Overcoming the constraints of low sample sizes to produce age and growth data for rare or threatened sharks

Overcoming the constraints of low sample sizes to produce age andgrowth data for rare or threatened sharks

JONATHAN J. SMART*, ALASTAIR V. HARRY, ANDREW J. TOBIN and COLIN A. SIMPFENDORFERCentre for Sustainable Tropical Fisheries and Aquaculture & School of Earth and Environmental Sciences, James Cook University,

Townsville, Queensland, Australia

ABSTRACT

1. Many sharks are listed as data deficient in assessment and management reports owing to a lack of basic lifehistory data, making decisions about conservation management difficult. As such, the collection of these data is apriority. However, rare or threatened species with populations that are already small can be difficult to sample.Thus there is a need for techniques that permit the use of small sample sizes to provide preliminary informationon life history parameters such as age and growth.

2. In this study, growth curves were fitted to length-at-age data for five rare or difficult to sample sharks fromnorth-eastern Australia: Carcharhinus coatesi (n= 56), Carcharhinus fitzroyensis (n = 39), Carcharhinus macloti(n = 37), Eusphyra blochii (n= 14) and Hemipristis elongata (n = 14) to provide the first estimates of growth forthese species. Vertebral centra from field collections were aged to obtain length-at-age data, and partial ageadjustments were used to increase the precision of age estimates. In addition, back calculation techniques wereapplied to add interpolated data to fill gaps in the growth curves caused by missing length classes.

3. Back calculation techniques did not substantially alter the growth curves of the species, which had an evenspread of data across size classes (C. fitzroyensis, E. blochii and H. elongata). However, the back calculationtechniques considerably improved the growth curves for C. coatesi and C. macloti where juveniles were missingfrom the samples.

4. Small sample sizes often provide a barrier to conducting growth studies because of the perception that growthestimates can only be obtained from ‘large’ sample sizes. However, by including individuals across all of the specieslength classes and maximizing the use of all available exogenous information using back calculation and partialage adjustments, as well as through judicious choice of growth models, it is possible to obtain practicalestimates of growth, even when sample sizes are extremely limited.Copyright # 2012 John Wiley & Sons, Ltd.

Received 7 February 2012; Revised 25 June 2012; Accepted 7 July 2012

KEY WORDS: conservation evaluation; endangered species; fishing; ocean; coastal; fish

INTRODUCTION

The conservation andmanagement of elasmobranchs(sharks and batoids) depends on accurate life historydata (Heupel and Simpfendorfer, 2010) on whichassessment tools such as ecological risk assessments,demographic models and stock assessments can be

based (Simpfendorfer et al., 2011). However, lifehistory data are mostly available for species that arecommonly taken in commercial fisheries (Davenportand Stevens, 1988; Natanson et al., 1995; Carlsonet al., 2003; Joung et al., 2005; McAuley et al.,2006), which represent only a fraction of all specieswithin the group. This uneven spread of research

*Correspondence to: J. J. Smart, Centre for Sustainable Tropical Fisheries and Aquaculture & School of Earth and Environmental Sciences,James Cook University, Townsville, Queensland, 4811, Australia. E-mail: [email protected]

Copyright # 2012 John Wiley & Sons, Ltd.

AQUATIC CONSERVATION: MARINE AND FRESHWATER ECOSYSTEMS

Aquatic Conserv: Mar. Freshw. Ecosyst. (2012)

Published online in Wiley Online Library(wileyonlinelibrary.com). DOI: 10.1002/aqc.2274

across the diversity of elasmobranch taxa means thatalmost half of the known species that are included onthe IUCN Red List of Threatened Species are datadeficient (IUCN, 2011).

The inability to obtain sufficient samples, especiallyfrom rare or threatened species, on which to base lifehistory research is a major impediment to addressingknowledge gaps. For age and growth studies aminimum sample size of 200 has been recommendedto obtain unbiased estimates of age and growthparameters (Kritzer et al., 2001; Thorson andSimpfendorfer, 2009). However, this sample size isunrealistic for many species as they can be difficult tosample because of low abundances (either naturallyor because of the effects of human activities), gearselectivity (Thorson and Simpfendorfer, 2009) orimposed permitting restrictions that limit the abilityof scientists to collect samples (Simpfendorfer et al.,2008). The ability to produce precise estimates ofage and growth parameters from small sample sizeswould overcome these limitations and improve theconservation management of many rare orthreatened species of elasmobranchs.

One technique that is used to assist in the study ofage and growth is back calculation, where the lengthof individuals at earlier ages is estimated from thespacing of bands on the otoliths of bony fishes orvertebral centra of elasmobranchs (Campana, 1990;Francis, 1990; Cailliet and Goldman, 2004). Backcalculation can be particularly useful when samplesizes are low, if the younger age classes are missingor if the samples have not been collected over acontinuous period (Goldman, 2004; Tribuzio et al.,2010). Back calculation techniques allow the numberof length-at-age data points to be increased,effectively increasing the sample size used to modelgrowth (Cailliet and Goldman, 2004). Theapplication of techniques such as back calculationmay thus be of assistance when working with smallsample sizes in age and growth studies of rare orthreatened species.

To examine the feasibility of using small samplesizes to estimate age and growth parameters for rarespecies, this study used samples collected from fivespecies of shark occasionally caught in a gillnetfishery that operates along the east coast ofQueensland, Australia (Harry et al., 2011b): thecreek whaler Carcharhinus fitzroyensis, whitecheekshark Carcharhinus coatesi (previously identified asCarcharhinus dussumieri for northern Australia(White, 2012)), hardnose shark Carcharhinus macloti,winghead shark Eusphyra blochii, and fossil shark

Hemipristis elongata. The aim of this study was toprovide guidelines for researchers attempting todescribe growth characteristics of rare andthreatened species using small sample sizes. Methodsavailable for maximizing the use of exogenousinformation contained in a small number of samplesby using back calculation techniques and partialage-adjustments, and the appropriate choice ofgrowth models for small sample sizes are described.These techniques are applied to provide firstestimates of age and growth for the five specieslisted above and then the benefits and limitations ofthis approach are discussed.

MATERIALS AND METHODS

Sample collection

Samples were collected between March 2007 andNovember 2010 from within the Great Barrier ReefWorld Heritage Area (GBRWHA), Queensland,Australia. Samples were collected primarily froman onboard-vessel observer survey of a smallmesh, commercial gillnet fishery operating inthe region (East Coast Inshore Finfish Fishery).Full details of sample collection can be foundin Harry et al. (2011b). Additional samples werecollected opportunistically during fishery-independentsampling or were donated by fishermen. Thestretched total length (STL) was measured as thestraight line distance in millimetres taken bydepressing the upper lobe of the caudal fin into linewith the body axis (Compagno, 1984). Sex wasrecorded based on the presence of claspers in males.A section of the vertebral column was removedanterior to the first dorsal fin and stored frozen.

Vertebrae sectioning

Vertebrae were defrosted and a scalpel was used toseparate individual centra and remove the majorityof the remaining tissue, after which they were soakedin 5% sodium hypochlorite for 30min. The vertebraewere then washed under tap water and dried in anoven at 60�C for 24h. Longitudinal sections of thevertebrae, approximately 400mm thick, were takenthrough the focus using a low speed circular sawwith twin diamond tipped blades (Beuhler, Illinois,USA). They were then mounted on microscopeslides using crystal bond adhesive (SPI supplies,Pennsylvania, USA). Vertebrae that were too smallto be sectioned in this way were encased in clearcasting resin and then sectioned as above.

J. J. SMART ET AL.

Copyright # 2012 John Wiley & Sons, Ltd. Aquatic Conserv: Mar. Freshw. Ecosyst. (2012)

Age determination

Once sectioned, translucent and opaque bands werecounted in the corpus calcareum of each of thevertebrae (Goldman, 2004). The birth mark wasidentified by a change in the angle of the corpuscalcareum and represented an age of zero. Bandpairs after the birth mark were examined using adissecting microscope with transmitted light, countedand photographed. These were used to estimate theages of the individual; a pair of translucent andopaque bands was assumed to represent one year ofgrowth. Age validation could not be conducted forany of these species due to their low sample sizes,although several closely related species from theCarcharhinidae and Sphyrnidae have shown annualband pair deposition (McAuley et al., 2006; Harryet al., 2011a).

Counts were carried out by two independentreaders who had no knowledge of any biologicalinformation such as the sex or length of the specimen(Cailliet and Goldman, 2004; Goldman, 2004).Where there was a disagreement on the age ofan individual, the vertebra was re-examinedcollaboratively by both readers and a consensus agewas agreed upon. If a consensus could not beagreed then that specimen was excluded from theanalysis. Inter-reader precision was calculated usingpercentage agreement and percentage agreement+/� 1 year separated into length classes for three ofthe species (Goldman and Musick, 2006). Thesewere 50mm STL length classes for C. macloti andC. coatesi and 100mm STL length classes for C.fitzroyensis. Bias between reads was then evaluatedstatistically using Bowker’s test of symmetry(Bowker, 1948; Evans and Hoenig, 1998). Chang’s(1982) method for the coefficient of variation wasused to evaluate inter-reader precision. Hemipristiselongata and E. blochii were excluded from theseanalyses as the sample sizes available were too lowto warrant the use of these tests. However, since agebias plots were calculated for the same readers afterreading C. macloti, C. coatesi and C. fitzroyensis, itwas assumed that any bias that existed betweenthem would have been identified given that thevertebrae of all five species were very similar.

Partial ages

The reproductive cycles of many elasmobranchs arehighly synchronous (parturition occurring during afew discrete weeks or months of the year) (Wourms,1977). For synchronously reproducing species where

the timing of birth is known, it is possible to assign amean birth date to the population and moreprecisely estimate the age of individuals (e.g. if amean birth date of 1 January was assumed, the ageof a 1 year old individual caught on 1 July would be1.5 years). Four of the five study species are reportedto have a synchronous reproductive cycle in northernAustralian waters (Stevens and Lyle, 1989; Stevensand Mcloughlin, 1991). Carcharhinus macloti and H.elongata were assigned a mean birth-date of 1 Marchand 1 April, respectively (Stevens and Mcloughlin,1991). Carcharhinus fitzroyensis and E. blochii wereassigned a mean birth-date of 1 November based onthe capture of neonate individuals with unhealedumbilical scars.

If a species reproduces asynchronously and formsannual growth band pairs, then the birth date (andduration of first growth increment) will vary amongindividuals. Off northern Australia, C. coatesi isreported to reproduce asynchronously throughoutthe year (Stevens and Mcloughlin, 1991). For thisspecies, the first growth increment was adjusted to0.5 years for all individuals to account forasynchronous reproduction (Harry et al., 2010).

Back calculation techniques

Back calculation techniques were used to compensatefor the small sample sizes and missing length classes.Distances between growth band pairs were measuredusing a compound video microscope and an imageanalysis system, Image Pro Plus version 6.2 forWindows (Media Cybernetics 2002). The centrumradius (CR) was measured as the distance from thefocus to the edge of the vertebra in a straight line.The distance from the focus to each of the growthband pairs and the birth mark were also measuredalong this straight line. All of the distances measuredwere to the nearest 0.001mm. Once thesemeasurements were taken, a length-at-birth modifiedFraser–Lee method (Campana, 1990) was applied toall five species:

Li ¼ Lc þ CRi � CRcð Þ � Lc � Lbirthð ÞCRc � CRbirthð Þ

� �

where Li was the estimated STL at band i, Lc the STLat capture,CRc the centrum radius at capture,CRi thecentrum radius at band i,Lbirth the length-at-birth, andCRbirth the centrum radius at the birth mark.

A length-at-birth modified Fraser–Lee methodwas chosen as it incorporates exogenous informationsuch as length-at-birth (Cailliet and Goldman, 2004).This method is best used when the length-at-birth is

OVERCOMING SMALL SAMPLE SIZE CONSTRAINTS IN LENGTH-AT-AGE STUDIES


known and does not match the intercept of a modelapplied with another method. For C. fitzroyensisinformation on length-at-birth was based on theanimals in the sample with unhealed umbilical scars,which had a mean length of 515mm STL. Anindividual E. blochii (475mm STL) was capturedwith an unhealed umbilical scar from which itslength was assumed to represent length-at-birth. Nojuveniles with unhealed umbilical scars wereobtained for C. macloti or H. elongata, thereforelength-at-birth information was taken from Stevensand McLoughlin (1991) (C. macloti 425mm STL

and H. elongata 520mm STL). The length-at-birthfor C. coatesi was previously estimated as 350–400mm STL by Stevens and Mcloughlin (1991)under its previous taxonomic name, Carcharhinusdussumieri (White, 2012). However, an individual C.coatesi was captured on the east coast of Australiawith an unhealed umbilical scar at a length of439mm STL so this value was used as the lengthat birth.

Fitting growth models

A multi-model inference, information theoreticapproach incorporating Akaike’s informationcriterion (AIC MMI), was used to model the growthrates of all five species. The use of multiple modelshas been recommended over the use of a singlemodel (Cailliet et al., 2006) and is proposed as animprovement over a priori use of the von Bertalanffygrowth model (Katsanevakis and Maravelias, 2008;Thorson and Simpfendorfer, 2009). As part of thisapproach, three commonly used growth models inelasmobranch studies were included in the AIC MMIbased on results from Thorson and Simpfendorfer(2009). These models were a 3 parameter vonBertalanffy growth model (VB), a logistic model, andthe Gompertz model (Table 1). The best-fitparameter estimates were calculated using the NelderMead algorithm in the statistical package ‘R’

(R Development Core Team, 2009). Akaike’sinformation criterion with an incorporated biascorrection algorithm (AICc) was used to evaluatemodel performance. The AICc was chosen over astandard Akaike’s information criterion (AIC) as ithas been shown to perform better when sample sizesare below 200 (Zhu et al., 2009). The AICc wascalculated as:

AICc ¼ AIC þ 2k kþ 1ð Þn� k� 1

where AIC= nlog(s2) + 2 k, k is the total number ofparameters +1 for variance (s2) and n is the samplesize. Themost appropriate model was the one with thelowest AICc value (AICmin). The AIC difference (Δ)was used to rank the remaining models and wascalculated for each model (i = 1–3) as:

Δ ¼ AICc � AICmin

The models with the highest support had Δ of 0–2while models with considerably less support had Δ of2–10 and models with little or no support had Δ >10(Burnham and Anderson, 2001). AIC weights (w)were also calculated for each model (i = 1–3) andrepresent the probability of choosing the correctmodel from the set of candidates (Burnham andAnderson, 2001; Braccini et al., 2007; Harry et al.,2011a). This was calculated as:

wi ¼ exp �Δi=2ð ÞP3j¼1 exp �Δi=2ð Þ

RESULTS

Sample sizes ranged from 14 for E. blochii and H.elongata to 56 for C. coatesi (Table 2). For C.fitzroyensis there was obvious sexual dimorphism,with females growing c. 200mm STL larger thanmales. Consequently, separate growth models werefitted to males (n=19) and females (n=18)(Table 2). The data were spread evenly across alllength classes for C. fitzroyensis with a length rangeof 515–1070mm STL for males and 480–1250mmSTL for females. An even spread of data acrosslength classes was also present for E. blochii and H.elongata with length ranges of 475–1720mm STLand 788–1933mm STL, respectively. All of thelength ranges for these three species includedindividuals which were close to both maximum

Table 1. The equations of three growth models used in the multi-modelinference comparison

Model Growth function

von Bertalanffy L(t) =L0 + (L1�L0)(1� exp(�kt))logistic L tð Þ ¼ L1L0 exp ktð Þ

L1þL0 exp ktð Þ�1ð ÞGompertz L(t) =L1 exp(�L0 exp(�kt))

where L(t) is length-at-age t, L0 = length-at-age 0, L1=asymptoticlength and k= growth completion rate.

J. J. SMART ET AL.


Tab

le2.

Summaryof

multimod

elinferencegrow

than

alysisforfive

speciesof

sharkcompa

ring

mod

elsfitted

toob

served

andba

ck-calculatedda

ta.Ineach

case,d

atawerefitted

tothreemod

els,an

dmod

elaveragingwas

carriedou

tacross

asym

ptotic

leng

th,L1,as

thispa

rameter

was

common

toallmod

els(growth

rate

parameter

k,an

dleng

th-at-birthpa

rameter

L0wereno

tdirectly

compa

rablebetw

een

mod

els)

Observed

Back-calculated

Sex

Mod

elK

nAIC

cΔ

w(%

)RSE

L1

SEL0

SEk

SEn

AIC

Cw

(%)

RSE

L1

SEL0

SEk

SE

Carcharhinuscoatesi

Both

VB

456

534.75

034.18

35.2

839.1

4.9

439.5

35.2

3.042

0.824

258

3072.03

099.7

40.01

808.5

5.6

445.8

5.2

0.83

0.05

GOM

456

534.81

0.06

33.19

35.22

839

4.9

439.4

35.2

3.581

0.903

258

3083.65

11.61

0.3

40.79

801.8

5.1

448.9

5.2

1.01

0.05

LOG

456

534.84

0.09

32.62

35.23

838.9

4.9

439.3

35.2

4.177

0.985

258

3095.97

23.94

041.63

796.9

4.8

452.1

5.2

1.2

0.06

Average

838.9

4.9

808.4

5.6

Carcharhinusfitzroyensis

Male

VB

419

194.39

1.17

23.9

43.92

1079

60528

190.24

0.056

71720.07

063.91

39.39

996.1

22.8

533.7

9.7

0.37

0.04

GOM

419

193.73

0.51

33.25

43.17

1050

44529

180.324

0.057

71721.78

1.72

27.07

39.87

977.9

18.7

536.1

9.7

0.47

0.04

LOG

419

193.22

042.85

42.59

1032

35530

180.411

0.059

71723.98

3.92

9.02

40.49

965.5

16.4

538.8

9.6

0.58

0.05

Average

1049

47988.4

23.7

Fem

ale

VB

418

199.65

0.53

28.54

67.9

1412

166

514

270.145

0.048

76815.98

091.25

52.96

1258

43536

140.21

0.03

GOM

418

199.28

0.17

34.24

67.21

1332

108

517

260.224

0.048

76820.81

4.84

8.13

54.67

1211

33544

130.29

0.03

LOG

418

199.12

037.22

66.9

1288

83520

250.307

0.05

76825.96

9.99

0.62

56.55

1184

28552

130.38

0.03

Average

1339

125

1253

44Carcharhinusmacloti

Both

VB

437

348.54

033.46

28.03

1173

624

670

470.049

0.087

279

2734.58

099.77

32.69

879

9.9

432.7

4.9

0.26

0.01

GOM

437

348.54

0.01

33.33

28.03

1112

422

672

440.07

0.087

279

2746.7

12.11

0.23

33.41

858.9

8437.1

4.8

0.35

0.02

LOG

437

348.55

0.02

33.21

28.04

1073

318

674

410.09

0.087

279

2760.8

26.22

034.27

846

6.9

441.7

4.8

0.43

0.02

Average

1119

457

878.9

9.9

Eusphyrablochii

Both

VB

414

151.53

2.77

14.04

93.71

1893

130

536

580.117

0.026

136

932.83

098.68

72.8

1710

55496

210.12

0.01

GOM

414

150.02

1.27

29.76

88.45

1812

83546

520.179

0.026

136

941.47

8.64

1.31

76.74

1614

40525

200.19

0.01

LOG

414

148.75

056.2

84.23

1767

62553

480.25

0.029

136

950.68

17.85

0.01

81.17

1567

34549

190.26

0.02

Average

1798

871709

56Hem

ipristiselongata

Both

VB

414

167.13

037.18

106.75

1776

75538

159

0.313

0.079

941153.76

074.18

113.78

1691

47514

260.27

0.03

GOM

414

167.33

0.2

33.57

107.53

1754

66625

118

0.4

0.092

941156.09

2.32

23.21

115.2

1622

35530

250.4

0.03

LOG

414

167.61

0.48

29.24

108.6

1739

60675

102

0.492

0.109

941160.46

6.7

2.61

117.91

1585

30547

240.55

0.04

Average

1757

701672

54

Kisthenu

mberof

fitted

mod

elpa

rameters(pluson

eforvarian

ce),nisthesamplesize,A

ICCisthesm

all-samplebias

adjusted

form

ofAka

ike’sInform

ationCriteria,

Δisthedifference

inAIC

Cvalues

betw

eenmod

els,w(%

)are

theAIC

Cweigh

ts,R

SEistheresidu

alstan

dard

error,L1isasym

ptoticleng

thpa

rameter

inmm

,L0istheleng

th-at-birthpa

rameter

inmm,a

ndkisthegrow

thrate

parameter

inyear

-1.SE

isthestan

dard

errorforeach

adjacent

parameter.



length and the length-at-birth (Stevens and Lyle,1989; Stevens and Mcloughlin, 1991). However,there was a lack of spread across length classes forC. coatesi and C. macloti as both had juvenile lengthclasses missing from the samples. The lengthranges were 706–913mm STL for C. macloti and439–915mm STL for C. coatesi. Minimum ageestimates of 0 year were attained for C. coatesi,C. fitzroyensis and E. blochii where neonateindividuals were collected with unhealed umbilicalscars. The minimum age estimates for H. elongataand C. macloti were 0.8 year and 2.8 years,respectively. The maximum ages attained for eachspecies were 6.5 years for C. coatesi, 9.1 years(males) and 12.5 years (females) for C. fitzroyensis,11.8 years for C. macloti, 20.9 years for E. blochiiand 14.7 years for H. elongata.

The percentage agreement +/�1year betweenreads was 73.01% for C. coatesi, 87.77% for C.fitzroyensis, and 52.97% for C. macloti (Figure 1).No systematic bias was detected by the Bowker’s testof symmetry for C. coatesi (df=11, x2=17.33,P=0.10) or C. macloti (df=21, x2=19.86, P=0.52).However, systematic bias was detected for C.fitzroyensis (df=10, x2=20.8, P=0.022), althoughthe magnitude of this bias was minimal and restrictedto the smaller length classes (Figure 1(b)). Chang’scoefficient of variation was 12.6% for C. coatesi,28.8% for C. fitzroyensis and 18.1% for C. macloti.

When growth models were fitted to the observeddata only, there was approximately equal supportfor each model for four of the species (Table 2;Figure 2). The exception to this was E. blochii, inwhich the logistic model (w=56.2%) had muchgreater support than the Gompertz (w=29.8%)and von Bertalanffy (w=14.0%) (Table 2). Thelack of a clear ‘best’ model for most of the speciesmay be related to the small sample sizes, and

supports the MMI approach to growth analysis.For each of the species the use of just a singlemodel could have resulted in an underestimationof standard error (Katsanevakis, 2006; Katsanevakisand Maravelias, 2008).

In comparison, the MMI results for the backcalculated data showed that the von Bertalanffygrowth model provided the majority of thesupport for all of the species (Table 2). Theincrease in interpolated sample size due to backcalculation resulted in lower standard errorsaround the model parameter estimates for all ofthe species except C. coatesi (Table 2). Thisindicates a higher level of statistical precision thanthe observed data alone. Despite this consistentimprovement in statistical precision, the biologicalaccuracy of the observed and back calculated datadiffered between one another for each of the fivespecies. When the observed and back calculatedgrowth curves are compared for C. fitzroyensis(Figure 2(c), (d)), E. blochii (Figure 2(g), (h)) andH. elongata (Figure 2(i), (j)), little difference couldbe observed between the curves produced.However, the model average L1 parameterestimate of the observed data provided a morebiologically reasonable representation of L1 foreach of these three species (Table 2). Therefore,modelling the observed data gave more biologicallyappropriate results; despite the back calculatedmodels providing higher statistical precision.However, the observed data could not providebiologically reasonable growth curves for C. maclotinor C. coatesi owing to the missing juvenile lengthclasses. For example, in C. macloti as the L0

parameter estimate did not match the knownlength-at-birth (Figure 2(e)) (Stevens andMcloughlin, 1991). Therefore, for C. macloti theback calculated data provided the most biologically

0 2 4 6 8

0

2

4

6

8

1

12

4

3

5

3

5

7

8

8

4 2

2

1

4

2

6

1

(a) C.coatesi

Rea

ding

2 (

year

s) m

ean

± 2S

E

0 2 4 6 8 10 12

0

2

4

6

8

10

12

14

10

12

7

12

3

5

2

4

4

3

10

4

9

2

4

5

4

3

5 3

2

22

(b) C.fitzroyensis

Reader 1 Age (years)0 2 4 6 8 10

0

2

4

6

8

10

2

5

1

3

3

3

2

1

1

3

2

2

3

3

3

1

5

8

1

2

2

4

4

2 2

2

1

4

2

3

2

1

(c) C.macloti

Figure 1. Age-bias plot for (a) Carcharhinus coatesi, (b) Carcharhinus fitzroyensis, and (c) Carcharhinus macloti incorporating age-specific agreementsbetween Reading 1 and 2 used for Bowker’s test of symmetry. Mean age-specific agreements �2 standard errors are plotted along with the 1–1

equivalence line for comparison.

J. J. SMART ET AL.


reasonable growth curve (Figure 2, (f)). Similarly, thelack of smaller C. coatesi caused an unusual shapedgrowth curve, which did not appear to bebiologically realistic (Figure 2(a)) and a morerealistic fit was obtained when the back calculateddata were used (Table 2; Figure 2(b)).

DISCUSSION

These results demonstrate that reasonable estimates ofage and growth can be produced from rare orthreatened elasmobranch species with limited samplesizes. Sample sizes of less than 20 have rarely beenused to produce age and growth information as

samples this small usually suffer from length classbias which can alter parameters such as theasymptotic length or curvature. However, in thisstudy biologically appropriate age and growth curvesfor three species (C. fitzroyensis, E. blochii and H.elongata) were produced successfully despite havingsample sizes as low as 14. The remaining two species(C. coatesi and C. macloti) required the use of backcalculation techniques to attain biologicallyappropriate age and growth estimates as missingjuvenile length classes gave estimates that didnot initially match known parameters, such as lengthat birth.

The omission of length classes was the primaryfactor affecting model accuracy rather than sample

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Figure 2. Length-at-age determined by vertebral analysis for the observed data and Fraser Lee length-at-birth modified back calculation technique forall five species. Solid lines are the weighted model average of mean length-at-age from all growth models. Sexes have been pooled for C. coatesi, C.

macloti, E. blochii and H. elongata but were separated for C. fitzroyensis.



size itself. This was demonstrated by the results for C.coatesi which had the largest sample size but stillrequired back calculation techniques to account formissing length classes. Length class bias is typicallycaused by gear selectivity, where all of the lengthclasses of the population have disproportionatechances of being caught owing to factors such ashook size or mesh size in gill nets (Kirkwood andWalker, 1986; Thorson and Simpfendorfer, 2009).When length class bias omits the juvenile classesfrom a sample, back calculation techniques canbe used to account for them (Cailliet andGoldman, 2004; Tribuzio et al., 2010). The observedmodels for C. coatesi and C. macloti were initiallybiologically inappropriate as the length at birth wasoverestimated for C. macloti and neither species hada point of inflection which matched their knownlengths at maturity, which is common in othercarcharhinid species (Davenport and Stevens, 1988).However, once back calculation was performed,these parameters more closely matched their knownlengths at birth and provided points of inflectionthat matched their known lengths at maturity.Therefore the back calculated models provided themost biologically appropriate estimates for thesetwo species.

While back calculation can effectively accountfor missing juvenile length classes, it cannotaccount for missing larger length classes thatinclude mature and fully grown individuals. Whenthese length classes are absent from the sample theasymptotic length (L1) will be substantiallydifferent to the true average maximum size of thespecies and therefore the growth coefficient (k) willalso be inaccurate. This was demonstrated forspinner sharks Carcharhinus brevipinna, where ageand growth estimates that were produced from asample which lacked mature individuals(Branstetter, 1987a) were later shown to beinaccurate by a study that included these lengthclasses (Joung et al., 2005). Therefore a samplemust include mature or fully grown individuals inorder to produce reliable estimates of age andgrowth, although errors can still occur with theinclusion of these length classes. Rosa Lee’sphenomenon probably occurred for E. blochii andH. elongata as the age estimates produced by theback calculation were lower than the estimatesproduced by the observed data for the juveniles.Rosa Lee’s phenomenon occurs when individualswith slower growth rates suffer less mortality whenyoung (Ricker, 1969) therefore when they attainmaximum size they will produce slower growth

rates than is true for the population when backcalculation is performed on them (Ricker, 1969,1992; Campana, 1990; Walker et al., 1998).Therefore despite having lower statistical accuracy,the observed model was considered the mostbiologically appropriate for both of these species.This shows that when sample sizes are small, backcalculation may be unnecessary when there is aneven spread of data across length classes, althoughthis may limit the precision of the age and growthestimates because of smaller sample sizes.

Assigning partial ages can theoretically increasemodel precision by categorizing an individual’s ageinto fractions of a year rather than discrete yearclasses (Ballagh et al., 2011). This avoids aligningthe individuals into year classes, thus increasing thespread of data across the samples age range.However, partial ages can only be assigned toseasonally reproducing species when the timing ofspawning or birth is known (Ballagh et al., 2011).This is a good example of how the judicious use ofexogenous biological information can benefit theseanalyses.

Sexual dimorphism can also have importantimplications for length-at-age studies as sexes areoften combined to increase the sample size fordata-limited species (Branstetter, 1987a,b; Harryet al., 2011a). Combining sexes allows gaps in thedata to be filled but can be detrimental to the finalmodel if sexual dimorphism in size occurs. Thiswas the case for C. fitzroyensis where females grewnoticeably larger than males, and as such wereanalysed separately. Although this meantinferences on growth were based on much smallersamples sizes (leading to higher standard errors),this trade off was considered appropriate. Forboth sexes, individuals ranged in size fromneonates to large adults so it was possible to fitgrowth curves that were in keeping with thebiology of the species.

The growth curves attained for each of these fivespecies emphasize the diversity that not only existsamong all shark species, but also between specieswithin the same families. Two growth patternswere observed in this study. First, a steady growthrate which asymptoted gradually after maturity, asdisplayed by C. fitzroyensis, C. macloti, E. blochiiand H. elongata. This is similar to many otherspecies of carcharhinid and sphyrnid sharks suchas the sandbar shark Carcharhinus plumbeus(Joung et al., 2004; McAuley et al., 2006; Romineet al., 2006), common blacktip shark Carcharhinuslimbatus (Wintner and Cliff, 1996) and great

J. J. SMART ET AL.


hammerhead Sphyrna mokarran (Piercy et al., 2007,2010; Harry et al., 2011a). The second growthpattern demonstrated fast juvenile growth rateswith the rapid attainment of maximum length,such as that displayed by C. coatesi. This type oflife history is usually caused by natural selectionpressures such as predation which favour fasterjuvenile growth (Simpfendorfer, 1993). Thisgrowth pattern is typical of smaller species such asthe milk shark Rhizoprionodon acutus (Harryet al., 2010) and the Australian sharpnose sharkRhizoprionodon taylori (Simpfendorfer, 1993).

Estimates of age and growth rates in sharks areinfluenced by the periodicity of growth band pairformation and whether or not this is annual(Goldman, 2004). This requires the use of agevalidation techniques such as chemical marking,tag recapture of known age individuals ormarginal increment analysis which are commonlyattempted in conjunction with age and growthstudies (Simpfendorfer, 1993; Simpfendorfer et al.,2002; McAuley et al., 2006; Harry et al., 2011a).However, the use of these techniques was notpossible owing to the small sample sizes attainedfor these five species. In order to conduct marginalincrement analysis monthly samples are required,while chemical marking requires marked individualsto be recaptured, both of which are difficult toachieve when initial samples are already rare. Thereis a growing body of literature that reports thatmany elasmobranch families such as Carcharhinidaeand Sphyrnidae have annual band deposition(McAuley et al., 2006; Harry et al., 2011a).However, there are some exceptions reported fromthe families Squatinidae (Natanson and Cailliet,1990), Cetorhinidae (Natanson et al., 2008), andOrectoloblidae (Chidlow et al., 2007). Studies on theporbeagle Lamna nasus have also shown thatyounger individuals produce band pairs annually(Campana et al., 2002; Natanson et al., 2002) butonce they reach maximum size cease to deposit bandpairs due to the cessation of growth, leading to theunder-aging of older animals by as much as 50%(Francis et al., 2007). Therefore validation is still apriority and should be conducted as soon assufficient samples become available, given theassumption of annual band pair formation isessential for growth studies. However, while theconfidence in unvalidated results may be diminished,they are still important because preliminary age andgrowth information is needed for many specieswhose management and conservation may havepressing need of this information.

CONCLUSIONS

Elasmobranchs in general are a data-poor taxon,and uncertainty about aspects of their biologycan confound management decisions. Therefore,techniques which are suitable for smaller samplesizes need to be highlighted in order to improve themanagement and conservation of these data-limitedtaxa. This study has shown that techniques that arealready widely available and frequently used canproduce preliminary results for species when only alimited number of samples can be obtained. Earlypapers from the 1970s and 1980s regularly usedlimited (n <200) (Stevens, 1975; Pratt and Casey,1983; Martin and Cailliet, 1988; Yudin and Cailliet,1990) or low (n <50) (DeCrosta, 1981; Caillietet al., 1983, 1985; Schwartz, 1983) sample sizesbecause baseline life history information for manyspecies was needed immediately. Managementdecisions were then based on such studies untilvalidated age and growth information becameavailable. Today’s scenario has changed little asinformation is still lacking for many elasmobranchspecies, yet the use of small sample sizes hasbecome scarce.

The results of this research show that reasonableestimates of age and growth can be attained fromlimited samples so long as certain guidelines arefollowed. These are: (1) including an even spread ofdata across length classes or using back calculationthat includes fully grown individuals; (2) carefulconsideration of whether sexes should be pooled orseparated; (3) assigning partial ages when possible toincrease model precision; and (4) performingvalidation techniques when possible or providingevidence to suggest that band pair formation isannual until validation can be attempted. Thelimitations of precluding age validation andcalculating reader bias can be justified given theimmediate benefit of making these preliminaryresults available to managers.

This study serves as an example that preliminaryage and growth estimates can improve elasmobranchmanagement and conservation as these results havealready been included in a semi-quantitativeecological risk assessment (Tobin et al., 2010). Whilethe data deficiency of many elasmobranch specieswill also rely on several factors such as populationtrends, distribution, and threats (Dulvy et al., 2008),the procurement of basic life history information(even in a preliminary form) is an important steptowards reducing the number of data deficient taxa,thus improving their management and conservation.



ACKNOWLEDGEMENTS

This project was supported by the AustralianGovernment funded Marine and Tropical SciencesResearch Facility under Project 4.8.4. The authorswould like to thank the staff, students andvolunteers from the JCU Fishing & FisheriesResearch Team for their contributions, especiallythe fisheries observers Jimmy White and OlivierBittar. We would also like to thank the fishers ofthe Queensland ECIFF, without whose help andcooperation, this work would not have beenpossible. We would also like to thank the threeanonymous reviewers whose comments helped toimprove this paper.

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Overcoming the constraints of low sample sizes to produce age and growth data for rare or threatened sharks