Monitoring mammal populations with line transect

techniques in African forests

ANDREW J. PLUMPTRE

The Wildlife Conservation Society, 185th Street and Southern Boulevard, Bronx, New York, NY 10460±1099,

USA

Summary

1. Line transect survey techniques have been used to estimate population density

for a variety of mammal species in tropical forests. In many cases indirect methods,

surveying signs of animals such as counts of dung or nests, have been used because

of the poor visibility in these forests. The estimates of the production and decom-

position rates of these signs each have their associated errors; however, for the

majority of published studies these errors have not been incorporated into the esti-

mate of the standard errors or con®dence limits of the density estimate. An equa-

tion is given showing how this should be done.

2. An equation is also given relating the resolution (R) of a density estimate to the

coe�cient of variation (CV) of the estimate. This shows that to detect a 10%

change in a population the CV must be 3�6% (with a power of 50%) or 2�4% (with

80% power). Using this equation and data from studies in Africa, it is shown that

di�erences of less than 10±30% change in the population are unlikely to be

detected between two surveys where visual sightings of animals are made. When

indirect methods of estimating the population are used, it is unlikely that less than

a 30±50% change in the population could be detected.

3. Some studies have surveyed primate groups using estimates of an average group

spread. Data from primate groups in Budongo Forest, Uganda, show that group

spread is highly variable and varies at di�erent times of day and between months.

This survey technique is not recommended.

4. If line transects are used for monitoring populations, conversion factors should

be minimized as each contributes to an increase in the CV and a reduction in the

ability to detect small changes in population density.

5. Monitoring trends in abundance over several survey periods can improve the

detection of change, although this is costly and requires several surveys before any

conclusions can be reached. Re-using transects in subsequent surveys can also

reduce the variation around the estimate and will improve the resolution. Focusing

survey e�orts in areas of high density is an alternative strategy, but one that could

lead to other errors as high-density areas may be the safest and hence the last to

show change. Using biased survey methods is also a promising technique that can

increase the precision of surveys. It is concluded that a combination of di�erent

survey methods will ensure that changes in abundance are identi®ed.

Key-words: elephants, population errors, primates, surveying mammals.

Journal of Applied Ecology (2000) 37, 356±368

Introduction

Ecological monitoring should be a vital component

of any conservation project so that the e�ects ofCorrespondence: A.J. Plumptre (fax 718 3644275; e-mail

aplumptre@wcs.org).

Journal of

Applied Ecology

2000, 37,

356±368

# 2000 British

Ecological Society

management can be assessed (Kremen, Merenlender

& Murphy 1994). Management plans always empha-

size that monitoring should take place and, more

recently, some have attempted to de®ne limits of

acceptable change beyond which management action

should be taken (Alexander 1996). However, if we

are to de®ne these limits, we must be certain that

our survey techniques can detect them.

The use of distance sampling techniques to esti-

mate animal population densities has become

increasingly popular since the production of the

computer package TRANSECT (Laake, Burnham &

Anderson 1979) and subsequently DISTANCE

(Buckland et al. 1993; Laake et al. 1994). In African

forests this technique has mainly been used to esti-

mate the density of primate groups (Whitesides et al.

1988; White 1992, 1994; Plumptre & Reynolds

1994), as many species are highly visible. Surveyors

of most other mammals in these forests have

resorted to indirect estimation techniques rather

than direct observation because visibility is often

poor and some species cannot be approached in

safety. In these surveys animal densities were calcu-

lated from line transects, counting signs that animals

leave behind, usually nests (apes: Ghiglieri 1984;

Tutin & Fernandez 1984; Wrogeman 1992; White

1994; Hashimoto 1995; Ihobe 1995; Marchesi et al.

1995; Plumptre & Reynolds 1996, 1997; Hall et al.,

1998a) or dung (elephants Loxodonta africana: Wing

& Buss 1970; Short 1983; Merz 1986; Barnes & Jen-

sen 1987; Dawson 1990; Ruggiero 1990; Fay &

Agnagna 1991; Barnes 1993; Plumptre & Harris

1995; ungulates: Plumptre 1991; White 1992, 1994;

Plumptre & Harris 1995). Indirect counts require

conversion factors to be calculated to convert the

count of dung or nests to animal density. These fac-

tors include the rates of production and the decay

rates of dung/nests. Some studies have avoided the

need to correct for the rate of decomposition of

dung or nests by counting the number that appear

over a certain time period. The same transects are

visited repeatedly during this period at intervals

shorter than the quickest time to decay. These are

referred to here as marked nest counts or clearance

plot dung counts (Plumptre & Reynolds 1996;

Staines & Ratcli�e 1987).

Where the animals/signs of interest occur in

groups, then conversions have to be made to calcu-

late animal/sign density from group density. This

has been particularly common in primate surveys

(Whitesides et al. 1988; Plumptre & Reynolds 1994),

where individual density has been calculated using

mean group size. Whitesides et al. (1988), in addi-

tion, recommended that a measure of mean group

spread be calculated for primate studies, using a per-

pendicular distance measure to the nearest animal to

the transect to calculate the perpendicular distance

from the transect to the centre of the group. They

argued that this was necessary because monkeys

further from the transect tended to be missed.

Each of these conversion factors has an associated

error. Few studies report their standard errors or

95% con®dence limits, and where they do these

errors are of the count only and rarely include errors

from conversion factors. If line transects are to be

used for monitoring populations of mammals then

the true errors of the estimate should be calculated.

This paper investigates how variation in conversion

factors and measures of e�ort a�ect the error of the

density estimate. Table 1 summarizes the errors asso-

ciated with di�erent methods of analysis.

Methods

LINE TRANSECT TECHNIQUES

Line transects are commonly established using a

strati®ed random sampling procedure (Plumptre &

Reynolds 1994). In African forests transects have

usually been walked at approximately 1 km hÿ1,counting all groups of animals seen from the trans-

ect. The perpendicular distance from the transect

line to the centre of the group seen is measured and

the number of animals seen in the group recorded

(Plumptre & Reynolds 1994; White 1994). The per-

pendicular distances are used to calculate a prob-

Table 1. The additional errors associated with direct and indirect counts of mammals from transects. These associated

errors should be calculated in addition to the error of the basic count.� � error associated with survey estimate; ±�noerror;�/±� can be an error depending on method used

Method Production rate Decomposition rate Group size Group spread

Direct counts

Sightings of single animals ± ± ± ±

Sightings of groups ± ± � � / ±Indirect counts

Dung counts � � � ±

Nest counts � � � ±

Clearance plot dung counts � ± � ±

Marked nest counts � ± � ±

357A.J. Plumptre

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ability density function that models the decrease in

sightings of animals with distance from the centre

line of the transect. This function is used to calculate

a density of groups with standard error and 95%

con®dence limits (Buckland et al. 1993). Individual

density can be calculated from group density by

multiplying by mean group size (see below). Esti-

mating density using line transects has been thor-

oughly covered by Buckland et al. (1993) and the

reader is referred to this book for details.

A Z-test is used to test whether two population

(Buckland et al. 1993, p. 381):

Z � D2 ÿD1

�p se�D2�2 � se�D1�2�where Dn � density estimate of population n or the

same population at time n; and se(Dn) � standard

error of this estimate

The assumptions for this test are that se(D2)�se(D1) and that the sample units from the ®rst sur-

vey are drawn independently from the sample units

in the second survey. An additional assumption is

that sample sizes are su�ciently large that the distri-

bution is close to normal. Sample size in transect

analyses is a function of the number of objects seen

and the number of transects censused. Buckland

et al. (1993) recommend that at least 10 transects

are censused to meet this assumption, although stu-

dies of elephant dung in Gabon indicate that 20±25

transects are required to approach normality (P.

Walsh, personal communication). With fewer than

this number of transects, it is better to use a t-distri-

bution (see Appendix 1 for a possible test).

Line transect surveying makes several assump-

tions (for details see Buckland et al. 1993): (i)

objects on the centre line are detected with certainty;

(ii) objects are detected at their initial location; (iii)

measurements are exact. Some papers state that an

object should not be counted on more than one

transect line, but this is not in fact an assumption of

this technique provided movement is random with

respect to the lines (Buckland et al. 1993, p. 37).

CALCULATING RESOLUTION OF DENSITY

ESTIMATION FROM TWO INDEPENDENT

SURVEYS

The resolution of a density estimate is de®ned here

as the percentage change that will be detectable

between two independent surveys. Surveys in Afri-

can forests are costly and there are few places where

more than two surveys have been carried out to date

(see Discussion). The resolution will depend on the

standard errors of the two density estimates. If initi-

ally we make an assumption that the standard error

of a density estimate is equal to the standard error

of a second density estimate, which is changed by a

factor R, i.e. D2�D1�D1*R, where D1 � density

estimate and R � proportional change or resolution

(100R�% change), then we can derive a simple

equation from the Z-test equation above to calculate

the resolution (R). Substituting D2�D1�D1*R in

the equation above:

Z � D1 ÿD1 �D1�R

�p se�D2�2 � se�D1�2�Therefore:

Z � D1�R

�p 2�se�D1�2���21:96

(for P� 0�05, 2-tailed test; but see below).Therefore:

R � 2:77se�D1�D1

� 2:77�CV=100� eqn 1

where CV � coe�cient of variation calculated by

DISTANCE.

For example, if we want to detect a 10% change

in the population then R� 0�1 and CV� 3�61%.

However, the power of the Z-test to detect a di�er-

ence at P� 0�05 is low (see Appendix 2), only

around 50%. If we want the power of the test to be

around 80% (as most textbooks suggest) then we

need to calculate the Z-test for 2�8 standard errors.

In this case CV� 2�4% (Appendix 2).

If the standard error of the second density esti-

mate di�ers from the ®rst (a violation of one of the

assumptions of the test, see above) then the number

in equation 1 changes and the resolution that is

detectable changes, although not greatly (Fig. 1).

This test provides a measure of the percentage

change in a population. However, a 100% increase

(population doubling) is di�erent to a 100%

decrease (population extinction). One way to deal

with this is to use di�erences between densities on a

logarithmic scale and the fact that the CV of the

density is approximately equal to the standard

deviation of the loge transformed density (P. Roth-

ery, personal communication). This method has the

advantage that working with log densities helps to

approximate a normal distribution. However, for

the purposes of this paper, percentage increases/

decreases will be used as examples because it is

easier to visualize references to 20% changes in the

text rather than di�erences on a logarithmic scale.

With indirect counts there are errors and CVs

associated with each conversion factor used. A stan-

dard dung survey, for example, corrects the dung

density for the decomposition rate and the deposi-

tion rate of dung:

T � DP=Q

where T � density of animals; D � density of dung

on transects; P � mean rate of decay (1/mean days);

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and Q � mean number of dung piles produced per

day.

Barnes (1993) gives an equation (derived using the

delta method) that provides an approximate esti-

mate of the CV for the product of several variables:

CV2�T� � CV2�D� � CV2�P� � CV2�Q� eqn 2

where CV(X) � coe�cient of variation of variable X

(standard error/mean *100%) [CV(Q) is approxi-

mately � CV(1/Q)].

This equation assumes that the values of the com-

ponent variables are not correlated (for example it is

possible that dung decay is faster if dung density is

high because dung beetles are more abundant, in

which case this assumption would be invalid).

The variance of the corrected estimate is:

Var�T� � �D�P=Q�2���CV�D��2 � �CV�P��2

� �CV�Q��2�

RESOLUTION OF DIRECT OBSERVATIONS

FROM TRANSECT DATA IN AFRICA

Primate sightings

Data from primate surveys in the Budongo Forest

in western Uganda (Plumptre & Reynolds 1994,

1996) were used to investigate the e�ects of total dis-

tance walked and number of groups sighted. Data

were used from surveys of blue monkeys Cercopithe-

cus mitis Matschie and black and white colobus

monkeys Colobus guereza Ruppell in several com-

partments in the forest. In each compartment ®ve

transects were established using a strati®ed random

sampling procedure (Plumptre & Reynolds 1994),

and were walked twice each month during 1993.

The total length of transects was at least 10 km in

each compartment. The data were analysed each

time the transects were walked three times, until

they had been walked 21 times. This allowed the

change in the CV to be monitored with survey e�ort

and number of groups seen.

Nest counts

Data from gorilla Gorilla gorilla graueri Matschie

surveys (Hall et al. 1998b) and chimpanzee Pan

troglodytes schweinfurthi Blumenbach surveys

(Plumptre & Reynolds 1996; Hall et al. 1998b) were

used to investigate the e�ect of sample size on CV

of nest counts.

EFFECTS OF CORRECTION FACTORS USING

DATA FROM AFRICA

Dung defaecation rates

Standard errors and CVs of data for defaecation

rates that could be found in the literature (for large

African mammals) were calculated.

Fig. 1. The percentage change detectable (resolution) with a Z-test as the coe�cient of variation changes and the standard

errors of the density estimates change. The lines plotted are where the standard errors of two density estimates are equal

(SE1� SE2; assumed in equation 1) and also where one is half (SE1� 2SE2) or double (2SE1�SE2) the size of the other.Lines are plotted where the power of the test is around 50%.

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Nest construction rates

Estimates of nest construction rate and its CV were

calculated from dawn to dusk follows of habituated

individuals in a community of chimpanzees in the

Budongo Forest in western Uganda. Only data from

complete dawn to dusk follows were used (Plumptre

& Reynolds 1997).

Nest decay rates

Mean time to nest decay has traditionally been cal-

culated from nest decay rates in the literature,

although nest decay can also be calculated in a simi-

lar way to decay of dung by ®tting an equation to

the decay curve and obtaining bootstrap estimates

of the error (Barnes & Barnes 1992; Barnes et al.

1994; Plumptre & Reynolds 1996). Fitting a decay

rate equation such as an exponential decay (Barnes

& Barnes 1992) has advantages in that the slowest

decomposing nests/dung do not need to be moni-

tored until they have disappeared before an estimate

for the rate can be obtained. However, this method

measures the median rate of decay rather than the

mean rate and it is recommended that mean rate is

used (Barnes & Barnes 1992; White 1995). CVs of

published mean time to nest decay studies were cal-

culated where the data were available to do so.

Dung decay rates

Barnes et al. (1994) provided data on bootstrapped

estimates of the median decay rate of elephant Lox-

odonta africana Blumenbach dung and its associated

errors for dung monitored in Ghana and Cameroon.

The e�ects of sample size on bootstrapped CV were

analysed using these data.

The combined e�ects of these errors for these con-

version factors were investigated using equation 2.

EFFECTS OF MEASURES OF GROUP SIZE

AND SPREAD ON PRIMATE SURVEYS

Individual animal density is calculated by multiply-

ing the group density by the mean group size. It is

sometimes found that large groups are seen at

further distances from the transects than small

groups, in which case it is necessary to correct for

this bias. Buckland et al. (1993, pp. 130±134) give

four methods to do this: (i) calculate mean group

size from observations within a strip width where

there is no bias observed; (ii) use the perpendicular

distance for the group to replace the group by n

individuals with the same perpendicular distance

(where n � number of animals seen); (iii) stratify the

density estimation procedures by group size

(requires a large sample size to do this); (iv) regress

group size with distance or estimated detection

probability. DISTANCE can carry out the last

method and by default regresses log(group size) on

the estimated detection probability. The e�ects of

correcting for group size on CV was investigated

with the primate data, correlating CV of group den-

sity with CV of individual monkey density calcu-

lated by DISTANCE.

Many primatologists have surveyed groups of pri-

mates by measuring the perpendicular distance to

the nearest animal in a group and then computing

an average group spread to calculate the true per-

pendicular distance to the group centre (Whitesides

et al. 1988; White 1994). This method assumes that

group spread on average is circular, constant

throughout the day and has no error associated with

its measurement. As Struhsaker (1997) pointed out,

primates often move in a linear fashion and are very

unlikely to be distributed in a circle. To test the

assumption that group spread is fairly constant,

measurements were made during dawn to dusk fol-

lows of 17 groups of monkeys (six blue monkey, six

black and white colobus monkey and ®ve redtail

monkey Cercopithecus ascanius Matschie) made

between October 1994 and January 1996 in the

Budongo Forest. Groups were located at around

16.00 h on day 1 and followed until dusk, then from

dawn until dusk on day 2 and on the third day from

dawn until the time at which they were found on

day 1. Each group was followed using this protocol

once each month. Group spread was measured

using a range®nder (often several measurements

were required to measure across the whole group as

visibility was not much greater than 30m; these

would be made to tree stems and summed across the

group). Group spread was measured in this manner

every 30min throughout the day.

Results

DIRECT OBSERVATIONS FROM TRANSECTS

Distance walked

Not surprisingly, increasing the distance walked

reduced the CV of group density in primates in

Budongo Forest (Table 2) because it increased the

numbers of groups encountered. What is of interest

here is that the CV remained fairly high (10±20%)

even when the distance walked was large (200� km),and the forest supports a relatively high density of

primates (Plumptre & Reynolds 1994). Conse-

quently, in order to detect this degree of change in

primate populations in Africa, it is necessary to

walk at least 200 km and probably further because

most other sites will have a lower sighting fre-

quency.

Number of groups seen

The number of groups seen strongly reduced the CV

for primate groups in Budongo Forest (Fig. 2). This

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was expected as standard error (and hence CV) is

always reduced by increased sample size. By ®tting a

curve of the equation CV� a/p(N) (where N �number of groups seen; a� a constant) to these

points (Radj2 =0�93, F� 685�8, P<0�001) it can be

calculated that to detect a 10% change

(CV� 3�61%) in the group density you would need

to see about 1671 primate groups, and to detect a

20% change (CV� 7�22%) about 418 groups. How-

ever, as stated previously, the power to detect this

change is only about 50%. For a power of 80% the

respective values are 3781 (CV� 2�4%) and 1029

groups (CV� 4�6%).

Number of nests seen

Variation around group density estimates (chimpan-

zees and gorillas combined) for the number of nest

sites seen from transects was high. Fitting a similar

curve (CV� a/p(N)) of nest sites seen on CV gives

a reasonable regression (Radj2 =0�67, F� 36�2,

P<0�001). Using the equation derived, 349 nests

would need to be found to detect a 20% di�erence

and 1395 nests to detect a 10% change (again with

only a power of 50% to detect this change). For a

power of 80% the values are 3157 (10% change)

and 859 nests (20% change).

INDIRECT SURVEYING

Production rates

The defaecation rates of various mammals have

been calculated and published in the literature.

However, few studies have published the errors

around these rates. The CV for those that have are

Table 2. The number of groups seen, distance walked and coe�cient of variation (CV) for two monkey species in di�erent

compartments in Budongo Forest

Species Compartment Number of groups Distance walked (km) Density (groups kmÿ2) CV (%)

Blue monkey B1 163 210 21�0 9�7Cercopithecus mitis K11±13 16 210 2�9 37�9

W21 76 210 9�4 17�9K4 74 212 9�4 13�5N3 133 227 13�8 10�8

Black and white colobus B1 58 210 6�5 16�7Colobus guereza K11±13 47 210 6�6 16�7

K4 68 212 8�8 15�0N3 95 227 9�9 13�7

Fig. 2. Changes in coe�cient of variation with numbers of primate groups seen for surveys of blue and colobus monkeys in

di�erent forest compartments.

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not too high (Table 3) and very much depend on the

number of days over which production was mea-

sured. For elephants, production has been calculated

by following the trails of a group over several days

for each estimate (Wing & Buss 1970; Tchamba

1991), providing a large sample size. For other esti-

mates individual animals have been monitored over

much less time and hence the CV is larger.

There is no published literature on the production

rates of nests by gorillas and only one for chimpan-

zees (Plumptre & Reynolds 1997). The mean pro-

duction rate from the dawn±dusk follows of

chimpanzees in Budongo was 1�15 nests per day

with a CV of 4�1%. This was based on 201 dawn±

dusk follows.

Decay rates

For nest decay, the mean number of days to com-

plete decay has been calculated to correct the nest

density estimate to an animal density. Two pub-

lished studies have provided measures of variance/

error around these mean estimates. In the Tai For-

est, mean decay was 73�3 days, SE� 9�7,CV� 13�3% (Marchesi et al. 1995), and in Budongo

Forest, mean decay was 45�9 days, SE� 3�6,CV� 7�8% (Plumptre & Reynolds 1996).

Barnes et al. (1994) used bootstrapping of median

time to decay (1000 replications) as a procedure to

calculate the standard error of the mean number of

days for elephant dung to decay. Dung was moni-

tored in di�erent sites or at di�erent times of year in

Ghana and Cameroon to provide 12 estimates of

decay rate with standard errors. The CV was about

5% with 70 monitored dung piles and 10% with 40

monitored piles.

Combining CVs for two independent surveys

A CV of 10% allows measurement of a 27�7%change in the population in a second survey (with

50% power). Counts of primates (Fig. 3) and nests

rarely had lower CVs, even with large sample sizes.

If CVs of dung/nest deposition and decay are

around 5% as well, then the total CV of the group

density estimate is:

�CV total�2 � �CV density�2 � �CV deposition�2

� �CV decay�2 � p�150� � 12�2%

This CV will allow detection of a 34% change in

the population (with 50% power) or a 67% change

(with 80% power). This is using fairly optimistic

estimates of CV for dung decay and deposition; sev-

eral estimates given above are larger than 5%. If

decay and deposition are both 10%, then only a

48% change in the population can be detected (50%

Table 3. The coe�cient of variation in the deposition rate of dung for various species, and construction rate of chimpanzee

nests from published studies. N � number of sample intervals over which dung/nest production was measured to obtain a

mean

Species N

Deposition

rate

(no. dayÿ1)CV

(%) Reference

Dung

Elephant Loxodonta africana Blumenbach 6 17�0 3�4 Wing & Buss (1970)

Elephant Loxodonta africana 16 19�8 1�2 Tchamba (1991)

Elephant Loxodonta africana 2 16�2 2�8 Plumptre (1991); A.J. Plumptre,

unpublished data

Bu�alo Syncerus ca�er Sparrmann 15 5�1 5�2 Plumptre (1991); A.J. Plumptre,

unpublished data

Okapi Okapia johnstoni P.Sclater 5 5�2 14�1 J. Hart, unpublished data

Blue duiker Cephalophus monticola Thunberg 4 4�9 26�5 Koster & Hart (1988)

Bay duiker Cephalophus dorsalis Gray 4 4�4 29�5 Koster & Hart (1988)

Bushbuck Tragelaphus scriptus Pallas 5 19�0 49�6 Plumptre (1991); A.J. Plumptre,

unpublished data

Blackbuck Antilope cervicapra L. 12 10�4 7�7 Rollins, Bryant & Montandon (1984)

Fallow deer Dama dama L. 12 11�3 11�5 Rollins, Bryant & Montandon (1984)

Sika deer Cervus nippon Temminick 20 6�9 4�3 Rollins, Bryant & Montandon (1984)

Axis deer Axis axis Erxleben 12 12�6 11�9 Rollins, Bryant & Montandon (1984)

White-tailed deer 12 19�6 11�7 Rollins, Bryant & Montandon (1984)

Odocoileus virginianus Zimmermann

Moose Alces alces L. 22 10�9 2�3 Miquelle (1983)

Nests

Chimpanzee P. troglodytes Blumenbach 14 1�15 4�1 A.J. Plumptre, unpublished data

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power). For 80% power, not even 100% change can

be detected.

GROUP SIZE AND SPREAD

The primate groups followed in Budongo often split

up into two or more subgroups that could be sepa-

rated by 200� m. During a survey these would be

counted as separate groups, and hence the density

estimate would be overestimated if these were multi-

plied by a mean group size calculated from follow-

ing di�erent groups and counting all individuals

present. Consequently, it is recommended that the

number of animals seen from the transect should be

used as the group size in DISTANCE.

Density estimates of group density and total mon-

key density were calculated from the Budongo sur-

vey data using the corrected mean group size

(observed from the transects) and the default

method in DISTANCE. Regressing the CV of pri-

mate group density on the CV of total monkey den-

sity gave the following equation:

CV �total� � 1�005�CV group�

� 3�333�R2adj � 0�99; F � 4802; P < 0�001�

Therefore calculating total density from group

density increases the CV by 3�3% for the Budongo

data.

The CV of group spread was very low after a very

large sample size for all species (blue monkeys:

n� 3163, mean � 65�6m, CV� 1�0%; redtail mon-

key: n� 2426, mean � 64�6m, CV� 1�1%; colobus

monkey: n� 2698, mean � 31�5m, CV� 1�7%).

This small variation should be included in the total

survey variation if average group spreads are used

to calculate perpendicular distance.

A repeated measures general linear model analysis

was carried out to investigate the time of day and

month of the year on group spread. For each species

the natural logarithm of group spread was taken to

normalize the data. Primate group spread varied sig-

ni®cantly throughout the day (blue monkey:

F� 8480�2, d.f.� 1,5, P<0�001, range 6±321m;

redtail monkey: F� 4260�9, d.f.� 1,4, P<0�001,range 7±267m; colobus monkey: F� 8281�6,d.f.� 1,5, P<0�001, range 1±212m), increasing

between 06.00 and 08.00 h (Fig. 3), the time when

most surveys are taking place. Group spread also

varied signi®cantly between months (blue monkey:

F� 7622�1, d.f.� 1,5, P<0�001; redtail monkey:

F� 5140�6, d.f.� 1,4, P<0�001; colobus monkey:

F� 5678�9, d.f.� 1,5, P<0�001).Due to this variation in group spread it is con-

cluded that correcting perpendicular distance data

to the nearest individual in a group with a measure

of the radius of mean group spread (Whitesides et al.

1988) is not a good method and should be avoided.

It is better to measure the perpendicular distance to

the centre of the group of animals seen and count

these, or to measure distance to every individual in

the group and analyse the data for individuals (S.

Buckland, personal communication).

Fig. 3. Mean group spread for three primate species at di�erent times of day in Budongo Forest, Uganda.

363A.J. Plumptre

# 2000 British

Ecological Society

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Ecology, 37,

356±368

Discussion

MONITORING

In African forests line transect surveys have mainly

been used to obtain density estimates of large mam-

mals, and few studies have established monitoring

programmes. It is often implied that subsequent sur-

veys will show whether the population is changing,

but little thought is given to planning future surveys.

If future surveys are to detect change then the

results in this paper show that both surveys must be

intensive. Where monitoring has occurred in Africa

it has provided useful data for conservation. For

example, detection of population changes of ele-

phants following aerial monitoring of several popu-

lations in savannas led to the placing of this species

on Appendix 1 of CITES (Douglas-Hamilton 1987;

Douglas-Hamilton, Michelmore & Inamdar 1992).

With the recent concessions made to allow limited

trade of ivory, it is vital that elephant populations

continue to be monitored. In forests this can cur-

rently only be achieved using line transect dung

counts (Barnes et al. 1994).

IMPROVING THE RESOLUTION BY

REPEATED SURVEYING OR REPEATED USE

OF TRANSECTS

If line transect methods are to be used for monitor-

ing animal populations in Africa, the results from

this study show that at best a 10±30% change in the

population will be detectable between two surveys,

and if high power is required for the test then the

percentage change detectable will be higher still.

Estimations of density using indirect methods (dung

or nest counts) will at best be able to detect a 30±

50% change in the population. These results are,

however, obtained on the assumption that two inde-

pendent surveys are made and that the two density

estimates obtained are tested for di�erences. The

resolution can be improved in two ways if this

assumption is not made:

1. carrying out regular surveys and ®tting a

trendline to the data obtained (Buckland & Anga-

nuzzi 1988; Buckland et al. 1993, pp. 392±396).

2. using the same transects for the second survey.

In this case the variance of the di�erence in the den-

sity estimate of the two surveys is reduced by the

covariance of the two estimates:

V�D2 ÿ D1� � V�D2� � V�D1� ÿ 2 cov �D2;D1�In this case it would be better to estimate density

for each transect separately (using the detection

function obtained by pooling data across all trans-

ects), and then use Wilcoxon's signed ranks test (or

a paired t-test if the data are normal) on the paired

data to assess whether there has been a signi®cant

change in the population (P. Rothery, personal com-

munication). This will be a more robust test than

the Z-test.

Both these improvements assume that funding for

surveys is regular, something that is rare in Africa.

Transect lines can become overgrown and di�cult

to ®nd after only 6 months, so that if regular sur-

veyors are to revisit lines then it will be necessary to

employ labourers to keep the lines open. Even for a

single survey the costs can be prohibitive if large

areas are being surveyed. The Wildlife Conservation

Society's Grauer's gorilla Gorilla gorilla graueri

Matschie survey in Kahuzi Biega National Park in

the Democratic Republic of Congo cost around

$80 000, and a recent survey of the mountain goril-

las in Bwindi Impenetrable National Park in

Uganda, covering only 325 km2, cost around

$35 000.

IMPROVING THE RESOLUTION TO DETECT

CHANGES IN TWO INDEPENDENT SURVEYS

Accuracy, bias and precision

The accuracy of a population estimate is a function

of the bias of the estimate and the precision of the

estimate. In most surveys line transects are estab-

lished using strati®ed random sampling methods to

eliminate any potential bias. However, the e�ort

required to do this may be at the expense of a larger

sample size because it takes more time to establish

transects than to use paths that already exist in the

forest. It is possible to census from paths in the for-

est, but this will give a biased estimate of the popu-

lation density. However, this biased estimate is

likely to be more precise for the same e�ort

(human-days) as a transect census because more

ground will be covered and a larger sample size is

more likely to be obtained. In order to improve the

ability to detect changes in a population, the preci-

sion of the two estimates must be high. If the bias

can be corrected, obtaining biased estimates may in

fact allow greater resolution.

Walsh & White (1999) have developed a method

that they call `reconnaissance (recce) walks' that fol-

low a path of least resistance through the forest.

They have found that elephant dung encounter rate

(Walsh & White 1999) and gorilla nest encounter

rate (Hall et al. 1998b) on recce walks are highly

correlated with encounter rates on nearby line trans-

ects. Thus, a statistically rigorous estimate of density

can be made from recce data if some e�ort is made

to calibrate the functional relationship between

recce and transect encounter rates and thereby cor-

rect for the bias. Therefore a combination of recce

and transect sampling should provide a more precise

estimate of density than transect sampling alone,

because transect sampling requires roughly three

364Line transect

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tropical forests

# 2000 British

Ecological Society

Journal of Applied

Ecology, 37,

356±368

times the e�ort necessary for recce sampling (Walsh

& White 1999).

Decay rates

The resolution of indirect counts can also be

improved by reducing the number of conversion fac-

tors involved. Transects that are visited regularly

can measure the accumulation of nests and dung

and thereby avoid the need to correct for decay

(marked nest counts in Plumptre & Reynolds 1996,

1997; clearance counts of dung in Staines & Ratcli�e

1987). Given the inter-seasonal variation in decay

rates of nests (Plumptre & Reynolds 1996) and dung

(Plumptre 1991; Plumptre & Harris 1995; A.

Nchanji, unpublished elephant dung data), dung

and nest count resolution is poor where decay rates

are calculated. It is not valid to calculate separate

dung decay rates for wet and dry seasons because

long-lived dung (such as elephant and bu�alo) sur-

vives from one season into the next and decays at a

di�erent rate to dung deposited in that subsequent

season (A. Nchanji, unpublished data). Many stu-

dies utilize nest or dung decay data from other sites

but, given the variation that occurs, these data are

likely to be inappropriate. However, repeatedly visit-

ing transects is more labour intensive and costly

than one-o� counts, and counting only fresh dung/

nests will result in lower sample sizes. Consequently

there is a trade-o� between the loss of precision due

to lower sample sizes and the decrease in resolution

as a result of correcting for decay rates. This should

be investigated further.

Defaecation rates

If surveys use indirect signs to estimate population

size, better estimates of defaecation rates and nest

production rates are needed with smaller CVs.

Many of the values for CV in Table 3 are high

because the observation time was short. Elephant

defaecation rates had the lowest CV because it is

possible to follow a group for several days and

hence obtain a large sample size. Population esti-

mates from indirect counts should incorporate the

errors of the deposition and decay rates in the error

of the estimate and the errors should be published

in papers.

Sample sizes

Sample sizes in surveys should reach at least 100

groups if the objective of the study is to monitor the

population changes in future. A pilot study should

be carried out to determine the sighting rate prior to

commencing the main survey. For rare species,

obtaining 100 sightings is likely to require many

hundreds of kilometres of transects, and conse-

quently line transects may not be appropriate and

recce walks may be a better method. One option is

to concentrate transects in areas where densities are

known to be high or that are visited regularly by the

animals, and to monitor these areas. In the forests

of central Africa many animals visit waterholes/salt

licks or `bais' (Turkalo & Fay 1995), and monitor-

ing could be better concentrated at sites such as

these. This method would assume that habitat use

does not change over time, however, and care must

be taken to ensure that monitoring also occurs else-

where at the same time to con®rm this. It is possible

that populations will concentrate at these sites when

they are declining elsewhere if these sites are consid-

ered `safe' or `good habitat', and general population

declines will not be detected until it is too late to do

anything.

Monitoring of animal populations in African for-

ests must rely on information from various sources

in order to adapt management practices in time to

assist declining populations. Relying solely on trans-

ect counts is inadvisable because of the low resolu-

tion of changes that can be detected. For example, if

elephant populations are to be monitored in forests

it would be advisable to focus dung counts in

regions where the population is known to be high,

whilst at the same time having some transects or

camera traps in low density regions (where the data

of interest will be presence or absence, rather than

density or encounter rates). In addition, records of

carcasses should be collected and surveys of meat in

markets conducted so that additional data are avail-

able from other sources. Using a multi-method

approach such as this is likely to give a clearer pic-

ture of changes in mammal abundance.

RECOMMENDATIONS FOR MONITORING IN

TROPICAL FORESTS

1. Carry out a pilot study prior to a survey to deter-

mine the encounter rate along transects: are trans-

ects going to be a suitable method to use? At the

same time test the possible use of recce walks or

other biased survey methods that may give more

precise but biased estimates (if the bias can be cor-

rected).

2. Obtain data on decay rates of signs and, if the

variation is high, consider the use of repeated sur-

veys along transects.

3. Obtain at least 100 sightings of groups or sepa-

rate sightings of individuals.

4. If possible and if the budget allows it, survey reg-

ularly and ®t trendlines to the data. Re-use the same

transects wherever possible.

5. Record the number of animals seen whenever a

group is sighted and do not use measures of group

spread to correct the perpendicular distance.

6. Obtain good measures of the production rate of

signs so that the associated CV is small.

365A.J. Plumptre

# 2000 British

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Journal of Applied

Ecology, 37,

356±368

7. Think about a variety of methods that can be

used to monitor the population in question and do

not rely on one method.

Acknowledgements

I would like to thank many of the people who have

contributed through informal discussion to the ideas

in this paper. In particular John Hart (who also pro-

vided data for Table 2), Peter Walsh and Lee White

have made me think hardest about survey methods

and monitoring. Len Thomas, Peter Rothery and

Peter Walsh have all provided helpful advice on the

statistics given here, and provided solutions given in

the Appendices. I am also grateful to the two anon-

ymous referees whose advice greatly improved this

paper. Data collected in the Virungas, Rwanda, on

dung production was funded by Bristol University,

Fauna and Flora International and the Dian Fossey

Gorilla Fund. Data collected in Budongo Forest,

Uganda, was funded by ODA, National Geographi-

cal Society, Jane Goodall Institute and the Wildlife

Conservation Society. I am grateful to the Ugandan

and Rwandan ®eld assistants who helped collect

these data, particularly Mutungire Nabert, Muhu-

muza Geresomu, Kyamanywa Julius, Uwimana

Fidele, Tolith Alfred, Hatari Stephen, Biroch God-

frey, Tuka Zephyr, Tinka John, Kugonza Dissan,

Kakura James and Akanya Martin and other sta�

of the Budongo Forest Project and the Karisoke

Research Centre. I am also grateful to the Institute

of Biological Anthropology at Oxford University

and in particular Professor Vernon Reynolds for

support whilst working in Uganda.

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Appendix 1

t-test to test di�erences in density estimates (L. Tho-

mas, personal communication).

This test may be more appropriate than the Z-test

for small sample sizes. The only approximations

available are designed for the case where the t distri-

bution is being used to compare two sample means.

Their performance when comparing two estimates is

unknown. However, an approximation is as follows:

t � �densityÿ1ÿ densityÿ2�=sigmawhere sigma (the standard error, or standard devia-

tion of the di�erence in estimates) is estimated by:

p��SE survey 1�2 � �SE survey 2�2�The degrees of freedom for this t-test are:

� ��SE 1�2 � �SE 2�2��p

��SE 1�4=dfÿ1� �SE 2�4=dfÿ2�d.f._1 and d.f._2 come from the formulae in Buck-

land et al. (1993, pp. 89±90).

Appendix 2

Statistical power of Z-test (P. Rothery, personal com-

munication; L. Thomas, personal communication).

To approximate the power of the Z-test the actual

di�erence and the standard error of the estimated

di�erence are required. This can be seen as follows.

A di�erence is detected at the 5% level when the

standardized di�erence D/s[D] is larger than 1�96 or

less than ÿ1�96, where D is the estimated di�erence.

The power of the test is then given by:

Power � 1 ÿ Prob� ÿ 1�96 < D=SE�D�

< 1�96� � 1 ÿ Prob� ÿ 1�96�SE�D�

< D < 1�96�SE�D��

If Dtrue is the true di�erence, then the above

expression for power can be written as:

Power � 1 ÿ Prob� ÿ 1�96�SE�D� ÿ Dtrue

< D ÿ Dtrue < 1�96�SE�D� ÿ Dtrue�

or

Power � 1 ÿ Prob� ÿ 1�96 ÿ Dtrue=SE�D�

< �D ÿ Dtrue�=SE�D�

< 1�96 ÿ Dtrue=SE�D��If D follows a normal distribution with mean

Dtrue and standard error SE[D], then the quantity

Z� (DÿDtrue)/SE[D] follows a standardized nor-

mal distribution with mean zero and standard devia-

tion of one. The power is then given by:

Power � 1 ÿ Prob� ÿ 1�96 ÿ Dtrue=SE�D�

< Z < 1�96 ÿ Dtrue=SE�D��The probability can be looked up in tables of the

367A.J. Plumptre

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Ecology, 37,

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standardized normal distribution or calculated using

a statistical package such as Minitab.

If we apply the above formula to calculate power

for detecting a di�erence of two standard errors, i.e.

Dtrue � 2*SE[D], then we have:

Power � 1 ÿ Prob� ÿ 3�96 < Z

< ÿ 0�04� � 0�52The corresponding power for detecting a di�er-

ence of three standard errors is give by:

Power � 1 ÿ Prob� ÿ 4�96 < Z

< ÿ 1�04� � 0�85The method can be related to the estimation of

changes in density as follows. Let D1true and

D2true denote the true densities at times 1 and 2,

with change in density given by:

Dtrue � D2true ÿ D1true � R�D1true

Let D1 and D2 be estimated densities at times 1

and 2, respectively, with change estimated as

D�D2ÿD1. If the coe�cient of variation of each

estimated density is equal to C, then:

SE�D1� � C�D1;SE�D2� � C�D2

The standard error of the estimated di�erence is

then given by:

SE�D� � C�D1true�p�1 � �1 � R�2�

So:

Dtrue=SE�D� � R=fC�p�1 � �1 � R�2�gFor a 10% change (R� 0�10) and C� 0�036 then:

Dtrue=SE�D� � 0�10=�0�036�1�49� � 1�87with corresponding power of about 53%. For 80%

power, Dtrue/SE[D]� 2�8 and C� 0�024.

368Line transect

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tropical forests

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