryingcapacity of the forest Hxt is the human har-vest of the prey biomass de ned in equation[3c] and Yt is the harvest of the prey by ti-gers which is described below

Field studies suggest that on average a ti-ger requires approximately 3000 kg of preyper year to survive (Sunquist Karanth andSunquist 1999) We therefore de ne the min-imum food intake of a tiger as M 5 3000kg Field observations also reveal that tigerssucceed in capturing between 10ndash20 ofthe available prey biomass in their homeranges (Schaller 1967 Sunquist 1981 John-singh 1983) In the presence of competingpredators such as wild dogs (Cuon alpinus)and leopards (Panthera pardus) a predationrate of 10 is deemed more appropriate(Karanth 2001) Thus the predation rate isde ned as r 5 010 It follows that the maxi-mum number of tigers that can be sustainedwith a prey base of Xt is rXtM Accord-

12 The random numbers were generated in Excel us-ing a random seed of 1 and mean of 3

206 Land Economics May 2003

ingly the prey biomass consumed by tigersis given by

Yt 5 MTt if rXt MTt

Yt 5 rXt otherwise [6a]

where Tt is the total number of tigers in pe-riod t M is the minimum food intake and ris the predation rate

Thus when prey are plentiful (ie rXt MTt) each tiger is able to meet its nutritionalneeds and successfully captures Mkg of preyper annum hence Yt 5 MTt On the otherhand if there is insuf cient prey to meet theneeds of the total population the level of pre-dation is at its maximum level Yt 5 rXt

A shortage of prey could have two effectson tiger survival prospects First prey deple-tion is likely to depress survival rates acrossall demographic stages Second a shortageof prey may also lower the carrying capacityof the habitat and thus lead to an expansionin the home ranges of breeding adult femalesIn the absence of data on the effects of preydepletion across demographic groups wefollow Karanth and Stith and assume thatprey depletion effects only (i) the carryingcapacity of the habitat and (ii) the survivalrates of cubs Thus under conditions of preydepletion the survival rates of cubs and thecarrying capacity are depressed by a preydepletion factor that is de ned as

h t11 5 51 if rXt 2 MTt $ 0

rXi

MTt

if rXt 2 MTt 0 [6b]

The cub survival rate (s c) and the carryingcapacity (Ks) are pre-multiplied by [6b]

It is acknowledged that the neglect of preydepletion effects on the survival rates acrossother demographic categories is unsatisfac-tory This approach can therefore be ex-pected to underestimate the true impact ofprey depletion if survival rates are depressedmore generally across all demographicstages However re nements of the modelmust await further research on this issue

Turning next to the effects of poachingPoachers target juveniles transients and

adults The number of tigers killed at eachstage is assumed to be proportional to the ex-isting distribution of tigers across the variousdemographic stages Let superscript i(i 5 jt a) denote demographic stages and recallthat superscript s 5 M F denotes genderDe ne k is

t as the proportion of male or femaletigers at demographic stage i(i 5 j t a) Thenthe numberofgenders tigers poachedatdemo-graphic stage i(i 5 j t a) is de ned as

HisTt11 5 HTtk is

t [6c]

where HTt is the total harvest of tigers as de-termined in equation [2b] k is

t 5 (T ist Tt) is

the proportion of gender s tigers at stagei(i 5 j t a) T is

t 5 number of gender s ti-gers at stage i and Tt is the total populationof tigers The number of tigers at each stageis thus lowered by the amount de ned inequation [6c]

V SIMULATION RESULTS

We now combine the economic models ofbehavior (equations [2b] and [3c]) and tigerpopulation growth (equations [4a]ndash[6c]) todetermine the time paths of lsquotiger stocksrsquo un-der alternative scenarios For given parame-ters the level of poaching emerges from theoptimising decisions of farmers and poach-ers This in turn affects tiger stock levelsModel parameters are varied to determinethe sensitivity of tiger population levels tochanges in economic circumstances

In the model labor is allocated across dif-ferent activities until the marginal returns areequalised The returns to off-farm work areexogenously xed and hence de ne the mini-mum payoffs to any activity that a householdwill accept The returns to agriculture varywith the price of agricultural commoditiesand the losses due to wildlife predation Thepayoffs to poaching also vary with wildlifestocks and the expected penalties for convic-tion It follows that changes in the returns toany one activity may induce a reallocation oflabor across other activities and thereforecould alter the level of poaching

The parameters for the basic tiger popula-tion model (equations [4a]ndash[4e]) are fromKaranth and Stith (1999) and are based on

79(2) Damania et al The Economics of Protecting Tiger Populations 207

eld research in India and Nepal Behavioraldata for subsistence farmers are drawn froma variety of sources13 The Data Appendixprovides details of the sources of informa-tion assumptions estimation methods andparameter values

The benchmark simulation draws on pa-rameter estimates based on the best availabledata for those regions with reasonablyhealthy tiger populations (eg the Kanha andBandipur Tiger Reserves in India) The habi-tat is assumed to comprise an area of approx-imately 1000 km2 with a prey carrying ca-pacity of 4500 kgkm214 It is supposed thatwhen prey are plentiful (rXt MTt) the un-disturbed habitat can sustain Kf 5 24 breed-ing adult females and Km 5 12 adult males(Karanth and Stith 1999 Kenney et al1995) In the base case farmers receive Rs1000 for each tiger killed face a ne of Rs25000 and a 2 probability of conviction(WPSI 2001)15 The off-farm wage rate is setat Rs 40 per day and the price of agriculturalproduce at Rs 85kg We begin by assuminga human population density of N 5 400households

It is important to distinguish between theecological effects and economic causes ofprey depletion from those of tiger poachingIn order to gain some understanding of theselinkages we begin by presenting simulationsfor the stylized case when only tiger poach-ing occurs We then assume that there is notiger poaching and consider the impact ofprey poaching on tiger populations Finallysimulations are presented for the completemodel where both tigers and their prey arehunted by subsistence farmers

Consider rst the effects of tiger poachingin isolation16 Curve A in Figure 1 shows thetiger population trajectory in a pristine habi-tat with no tiger poaching or prey depletionThe population achieves a stable equilibriumat 87 adult and juvenile tigers suggesting adensity of 9 tigers100 km2 This outcomeapproximates population levels in the frag-mented yet relatively healthy habitats foundin India and Nepal Curve B simulates the ef-fects of tiger poaching when the parametersare at the base case levels17 The tiger popula-tion declines to a stable 53 adult and juveniletigers with poachers harvesting 6 tigers per

year (approximately 11 percent of the popu-lation) Curve C simulates the effects of a50 increase in the price per tiger killed (Rs1500) The population falls substantially to27 tigers with 4 tigers harvested each year(approximately 12 of the population)

The simulation presented in Curve Dillus-trates the effects of an 80 increase in theprice paid to tiger poachers When the priceis increased to Rs 1800 the population de-clines to 19 tigers with 3 harvested each yearIn curve E when the poaching price is in-creased from Rs 1800 to Rs 1900 the tigerpopulation collapses within 50 years

This nding suggests that a relativelysmall increase in the payoffs to poaching(from Rs 1800 to Rs 1900) can drive a smallpopulation to extinction in a relatively shorttime period This is a signi cant resultwhich is consistent with Karanth and Stithrsquos(1999) simulations and related evidence thathunting of large felids can lead to sudden ex-tinction when it exceeds a certain thresholdlevel (Martin and de Meulanaer 1988 Bailey1993) The impact of poaching may thus bediscontinuous and prone to induce collapsesin populations This appears to be an exam-ple of the unstable equilibria frequently en-countered in discrete time predator-prey

13 Many of the tiger reserves are in tribal areas Itseems likely that behavior of tribal agriculturalistswould differ from those of other non-tribal agricultural-ists We have been compelled to use the only availabledata on agriculture which is based on non-tribal agri-culture There is clearly an urgent need for eldworkin and around tiger reserves to obtain more accurateinformation

14 The estimates of prey biomass in prime areas withtiger densities of between 10ndash12 per 100 km2 is derivedfrom data in Karanth and Nichols (2000) It is useful tonote that this estimate is also consistent with earlierstudies conducted using less advanced techniques Forinstance Johnsingh (1983) estimates a prey density of3382 kgkm2 in Bandipur reserve and a predation rateof 30 suggesting a possible carrying capacity of3382 (1 1 30) 5 4397 kgkm2

15 The assumption of a 2 conviction rate is a clearoverestimate of the true conviction probabilities ourbase case results thus underestimate the most likelyconsequence of poaching (WPSI 2001)

16 Formally this can be achieved by setting all thecoef cient of prey poaching to zero

17 In the base case farmers receive Rs 1000 for eachtiger killed face a ne of Rs 25000 and a 2 probabil-ity of conviction N is xed at 400 households

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

79(2) Damania et al The Economics of Protecting Tiger Populations 201

can be a much more effective way to protectforests than policies aimed at using forest re-sources The issues concerning participatorymanagement addressed in these studies raiseimportant questions about the appropriate-ness of the widespread promotion of JFM inIndia for protecting tigers

The model and simulations presented hereexamine how the tigerrsquos biological needs in-teract with economics incentives facinghouseholds living in and around their habi-tats The analysis aims to contribute to thepolicy debate about how best to protect tigerpopulations

III THE MODEL

Most of Indiarsquos tiger habitats are in parksand protected areas that also support variousforms of land uses including agriculturelivestock grazing and fuelwood collection(Mishra 1997 Sekhar 1998) The intersper-sion of humans in and around these parksleads inevitably to con icts over resource use(Schultz and Skonhoft 1996) Two motivesfor local people hunting the tigerrsquos prey spe-cies are considered The rst is when thelarge ungulates cause damage to crops in ad-joining agricultural areas termed the lsquolsquonui-sance effectrsquorsquo by Marks (1984) The secondmotive arises from the incentive of subsis-tence producers to hunt ungulates as a sup-plementary food source On the other handthe incentive to hunt tigers is driven entirelyby the demand for tiger products

The context for this model is a wild tigerpopulation in an insular forest patch sur-rounded by agricultural landmdasha typical char-acteristic of tiger reserves on the Indian sub-continent We extend the most recent modelof tiger population dynamics developed byKaranth and Stith (1999) to include preda-tor-prey interactions The biological model isincorporated into a household productionmodel in which subsistence farmers hunt ti-gers and their prey

The model presented here is similar toBluffstonersquos (1995) analysis of fuelwood ex-traction by subsistence farmers in Nepal It ismore closely related to Barrett and Arcesersquos(1998) model of the hunting incentives forfarmers in an integrated conservation and de-

velopment project (ICDP) in Tanzania3 Thispaper extends this literature by incorporatingan economic model of poaching behaviorinto a multiple species predator-prey model

The Household Model

As noted earlier we consider a tiger re-serve that is surrounded by agricultural landThe production and consumption units arehouseholds engaged in four kinds of activi-ties agricultural production off-farm workhunting tigers and hunting herbivores (iethe tigerrsquos prey) Income from agriculturalproduction and off-farm work is used to pur-chase food and other commodities House-holds hunt prey animals as a supplementarysource of food and to protect crops fromdamage4 The incentive to poach tigers isdriven entirely by the illegal trade in tigerproducts that is controlled by criminal gangswho determine the price paid to farmers foreach tiger killed5 Since very little is knownabout the nature of such poaching we adoptfunctional forms with parsimonious data re-quirements There are N households in thearea surrounding the tiger reserve A Cobb-Douglas function is employed to representhousehold utility

U 5 aF log(F ) 1 azlog(Z) 1 axlog(hx) [1a]

3 Barrett and Arcesersquos (1998) work is of consider-able relevance for wildlife conservation policies Theauthors develop a bio-economic simulation model thatshows that ICDP programs may be time inconsistent ina stochastic environment

4 In contrast to conditions in Africa there appears tobe no substantial market for game meat on the Indiansubcontinentand limited demand for the hides of ungu-lates Thus we ignore the possibility that hunted preyare sold in open markets

5 Tigers that stray into agricultural lands and preyupon domestic livestock are often killed by farmersWhile this issue is clearly important we do not considersuch lsquolsquonuisancersquorsquo killing of tigers for two reasons Firstsuch kills appear to be concentrated on animals thatstray outside reserves while our attention is mainly fo-cused upon the condition of animals with home rangeswithin a reserve However the main reason we haveneglected this problem is that in the absence of suf -cient data there appears to be no obvious manner inwhich to parameterize the extent of nuisance killing inthe simulations presented in Section 5 This suggeststhat our results may underestimate the true impacts oftiger poaching

202 Land Economics May 2003

where F represents consumption of food Zconsumption of non-food items hx consump-tion of prey animals ai 0 (i 5 F Z x) arethe parameters of the utility function withaF 1 aZ 1 ax 5 1

Equation [1a] is maximized subject to theconstraints

wLo 1 pgG 1 (PT 2 qTWT)hT

5 pzZ 1 pFF 1 qxWxhx [1b]

G 5 kLbg(1 2 mX) [1c]

hx 5 dLxX [1d]

hT 5 LgT1T

R2e

[1e]

L 5 Lo 1 Lg 1 Lx 1 LT [1f]

where G is agricultural output X is the bio-mass of prey animals Lg is labor time de-voted to agriculture Lo is labor time devotedto off-farm work Lx is labor time spent hunt-ing prey animals LT is labor time on huntingtigers and pg pF pz PT are the prices of ag-ricultural produce food non-food commodi-ties and tigers respectively qi(i 5 T X) is theprobability of being convicted for poachingtigers (T) and their prey (X) and W i(i 5 TX) is the ne per unit harvest if convicted forpoaching tigers or their prey T is the numberof tigers and R the area of the reserve k xb g m d 0 are parameters

By equation [1a] household utility de-pends on the consumption of food (F ) othergoods (a non-food composite commodity[Z]) and the quantity of prey animalsconsumed (hx)

Equation [1b] is the household budgetconstraint Food and other goods are pur-chased at given prices pz and pF respectivelyThese purchases are nanced by (i) the saleof agricultural produce (G) which is sold ata price pg (ii) off farm labor (Lo) which isremunerated at a wage rate of w and (iii) ti-ger poaching (hT) The farmers receive anamount PT for each tiger killed which is de-termined by traders Since poaching is ille-gal it may result in conviction The expected

penalty for poaching tigers is qT WT whereqT is the probability of detection and convic-tion WT is the ne per tiger killed Thus theexpected payoffs from tiger poaching is de- ned by pT 5 (PT 2 qTWT) Finally sincepoaching prey is also illegal the householdmay incur an expected penalty qxWxhxwhere qx is the probability of detection andconviction Wx is the ne per prey animalpoached (hx)

Equation [1c] describes the agriculturalproduction function Following empiricalstudies on subsistence farming in India ag-ricultural production (G) is assumed to de-pend upon labor inputs (Lg) where b is theelasticity and ka constant (Deninger and Bis-wanger 1998 Saha 1994)6 The productionfunction also takes into account the damageto crops by the grazing and trampling of wildtiger prey This is given by (mX where X isthe biomass of prey animals and m is thedamage coef cient

Equation [1d] describes the prey harvestproduction function In the absence of dataon poaching of ungulate-prey in tiger habi-tats we adopt a functional form that hasbeen used in African studies of ungulatehunting (Kinyua van Kooten and Bulte2000) Thus the harvest of herbivores (hx) isa function of labor inputs (Lx) and the popu-lation of ungulate prey (X) with unit elastici-ties with respect to labor inputs and preypopulations

Equation [1e] is the tiger poaching pro-duction function There is no data availableon the nature of tiger poaching Hence anyfunctional form that is adopted is necessarilyconjectural Existing evidence suggests thattigers are usually killed by poisoning shoot-ing or setting traps and snares (WPSI 2001)techniques requiring only minimal invest-ment in capital equipment To economize onparameters we abstract from the need forcapital equipment and assume that the har-vest rate depends on the density of tigers and

6 The models used by Deninger and Biswanger(1999) and by Saha (1994) focus on agricultural house-holds While it is unclear how appropriate their models t the type of agriculture practiced in and around tigerhabitats in India the lack of better data limits our op-tions

79(2) Damania et al The Economics of Protecting Tiger Populations 203

the amount of search effort7 Tiger poachingis thus speci ed using a Cobb-Douglas func-tion with search effort and tiger densities asthe only arguments in the production func-tion The method by which the parameters onsearch effort (LT) and tiger density (TR) areestimated is described in the Data Appendix

Equation [1f ] is the time allocation con-straint which requires that labor time devotedto off-farm work (Lo) agriculture (Lg) andhunting tigers and their prey (LT Lx) mustequal the xed endowment of time (L) avail-able to the household Leisure is not includedas a choice variable as existing householdsurvey data in potential tiger habitats in Ne-pal suggest that opportunities for leisure con-sumption are limited in such poor ruralhouseholds (Bluffstone 1995)8

The utility maximization problem is basedon the notion that households take the timepath of exogenous variables such as thestock of herbivores (X) as given This re- ects the fact that there are assumed to bemany such households who have no propertyrights in wild animals Hence they have littleincentive to take account of the future conse-quences of their current actions Formallythis implies that households solve a static op-timisation problem Thus for notationalbrevity time symbols are suppressed in theabove equations9

Of particular interest in this context arethe solutions for poaching tigers and prey an-imals Solving the utility maximisation prob-lem in equations [1a]ndash[1f ] yields the follow-ing solution for the allocation of effortexpended on hunting tigers in each house-hold

LT 5 1gpTDe

w 21(12g)

[2a]

where pT 5 (PT 2 qTWT) is the net expectedpayoff from poaching a tiger D 5 TR is thedensity of tigers

Using [1e] the aggregate harvest of tigersis given by

HT NhT 5 N1gpTDe

w 2g12g

(D)e [2b]

The returns to off-farm work are exoge-nous and de ne the minimum payoffs to anyactivity that the household will accept Thusan increase in the wages paid for off-farmwork lowers poaching effort while an in-crease in the net expected payoffs frompoaching pT or an increase in the density oftigers D increases poaching effort

Labor time spent on hunting prey animalsis given by

Lc 5ax(w(L 2 Lg 2 LT) 1 pgG 1 pThT)

(w 1 qxWxdX)

[3a]

where

Lg 5 1 wbpgk(1 2 mX)2

1(b21)

[3b]

Substituting [3a] and [3b] in [1d] and aggre-gating over the N households gives the totallevel of prey animals hunted

Hx 5 NdLxX [3c]

The implicit price of hunting prey is againdetermined by the opportunity cost of timewhich is de ned by the off-farm wage rateThe hunted prey animals are consumedrather than sold hence an increase in thewage rate has con icting income and substi-tution effects on prey hunting levels (ie

7 Unlike many other species tigers are highly secre-tive animals inhabiting dense forests Therefore themain poaching constraint is likely to be the dif cultyinvolved in nding a tiger Field studies suggest that thelikelihood of an encounter depends on inter alia thedensity of tigers and the amount of search effort (Kar-anth and Nichols 2000)These key features are capturedin equation [1e]

8 Note also that since the analysis focuses on subsis-tence households with limited incomes we ignore thepossibility that households may hire labor In the ab-sence of adequate data we also ignore several othercomponents of agricultural household behavior includ-ing production and use of livestock (which may bepreyed upon by tigers) different types of farm outputconsumption of part of the farm output and the use ofother non-labor inputs (eg fertilizers)

9 It is perhaps worth noting that such myopic behav-iour has also been observed on communally held triballands where users own property rights to forest re-sources (Madhusudan and Karanth 1997)

204 Land Economics May 2003

paraHxparaw () 0) Speci cally the incomeeffect of higher wages increases the demandfor prey animals as a consumption goodwhile the substitution effect of higher off-farm wages raises the opportunity costs oftime devoted to hunting prey The net impactof higher off-farm wages therefore dependson the relative parameters of the model Incontrast an increase in the price of agricul-tural goods raises both income and the valueof crops damaged by prey This leads to in-creases in prey hunting levels (paraHxparapg 0)Similarly as expected a reduction in the ex-pected ne (qxWx) or an increase in the cropdamage coef cient (m) both lead to higherlevels of prey poaching (ie paraHxpara(qxWx) 0 paraHxparam 0)

This simple model of household behaviorignores a number of signi cant issues thatare of relevance in the context of wild animalpoaching in India10 For example anecdotalevidence suggests that corruption amongstforest of cials may be widespread in sometiger reserves in India (Breeden and Wright1996) This is perhaps a consequence of therelatively low wages that are paid to forestof cialsmdashoften in arrears In the absence ofdata on the incidence of corruption we donot explicitly deal with the modeling com-plications that arise when corruption ispervasive However it can be shown thatthe expected penalty for poaching in equa-tion [1b] is formally equivalent to the re-duced form payoff function that ariseswhen poachers bribe corrupt of cials11 Themodel also assumes that the probability ofconviction is xed In practice the proba-bility of a successful prosecution is likelyto depend on the level of expenditure bypoachers on their legal defense and the atti-tudes of local magistrates to wildlife pro-tection Moreover conviction rates andthe formal penalties for poaching may notcapture all the costs associated with beingdetected if caught poaching suggesting con-siderable uncertainty in the payoffs topoaching

IV TIGER BIOLOGY

The use of a single equation to model pop-ulation dynamics is often considered inap-

propriate for large predators that exhibitcomplex patterns of behaviour and face dif-ferent mortality rates over various stages intheir life cycle (see Burgman Ferson andAkcakaya 1993) Accordingly the existingliterature describes tiger population dy-namics using stage based stochastic demo-graphic models In this paper we follow thisconvention and extend the most recent modelof tiger demography by Karanth and Stith(1999) to incorporate predator-prey interac-tions

The Karanth-Stith model identi es tigersof both sexes in four distinct demographicstages cubs (younger than one year) juve-niles (one to two years) transients (tigersolder than two years in search of a homerange) and adults (breeding tigers with ahome range) In the absence of human pres-sures mortality rates at each stage of the lifecycle depend on intrinsic survival rateswhich incorporate deaths from natural fac-tors such as disease and intraspeci c compe-tition For expositional ease we begin bydescribing the dynamics of tiger populationswhen prey are plentiful and there is nopoaching

The number of cubs that survive in anyyear is determined by the birth rate of breed-ing females and the survival rate of cubs

Tct11 5 s cbTaf

t [4a]

where subscripts denote time periods Tct1 1 is

the number of surviving cubs in period t 11 s c is the survival rate of cubs b is the birth

10 We are grateful to a referee for suggesting theseissues

11 To see this suppose for simplicity that a fractionh of forest of cials are corruptible perhaps because ofthe low wages they receive The Indian forest serviceis a hierarchical organisation and the anecdotal accountsof corruption allege that bribery is most pervasiveamongst the lowestpaid of cials Let w be the probabil-ity that a poacher encounters a forest of cial Then cet-eris paribus the probability of being prosecuted isgiven by w(1 2 h) Furthermore if l is the probabilityof a successful conviction then q j 5 l jw j(1 2 h) ( j5 T X) is the total probability of being convicted forpoaching Damania (2002) assesses the complicationsthat arise in determining optimal environmental regula-tions under corruption We do not explore these impor-tant and complex issues in this paper

79(2) Damania et al The Economics of Protecting Tiger Populations 205

rate per breeding adult female and Taft is the

number of breeding adult females FollowingKaranth and Stith (1999) we assume anequal sex ratio at birth and mean litter size ofthree The birth rate b is treated as a Poissonvariable with a mean of three Randomnessis included in the model to capture demo-graphic stochasticity12

The surviving cubs move to the juvenilestage in the following period The number ofjuveniles who survive is

T jst11 5 s jsT cs

t (s 5 m f ) [4b]

where T jst1 1 is the number of surviving juve-

nile males (m) and females ( f ) in period t 11 s js(s 5 m f ) is the intrinsic survival rateof juvenile males (m) and females ( f )

At two years the surviving juveniles be-come transients Transients are de ned asadult tigers in search of home territories inwhich to hunt and breed If a vacant homerange is available a transient immediatelyoccupies the territory and is classi ed as abreeding adult Let Ks (s 5 m f ) denote themaximum number of territories available foradults of gender s 5 m f Let Tas

t be the num-ber of surviving adults of gender s 5 m fwith existing home ranges Then the numberof vacant territories available for the tran-sients to occupy is given by

V st11 5 Max(0 Ks 2 Tas

t )(s 5 m f ) [4c]

The number of transients in period (t 1 1) isde ned by (i) the number of transients whosurvive from the previous period (ii) juve-niles who progress to the transient stage (iii)minus the transients who nd home rangesand thus exit to the breeding adult stage

Ttst11 5 sts(s jsT js

t 1 Ttst ) 2 Vs

t11(s 5 m f ) [4d]

where Tt st1 1 is the number of surviving tran-

sients in period t 1 1 st s is the survival rateof transients of gender s 5 m f

Finally the number of breeding adults isgiven by the existing number of survivingadults and the new recruits to the category ofbreeding adult

T ast11 5 (s asTas

t 1 Vst11) [4e]

where s as is the survival rate of adults of gen-der s 5 m f The total population of non-cubtigers (T) is de ned to include the sum of ju-veniles transients and adults of both sexesThe model thus far assumes that prey areplentiful The only constraints on populationgrowth considered so far are the intrinsic sur-vival rates and the amount of territory avail-able to establish home ranges (ie Ks) Ifprey depletion lowers hunting success ratesit will lead to greater mortality of tigers Wetherefore extend the model to take account ofthe impact of prey availability on tiger popu-lation growth

Data on the intrinsic growth rates of indi-vidual prey species and the effects of browseand forage competition between species in ti-ger habitats is unavailable Hence we adopta simple approach and model the combinedbiomass of all prey species using a logisticequation of the form

Xt11 2 Xt 5 Xtr(1 2 XtX) 2 Hxt 2 Yt [5]

where Xt is the prey biomass at time t r is theintrinsic growth rate X is the prey carryingcapacity of the forest Hxt is the human har-vest of the prey biomass de ned in equation[3c] and Yt is the harvest of the prey by ti-gers which is described below

Field studies suggest that on average a ti-ger requires approximately 3000 kg of preyper year to survive (Sunquist Karanth andSunquist 1999) We therefore de ne the min-imum food intake of a tiger as M 5 3000kg Field observations also reveal that tigerssucceed in capturing between 10ndash20 ofthe available prey biomass in their homeranges (Schaller 1967 Sunquist 1981 John-singh 1983) In the presence of competingpredators such as wild dogs (Cuon alpinus)and leopards (Panthera pardus) a predationrate of 10 is deemed more appropriate(Karanth 2001) Thus the predation rate isde ned as r 5 010 It follows that the maxi-mum number of tigers that can be sustainedwith a prey base of Xt is rXtM Accord-

12 The random numbers were generated in Excel us-ing a random seed of 1 and mean of 3

206 Land Economics May 2003

ingly the prey biomass consumed by tigersis given by

Yt 5 MTt if rXt MTt

Yt 5 rXt otherwise [6a]

where Tt is the total number of tigers in pe-riod t M is the minimum food intake and ris the predation rate

Thus when prey are plentiful (ie rXt MTt) each tiger is able to meet its nutritionalneeds and successfully captures Mkg of preyper annum hence Yt 5 MTt On the otherhand if there is insuf cient prey to meet theneeds of the total population the level of pre-dation is at its maximum level Yt 5 rXt

A shortage of prey could have two effectson tiger survival prospects First prey deple-tion is likely to depress survival rates acrossall demographic stages Second a shortageof prey may also lower the carrying capacityof the habitat and thus lead to an expansionin the home ranges of breeding adult femalesIn the absence of data on the effects of preydepletion across demographic groups wefollow Karanth and Stith and assume thatprey depletion effects only (i) the carryingcapacity of the habitat and (ii) the survivalrates of cubs Thus under conditions of preydepletion the survival rates of cubs and thecarrying capacity are depressed by a preydepletion factor that is de ned as

h t11 5 51 if rXt 2 MTt $ 0

rXi

MTt

if rXt 2 MTt 0 [6b]

The cub survival rate (s c) and the carryingcapacity (Ks) are pre-multiplied by [6b]

It is acknowledged that the neglect of preydepletion effects on the survival rates acrossother demographic categories is unsatisfac-tory This approach can therefore be ex-pected to underestimate the true impact ofprey depletion if survival rates are depressedmore generally across all demographicstages However re nements of the modelmust await further research on this issue

Turning next to the effects of poachingPoachers target juveniles transients and

adults The number of tigers killed at eachstage is assumed to be proportional to the ex-isting distribution of tigers across the variousdemographic stages Let superscript i(i 5 jt a) denote demographic stages and recallthat superscript s 5 M F denotes genderDe ne k is

t as the proportion of male or femaletigers at demographic stage i(i 5 j t a) Thenthe numberofgenders tigers poachedatdemo-graphic stage i(i 5 j t a) is de ned as

HisTt11 5 HTtk is

t [6c]

where HTt is the total harvest of tigers as de-termined in equation [2b] k is

t 5 (T ist Tt) is

the proportion of gender s tigers at stagei(i 5 j t a) T is

t 5 number of gender s ti-gers at stage i and Tt is the total populationof tigers The number of tigers at each stageis thus lowered by the amount de ned inequation [6c]

V SIMULATION RESULTS

We now combine the economic models ofbehavior (equations [2b] and [3c]) and tigerpopulation growth (equations [4a]ndash[6c]) todetermine the time paths of lsquotiger stocksrsquo un-der alternative scenarios For given parame-ters the level of poaching emerges from theoptimising decisions of farmers and poach-ers This in turn affects tiger stock levelsModel parameters are varied to determinethe sensitivity of tiger population levels tochanges in economic circumstances

In the model labor is allocated across dif-ferent activities until the marginal returns areequalised The returns to off-farm work areexogenously xed and hence de ne the mini-mum payoffs to any activity that a householdwill accept The returns to agriculture varywith the price of agricultural commoditiesand the losses due to wildlife predation Thepayoffs to poaching also vary with wildlifestocks and the expected penalties for convic-tion It follows that changes in the returns toany one activity may induce a reallocation oflabor across other activities and thereforecould alter the level of poaching

The parameters for the basic tiger popula-tion model (equations [4a]ndash[4e]) are fromKaranth and Stith (1999) and are based on

79(2) Damania et al The Economics of Protecting Tiger Populations 207

eld research in India and Nepal Behavioraldata for subsistence farmers are drawn froma variety of sources13 The Data Appendixprovides details of the sources of informa-tion assumptions estimation methods andparameter values

The benchmark simulation draws on pa-rameter estimates based on the best availabledata for those regions with reasonablyhealthy tiger populations (eg the Kanha andBandipur Tiger Reserves in India) The habi-tat is assumed to comprise an area of approx-imately 1000 km2 with a prey carrying ca-pacity of 4500 kgkm214 It is supposed thatwhen prey are plentiful (rXt MTt) the un-disturbed habitat can sustain Kf 5 24 breed-ing adult females and Km 5 12 adult males(Karanth and Stith 1999 Kenney et al1995) In the base case farmers receive Rs1000 for each tiger killed face a ne of Rs25000 and a 2 probability of conviction(WPSI 2001)15 The off-farm wage rate is setat Rs 40 per day and the price of agriculturalproduce at Rs 85kg We begin by assuminga human population density of N 5 400households

It is important to distinguish between theecological effects and economic causes ofprey depletion from those of tiger poachingIn order to gain some understanding of theselinkages we begin by presenting simulationsfor the stylized case when only tiger poach-ing occurs We then assume that there is notiger poaching and consider the impact ofprey poaching on tiger populations Finallysimulations are presented for the completemodel where both tigers and their prey arehunted by subsistence farmers

Consider rst the effects of tiger poachingin isolation16 Curve A in Figure 1 shows thetiger population trajectory in a pristine habi-tat with no tiger poaching or prey depletionThe population achieves a stable equilibriumat 87 adult and juvenile tigers suggesting adensity of 9 tigers100 km2 This outcomeapproximates population levels in the frag-mented yet relatively healthy habitats foundin India and Nepal Curve B simulates the ef-fects of tiger poaching when the parametersare at the base case levels17 The tiger popula-tion declines to a stable 53 adult and juveniletigers with poachers harvesting 6 tigers per

year (approximately 11 percent of the popu-lation) Curve C simulates the effects of a50 increase in the price per tiger killed (Rs1500) The population falls substantially to27 tigers with 4 tigers harvested each year(approximately 12 of the population)

The simulation presented in Curve Dillus-trates the effects of an 80 increase in theprice paid to tiger poachers When the priceis increased to Rs 1800 the population de-clines to 19 tigers with 3 harvested each yearIn curve E when the poaching price is in-creased from Rs 1800 to Rs 1900 the tigerpopulation collapses within 50 years

This nding suggests that a relativelysmall increase in the payoffs to poaching(from Rs 1800 to Rs 1900) can drive a smallpopulation to extinction in a relatively shorttime period This is a signi cant resultwhich is consistent with Karanth and Stithrsquos(1999) simulations and related evidence thathunting of large felids can lead to sudden ex-tinction when it exceeds a certain thresholdlevel (Martin and de Meulanaer 1988 Bailey1993) The impact of poaching may thus bediscontinuous and prone to induce collapsesin populations This appears to be an exam-ple of the unstable equilibria frequently en-countered in discrete time predator-prey

13 Many of the tiger reserves are in tribal areas Itseems likely that behavior of tribal agriculturalistswould differ from those of other non-tribal agricultural-ists We have been compelled to use the only availabledata on agriculture which is based on non-tribal agri-culture There is clearly an urgent need for eldworkin and around tiger reserves to obtain more accurateinformation

14 The estimates of prey biomass in prime areas withtiger densities of between 10ndash12 per 100 km2 is derivedfrom data in Karanth and Nichols (2000) It is useful tonote that this estimate is also consistent with earlierstudies conducted using less advanced techniques Forinstance Johnsingh (1983) estimates a prey density of3382 kgkm2 in Bandipur reserve and a predation rateof 30 suggesting a possible carrying capacity of3382 (1 1 30) 5 4397 kgkm2

15 The assumption of a 2 conviction rate is a clearoverestimate of the true conviction probabilities ourbase case results thus underestimate the most likelyconsequence of poaching (WPSI 2001)

16 Formally this can be achieved by setting all thecoef cient of prey poaching to zero

17 In the base case farmers receive Rs 1000 for eachtiger killed face a ne of Rs 25000 and a 2 probabil-ity of conviction N is xed at 400 households

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

202 Land Economics May 2003

where F represents consumption of food Zconsumption of non-food items hx consump-tion of prey animals ai 0 (i 5 F Z x) arethe parameters of the utility function withaF 1 aZ 1 ax 5 1

Equation [1a] is maximized subject to theconstraints

wLo 1 pgG 1 (PT 2 qTWT)hT

5 pzZ 1 pFF 1 qxWxhx [1b]

G 5 kLbg(1 2 mX) [1c]

hx 5 dLxX [1d]

hT 5 LgT1T

R2e

[1e]

L 5 Lo 1 Lg 1 Lx 1 LT [1f]

where G is agricultural output X is the bio-mass of prey animals Lg is labor time de-voted to agriculture Lo is labor time devotedto off-farm work Lx is labor time spent hunt-ing prey animals LT is labor time on huntingtigers and pg pF pz PT are the prices of ag-ricultural produce food non-food commodi-ties and tigers respectively qi(i 5 T X) is theprobability of being convicted for poachingtigers (T) and their prey (X) and W i(i 5 TX) is the ne per unit harvest if convicted forpoaching tigers or their prey T is the numberof tigers and R the area of the reserve k xb g m d 0 are parameters

By equation [1a] household utility de-pends on the consumption of food (F ) othergoods (a non-food composite commodity[Z]) and the quantity of prey animalsconsumed (hx)

Equation [1b] is the household budgetconstraint Food and other goods are pur-chased at given prices pz and pF respectivelyThese purchases are nanced by (i) the saleof agricultural produce (G) which is sold ata price pg (ii) off farm labor (Lo) which isremunerated at a wage rate of w and (iii) ti-ger poaching (hT) The farmers receive anamount PT for each tiger killed which is de-termined by traders Since poaching is ille-gal it may result in conviction The expected

penalty for poaching tigers is qT WT whereqT is the probability of detection and convic-tion WT is the ne per tiger killed Thus theexpected payoffs from tiger poaching is de- ned by pT 5 (PT 2 qTWT) Finally sincepoaching prey is also illegal the householdmay incur an expected penalty qxWxhxwhere qx is the probability of detection andconviction Wx is the ne per prey animalpoached (hx)

Equation [1c] describes the agriculturalproduction function Following empiricalstudies on subsistence farming in India ag-ricultural production (G) is assumed to de-pend upon labor inputs (Lg) where b is theelasticity and ka constant (Deninger and Bis-wanger 1998 Saha 1994)6 The productionfunction also takes into account the damageto crops by the grazing and trampling of wildtiger prey This is given by (mX where X isthe biomass of prey animals and m is thedamage coef cient

Equation [1d] describes the prey harvestproduction function In the absence of dataon poaching of ungulate-prey in tiger habi-tats we adopt a functional form that hasbeen used in African studies of ungulatehunting (Kinyua van Kooten and Bulte2000) Thus the harvest of herbivores (hx) isa function of labor inputs (Lx) and the popu-lation of ungulate prey (X) with unit elastici-ties with respect to labor inputs and preypopulations

Equation [1e] is the tiger poaching pro-duction function There is no data availableon the nature of tiger poaching Hence anyfunctional form that is adopted is necessarilyconjectural Existing evidence suggests thattigers are usually killed by poisoning shoot-ing or setting traps and snares (WPSI 2001)techniques requiring only minimal invest-ment in capital equipment To economize onparameters we abstract from the need forcapital equipment and assume that the har-vest rate depends on the density of tigers and

6 The models used by Deninger and Biswanger(1999) and by Saha (1994) focus on agricultural house-holds While it is unclear how appropriate their models t the type of agriculture practiced in and around tigerhabitats in India the lack of better data limits our op-tions

79(2) Damania et al The Economics of Protecting Tiger Populations 203

the amount of search effort7 Tiger poachingis thus speci ed using a Cobb-Douglas func-tion with search effort and tiger densities asthe only arguments in the production func-tion The method by which the parameters onsearch effort (LT) and tiger density (TR) areestimated is described in the Data Appendix

Equation [1f ] is the time allocation con-straint which requires that labor time devotedto off-farm work (Lo) agriculture (Lg) andhunting tigers and their prey (LT Lx) mustequal the xed endowment of time (L) avail-able to the household Leisure is not includedas a choice variable as existing householdsurvey data in potential tiger habitats in Ne-pal suggest that opportunities for leisure con-sumption are limited in such poor ruralhouseholds (Bluffstone 1995)8

The utility maximization problem is basedon the notion that households take the timepath of exogenous variables such as thestock of herbivores (X) as given This re- ects the fact that there are assumed to bemany such households who have no propertyrights in wild animals Hence they have littleincentive to take account of the future conse-quences of their current actions Formallythis implies that households solve a static op-timisation problem Thus for notationalbrevity time symbols are suppressed in theabove equations9

Of particular interest in this context arethe solutions for poaching tigers and prey an-imals Solving the utility maximisation prob-lem in equations [1a]ndash[1f ] yields the follow-ing solution for the allocation of effortexpended on hunting tigers in each house-hold

LT 5 1gpTDe

w 21(12g)

[2a]

where pT 5 (PT 2 qTWT) is the net expectedpayoff from poaching a tiger D 5 TR is thedensity of tigers

Using [1e] the aggregate harvest of tigersis given by

HT NhT 5 N1gpTDe

w 2g12g

(D)e [2b]

The returns to off-farm work are exoge-nous and de ne the minimum payoffs to anyactivity that the household will accept Thusan increase in the wages paid for off-farmwork lowers poaching effort while an in-crease in the net expected payoffs frompoaching pT or an increase in the density oftigers D increases poaching effort

Labor time spent on hunting prey animalsis given by

Lc 5ax(w(L 2 Lg 2 LT) 1 pgG 1 pThT)

(w 1 qxWxdX)

[3a]

where

Lg 5 1 wbpgk(1 2 mX)2

1(b21)

[3b]

Substituting [3a] and [3b] in [1d] and aggre-gating over the N households gives the totallevel of prey animals hunted

Hx 5 NdLxX [3c]

The implicit price of hunting prey is againdetermined by the opportunity cost of timewhich is de ned by the off-farm wage rateThe hunted prey animals are consumedrather than sold hence an increase in thewage rate has con icting income and substi-tution effects on prey hunting levels (ie

7 Unlike many other species tigers are highly secre-tive animals inhabiting dense forests Therefore themain poaching constraint is likely to be the dif cultyinvolved in nding a tiger Field studies suggest that thelikelihood of an encounter depends on inter alia thedensity of tigers and the amount of search effort (Kar-anth and Nichols 2000)These key features are capturedin equation [1e]

8 Note also that since the analysis focuses on subsis-tence households with limited incomes we ignore thepossibility that households may hire labor In the ab-sence of adequate data we also ignore several othercomponents of agricultural household behavior includ-ing production and use of livestock (which may bepreyed upon by tigers) different types of farm outputconsumption of part of the farm output and the use ofother non-labor inputs (eg fertilizers)

9 It is perhaps worth noting that such myopic behav-iour has also been observed on communally held triballands where users own property rights to forest re-sources (Madhusudan and Karanth 1997)

204 Land Economics May 2003

paraHxparaw () 0) Speci cally the incomeeffect of higher wages increases the demandfor prey animals as a consumption goodwhile the substitution effect of higher off-farm wages raises the opportunity costs oftime devoted to hunting prey The net impactof higher off-farm wages therefore dependson the relative parameters of the model Incontrast an increase in the price of agricul-tural goods raises both income and the valueof crops damaged by prey This leads to in-creases in prey hunting levels (paraHxparapg 0)Similarly as expected a reduction in the ex-pected ne (qxWx) or an increase in the cropdamage coef cient (m) both lead to higherlevels of prey poaching (ie paraHxpara(qxWx) 0 paraHxparam 0)

This simple model of household behaviorignores a number of signi cant issues thatare of relevance in the context of wild animalpoaching in India10 For example anecdotalevidence suggests that corruption amongstforest of cials may be widespread in sometiger reserves in India (Breeden and Wright1996) This is perhaps a consequence of therelatively low wages that are paid to forestof cialsmdashoften in arrears In the absence ofdata on the incidence of corruption we donot explicitly deal with the modeling com-plications that arise when corruption ispervasive However it can be shown thatthe expected penalty for poaching in equa-tion [1b] is formally equivalent to the re-duced form payoff function that ariseswhen poachers bribe corrupt of cials11 Themodel also assumes that the probability ofconviction is xed In practice the proba-bility of a successful prosecution is likelyto depend on the level of expenditure bypoachers on their legal defense and the atti-tudes of local magistrates to wildlife pro-tection Moreover conviction rates andthe formal penalties for poaching may notcapture all the costs associated with beingdetected if caught poaching suggesting con-siderable uncertainty in the payoffs topoaching

IV TIGER BIOLOGY

The use of a single equation to model pop-ulation dynamics is often considered inap-

propriate for large predators that exhibitcomplex patterns of behaviour and face dif-ferent mortality rates over various stages intheir life cycle (see Burgman Ferson andAkcakaya 1993) Accordingly the existingliterature describes tiger population dy-namics using stage based stochastic demo-graphic models In this paper we follow thisconvention and extend the most recent modelof tiger demography by Karanth and Stith(1999) to incorporate predator-prey interac-tions

The Karanth-Stith model identi es tigersof both sexes in four distinct demographicstages cubs (younger than one year) juve-niles (one to two years) transients (tigersolder than two years in search of a homerange) and adults (breeding tigers with ahome range) In the absence of human pres-sures mortality rates at each stage of the lifecycle depend on intrinsic survival rateswhich incorporate deaths from natural fac-tors such as disease and intraspeci c compe-tition For expositional ease we begin bydescribing the dynamics of tiger populationswhen prey are plentiful and there is nopoaching

The number of cubs that survive in anyyear is determined by the birth rate of breed-ing females and the survival rate of cubs

Tct11 5 s cbTaf

t [4a]

where subscripts denote time periods Tct1 1 is

the number of surviving cubs in period t 11 s c is the survival rate of cubs b is the birth

10 We are grateful to a referee for suggesting theseissues

11 To see this suppose for simplicity that a fractionh of forest of cials are corruptible perhaps because ofthe low wages they receive The Indian forest serviceis a hierarchical organisation and the anecdotal accountsof corruption allege that bribery is most pervasiveamongst the lowestpaid of cials Let w be the probabil-ity that a poacher encounters a forest of cial Then cet-eris paribus the probability of being prosecuted isgiven by w(1 2 h) Furthermore if l is the probabilityof a successful conviction then q j 5 l jw j(1 2 h) ( j5 T X) is the total probability of being convicted forpoaching Damania (2002) assesses the complicationsthat arise in determining optimal environmental regula-tions under corruption We do not explore these impor-tant and complex issues in this paper

79(2) Damania et al The Economics of Protecting Tiger Populations 205

rate per breeding adult female and Taft is the

number of breeding adult females FollowingKaranth and Stith (1999) we assume anequal sex ratio at birth and mean litter size ofthree The birth rate b is treated as a Poissonvariable with a mean of three Randomnessis included in the model to capture demo-graphic stochasticity12

The surviving cubs move to the juvenilestage in the following period The number ofjuveniles who survive is

T jst11 5 s jsT cs

t (s 5 m f ) [4b]

where T jst1 1 is the number of surviving juve-

nile males (m) and females ( f ) in period t 11 s js(s 5 m f ) is the intrinsic survival rateof juvenile males (m) and females ( f )

At two years the surviving juveniles be-come transients Transients are de ned asadult tigers in search of home territories inwhich to hunt and breed If a vacant homerange is available a transient immediatelyoccupies the territory and is classi ed as abreeding adult Let Ks (s 5 m f ) denote themaximum number of territories available foradults of gender s 5 m f Let Tas

t be the num-ber of surviving adults of gender s 5 m fwith existing home ranges Then the numberof vacant territories available for the tran-sients to occupy is given by

V st11 5 Max(0 Ks 2 Tas

t )(s 5 m f ) [4c]

The number of transients in period (t 1 1) isde ned by (i) the number of transients whosurvive from the previous period (ii) juve-niles who progress to the transient stage (iii)minus the transients who nd home rangesand thus exit to the breeding adult stage

Ttst11 5 sts(s jsT js

t 1 Ttst ) 2 Vs

t11(s 5 m f ) [4d]

where Tt st1 1 is the number of surviving tran-

sients in period t 1 1 st s is the survival rateof transients of gender s 5 m f

Finally the number of breeding adults isgiven by the existing number of survivingadults and the new recruits to the category ofbreeding adult

T ast11 5 (s asTas

t 1 Vst11) [4e]

where s as is the survival rate of adults of gen-der s 5 m f The total population of non-cubtigers (T) is de ned to include the sum of ju-veniles transients and adults of both sexesThe model thus far assumes that prey areplentiful The only constraints on populationgrowth considered so far are the intrinsic sur-vival rates and the amount of territory avail-able to establish home ranges (ie Ks) Ifprey depletion lowers hunting success ratesit will lead to greater mortality of tigers Wetherefore extend the model to take account ofthe impact of prey availability on tiger popu-lation growth

Data on the intrinsic growth rates of indi-vidual prey species and the effects of browseand forage competition between species in ti-ger habitats is unavailable Hence we adopta simple approach and model the combinedbiomass of all prey species using a logisticequation of the form

Xt11 2 Xt 5 Xtr(1 2 XtX) 2 Hxt 2 Yt [5]

where Xt is the prey biomass at time t r is theintrinsic growth rate X is the prey carryingcapacity of the forest Hxt is the human har-vest of the prey biomass de ned in equation[3c] and Yt is the harvest of the prey by ti-gers which is described below

Field studies suggest that on average a ti-ger requires approximately 3000 kg of preyper year to survive (Sunquist Karanth andSunquist 1999) We therefore de ne the min-imum food intake of a tiger as M 5 3000kg Field observations also reveal that tigerssucceed in capturing between 10ndash20 ofthe available prey biomass in their homeranges (Schaller 1967 Sunquist 1981 John-singh 1983) In the presence of competingpredators such as wild dogs (Cuon alpinus)and leopards (Panthera pardus) a predationrate of 10 is deemed more appropriate(Karanth 2001) Thus the predation rate isde ned as r 5 010 It follows that the maxi-mum number of tigers that can be sustainedwith a prey base of Xt is rXtM Accord-

12 The random numbers were generated in Excel us-ing a random seed of 1 and mean of 3

206 Land Economics May 2003

ingly the prey biomass consumed by tigersis given by

Yt 5 MTt if rXt MTt

Yt 5 rXt otherwise [6a]

where Tt is the total number of tigers in pe-riod t M is the minimum food intake and ris the predation rate

Thus when prey are plentiful (ie rXt MTt) each tiger is able to meet its nutritionalneeds and successfully captures Mkg of preyper annum hence Yt 5 MTt On the otherhand if there is insuf cient prey to meet theneeds of the total population the level of pre-dation is at its maximum level Yt 5 rXt

A shortage of prey could have two effectson tiger survival prospects First prey deple-tion is likely to depress survival rates acrossall demographic stages Second a shortageof prey may also lower the carrying capacityof the habitat and thus lead to an expansionin the home ranges of breeding adult femalesIn the absence of data on the effects of preydepletion across demographic groups wefollow Karanth and Stith and assume thatprey depletion effects only (i) the carryingcapacity of the habitat and (ii) the survivalrates of cubs Thus under conditions of preydepletion the survival rates of cubs and thecarrying capacity are depressed by a preydepletion factor that is de ned as

h t11 5 51 if rXt 2 MTt $ 0

rXi

MTt

if rXt 2 MTt 0 [6b]

The cub survival rate (s c) and the carryingcapacity (Ks) are pre-multiplied by [6b]

It is acknowledged that the neglect of preydepletion effects on the survival rates acrossother demographic categories is unsatisfac-tory This approach can therefore be ex-pected to underestimate the true impact ofprey depletion if survival rates are depressedmore generally across all demographicstages However re nements of the modelmust await further research on this issue

Turning next to the effects of poachingPoachers target juveniles transients and

adults The number of tigers killed at eachstage is assumed to be proportional to the ex-isting distribution of tigers across the variousdemographic stages Let superscript i(i 5 jt a) denote demographic stages and recallthat superscript s 5 M F denotes genderDe ne k is

t as the proportion of male or femaletigers at demographic stage i(i 5 j t a) Thenthe numberofgenders tigers poachedatdemo-graphic stage i(i 5 j t a) is de ned as

HisTt11 5 HTtk is

t [6c]

where HTt is the total harvest of tigers as de-termined in equation [2b] k is

t 5 (T ist Tt) is

the proportion of gender s tigers at stagei(i 5 j t a) T is

t 5 number of gender s ti-gers at stage i and Tt is the total populationof tigers The number of tigers at each stageis thus lowered by the amount de ned inequation [6c]

V SIMULATION RESULTS

We now combine the economic models ofbehavior (equations [2b] and [3c]) and tigerpopulation growth (equations [4a]ndash[6c]) todetermine the time paths of lsquotiger stocksrsquo un-der alternative scenarios For given parame-ters the level of poaching emerges from theoptimising decisions of farmers and poach-ers This in turn affects tiger stock levelsModel parameters are varied to determinethe sensitivity of tiger population levels tochanges in economic circumstances

In the model labor is allocated across dif-ferent activities until the marginal returns areequalised The returns to off-farm work areexogenously xed and hence de ne the mini-mum payoffs to any activity that a householdwill accept The returns to agriculture varywith the price of agricultural commoditiesand the losses due to wildlife predation Thepayoffs to poaching also vary with wildlifestocks and the expected penalties for convic-tion It follows that changes in the returns toany one activity may induce a reallocation oflabor across other activities and thereforecould alter the level of poaching

The parameters for the basic tiger popula-tion model (equations [4a]ndash[4e]) are fromKaranth and Stith (1999) and are based on

79(2) Damania et al The Economics of Protecting Tiger Populations 207

eld research in India and Nepal Behavioraldata for subsistence farmers are drawn froma variety of sources13 The Data Appendixprovides details of the sources of informa-tion assumptions estimation methods andparameter values

The benchmark simulation draws on pa-rameter estimates based on the best availabledata for those regions with reasonablyhealthy tiger populations (eg the Kanha andBandipur Tiger Reserves in India) The habi-tat is assumed to comprise an area of approx-imately 1000 km2 with a prey carrying ca-pacity of 4500 kgkm214 It is supposed thatwhen prey are plentiful (rXt MTt) the un-disturbed habitat can sustain Kf 5 24 breed-ing adult females and Km 5 12 adult males(Karanth and Stith 1999 Kenney et al1995) In the base case farmers receive Rs1000 for each tiger killed face a ne of Rs25000 and a 2 probability of conviction(WPSI 2001)15 The off-farm wage rate is setat Rs 40 per day and the price of agriculturalproduce at Rs 85kg We begin by assuminga human population density of N 5 400households

It is important to distinguish between theecological effects and economic causes ofprey depletion from those of tiger poachingIn order to gain some understanding of theselinkages we begin by presenting simulationsfor the stylized case when only tiger poach-ing occurs We then assume that there is notiger poaching and consider the impact ofprey poaching on tiger populations Finallysimulations are presented for the completemodel where both tigers and their prey arehunted by subsistence farmers

Consider rst the effects of tiger poachingin isolation16 Curve A in Figure 1 shows thetiger population trajectory in a pristine habi-tat with no tiger poaching or prey depletionThe population achieves a stable equilibriumat 87 adult and juvenile tigers suggesting adensity of 9 tigers100 km2 This outcomeapproximates population levels in the frag-mented yet relatively healthy habitats foundin India and Nepal Curve B simulates the ef-fects of tiger poaching when the parametersare at the base case levels17 The tiger popula-tion declines to a stable 53 adult and juveniletigers with poachers harvesting 6 tigers per

year (approximately 11 percent of the popu-lation) Curve C simulates the effects of a50 increase in the price per tiger killed (Rs1500) The population falls substantially to27 tigers with 4 tigers harvested each year(approximately 12 of the population)

The simulation presented in Curve Dillus-trates the effects of an 80 increase in theprice paid to tiger poachers When the priceis increased to Rs 1800 the population de-clines to 19 tigers with 3 harvested each yearIn curve E when the poaching price is in-creased from Rs 1800 to Rs 1900 the tigerpopulation collapses within 50 years

This nding suggests that a relativelysmall increase in the payoffs to poaching(from Rs 1800 to Rs 1900) can drive a smallpopulation to extinction in a relatively shorttime period This is a signi cant resultwhich is consistent with Karanth and Stithrsquos(1999) simulations and related evidence thathunting of large felids can lead to sudden ex-tinction when it exceeds a certain thresholdlevel (Martin and de Meulanaer 1988 Bailey1993) The impact of poaching may thus bediscontinuous and prone to induce collapsesin populations This appears to be an exam-ple of the unstable equilibria frequently en-countered in discrete time predator-prey

13 Many of the tiger reserves are in tribal areas Itseems likely that behavior of tribal agriculturalistswould differ from those of other non-tribal agricultural-ists We have been compelled to use the only availabledata on agriculture which is based on non-tribal agri-culture There is clearly an urgent need for eldworkin and around tiger reserves to obtain more accurateinformation

14 The estimates of prey biomass in prime areas withtiger densities of between 10ndash12 per 100 km2 is derivedfrom data in Karanth and Nichols (2000) It is useful tonote that this estimate is also consistent with earlierstudies conducted using less advanced techniques Forinstance Johnsingh (1983) estimates a prey density of3382 kgkm2 in Bandipur reserve and a predation rateof 30 suggesting a possible carrying capacity of3382 (1 1 30) 5 4397 kgkm2

15 The assumption of a 2 conviction rate is a clearoverestimate of the true conviction probabilities ourbase case results thus underestimate the most likelyconsequence of poaching (WPSI 2001)

16 Formally this can be achieved by setting all thecoef cient of prey poaching to zero

17 In the base case farmers receive Rs 1000 for eachtiger killed face a ne of Rs 25000 and a 2 probabil-ity of conviction N is xed at 400 households

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

79(2) Damania et al The Economics of Protecting Tiger Populations 203

the amount of search effort7 Tiger poachingis thus speci ed using a Cobb-Douglas func-tion with search effort and tiger densities asthe only arguments in the production func-tion The method by which the parameters onsearch effort (LT) and tiger density (TR) areestimated is described in the Data Appendix

Equation [1f ] is the time allocation con-straint which requires that labor time devotedto off-farm work (Lo) agriculture (Lg) andhunting tigers and their prey (LT Lx) mustequal the xed endowment of time (L) avail-able to the household Leisure is not includedas a choice variable as existing householdsurvey data in potential tiger habitats in Ne-pal suggest that opportunities for leisure con-sumption are limited in such poor ruralhouseholds (Bluffstone 1995)8

The utility maximization problem is basedon the notion that households take the timepath of exogenous variables such as thestock of herbivores (X) as given This re- ects the fact that there are assumed to bemany such households who have no propertyrights in wild animals Hence they have littleincentive to take account of the future conse-quences of their current actions Formallythis implies that households solve a static op-timisation problem Thus for notationalbrevity time symbols are suppressed in theabove equations9

Of particular interest in this context arethe solutions for poaching tigers and prey an-imals Solving the utility maximisation prob-lem in equations [1a]ndash[1f ] yields the follow-ing solution for the allocation of effortexpended on hunting tigers in each house-hold

LT 5 1gpTDe

w 21(12g)

[2a]

where pT 5 (PT 2 qTWT) is the net expectedpayoff from poaching a tiger D 5 TR is thedensity of tigers

Using [1e] the aggregate harvest of tigersis given by

HT NhT 5 N1gpTDe

w 2g12g

(D)e [2b]

The returns to off-farm work are exoge-nous and de ne the minimum payoffs to anyactivity that the household will accept Thusan increase in the wages paid for off-farmwork lowers poaching effort while an in-crease in the net expected payoffs frompoaching pT or an increase in the density oftigers D increases poaching effort

Labor time spent on hunting prey animalsis given by

Lc 5ax(w(L 2 Lg 2 LT) 1 pgG 1 pThT)

(w 1 qxWxdX)

[3a]

where

Lg 5 1 wbpgk(1 2 mX)2

1(b21)

[3b]

Substituting [3a] and [3b] in [1d] and aggre-gating over the N households gives the totallevel of prey animals hunted

Hx 5 NdLxX [3c]

The implicit price of hunting prey is againdetermined by the opportunity cost of timewhich is de ned by the off-farm wage rateThe hunted prey animals are consumedrather than sold hence an increase in thewage rate has con icting income and substi-tution effects on prey hunting levels (ie

7 Unlike many other species tigers are highly secre-tive animals inhabiting dense forests Therefore themain poaching constraint is likely to be the dif cultyinvolved in nding a tiger Field studies suggest that thelikelihood of an encounter depends on inter alia thedensity of tigers and the amount of search effort (Kar-anth and Nichols 2000)These key features are capturedin equation [1e]

8 Note also that since the analysis focuses on subsis-tence households with limited incomes we ignore thepossibility that households may hire labor In the ab-sence of adequate data we also ignore several othercomponents of agricultural household behavior includ-ing production and use of livestock (which may bepreyed upon by tigers) different types of farm outputconsumption of part of the farm output and the use ofother non-labor inputs (eg fertilizers)

9 It is perhaps worth noting that such myopic behav-iour has also been observed on communally held triballands where users own property rights to forest re-sources (Madhusudan and Karanth 1997)

204 Land Economics May 2003

paraHxparaw () 0) Speci cally the incomeeffect of higher wages increases the demandfor prey animals as a consumption goodwhile the substitution effect of higher off-farm wages raises the opportunity costs oftime devoted to hunting prey The net impactof higher off-farm wages therefore dependson the relative parameters of the model Incontrast an increase in the price of agricul-tural goods raises both income and the valueof crops damaged by prey This leads to in-creases in prey hunting levels (paraHxparapg 0)Similarly as expected a reduction in the ex-pected ne (qxWx) or an increase in the cropdamage coef cient (m) both lead to higherlevels of prey poaching (ie paraHxpara(qxWx) 0 paraHxparam 0)

This simple model of household behaviorignores a number of signi cant issues thatare of relevance in the context of wild animalpoaching in India10 For example anecdotalevidence suggests that corruption amongstforest of cials may be widespread in sometiger reserves in India (Breeden and Wright1996) This is perhaps a consequence of therelatively low wages that are paid to forestof cialsmdashoften in arrears In the absence ofdata on the incidence of corruption we donot explicitly deal with the modeling com-plications that arise when corruption ispervasive However it can be shown thatthe expected penalty for poaching in equa-tion [1b] is formally equivalent to the re-duced form payoff function that ariseswhen poachers bribe corrupt of cials11 Themodel also assumes that the probability ofconviction is xed In practice the proba-bility of a successful prosecution is likelyto depend on the level of expenditure bypoachers on their legal defense and the atti-tudes of local magistrates to wildlife pro-tection Moreover conviction rates andthe formal penalties for poaching may notcapture all the costs associated with beingdetected if caught poaching suggesting con-siderable uncertainty in the payoffs topoaching

IV TIGER BIOLOGY

The use of a single equation to model pop-ulation dynamics is often considered inap-

propriate for large predators that exhibitcomplex patterns of behaviour and face dif-ferent mortality rates over various stages intheir life cycle (see Burgman Ferson andAkcakaya 1993) Accordingly the existingliterature describes tiger population dy-namics using stage based stochastic demo-graphic models In this paper we follow thisconvention and extend the most recent modelof tiger demography by Karanth and Stith(1999) to incorporate predator-prey interac-tions

The Karanth-Stith model identi es tigersof both sexes in four distinct demographicstages cubs (younger than one year) juve-niles (one to two years) transients (tigersolder than two years in search of a homerange) and adults (breeding tigers with ahome range) In the absence of human pres-sures mortality rates at each stage of the lifecycle depend on intrinsic survival rateswhich incorporate deaths from natural fac-tors such as disease and intraspeci c compe-tition For expositional ease we begin bydescribing the dynamics of tiger populationswhen prey are plentiful and there is nopoaching

The number of cubs that survive in anyyear is determined by the birth rate of breed-ing females and the survival rate of cubs

Tct11 5 s cbTaf

t [4a]

where subscripts denote time periods Tct1 1 is

the number of surviving cubs in period t 11 s c is the survival rate of cubs b is the birth

10 We are grateful to a referee for suggesting theseissues

11 To see this suppose for simplicity that a fractionh of forest of cials are corruptible perhaps because ofthe low wages they receive The Indian forest serviceis a hierarchical organisation and the anecdotal accountsof corruption allege that bribery is most pervasiveamongst the lowestpaid of cials Let w be the probabil-ity that a poacher encounters a forest of cial Then cet-eris paribus the probability of being prosecuted isgiven by w(1 2 h) Furthermore if l is the probabilityof a successful conviction then q j 5 l jw j(1 2 h) ( j5 T X) is the total probability of being convicted forpoaching Damania (2002) assesses the complicationsthat arise in determining optimal environmental regula-tions under corruption We do not explore these impor-tant and complex issues in this paper

79(2) Damania et al The Economics of Protecting Tiger Populations 205

rate per breeding adult female and Taft is the

number of breeding adult females FollowingKaranth and Stith (1999) we assume anequal sex ratio at birth and mean litter size ofthree The birth rate b is treated as a Poissonvariable with a mean of three Randomnessis included in the model to capture demo-graphic stochasticity12

The surviving cubs move to the juvenilestage in the following period The number ofjuveniles who survive is

T jst11 5 s jsT cs

t (s 5 m f ) [4b]

where T jst1 1 is the number of surviving juve-

nile males (m) and females ( f ) in period t 11 s js(s 5 m f ) is the intrinsic survival rateof juvenile males (m) and females ( f )

At two years the surviving juveniles be-come transients Transients are de ned asadult tigers in search of home territories inwhich to hunt and breed If a vacant homerange is available a transient immediatelyoccupies the territory and is classi ed as abreeding adult Let Ks (s 5 m f ) denote themaximum number of territories available foradults of gender s 5 m f Let Tas

t be the num-ber of surviving adults of gender s 5 m fwith existing home ranges Then the numberof vacant territories available for the tran-sients to occupy is given by

V st11 5 Max(0 Ks 2 Tas

t )(s 5 m f ) [4c]

The number of transients in period (t 1 1) isde ned by (i) the number of transients whosurvive from the previous period (ii) juve-niles who progress to the transient stage (iii)minus the transients who nd home rangesand thus exit to the breeding adult stage

Ttst11 5 sts(s jsT js

t 1 Ttst ) 2 Vs

t11(s 5 m f ) [4d]

where Tt st1 1 is the number of surviving tran-

sients in period t 1 1 st s is the survival rateof transients of gender s 5 m f

Finally the number of breeding adults isgiven by the existing number of survivingadults and the new recruits to the category ofbreeding adult

T ast11 5 (s asTas

t 1 Vst11) [4e]

where s as is the survival rate of adults of gen-der s 5 m f The total population of non-cubtigers (T) is de ned to include the sum of ju-veniles transients and adults of both sexesThe model thus far assumes that prey areplentiful The only constraints on populationgrowth considered so far are the intrinsic sur-vival rates and the amount of territory avail-able to establish home ranges (ie Ks) Ifprey depletion lowers hunting success ratesit will lead to greater mortality of tigers Wetherefore extend the model to take account ofthe impact of prey availability on tiger popu-lation growth

Data on the intrinsic growth rates of indi-vidual prey species and the effects of browseand forage competition between species in ti-ger habitats is unavailable Hence we adopta simple approach and model the combinedbiomass of all prey species using a logisticequation of the form

Xt11 2 Xt 5 Xtr(1 2 XtX) 2 Hxt 2 Yt [5]

where Xt is the prey biomass at time t r is theintrinsic growth rate X is the prey carryingcapacity of the forest Hxt is the human har-vest of the prey biomass de ned in equation[3c] and Yt is the harvest of the prey by ti-gers which is described below

Field studies suggest that on average a ti-ger requires approximately 3000 kg of preyper year to survive (Sunquist Karanth andSunquist 1999) We therefore de ne the min-imum food intake of a tiger as M 5 3000kg Field observations also reveal that tigerssucceed in capturing between 10ndash20 ofthe available prey biomass in their homeranges (Schaller 1967 Sunquist 1981 John-singh 1983) In the presence of competingpredators such as wild dogs (Cuon alpinus)and leopards (Panthera pardus) a predationrate of 10 is deemed more appropriate(Karanth 2001) Thus the predation rate isde ned as r 5 010 It follows that the maxi-mum number of tigers that can be sustainedwith a prey base of Xt is rXtM Accord-

12 The random numbers were generated in Excel us-ing a random seed of 1 and mean of 3

206 Land Economics May 2003

ingly the prey biomass consumed by tigersis given by

Yt 5 MTt if rXt MTt

Yt 5 rXt otherwise [6a]

where Tt is the total number of tigers in pe-riod t M is the minimum food intake and ris the predation rate

Thus when prey are plentiful (ie rXt MTt) each tiger is able to meet its nutritionalneeds and successfully captures Mkg of preyper annum hence Yt 5 MTt On the otherhand if there is insuf cient prey to meet theneeds of the total population the level of pre-dation is at its maximum level Yt 5 rXt

A shortage of prey could have two effectson tiger survival prospects First prey deple-tion is likely to depress survival rates acrossall demographic stages Second a shortageof prey may also lower the carrying capacityof the habitat and thus lead to an expansionin the home ranges of breeding adult femalesIn the absence of data on the effects of preydepletion across demographic groups wefollow Karanth and Stith and assume thatprey depletion effects only (i) the carryingcapacity of the habitat and (ii) the survivalrates of cubs Thus under conditions of preydepletion the survival rates of cubs and thecarrying capacity are depressed by a preydepletion factor that is de ned as

h t11 5 51 if rXt 2 MTt $ 0

rXi

MTt

if rXt 2 MTt 0 [6b]

The cub survival rate (s c) and the carryingcapacity (Ks) are pre-multiplied by [6b]

It is acknowledged that the neglect of preydepletion effects on the survival rates acrossother demographic categories is unsatisfac-tory This approach can therefore be ex-pected to underestimate the true impact ofprey depletion if survival rates are depressedmore generally across all demographicstages However re nements of the modelmust await further research on this issue

Turning next to the effects of poachingPoachers target juveniles transients and

adults The number of tigers killed at eachstage is assumed to be proportional to the ex-isting distribution of tigers across the variousdemographic stages Let superscript i(i 5 jt a) denote demographic stages and recallthat superscript s 5 M F denotes genderDe ne k is

t as the proportion of male or femaletigers at demographic stage i(i 5 j t a) Thenthe numberofgenders tigers poachedatdemo-graphic stage i(i 5 j t a) is de ned as

HisTt11 5 HTtk is

t [6c]

where HTt is the total harvest of tigers as de-termined in equation [2b] k is

t 5 (T ist Tt) is

the proportion of gender s tigers at stagei(i 5 j t a) T is

t 5 number of gender s ti-gers at stage i and Tt is the total populationof tigers The number of tigers at each stageis thus lowered by the amount de ned inequation [6c]

V SIMULATION RESULTS

We now combine the economic models ofbehavior (equations [2b] and [3c]) and tigerpopulation growth (equations [4a]ndash[6c]) todetermine the time paths of lsquotiger stocksrsquo un-der alternative scenarios For given parame-ters the level of poaching emerges from theoptimising decisions of farmers and poach-ers This in turn affects tiger stock levelsModel parameters are varied to determinethe sensitivity of tiger population levels tochanges in economic circumstances

In the model labor is allocated across dif-ferent activities until the marginal returns areequalised The returns to off-farm work areexogenously xed and hence de ne the mini-mum payoffs to any activity that a householdwill accept The returns to agriculture varywith the price of agricultural commoditiesand the losses due to wildlife predation Thepayoffs to poaching also vary with wildlifestocks and the expected penalties for convic-tion It follows that changes in the returns toany one activity may induce a reallocation oflabor across other activities and thereforecould alter the level of poaching

The parameters for the basic tiger popula-tion model (equations [4a]ndash[4e]) are fromKaranth and Stith (1999) and are based on

79(2) Damania et al The Economics of Protecting Tiger Populations 207

eld research in India and Nepal Behavioraldata for subsistence farmers are drawn froma variety of sources13 The Data Appendixprovides details of the sources of informa-tion assumptions estimation methods andparameter values

The benchmark simulation draws on pa-rameter estimates based on the best availabledata for those regions with reasonablyhealthy tiger populations (eg the Kanha andBandipur Tiger Reserves in India) The habi-tat is assumed to comprise an area of approx-imately 1000 km2 with a prey carrying ca-pacity of 4500 kgkm214 It is supposed thatwhen prey are plentiful (rXt MTt) the un-disturbed habitat can sustain Kf 5 24 breed-ing adult females and Km 5 12 adult males(Karanth and Stith 1999 Kenney et al1995) In the base case farmers receive Rs1000 for each tiger killed face a ne of Rs25000 and a 2 probability of conviction(WPSI 2001)15 The off-farm wage rate is setat Rs 40 per day and the price of agriculturalproduce at Rs 85kg We begin by assuminga human population density of N 5 400households

It is important to distinguish between theecological effects and economic causes ofprey depletion from those of tiger poachingIn order to gain some understanding of theselinkages we begin by presenting simulationsfor the stylized case when only tiger poach-ing occurs We then assume that there is notiger poaching and consider the impact ofprey poaching on tiger populations Finallysimulations are presented for the completemodel where both tigers and their prey arehunted by subsistence farmers

Consider rst the effects of tiger poachingin isolation16 Curve A in Figure 1 shows thetiger population trajectory in a pristine habi-tat with no tiger poaching or prey depletionThe population achieves a stable equilibriumat 87 adult and juvenile tigers suggesting adensity of 9 tigers100 km2 This outcomeapproximates population levels in the frag-mented yet relatively healthy habitats foundin India and Nepal Curve B simulates the ef-fects of tiger poaching when the parametersare at the base case levels17 The tiger popula-tion declines to a stable 53 adult and juveniletigers with poachers harvesting 6 tigers per

year (approximately 11 percent of the popu-lation) Curve C simulates the effects of a50 increase in the price per tiger killed (Rs1500) The population falls substantially to27 tigers with 4 tigers harvested each year(approximately 12 of the population)

The simulation presented in Curve Dillus-trates the effects of an 80 increase in theprice paid to tiger poachers When the priceis increased to Rs 1800 the population de-clines to 19 tigers with 3 harvested each yearIn curve E when the poaching price is in-creased from Rs 1800 to Rs 1900 the tigerpopulation collapses within 50 years

This nding suggests that a relativelysmall increase in the payoffs to poaching(from Rs 1800 to Rs 1900) can drive a smallpopulation to extinction in a relatively shorttime period This is a signi cant resultwhich is consistent with Karanth and Stithrsquos(1999) simulations and related evidence thathunting of large felids can lead to sudden ex-tinction when it exceeds a certain thresholdlevel (Martin and de Meulanaer 1988 Bailey1993) The impact of poaching may thus bediscontinuous and prone to induce collapsesin populations This appears to be an exam-ple of the unstable equilibria frequently en-countered in discrete time predator-prey

13 Many of the tiger reserves are in tribal areas Itseems likely that behavior of tribal agriculturalistswould differ from those of other non-tribal agricultural-ists We have been compelled to use the only availabledata on agriculture which is based on non-tribal agri-culture There is clearly an urgent need for eldworkin and around tiger reserves to obtain more accurateinformation

14 The estimates of prey biomass in prime areas withtiger densities of between 10ndash12 per 100 km2 is derivedfrom data in Karanth and Nichols (2000) It is useful tonote that this estimate is also consistent with earlierstudies conducted using less advanced techniques Forinstance Johnsingh (1983) estimates a prey density of3382 kgkm2 in Bandipur reserve and a predation rateof 30 suggesting a possible carrying capacity of3382 (1 1 30) 5 4397 kgkm2

15 The assumption of a 2 conviction rate is a clearoverestimate of the true conviction probabilities ourbase case results thus underestimate the most likelyconsequence of poaching (WPSI 2001)

16 Formally this can be achieved by setting all thecoef cient of prey poaching to zero

17 In the base case farmers receive Rs 1000 for eachtiger killed face a ne of Rs 25000 and a 2 probabil-ity of conviction N is xed at 400 households

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

204 Land Economics May 2003

paraHxparaw () 0) Speci cally the incomeeffect of higher wages increases the demandfor prey animals as a consumption goodwhile the substitution effect of higher off-farm wages raises the opportunity costs oftime devoted to hunting prey The net impactof higher off-farm wages therefore dependson the relative parameters of the model Incontrast an increase in the price of agricul-tural goods raises both income and the valueof crops damaged by prey This leads to in-creases in prey hunting levels (paraHxparapg 0)Similarly as expected a reduction in the ex-pected ne (qxWx) or an increase in the cropdamage coef cient (m) both lead to higherlevels of prey poaching (ie paraHxpara(qxWx) 0 paraHxparam 0)

This simple model of household behaviorignores a number of signi cant issues thatare of relevance in the context of wild animalpoaching in India10 For example anecdotalevidence suggests that corruption amongstforest of cials may be widespread in sometiger reserves in India (Breeden and Wright1996) This is perhaps a consequence of therelatively low wages that are paid to forestof cialsmdashoften in arrears In the absence ofdata on the incidence of corruption we donot explicitly deal with the modeling com-plications that arise when corruption ispervasive However it can be shown thatthe expected penalty for poaching in equa-tion [1b] is formally equivalent to the re-duced form payoff function that ariseswhen poachers bribe corrupt of cials11 Themodel also assumes that the probability ofconviction is xed In practice the proba-bility of a successful prosecution is likelyto depend on the level of expenditure bypoachers on their legal defense and the atti-tudes of local magistrates to wildlife pro-tection Moreover conviction rates andthe formal penalties for poaching may notcapture all the costs associated with beingdetected if caught poaching suggesting con-siderable uncertainty in the payoffs topoaching

IV TIGER BIOLOGY

The use of a single equation to model pop-ulation dynamics is often considered inap-

propriate for large predators that exhibitcomplex patterns of behaviour and face dif-ferent mortality rates over various stages intheir life cycle (see Burgman Ferson andAkcakaya 1993) Accordingly the existingliterature describes tiger population dy-namics using stage based stochastic demo-graphic models In this paper we follow thisconvention and extend the most recent modelof tiger demography by Karanth and Stith(1999) to incorporate predator-prey interac-tions

The Karanth-Stith model identi es tigersof both sexes in four distinct demographicstages cubs (younger than one year) juve-niles (one to two years) transients (tigersolder than two years in search of a homerange) and adults (breeding tigers with ahome range) In the absence of human pres-sures mortality rates at each stage of the lifecycle depend on intrinsic survival rateswhich incorporate deaths from natural fac-tors such as disease and intraspeci c compe-tition For expositional ease we begin bydescribing the dynamics of tiger populationswhen prey are plentiful and there is nopoaching

The number of cubs that survive in anyyear is determined by the birth rate of breed-ing females and the survival rate of cubs

Tct11 5 s cbTaf

t [4a]

where subscripts denote time periods Tct1 1 is

the number of surviving cubs in period t 11 s c is the survival rate of cubs b is the birth

10 We are grateful to a referee for suggesting theseissues

11 To see this suppose for simplicity that a fractionh of forest of cials are corruptible perhaps because ofthe low wages they receive The Indian forest serviceis a hierarchical organisation and the anecdotal accountsof corruption allege that bribery is most pervasiveamongst the lowestpaid of cials Let w be the probabil-ity that a poacher encounters a forest of cial Then cet-eris paribus the probability of being prosecuted isgiven by w(1 2 h) Furthermore if l is the probabilityof a successful conviction then q j 5 l jw j(1 2 h) ( j5 T X) is the total probability of being convicted forpoaching Damania (2002) assesses the complicationsthat arise in determining optimal environmental regula-tions under corruption We do not explore these impor-tant and complex issues in this paper

79(2) Damania et al The Economics of Protecting Tiger Populations 205

rate per breeding adult female and Taft is the

number of breeding adult females FollowingKaranth and Stith (1999) we assume anequal sex ratio at birth and mean litter size ofthree The birth rate b is treated as a Poissonvariable with a mean of three Randomnessis included in the model to capture demo-graphic stochasticity12

The surviving cubs move to the juvenilestage in the following period The number ofjuveniles who survive is

T jst11 5 s jsT cs

t (s 5 m f ) [4b]

where T jst1 1 is the number of surviving juve-

nile males (m) and females ( f ) in period t 11 s js(s 5 m f ) is the intrinsic survival rateof juvenile males (m) and females ( f )

At two years the surviving juveniles be-come transients Transients are de ned asadult tigers in search of home territories inwhich to hunt and breed If a vacant homerange is available a transient immediatelyoccupies the territory and is classi ed as abreeding adult Let Ks (s 5 m f ) denote themaximum number of territories available foradults of gender s 5 m f Let Tas

t be the num-ber of surviving adults of gender s 5 m fwith existing home ranges Then the numberof vacant territories available for the tran-sients to occupy is given by

V st11 5 Max(0 Ks 2 Tas

t )(s 5 m f ) [4c]

The number of transients in period (t 1 1) isde ned by (i) the number of transients whosurvive from the previous period (ii) juve-niles who progress to the transient stage (iii)minus the transients who nd home rangesand thus exit to the breeding adult stage

Ttst11 5 sts(s jsT js

t 1 Ttst ) 2 Vs

t11(s 5 m f ) [4d]

where Tt st1 1 is the number of surviving tran-

sients in period t 1 1 st s is the survival rateof transients of gender s 5 m f

Finally the number of breeding adults isgiven by the existing number of survivingadults and the new recruits to the category ofbreeding adult

T ast11 5 (s asTas

t 1 Vst11) [4e]

where s as is the survival rate of adults of gen-der s 5 m f The total population of non-cubtigers (T) is de ned to include the sum of ju-veniles transients and adults of both sexesThe model thus far assumes that prey areplentiful The only constraints on populationgrowth considered so far are the intrinsic sur-vival rates and the amount of territory avail-able to establish home ranges (ie Ks) Ifprey depletion lowers hunting success ratesit will lead to greater mortality of tigers Wetherefore extend the model to take account ofthe impact of prey availability on tiger popu-lation growth

Data on the intrinsic growth rates of indi-vidual prey species and the effects of browseand forage competition between species in ti-ger habitats is unavailable Hence we adopta simple approach and model the combinedbiomass of all prey species using a logisticequation of the form

Xt11 2 Xt 5 Xtr(1 2 XtX) 2 Hxt 2 Yt [5]

where Xt is the prey biomass at time t r is theintrinsic growth rate X is the prey carryingcapacity of the forest Hxt is the human har-vest of the prey biomass de ned in equation[3c] and Yt is the harvest of the prey by ti-gers which is described below

Field studies suggest that on average a ti-ger requires approximately 3000 kg of preyper year to survive (Sunquist Karanth andSunquist 1999) We therefore de ne the min-imum food intake of a tiger as M 5 3000kg Field observations also reveal that tigerssucceed in capturing between 10ndash20 ofthe available prey biomass in their homeranges (Schaller 1967 Sunquist 1981 John-singh 1983) In the presence of competingpredators such as wild dogs (Cuon alpinus)and leopards (Panthera pardus) a predationrate of 10 is deemed more appropriate(Karanth 2001) Thus the predation rate isde ned as r 5 010 It follows that the maxi-mum number of tigers that can be sustainedwith a prey base of Xt is rXtM Accord-

12 The random numbers were generated in Excel us-ing a random seed of 1 and mean of 3

206 Land Economics May 2003

ingly the prey biomass consumed by tigersis given by

Yt 5 MTt if rXt MTt

Yt 5 rXt otherwise [6a]

where Tt is the total number of tigers in pe-riod t M is the minimum food intake and ris the predation rate

Thus when prey are plentiful (ie rXt MTt) each tiger is able to meet its nutritionalneeds and successfully captures Mkg of preyper annum hence Yt 5 MTt On the otherhand if there is insuf cient prey to meet theneeds of the total population the level of pre-dation is at its maximum level Yt 5 rXt

A shortage of prey could have two effectson tiger survival prospects First prey deple-tion is likely to depress survival rates acrossall demographic stages Second a shortageof prey may also lower the carrying capacityof the habitat and thus lead to an expansionin the home ranges of breeding adult femalesIn the absence of data on the effects of preydepletion across demographic groups wefollow Karanth and Stith and assume thatprey depletion effects only (i) the carryingcapacity of the habitat and (ii) the survivalrates of cubs Thus under conditions of preydepletion the survival rates of cubs and thecarrying capacity are depressed by a preydepletion factor that is de ned as

h t11 5 51 if rXt 2 MTt $ 0

rXi

MTt

if rXt 2 MTt 0 [6b]

The cub survival rate (s c) and the carryingcapacity (Ks) are pre-multiplied by [6b]

It is acknowledged that the neglect of preydepletion effects on the survival rates acrossother demographic categories is unsatisfac-tory This approach can therefore be ex-pected to underestimate the true impact ofprey depletion if survival rates are depressedmore generally across all demographicstages However re nements of the modelmust await further research on this issue

Turning next to the effects of poachingPoachers target juveniles transients and

adults The number of tigers killed at eachstage is assumed to be proportional to the ex-isting distribution of tigers across the variousdemographic stages Let superscript i(i 5 jt a) denote demographic stages and recallthat superscript s 5 M F denotes genderDe ne k is

t as the proportion of male or femaletigers at demographic stage i(i 5 j t a) Thenthe numberofgenders tigers poachedatdemo-graphic stage i(i 5 j t a) is de ned as

HisTt11 5 HTtk is

t [6c]

where HTt is the total harvest of tigers as de-termined in equation [2b] k is

t 5 (T ist Tt) is

the proportion of gender s tigers at stagei(i 5 j t a) T is

t 5 number of gender s ti-gers at stage i and Tt is the total populationof tigers The number of tigers at each stageis thus lowered by the amount de ned inequation [6c]

V SIMULATION RESULTS

We now combine the economic models ofbehavior (equations [2b] and [3c]) and tigerpopulation growth (equations [4a]ndash[6c]) todetermine the time paths of lsquotiger stocksrsquo un-der alternative scenarios For given parame-ters the level of poaching emerges from theoptimising decisions of farmers and poach-ers This in turn affects tiger stock levelsModel parameters are varied to determinethe sensitivity of tiger population levels tochanges in economic circumstances

In the model labor is allocated across dif-ferent activities until the marginal returns areequalised The returns to off-farm work areexogenously xed and hence de ne the mini-mum payoffs to any activity that a householdwill accept The returns to agriculture varywith the price of agricultural commoditiesand the losses due to wildlife predation Thepayoffs to poaching also vary with wildlifestocks and the expected penalties for convic-tion It follows that changes in the returns toany one activity may induce a reallocation oflabor across other activities and thereforecould alter the level of poaching

The parameters for the basic tiger popula-tion model (equations [4a]ndash[4e]) are fromKaranth and Stith (1999) and are based on

79(2) Damania et al The Economics of Protecting Tiger Populations 207

eld research in India and Nepal Behavioraldata for subsistence farmers are drawn froma variety of sources13 The Data Appendixprovides details of the sources of informa-tion assumptions estimation methods andparameter values

The benchmark simulation draws on pa-rameter estimates based on the best availabledata for those regions with reasonablyhealthy tiger populations (eg the Kanha andBandipur Tiger Reserves in India) The habi-tat is assumed to comprise an area of approx-imately 1000 km2 with a prey carrying ca-pacity of 4500 kgkm214 It is supposed thatwhen prey are plentiful (rXt MTt) the un-disturbed habitat can sustain Kf 5 24 breed-ing adult females and Km 5 12 adult males(Karanth and Stith 1999 Kenney et al1995) In the base case farmers receive Rs1000 for each tiger killed face a ne of Rs25000 and a 2 probability of conviction(WPSI 2001)15 The off-farm wage rate is setat Rs 40 per day and the price of agriculturalproduce at Rs 85kg We begin by assuminga human population density of N 5 400households

It is important to distinguish between theecological effects and economic causes ofprey depletion from those of tiger poachingIn order to gain some understanding of theselinkages we begin by presenting simulationsfor the stylized case when only tiger poach-ing occurs We then assume that there is notiger poaching and consider the impact ofprey poaching on tiger populations Finallysimulations are presented for the completemodel where both tigers and their prey arehunted by subsistence farmers

Consider rst the effects of tiger poachingin isolation16 Curve A in Figure 1 shows thetiger population trajectory in a pristine habi-tat with no tiger poaching or prey depletionThe population achieves a stable equilibriumat 87 adult and juvenile tigers suggesting adensity of 9 tigers100 km2 This outcomeapproximates population levels in the frag-mented yet relatively healthy habitats foundin India and Nepal Curve B simulates the ef-fects of tiger poaching when the parametersare at the base case levels17 The tiger popula-tion declines to a stable 53 adult and juveniletigers with poachers harvesting 6 tigers per

year (approximately 11 percent of the popu-lation) Curve C simulates the effects of a50 increase in the price per tiger killed (Rs1500) The population falls substantially to27 tigers with 4 tigers harvested each year(approximately 12 of the population)

The simulation presented in Curve Dillus-trates the effects of an 80 increase in theprice paid to tiger poachers When the priceis increased to Rs 1800 the population de-clines to 19 tigers with 3 harvested each yearIn curve E when the poaching price is in-creased from Rs 1800 to Rs 1900 the tigerpopulation collapses within 50 years

This nding suggests that a relativelysmall increase in the payoffs to poaching(from Rs 1800 to Rs 1900) can drive a smallpopulation to extinction in a relatively shorttime period This is a signi cant resultwhich is consistent with Karanth and Stithrsquos(1999) simulations and related evidence thathunting of large felids can lead to sudden ex-tinction when it exceeds a certain thresholdlevel (Martin and de Meulanaer 1988 Bailey1993) The impact of poaching may thus bediscontinuous and prone to induce collapsesin populations This appears to be an exam-ple of the unstable equilibria frequently en-countered in discrete time predator-prey

13 Many of the tiger reserves are in tribal areas Itseems likely that behavior of tribal agriculturalistswould differ from those of other non-tribal agricultural-ists We have been compelled to use the only availabledata on agriculture which is based on non-tribal agri-culture There is clearly an urgent need for eldworkin and around tiger reserves to obtain more accurateinformation

14 The estimates of prey biomass in prime areas withtiger densities of between 10ndash12 per 100 km2 is derivedfrom data in Karanth and Nichols (2000) It is useful tonote that this estimate is also consistent with earlierstudies conducted using less advanced techniques Forinstance Johnsingh (1983) estimates a prey density of3382 kgkm2 in Bandipur reserve and a predation rateof 30 suggesting a possible carrying capacity of3382 (1 1 30) 5 4397 kgkm2

15 The assumption of a 2 conviction rate is a clearoverestimate of the true conviction probabilities ourbase case results thus underestimate the most likelyconsequence of poaching (WPSI 2001)

16 Formally this can be achieved by setting all thecoef cient of prey poaching to zero

17 In the base case farmers receive Rs 1000 for eachtiger killed face a ne of Rs 25000 and a 2 probabil-ity of conviction N is xed at 400 households

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

79(2) Damania et al The Economics of Protecting Tiger Populations 205

rate per breeding adult female and Taft is the

number of breeding adult females FollowingKaranth and Stith (1999) we assume anequal sex ratio at birth and mean litter size ofthree The birth rate b is treated as a Poissonvariable with a mean of three Randomnessis included in the model to capture demo-graphic stochasticity12

The surviving cubs move to the juvenilestage in the following period The number ofjuveniles who survive is

T jst11 5 s jsT cs

t (s 5 m f ) [4b]

where T jst1 1 is the number of surviving juve-

nile males (m) and females ( f ) in period t 11 s js(s 5 m f ) is the intrinsic survival rateof juvenile males (m) and females ( f )

At two years the surviving juveniles be-come transients Transients are de ned asadult tigers in search of home territories inwhich to hunt and breed If a vacant homerange is available a transient immediatelyoccupies the territory and is classi ed as abreeding adult Let Ks (s 5 m f ) denote themaximum number of territories available foradults of gender s 5 m f Let Tas

t be the num-ber of surviving adults of gender s 5 m fwith existing home ranges Then the numberof vacant territories available for the tran-sients to occupy is given by

V st11 5 Max(0 Ks 2 Tas

t )(s 5 m f ) [4c]

The number of transients in period (t 1 1) isde ned by (i) the number of transients whosurvive from the previous period (ii) juve-niles who progress to the transient stage (iii)minus the transients who nd home rangesand thus exit to the breeding adult stage

Ttst11 5 sts(s jsT js

t 1 Ttst ) 2 Vs

t11(s 5 m f ) [4d]

where Tt st1 1 is the number of surviving tran-

sients in period t 1 1 st s is the survival rateof transients of gender s 5 m f

Finally the number of breeding adults isgiven by the existing number of survivingadults and the new recruits to the category ofbreeding adult

T ast11 5 (s asTas

t 1 Vst11) [4e]

where s as is the survival rate of adults of gen-der s 5 m f The total population of non-cubtigers (T) is de ned to include the sum of ju-veniles transients and adults of both sexesThe model thus far assumes that prey areplentiful The only constraints on populationgrowth considered so far are the intrinsic sur-vival rates and the amount of territory avail-able to establish home ranges (ie Ks) Ifprey depletion lowers hunting success ratesit will lead to greater mortality of tigers Wetherefore extend the model to take account ofthe impact of prey availability on tiger popu-lation growth

Data on the intrinsic growth rates of indi-vidual prey species and the effects of browseand forage competition between species in ti-ger habitats is unavailable Hence we adopta simple approach and model the combinedbiomass of all prey species using a logisticequation of the form

Xt11 2 Xt 5 Xtr(1 2 XtX) 2 Hxt 2 Yt [5]

where Xt is the prey biomass at time t r is theintrinsic growth rate X is the prey carryingcapacity of the forest Hxt is the human har-vest of the prey biomass de ned in equation[3c] and Yt is the harvest of the prey by ti-gers which is described below

Field studies suggest that on average a ti-ger requires approximately 3000 kg of preyper year to survive (Sunquist Karanth andSunquist 1999) We therefore de ne the min-imum food intake of a tiger as M 5 3000kg Field observations also reveal that tigerssucceed in capturing between 10ndash20 ofthe available prey biomass in their homeranges (Schaller 1967 Sunquist 1981 John-singh 1983) In the presence of competingpredators such as wild dogs (Cuon alpinus)and leopards (Panthera pardus) a predationrate of 10 is deemed more appropriate(Karanth 2001) Thus the predation rate isde ned as r 5 010 It follows that the maxi-mum number of tigers that can be sustainedwith a prey base of Xt is rXtM Accord-

12 The random numbers were generated in Excel us-ing a random seed of 1 and mean of 3

206 Land Economics May 2003

ingly the prey biomass consumed by tigersis given by

Yt 5 MTt if rXt MTt

Yt 5 rXt otherwise [6a]

where Tt is the total number of tigers in pe-riod t M is the minimum food intake and ris the predation rate

Thus when prey are plentiful (ie rXt MTt) each tiger is able to meet its nutritionalneeds and successfully captures Mkg of preyper annum hence Yt 5 MTt On the otherhand if there is insuf cient prey to meet theneeds of the total population the level of pre-dation is at its maximum level Yt 5 rXt

A shortage of prey could have two effectson tiger survival prospects First prey deple-tion is likely to depress survival rates acrossall demographic stages Second a shortageof prey may also lower the carrying capacityof the habitat and thus lead to an expansionin the home ranges of breeding adult femalesIn the absence of data on the effects of preydepletion across demographic groups wefollow Karanth and Stith and assume thatprey depletion effects only (i) the carryingcapacity of the habitat and (ii) the survivalrates of cubs Thus under conditions of preydepletion the survival rates of cubs and thecarrying capacity are depressed by a preydepletion factor that is de ned as

h t11 5 51 if rXt 2 MTt $ 0

rXi

MTt

if rXt 2 MTt 0 [6b]

The cub survival rate (s c) and the carryingcapacity (Ks) are pre-multiplied by [6b]

It is acknowledged that the neglect of preydepletion effects on the survival rates acrossother demographic categories is unsatisfac-tory This approach can therefore be ex-pected to underestimate the true impact ofprey depletion if survival rates are depressedmore generally across all demographicstages However re nements of the modelmust await further research on this issue

Turning next to the effects of poachingPoachers target juveniles transients and

adults The number of tigers killed at eachstage is assumed to be proportional to the ex-isting distribution of tigers across the variousdemographic stages Let superscript i(i 5 jt a) denote demographic stages and recallthat superscript s 5 M F denotes genderDe ne k is

t as the proportion of male or femaletigers at demographic stage i(i 5 j t a) Thenthe numberofgenders tigers poachedatdemo-graphic stage i(i 5 j t a) is de ned as

HisTt11 5 HTtk is

t [6c]

where HTt is the total harvest of tigers as de-termined in equation [2b] k is

t 5 (T ist Tt) is

the proportion of gender s tigers at stagei(i 5 j t a) T is

t 5 number of gender s ti-gers at stage i and Tt is the total populationof tigers The number of tigers at each stageis thus lowered by the amount de ned inequation [6c]

V SIMULATION RESULTS

We now combine the economic models ofbehavior (equations [2b] and [3c]) and tigerpopulation growth (equations [4a]ndash[6c]) todetermine the time paths of lsquotiger stocksrsquo un-der alternative scenarios For given parame-ters the level of poaching emerges from theoptimising decisions of farmers and poach-ers This in turn affects tiger stock levelsModel parameters are varied to determinethe sensitivity of tiger population levels tochanges in economic circumstances

In the model labor is allocated across dif-ferent activities until the marginal returns areequalised The returns to off-farm work areexogenously xed and hence de ne the mini-mum payoffs to any activity that a householdwill accept The returns to agriculture varywith the price of agricultural commoditiesand the losses due to wildlife predation Thepayoffs to poaching also vary with wildlifestocks and the expected penalties for convic-tion It follows that changes in the returns toany one activity may induce a reallocation oflabor across other activities and thereforecould alter the level of poaching

The parameters for the basic tiger popula-tion model (equations [4a]ndash[4e]) are fromKaranth and Stith (1999) and are based on

79(2) Damania et al The Economics of Protecting Tiger Populations 207

eld research in India and Nepal Behavioraldata for subsistence farmers are drawn froma variety of sources13 The Data Appendixprovides details of the sources of informa-tion assumptions estimation methods andparameter values

The benchmark simulation draws on pa-rameter estimates based on the best availabledata for those regions with reasonablyhealthy tiger populations (eg the Kanha andBandipur Tiger Reserves in India) The habi-tat is assumed to comprise an area of approx-imately 1000 km2 with a prey carrying ca-pacity of 4500 kgkm214 It is supposed thatwhen prey are plentiful (rXt MTt) the un-disturbed habitat can sustain Kf 5 24 breed-ing adult females and Km 5 12 adult males(Karanth and Stith 1999 Kenney et al1995) In the base case farmers receive Rs1000 for each tiger killed face a ne of Rs25000 and a 2 probability of conviction(WPSI 2001)15 The off-farm wage rate is setat Rs 40 per day and the price of agriculturalproduce at Rs 85kg We begin by assuminga human population density of N 5 400households

It is important to distinguish between theecological effects and economic causes ofprey depletion from those of tiger poachingIn order to gain some understanding of theselinkages we begin by presenting simulationsfor the stylized case when only tiger poach-ing occurs We then assume that there is notiger poaching and consider the impact ofprey poaching on tiger populations Finallysimulations are presented for the completemodel where both tigers and their prey arehunted by subsistence farmers

Consider rst the effects of tiger poachingin isolation16 Curve A in Figure 1 shows thetiger population trajectory in a pristine habi-tat with no tiger poaching or prey depletionThe population achieves a stable equilibriumat 87 adult and juvenile tigers suggesting adensity of 9 tigers100 km2 This outcomeapproximates population levels in the frag-mented yet relatively healthy habitats foundin India and Nepal Curve B simulates the ef-fects of tiger poaching when the parametersare at the base case levels17 The tiger popula-tion declines to a stable 53 adult and juveniletigers with poachers harvesting 6 tigers per

year (approximately 11 percent of the popu-lation) Curve C simulates the effects of a50 increase in the price per tiger killed (Rs1500) The population falls substantially to27 tigers with 4 tigers harvested each year(approximately 12 of the population)

The simulation presented in Curve Dillus-trates the effects of an 80 increase in theprice paid to tiger poachers When the priceis increased to Rs 1800 the population de-clines to 19 tigers with 3 harvested each yearIn curve E when the poaching price is in-creased from Rs 1800 to Rs 1900 the tigerpopulation collapses within 50 years

This nding suggests that a relativelysmall increase in the payoffs to poaching(from Rs 1800 to Rs 1900) can drive a smallpopulation to extinction in a relatively shorttime period This is a signi cant resultwhich is consistent with Karanth and Stithrsquos(1999) simulations and related evidence thathunting of large felids can lead to sudden ex-tinction when it exceeds a certain thresholdlevel (Martin and de Meulanaer 1988 Bailey1993) The impact of poaching may thus bediscontinuous and prone to induce collapsesin populations This appears to be an exam-ple of the unstable equilibria frequently en-countered in discrete time predator-prey

13 Many of the tiger reserves are in tribal areas Itseems likely that behavior of tribal agriculturalistswould differ from those of other non-tribal agricultural-ists We have been compelled to use the only availabledata on agriculture which is based on non-tribal agri-culture There is clearly an urgent need for eldworkin and around tiger reserves to obtain more accurateinformation

14 The estimates of prey biomass in prime areas withtiger densities of between 10ndash12 per 100 km2 is derivedfrom data in Karanth and Nichols (2000) It is useful tonote that this estimate is also consistent with earlierstudies conducted using less advanced techniques Forinstance Johnsingh (1983) estimates a prey density of3382 kgkm2 in Bandipur reserve and a predation rateof 30 suggesting a possible carrying capacity of3382 (1 1 30) 5 4397 kgkm2

15 The assumption of a 2 conviction rate is a clearoverestimate of the true conviction probabilities ourbase case results thus underestimate the most likelyconsequence of poaching (WPSI 2001)

16 Formally this can be achieved by setting all thecoef cient of prey poaching to zero

17 In the base case farmers receive Rs 1000 for eachtiger killed face a ne of Rs 25000 and a 2 probabil-ity of conviction N is xed at 400 households

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

206 Land Economics May 2003

ingly the prey biomass consumed by tigersis given by

Yt 5 MTt if rXt MTt

Yt 5 rXt otherwise [6a]

where Tt is the total number of tigers in pe-riod t M is the minimum food intake and ris the predation rate

Thus when prey are plentiful (ie rXt MTt) each tiger is able to meet its nutritionalneeds and successfully captures Mkg of preyper annum hence Yt 5 MTt On the otherhand if there is insuf cient prey to meet theneeds of the total population the level of pre-dation is at its maximum level Yt 5 rXt

A shortage of prey could have two effectson tiger survival prospects First prey deple-tion is likely to depress survival rates acrossall demographic stages Second a shortageof prey may also lower the carrying capacityof the habitat and thus lead to an expansionin the home ranges of breeding adult femalesIn the absence of data on the effects of preydepletion across demographic groups wefollow Karanth and Stith and assume thatprey depletion effects only (i) the carryingcapacity of the habitat and (ii) the survivalrates of cubs Thus under conditions of preydepletion the survival rates of cubs and thecarrying capacity are depressed by a preydepletion factor that is de ned as

h t11 5 51 if rXt 2 MTt $ 0

rXi

MTt

if rXt 2 MTt 0 [6b]

The cub survival rate (s c) and the carryingcapacity (Ks) are pre-multiplied by [6b]

It is acknowledged that the neglect of preydepletion effects on the survival rates acrossother demographic categories is unsatisfac-tory This approach can therefore be ex-pected to underestimate the true impact ofprey depletion if survival rates are depressedmore generally across all demographicstages However re nements of the modelmust await further research on this issue

Turning next to the effects of poachingPoachers target juveniles transients and

adults The number of tigers killed at eachstage is assumed to be proportional to the ex-isting distribution of tigers across the variousdemographic stages Let superscript i(i 5 jt a) denote demographic stages and recallthat superscript s 5 M F denotes genderDe ne k is

t as the proportion of male or femaletigers at demographic stage i(i 5 j t a) Thenthe numberofgenders tigers poachedatdemo-graphic stage i(i 5 j t a) is de ned as

HisTt11 5 HTtk is

t [6c]

where HTt is the total harvest of tigers as de-termined in equation [2b] k is

t 5 (T ist Tt) is

the proportion of gender s tigers at stagei(i 5 j t a) T is

t 5 number of gender s ti-gers at stage i and Tt is the total populationof tigers The number of tigers at each stageis thus lowered by the amount de ned inequation [6c]

V SIMULATION RESULTS

We now combine the economic models ofbehavior (equations [2b] and [3c]) and tigerpopulation growth (equations [4a]ndash[6c]) todetermine the time paths of lsquotiger stocksrsquo un-der alternative scenarios For given parame-ters the level of poaching emerges from theoptimising decisions of farmers and poach-ers This in turn affects tiger stock levelsModel parameters are varied to determinethe sensitivity of tiger population levels tochanges in economic circumstances

In the model labor is allocated across dif-ferent activities until the marginal returns areequalised The returns to off-farm work areexogenously xed and hence de ne the mini-mum payoffs to any activity that a householdwill accept The returns to agriculture varywith the price of agricultural commoditiesand the losses due to wildlife predation Thepayoffs to poaching also vary with wildlifestocks and the expected penalties for convic-tion It follows that changes in the returns toany one activity may induce a reallocation oflabor across other activities and thereforecould alter the level of poaching

The parameters for the basic tiger popula-tion model (equations [4a]ndash[4e]) are fromKaranth and Stith (1999) and are based on

79(2) Damania et al The Economics of Protecting Tiger Populations 207

eld research in India and Nepal Behavioraldata for subsistence farmers are drawn froma variety of sources13 The Data Appendixprovides details of the sources of informa-tion assumptions estimation methods andparameter values

The benchmark simulation draws on pa-rameter estimates based on the best availabledata for those regions with reasonablyhealthy tiger populations (eg the Kanha andBandipur Tiger Reserves in India) The habi-tat is assumed to comprise an area of approx-imately 1000 km2 with a prey carrying ca-pacity of 4500 kgkm214 It is supposed thatwhen prey are plentiful (rXt MTt) the un-disturbed habitat can sustain Kf 5 24 breed-ing adult females and Km 5 12 adult males(Karanth and Stith 1999 Kenney et al1995) In the base case farmers receive Rs1000 for each tiger killed face a ne of Rs25000 and a 2 probability of conviction(WPSI 2001)15 The off-farm wage rate is setat Rs 40 per day and the price of agriculturalproduce at Rs 85kg We begin by assuminga human population density of N 5 400households

It is important to distinguish between theecological effects and economic causes ofprey depletion from those of tiger poachingIn order to gain some understanding of theselinkages we begin by presenting simulationsfor the stylized case when only tiger poach-ing occurs We then assume that there is notiger poaching and consider the impact ofprey poaching on tiger populations Finallysimulations are presented for the completemodel where both tigers and their prey arehunted by subsistence farmers

Consider rst the effects of tiger poachingin isolation16 Curve A in Figure 1 shows thetiger population trajectory in a pristine habi-tat with no tiger poaching or prey depletionThe population achieves a stable equilibriumat 87 adult and juvenile tigers suggesting adensity of 9 tigers100 km2 This outcomeapproximates population levels in the frag-mented yet relatively healthy habitats foundin India and Nepal Curve B simulates the ef-fects of tiger poaching when the parametersare at the base case levels17 The tiger popula-tion declines to a stable 53 adult and juveniletigers with poachers harvesting 6 tigers per

year (approximately 11 percent of the popu-lation) Curve C simulates the effects of a50 increase in the price per tiger killed (Rs1500) The population falls substantially to27 tigers with 4 tigers harvested each year(approximately 12 of the population)

The simulation presented in Curve Dillus-trates the effects of an 80 increase in theprice paid to tiger poachers When the priceis increased to Rs 1800 the population de-clines to 19 tigers with 3 harvested each yearIn curve E when the poaching price is in-creased from Rs 1800 to Rs 1900 the tigerpopulation collapses within 50 years

This nding suggests that a relativelysmall increase in the payoffs to poaching(from Rs 1800 to Rs 1900) can drive a smallpopulation to extinction in a relatively shorttime period This is a signi cant resultwhich is consistent with Karanth and Stithrsquos(1999) simulations and related evidence thathunting of large felids can lead to sudden ex-tinction when it exceeds a certain thresholdlevel (Martin and de Meulanaer 1988 Bailey1993) The impact of poaching may thus bediscontinuous and prone to induce collapsesin populations This appears to be an exam-ple of the unstable equilibria frequently en-countered in discrete time predator-prey

13 Many of the tiger reserves are in tribal areas Itseems likely that behavior of tribal agriculturalistswould differ from those of other non-tribal agricultural-ists We have been compelled to use the only availabledata on agriculture which is based on non-tribal agri-culture There is clearly an urgent need for eldworkin and around tiger reserves to obtain more accurateinformation

14 The estimates of prey biomass in prime areas withtiger densities of between 10ndash12 per 100 km2 is derivedfrom data in Karanth and Nichols (2000) It is useful tonote that this estimate is also consistent with earlierstudies conducted using less advanced techniques Forinstance Johnsingh (1983) estimates a prey density of3382 kgkm2 in Bandipur reserve and a predation rateof 30 suggesting a possible carrying capacity of3382 (1 1 30) 5 4397 kgkm2

15 The assumption of a 2 conviction rate is a clearoverestimate of the true conviction probabilities ourbase case results thus underestimate the most likelyconsequence of poaching (WPSI 2001)

16 Formally this can be achieved by setting all thecoef cient of prey poaching to zero

17 In the base case farmers receive Rs 1000 for eachtiger killed face a ne of Rs 25000 and a 2 probabil-ity of conviction N is xed at 400 households

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

79(2) Damania et al The Economics of Protecting Tiger Populations 207

eld research in India and Nepal Behavioraldata for subsistence farmers are drawn froma variety of sources13 The Data Appendixprovides details of the sources of informa-tion assumptions estimation methods andparameter values

The benchmark simulation draws on pa-rameter estimates based on the best availabledata for those regions with reasonablyhealthy tiger populations (eg the Kanha andBandipur Tiger Reserves in India) The habi-tat is assumed to comprise an area of approx-imately 1000 km2 with a prey carrying ca-pacity of 4500 kgkm214 It is supposed thatwhen prey are plentiful (rXt MTt) the un-disturbed habitat can sustain Kf 5 24 breed-ing adult females and Km 5 12 adult males(Karanth and Stith 1999 Kenney et al1995) In the base case farmers receive Rs1000 for each tiger killed face a ne of Rs25000 and a 2 probability of conviction(WPSI 2001)15 The off-farm wage rate is setat Rs 40 per day and the price of agriculturalproduce at Rs 85kg We begin by assuminga human population density of N 5 400households

It is important to distinguish between theecological effects and economic causes ofprey depletion from those of tiger poachingIn order to gain some understanding of theselinkages we begin by presenting simulationsfor the stylized case when only tiger poach-ing occurs We then assume that there is notiger poaching and consider the impact ofprey poaching on tiger populations Finallysimulations are presented for the completemodel where both tigers and their prey arehunted by subsistence farmers

Consider rst the effects of tiger poachingin isolation16 Curve A in Figure 1 shows thetiger population trajectory in a pristine habi-tat with no tiger poaching or prey depletionThe population achieves a stable equilibriumat 87 adult and juvenile tigers suggesting adensity of 9 tigers100 km2 This outcomeapproximates population levels in the frag-mented yet relatively healthy habitats foundin India and Nepal Curve B simulates the ef-fects of tiger poaching when the parametersare at the base case levels17 The tiger popula-tion declines to a stable 53 adult and juveniletigers with poachers harvesting 6 tigers per

year (approximately 11 percent of the popu-lation) Curve C simulates the effects of a50 increase in the price per tiger killed (Rs1500) The population falls substantially to27 tigers with 4 tigers harvested each year(approximately 12 of the population)

The simulation presented in Curve Dillus-trates the effects of an 80 increase in theprice paid to tiger poachers When the priceis increased to Rs 1800 the population de-clines to 19 tigers with 3 harvested each yearIn curve E when the poaching price is in-creased from Rs 1800 to Rs 1900 the tigerpopulation collapses within 50 years

This nding suggests that a relativelysmall increase in the payoffs to poaching(from Rs 1800 to Rs 1900) can drive a smallpopulation to extinction in a relatively shorttime period This is a signi cant resultwhich is consistent with Karanth and Stithrsquos(1999) simulations and related evidence thathunting of large felids can lead to sudden ex-tinction when it exceeds a certain thresholdlevel (Martin and de Meulanaer 1988 Bailey1993) The impact of poaching may thus bediscontinuous and prone to induce collapsesin populations This appears to be an exam-ple of the unstable equilibria frequently en-countered in discrete time predator-prey

13 Many of the tiger reserves are in tribal areas Itseems likely that behavior of tribal agriculturalistswould differ from those of other non-tribal agricultural-ists We have been compelled to use the only availabledata on agriculture which is based on non-tribal agri-culture There is clearly an urgent need for eldworkin and around tiger reserves to obtain more accurateinformation

14 The estimates of prey biomass in prime areas withtiger densities of between 10ndash12 per 100 km2 is derivedfrom data in Karanth and Nichols (2000) It is useful tonote that this estimate is also consistent with earlierstudies conducted using less advanced techniques Forinstance Johnsingh (1983) estimates a prey density of3382 kgkm2 in Bandipur reserve and a predation rateof 30 suggesting a possible carrying capacity of3382 (1 1 30) 5 4397 kgkm2

15 The assumption of a 2 conviction rate is a clearoverestimate of the true conviction probabilities ourbase case results thus underestimate the most likelyconsequence of poaching (WPSI 2001)

16 Formally this can be achieved by setting all thecoef cient of prey poaching to zero

17 In the base case farmers receive Rs 1000 for eachtiger killed face a ne of Rs 25000 and a 2 probabil-ity of conviction N is xed at 400 households

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

208 Land Economics May 2003

FIGURE 1The Impact of P oaching P rice on Tiger P opulations

models when the predator population is atlow levels (May 1978 Freedman 1979) This nding has important policy implicationssince a large number of reserves have low ti-ger numbers of less than 30 animals per1000km2 The simulations highlight the po-tential risks of extinction facing small tigerpopulations subjected to increased poachingpressure

Figure 2 summarizes the consequences ofprey depletion when there is no tiger poach-ing Curve A shows the wild tiger populationtrajectories when the parameters are held atbase levels in the model (ie a farm popula-tion of 400 households an off-farm wage ofRs 40 per day and an agricultural outputprice of Rs 85kg) In the base case there isa stable population of 86 tigers that approxi-mates that of a pristine habitat When thenumber of farm households is increased by

50 (from 400 to 600) and off-farm wageand agricultural production prices are heldconstant at base levels tigers are extinct inless than 60 years (Curve B) Higher humanpopulations increase the demand for ungu-lates as a supplementary food source whichleads to a shrinking prey base and hence adecline in the tiger population

The model simulations further highlightthe sensitivity of tiger populations to agricul-tural income Even when the number of farmhouseholds is reduced to 500 if agriculturalprices are increased by 20 (to Rs 102kg)tiger populations are eliminated in less than80 years (Curve C) On the other hand CurveD shows that a 20 decline in agriculturalprices leads to recovery of the populationThis result helps illustrate how direct and in-direct agricultural subsidies impact the envi-ronment and ecosystems The responsiveness

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

79(2) Damania et al The Economics of Protecting Tiger Populations 209

FIGURE 2The Impact of P rey P oaching on Tiger P opulation

of prey depletion to agricultural prices sug-gests that the withdrawal of agricultural sub-sidies may generate substantial improve-ments in habitat quality

We also consider the effects of a 100 in-crease in off-farm wage when the number ofhouseholds is set at N 5 500 with all otherparameters held at the base level This simu-lation slowed the extinction time suggestingthat the substitution effects of higher off-farm wages do not reduce hunting levels suf- ciently to outweigh the effects of a higherhuman population This is clearly a conse-quence of the assumed parameter values inthe simulations and highlights the need formore reliable parameter estimates based on eld studies in tiger reserves Finally a100 increase in either the ne for huntingor the probability of conviction both lead torecovery of the population (ie the popula-tion reaches the same levels as Curve D)

Figure 3 simulates the combinedeffects ofboth tiger poaching and prey poaching bysubsistence farm households In Figure 3Curve A portrays the tiger population trajec-tory when all parameters are at their base lev-els The population stabilizes at 53 tigerswith 6 tigers harvested each year A commonscenario faced by Indiarsquos tiger reserves is in-creasing human population pressure CurveB in Figure 3 simulates the impact on tigerpopulations when agricultural prices tigerpoaching prices and the number of farmhouseholds all increase by 50 The result isthat the reserversquos tiger population is extinctin less than 45 years

In Figure 3 Curve C the nes for bothprey poaching and tiger poaching are dou-bled to represent a reserve under pressurefrom human population The tiger populationstabilizes at 37 animals The higher neslower the payoffs from poaching both tigers

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

210 Land Economics May 2003

FIGURE 3The Impact of Tiger P oaching and P rey P oaching on Tiger P opulations

and their prey so that effort devoted to hunt-ing falls On the other hand if only the nefor tiger poaching is doubled while the nefor prey poaching is held constant the tigerpopulation declines to zero in 54 years18

The nal simulation in Figure 3 (Curve D)doubles off-farm wages and the nes for ti-ger poaching and prey poaching The resultis a tiger population stabilizing at 53 with 5killed each year The increase in off-farmwages raises the opportunity costs of time al-located to poaching while the higher ex-pected nes lower the payoffs from huntingboth tigers and their prey

Figure 4 illustrates how households allo-cate labor to tiger poaching in each of thefour scenarios presented in Figure 3 For ex-ample Curve A in Figure 4 presents the samebase case as Curve A in Figure 3 to demon-strate how the percentage of total household

labor allocated to tiger poaching changesover time Tiger poaching effort begins ini-tially at just less than 25 of household laborallocation declining gradually and stabiliz-ing at around 7 with 6 tigers poached eachyear and the tiger population stable at 53

For Curve B agricultural prices tigerpoaching prices and total farm householdnumbers all increase by 50 The initial tigerpoaching effort is slightly more than 25 ofhousehold labor allocation a higher initial al-location than the base case re ecting the in-creased price for tigers Simultaneously in-creased agricultural prices together with ahigher farm population leads to greater preypoaching and a reduction in the prey bio-mass thereby lowering tiger survival rates

18 This simulation which has a population trajectorysimilar to Curve B is not shown to avoid clutter

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

79(2) Damania et al The Economics of Protecting Tiger Populations 211

FIGURE 4Household Tiger P oaching Effort

As tiger densities decline the likelihood of nding a tiger decreases so that the relativepayoffs to labor allocated to hunting tigersfalls Hence the time allocated to hunting ti-gers declines to zero as the populationreaches extinction in around 40 years

Curve C uses the same parameter settingsas Curve B except for the tiger poaching andprey poaching nes are doubled The resultis less household time devoted to hunting ti-gers as the expected cost of hunting increasesdue to the higher penalties When off-farmwages and nes are doubled (Figure 4 CurveD) labor time devoted to tiger poaching de-clines and the tiger population stabilizes atmore than 60 The increased nes togetherwith a higher off-farm wage lower the rela-tive payoffs from poaching and thus leads tolower levels of poaching

We considered numerous other scenariosfor the case of a reserve under increasedpressure from human population and activi-ties The overall conclusion from a largenumber of simulations is that tiger popula-tions in habitats with a healthy prey base areable to withstand modest levels of poachingWhen the prey base is depleted tiger survivalprospects decline Hence recovery of thepopulation necessitates controls over boththe level of tiger and prey poaching

These results indicate that anti-poachingpolicies should be directed at increasing theopportunity costs of poaching activities Inpractical terms this might involve higher nes or more frequent and intensive patrolsand other related policies that require greateravoidance by poachers thus renderingpoaching more dif cult These initiatives

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

212 Land Economics May 2003

would increase the opportunity costs ofpoaching The provision of alternativesources of employment would also increasethe opportunity costs of poaching so long asit does not induce further migration into thearea The simulations suggest that higher off-farm wages when used in conjunction withother protective measures would induce arapid recovery of the tiger population (egcompare Curve C with D in Figure 3)

This outcome is suggestive of the reasonswhy tigers thrive in some prey abundant re-gions and not in others In areas where theopportunity cost of poaching is high due toeffective patrols for instance (eg theKanha Kaziranga Nagarahole Tiger Re-serves) tigers have survived in reasonablenumbers In more accessible and less pro-tected landscapes no tigers are found despitethe existence of suitable habitats (Wikrama-nayake et al 1998 Karanth 2001)

VI CONCLUSION

This paper extends the existing biologicalliterature on tiger populations by linking astochastic demographic model of tiger popu-lation with household behavior that endogen-izes two key threats to tiger populationspoaching tigers and poaching their prey Al-ternative scenarios simulate the impact of thenumber of households agricultural incomewage income and poaching intensity of ti-gers and their prey The results highlight thesensitivity fragility and instability of tigerpopulations to key economic parametersMost notable is the nding that the level ofhuman population is the most potent threat tothe tigerrsquos prey base and that the effects oflarge human populations may be dif cult toreverse with the economic instruments con-sidered in this paper

The sensitivity of tiger populations topoaching incentives in prey depleted reservesis another important concern Tiger popula-tions appear to exhibit threshold responses toincreases in poaching intensity In particularwhen prey levels are depleted a relativelysmall increase in tiger poaching may triggerextinction Thus the control of poaching inprey-depleted environments remains a matterof critical concern This suggests the need forincreasing the conviction rates for poaching

In practice this may be dif cult to achievefor it requires major institutional and judicialreform accompanied by substantial invest-ments in law enforcement

The modelling results suggest that an al-ternative and potentially more effective wayto reduce poaching is to increase the opportu-nity cost of poaching Policies such as theprovision of alternative employment and off-farm income accompanied by controls onforest access would have the desired effectof reducing the incidence of poaching

The modelling results also raise questionsabout conservation efforts and forest man-agement strategies that emphasize any typeof forest resource use in and around tigerhabitats including JFM The net social costsand bene ts of alternative rural developmentstrategies need to be examined Examples in-clude increasing non-farm and non-forestryemployment improving access to educationenhancing agricultural productivity promot-ing non-forest dependent commercial activi-ties and shifting private and public infrastruc-ture investments away from tiger habitatsThese are a formidable yet urgently neededset of tasks given that about two-thirds of In-diarsquos total forest cover is in districts wherethe incidence of poverty (mostly among thetribal people) is more than 50 percent (Ku-mar et al 2000)

A number of alternative measures havebeen suggested to tackle the problem of tigerpoaching These include strategies to reducethe demand for tiger products in traditionalOriental medicine and policies to control theillegal cross-border trade in tiger productswhich is controlled by criminal organizations(Nowell 2000) Captive breeding of tigers forthe Oriental medicine trade in bones and or-gans is yet another suggestion which hasgained some popularity Support for this pol-icy is based on the notion that generatingsupplies from captivendashbred animals com-modity prices are expected to fall therebylowering the incentive to poach species in thewild Damania and Bulte (2001) assess theprospects of captive breeding in considerabledetail The analysis reveals that when theillegal trade in wildlife commodities iscontrolled by cartelized oligopolies captivebreeding may lead to further poaching ofwild stocks as has occurred with the moon

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

79(2) Damania et al The Economics of Protecting Tiger Populations 213

bears of China and Vietnam and the croco-diles in Thailand (Meacham 1997) More im-portant however these initiatives would dolittle to prevent extinction of tigers throughdepletion of their prey base

The results in this paper are tentativeLack of data and information on key eco-nomic and biological factors means that themodelrsquos parameters are based on impreciseestimates To guard against exaggerating thethreat of extinction we have adopted conser-vative assumptions For instance the proba-bility of convicting poachers is assumed tobe considerably higher than the availabledata suggests Similarly we use the upperbound of estimates for ungulate intrinsicgrowth rate and the lower bound of estimatesfor the returns to agriculture Moreoverwhile prey depletion can be expected to ef-

DATA APPENDIX

Data Sources and P arameter Values

Parameter Description Value Source

s af Survival rate of adult female 9 Karanth and Stith (1999)s am Survival rate of adult male 8 Karanth and Stith (1999)stf Survival rate of transient female 7 Karanth and Stith (1999)stf Survival rate of transient male 65 Karanth and Stith (1999)s j Survival rate of juveniles 9 Karanth and Stith (1999)s c Survival rate of cubs 6 Karanth and Stith (1999)r Predation rate 10 Karanth (1988)M Minimum prey biomass for tiger survival 3000 Kg Karanth (1988)ax Coef cient for game meat demand in utility 05 World BankNepal Nutrition

function Based on proportion of meat in and Energy Surveydiet

L Total endowment of labor per household 500 days per Bluffstone (1995)annum

b Coef cient in agricultural output production 154 Saha (1994)function

m Damage to crops per unit prey biomass calcu- 00001 per Sekhar (1998) tables 1ndash4lated as percent crop loss per hectareprey 1000 Kgbiomass This data is based on survey work prey biomassat Sariska Tiger Reserve

X Prey carrying capacity 4500 kgkm2 See text footnote 5r Prey intrinsic growth rate 4 See textd Coef cient of prey hunting production function 002 Lower estimate from Kinyua

et al (2000)qx Probability of prey hunter being convicted 001 See notes belowWcentx WT Penalty for poaching prey and tigers Rs5000 Wildlife Protection Act

Rs25000 India 1972 Section 51w Daily wage rate for off-farm work Rs40 Reserve Bank of India (1999)pg Price of agricultural produce Rs850100 kg Dinar et al (1998)PT Price paid to poachers for each tiger Rs1000 WPSI (2001)qT Probability of being convicted for poaching a 02 WPSI (2001)

tigerl x Parameters of tiger poaching production 46 104 See notes below

function

fect survival prospects across all age classesthe model conservatively assumes that it hasno impact on juvenile or transient tigers butonly depresses cub survival rates and theadult carrying capacity

Finally it is important to note that this pa-per ignores a number of other importantthreats to the tiger Key amongst these is theunrelenting erosion of habitats and forestcorridors connecting tiger reserves Many ti-ger reserves are threatened with plans formajor development projects including minesroads and dams (World Bank 1996) The re-serves face further pressures from the steadyextraction of resources for timber fuelwoodfodder and livestock grazing all of whichare factors linked closely to human popula-tion growth The effects of habitat erosion re-main an area in need of urgent research

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

214 Land Economics May 2003

Data Appendix Notes

1 Coef cients for the poaching production func-tions

There are no studies on nor data available ontiger poaching We therefore seek to infer poach-ing production parameters using indirect proxiesOne of the more sophisticated methods used to es-timate tiger densities relies on a technique knownas lsquolsquocamera trap samplingrsquo rsquo Cameras are posi-tioned to sample an area within which some ofthe passing animals are photographed The popu-lation estimates are based on the number of tigersphotographed and the associated capture proba-bilities derived from the data (Karanth and Nich-ols 1998 2000) Many of the poaching tech-niques are lsquolsquopassiversquo rsquo and involve laying a snareor trap in areas where tigers are thought to resideIn the absence of any other information we as-sume that that the main constraint on poaching isthe dif culty involved in nding a tiger It is sup-posed that the probability of a tiger being caughtin a snare or trap is analogous to that of capturinga tiger with a camera in the area being sampledThus the probability of poaching is assumed todepend on the density of tigers and the number ofdays that a trap has been laid We use informationfrom the camera capture studies to proxy thepoaching technology parameters Using data fromthe most recent study (Karanth and Nichols2000) we regress the number of tigers capturedby cameras against trapping effort and tiger den-sity to obtain the coef cients of the poaching pro-duction function

Log(HT) 5 46 Log(Effort)(2409)

1 104 Log(Density)(441)

(R2 5 80 F 5 21244 SE of regression 5 33number of observations 5 7 t-statistics in paren-theses below the coef cients)

The estimates are based on data from thePench Kanha Kaziranga Nagarahole BhadraBandipur and Ranthambore Tiger Reserves

The parameters for poaching effort and densityeffects are based on these regression estimates Itis acknowledged that these estimates are at bestonly broadly indicative and likely to be biasedMoreover it is dif cult to determine the directionof the bias If bait is more (less) ef cient at cap-turing tigers than cameras we will have underes-timated (overestimated) the coef cient on effortand also biased the estimate of density This ishowever the best available information

The parameters used for the probability of de-tecting and convicting poachers are arbitrary TheWildlife Trust of India (www Wildlifetrust-o ndiaorg) has recorded only two convictions fortiger poaching which suggests that the rate of con-viction for poaching tigers may be lower than 02(WPSI 2001) It is likely that the parameters usedin this paper substantially overestimate the trueprobability of conviction There is no publisheddata on the conviction rates for poaching prey ani-mals though it is deemed to be lower than thatfor tiger poaching (Wildlife Trust of India perscomm) A higher conviction rate is used than issuggested by the anecdotal evidence since actualconvictions rates may not account for all the costsassociated with detection and prosecution2 Off farm wages

Average rural wages in India vary from Rs 40per day in some states (eg Haryana which hasno tiger reserve) to Rs 22 in other states (eg As-sam and Madhya Pradesh with tiger populations[Reserve Bank of India 1999]) We adopt the up-per bound of these gures and set the off-farmwage rate at Rs 40 which is higher than the aver-age wage in most tiger range states in IndiaMoreover as noted by a referee if rural wages uctuate seasonally then poaching is likely to beconcentrated in seasons of low labor demand andlow wages In this case we are likely to have fur-ther overestimated the true off-farm wage in theoff-peak seasons3 The Prey Intrinsic growth rate

Field data obtained by Karanth at Nagaraholesuggests the following intrinsic growth rates forthe major prey species chital (Axis axis) 32gaur (Bos gaurus ) 43 wild pig (Sus scrofa)150 The aggregate prey growth rate weightedby estimated prey densities (see Karanth andNichols 2000) yields an intrinsic growth rate ofat least r 5 04

References

Bailey T N 1993 The African Leopard Ecol-ogy and Behavior of a Solitary Felid NewYork Columbia University Press

Barbier E B 1992 lsquolsquoCommunity-Based Devel-opment in Africarsquo rsquo In Economics for theWilds ed E B Barbier and T SwansonWashington DC Island Press

Barrett C B and P Arcese 1995 lsquolsquoAre Inte-grated Conservation-Development Projects(ICDPs) Sustainable On the Conservation ofLarge Mammals in Sub-Saharan Africarsquo rsquoWorld Development 23 (7) 1073ndash84

79(2) Damania et al The Economics of Protecting Tiger Populations 215

mdashmdashmdash 1998 lsquolsquoWildlife Harvesting in IntegratedConservation and Development Projects Link-ing Harvest to Household Demand AgriculturalProduction and Environmental Shocks in theSerengetirsquo rsquo Land Economics 74 (Nov) 449ndash65

Bluffstone R A 1995 lsquolsquoThe Effect of LaborMarket Performance on Deforestation in De-veloping Countries Under Open Access AnExample from Rural Nepalrsquo rsquo Journal of Envi-ronmental Economics and Management 29(Jul) 42ndash63

Breeden S and B Wright 1996 Through the Ti-gerrsquos Eyes Berkeley Ten Speed Press

Burgman M A S Ferson and H R Akcakaya1993 Risk Assessment in Conservation Biol-ogy London Chapman Hall

Damania R 2002 lsquolsquoEnvironmental Controlswith Corrupt Bureaucratsrsquorsquo Environment andDevelopment Economics 7407ndash27

Damania R and E Bulte 2000 lsquolsquoThe Econom-ics of Captive Breeding and Endangered Spe-cies Conservationrsquo rsquo CIES Discussion Paper0139 Adelaide CIES

Deininger K and H Binswanger 1998 TheEvolution of the World Bankrsquos Land PolicyWashington DC World Bank

Dinar A R Mendelsohn R Ericson J ParikhA Sanghi and K Kumar 1998 lsquolsquoMeasuringthe Impact of Climate Change on Indian Agri-culturersquo rsquo World Bank Technical Paper 402Washington DC World Bank

drsquoSilvia E and B Nagnath 2002 lsquolsquoBehroon-guda A Rare Success Story in Joint ForestManagementrsquo rsquo Economics and PoliticalWeekly 27 (6) 551ndash57

Freedman H I 1979 Deterministic Mathemati-cal Models in Population Ecology New YorkMarcel Dekker Inc

Ghimire K B 1994 lsquolsquoParks and People Liveli-hood Issues in National Parks Management inThailand and Madagascarrsquorsquo Development andChange 25 (2) 195ndash229

Gunatilake H M 1994 lsquolsquoAn Economic ImpactAssessment of the Proposed Conservation Pro-gramme on Peripheral Communities of theKnuckles National Wilderness Area of SriLankarsquorsquo Journal of Sustainable Forestry 2 (1)1ndash12

mdashmdashmdash 1998 lsquolsquoThe Role of Rural Developmentin Protecting Tropical Rainforests Evidencefrom Sri Lankarsquo rsquo Journal of EnvironmentalManagement 53 (3) 273ndash92

Gunatilake H M and U Chakravorty 2000lsquolsquoForest Resource Extraction by Local Com-munities A Comparative Dynamic AnalysisrsquorsquoNota Di Lavoro 412000 Milano FondazioneEni Enrico Mattei

Johnsingh A J T 1983 lsquolsquoLarge MammalianPrey-Predators in Bandipurrsquorsquo Journal of theBombay Natural History Society 801ndash57

Karanth K U 1988 lsquolsquoPopulation Structure Den-sity and Biomass of Large Herbivores in aSouth Indian Tropical Forestrsquorsquo M S thesisUniversity of Florida Gainesville

mdashmdash 2001 Tigers Scotland UK Colin BaxterPhotography

Karanth K U and J D Nichols 1998 lsquolsquoEstima-tion of Tiger Densities in India Using Photo-graphic Captures and Recapturesrsquo rsquo Ecology79 (8) 2852ndash62

mdashmdashmdash 2000 lsquolsquoEcological Status and Conserva-tion of Tigers in Indiarsquorsquo Final Report to Divi-sion of International Conservation Washing-ton DC US Fish and Wildlife Service

Karanth KU and B M Stith 1999 lsquolsquoPreyDepletion as a Critical Determinant of TigerPopulation Viabilityrsquo rsquo In Riding the Tiger edJ Seidensticker S Christie and P JacksonCambridge UK Cambridge UniversityPress

Kenney J J L D Smith A M Star eld andC W McDougal 1995 lsquolsquoThe Long Term Ef-fect of Tiger Poaching on Population Viabil-ityrsquo rsquo Conservation Biology 91127ndash33

Kinyua Patrick I D G Cornelis van Kootenand Erwin H Bulte 2000 lsquolsquoAfrican WildlifePolicy Protecting Wildlife Herbivores on Pri-vate Game Ranchesrsquo rsquo European Review ofAgricultural Economics 27 (2) 227ndash44

Kothari A S Suri and N Singh 1995 lsquolsquoPeopleand Protected Areas Rethinking Conservationin Indiarsquo rsquo The Ecologist 25 (5) 188ndash97

Kumar N N Saxena Y Alagh and K Mitra2000 lsquolsquoIndia Alleviating Poverty throughForest Developmentrsquo rsquo OED Evaluation Coun-try Case Study Series Washington DCWorld Bank

Lele U N Kumar S Arif Husain A Zazuetaand L Kelly 2000 lsquolsquoThe World Bank ForestStrategy Striking the Right Balancersquo rsquo Wash-ington DC World Bank

Madhusudan M D and Karanth K U 2000lsquolsquoHunting for an Answer Local Hunters andLarge Mammal Conservation in Indiarsquo rsquo InHunting for Sustainability in Tropical Forestsed J G Robinson and E L Bennett NewYork Columbia University Press

Marks S A 1984 The Imperial Lion HumanDimensions of Wildlife Management in AfricaBoulder Westview Press

Martin R B and T de Meulanaer 1988 SurveyStatus of the Leopard Panthera Pardus in SubSaharan Africa Laussane SwitzerlandCITES

216 Land Economics May 2003

May R 1978 Stability and Complexity in ModelEcosystems Princeton Princeton UniversityPress

Meachem C J 1997 How the Tiger Lost itsStripes New York Harcourt Brace and Co

Mishra C 1997 lsquolsquoLivestock Depredation byLarge Carnivores in the Indian TransmdashHima-layan Con ict Perceptions and ConservationImplicationsrsquo rsquo Environmental Conservation24 (4) 338ndash43

Nepal S K and K E Weber 1995 lsquolsquoManagingResources and Resolving Con icts NationalParks and Local Peoplersquo rsquo International Jour-nal of Sustainable Development and WorldEcology 2 (1) 11ndash25

Nowell K 2000 Far from a Cure The TigerTrade Revisited Cambridge UK Traf c Re-port

Nowell K and P Jackson 1996 Wild Cats Sta-tus Survey and Conservation Action PlanCambridge UK IUCN Publications ServicesUnit

Panayotou T 1993 Green Markets The Econom-ics of Sustainable Development San Fran-cisco ICS Press

Reserve Bank of India 1999 Handbook of Statis-tics on the Indian Economy Mumbai IndiaReserve Bank of India

Saberwal V K 1996 lsquolsquoPastoral Politics GaddiGrazing Degradation and Biodiversity Con-servation in Himachal Pradech Indiarsquo rsquo Con-servation Biology 10 (6) 741ndash49

Saha A 1994 lsquolsquoA Two-Season AgriculturalHousehold Model of Output and Price Uncer-taintyrsquo rsquo Journal of Development Economics45 (2) 245ndash69

Schaller G B 1967 The Deer and the TigerChicago Chicago University Press

Schultz C and A Skonhoft 1996 lsquolsquoWildlifeManagement Land-use and Con ictsrsquorsquo Envi-ronment and Development Economics 1 (3)265ndash80

Seidensticker J S Christie and P Jackson1999 Riding the Tiger Cambridge UKCambridge University Press

Sekhar N U 1998 lsquolsquoCrop and Livestock Depre-dation Caused by Wild Animals in ProtectedAreas The Case of Sariska Tiger ReserveRajasthan Indiarsquo rsquo Environmental Conserva-tion 25 (2) 160ndash71

Shyamsundar P and R A Kramer 1996lsquolsquoTropical Forest Protection An EmpiricalAnalysis of the Costs Borne by Local Peoplersquo rsquoJournal of Environmental Economics andManagement 31 (2) 129ndash44

Simpson D R 1995 lsquolsquoWhy Integrated Conser-vation and Development Projects MayAchieve Neither Goalrsquo rsquo Resources for the Fu-ture Discussion Paper 95-2 Washington DCResources for the Future

Studsrod J E and P Wegge 1995 lsquolsquoPark Peo-ple Relationships The Case of DamagesCaused by Park Animals Around the RoyalBardia National Park Nepalrsquo rsquo EnvironmentalConservation 22 (2) 133ndash42

Sunquist M E 1981 lsquolsquoThe Social Organizationof Tigers in Royal Chitwan National Parkrsquo rsquoSmithsonian Contributions to Zoology 361ndash98

Sunquist M E K U Karanth and F Sunquist1999 lsquolsquoEcology Behavior and Resilience ofthe Tiger and its Conservation Needsrsquorsquo In Rid-ing the Tiger ed J Seidensticker S Christieand P Jackson Cambridge UK CambridgeUniversity Press

Terborgh J 1999 Requiem for Nature Washing-ton DC Island Press

Tisdell C A 1995 lsquolsquoIssues in Biodiversity Con-servation Including the Role of Local Commu-nitiesrsquo rsquo Environmental Conservation 22 (4)216ndash28

Wells M 1992 lsquolsquoBiodiversity Conservation Af- uence and Poverty Mismatched Costs andBene ts and Efforts to Remedy Themrsquorsquo Am-bio 21237ndash43

Wikramanayake E D E Dinerstein J GRobinson U Karanth A Rabinowitz DOlson T Mathew P Hedao M Conner GHemley and D Bolze 1998 lsquolsquoAn EcologyBased Method for De ning Prioirities forLarge Mamal Conservation The Tiger as aCase Studyrsquo rsquo Conservation Biology 12 (4)865ndash78

World Bank 1996 lsquolsquoIndia Ecodevelopment Proj-ectrsquo rsquo GEF Project Document South Asia De-partment II Agriculture and Water DivisionWashington DC World Bank

WPSI (Wildlife Protection Society of India)2001 Update on the Trade in Tiger Partshttp wwwaxxelit tigerTiger7html