EvalEvation of a Fisheries 

Model for the Harvest 

of Hk~ksbill Sea Turtles, 

Eivtmochelys imbricata,in Cuba 

U.S. Dqmh4nt of Commerce 

MatiWd 4k#i$#id acld Atmospheric Administration 

Natbmd Mathe %heries Service 

NOAA T~bMcal Memorandum NMFS-OPR-5 

, S~gteinbw 9995 

\+ \\ 

\ 

\ 

\ ' 

Evaluation of a Fisheries 

Model for the Harvest 

of Hawksbill Sea Turtles, 

Eretmochelys imbricata, in 

sellna S, Heppell 

Larry 3. Crowder 

~~ey Priddy 

Oepatment of Zoology 

No& Carolina State University 

hIeigh, North Carob 

Present address: 

Dake University School of the Environment 

135 Duke Matine Lab Road 

Beaufort, North Carolina 285 17-972 1 

NOAA Technical Memorandum 

WS-OPR-5 

September 1995 

IJ.S, Department of Commerce 

Ro&d & Br~wn, Secretary 

National Oceanic and Atmospheric Administration 

D. James Baker, Under Secretary for Oceans and Atmosphere 

JJI J 

I ' W&E Maqipe Fisheries Service 

&kk~d &. Schmitten, Assistat Administrator for Fisheries 

IJ I 

Cuba 
Contents 

Abstract 

Introduction 

Model Description 

Model Assumptions 

@OW& Curve and Length-Weight Relationship 

Matuxation Rate, Sex Ratio, and Fecundity 

bud Survival Rate and Availability 

Popuhtion Size and Sustainable Yield 

Mudel Modifications and Results 

M-ode1 Validation 

Sensitivity Analysis 

Sensitivity of Model Parameters 

Changesin Early Growth Rate 

DOIRAP Results Using Data from Other Sources 

Matrix Models 

Methods 

Results 

Discussion 

Age-Length Key 

Catch-length records 

Sustainable Yield 

Migration 

Life History Considerations for Management 

Final Analysis of DOW 

Acknowledgments 

Glossary 

Literature Cited 

Appendices 
Abstract 

Introduction 

The hawksbill sea turtle, Eretmochelys imbricata, 

seas worldwide (National Research Council, 1990). The 

(tortoisesheIl or bekko) is highly prized as a material for 

items. As a result of a growing tourist trade, ha 

numbers throughout the Caribbean and Pacific. Hi 

the green sea turtle, Chelonia mydas, and loggerh 

have not been studied extensively until recent ye 

there are indications of population decline in are 

Other sea tunle species have declined precipitously over the p 

Research Council, 1990). 

men it joined the Convention on International Trade of 

Wild Flora and Fauna (CITES), Japan, the largest importer of 

exemption for the hawksbill and two other sea turtle species. 

primarily by U.S. delegates, compelled Japan to cease bekk 

Currently, me Bekko Association is formulating a proposal to 

trade with Cuba (Bekko Association, 1992). 
At a meeting of sea We specialists, industry representatives, 

in 1992, Dr. Takeyulcj Doi, advisor to the Japan Nuclear Utility Se~ce 

a fisheries model to calculate sustainable harvest levels for hawksbills 

Archipelago. The Bekko Association hope 

of Cuban hawksbills by CITES. Strict size 

efforts, have been proposed to prevent hawksbii population decline while 

relatively high level of harvest. 

Balazs of the National Marine F 

rstand how hawksb'ill He history afEects the 

overy from exploitation), we created a series 

on growth rates from several hawksbi studies. These 

bstitute for DOW; rather, they served 

strongly sect the population growth rate. 

Mention of mde names or commercial firms does 

Service, NOAA. 

not imply 

2 

endorsement by the 


Xior hawksbills, the model is based on an asymptotic van Bertal- @owoh cum 

that assigm lengths to wes. Other data required by the model include sex ratio, she at 

rnatt&yi md size at full avilabii to the fishery estimated &om harvest recar&& %cm&ty, 

misting fr~quency, and egg hatchability were estimated ftom beach surveys conducted in 

Cuba (~rQhal data not provided). An estimate of current yield is assumed to be ~~t 

(243.7 t pryear of turtles >50 cm straight carapace length (SCL)) (App. 2). ThB re-@ 

model pwmders are inferred through a series of equations, determined by evaluiithg the! 

population at equilibrium or postulated by Doi et al. (1992) (Figure 3). 

M~d1 hmpfiow: Like all models, DOIRAP contains severd assumptiom &BO &Bm \ 

cdd&~m .of population size and sustainable yield (Table 1). Insufficient or ncmmistmt 

data on aumivd and growth rates require the model to assume that the present ppdatibili &$I 

at stad~mry equilibrium, and that the proportion of turtles caught in each age ckss odd&@& 

6om wvmt harvest records accurately reflects the age distribution and survival rates fsu-: 

Cuban hawksbills. 

Table 1. Model-related Assumptions in DOIRAP. 

Yield &hate for 1978-91 is constant and 

txwahable. 

old] mtkwted by the model depicts maximum 

production (adult:recmit ratio) . 

lkhxkwn~~for hawksbills is 50 years, and 

gs:~wth mtm of captive-reared hatchlings are years, 

similar to wild turtles. 

Natural mortality for age 1+ turtles is constant. Natural mortality is not siz 

turtles above age 1. 

independent. 

Population is closed. 

Caribbean islands 
The length-weight relationship fitted to fishery data is: 

w t = 0.0001291t3 , 

whae w is weight (kg). The coefficient in equation 2 is similar to that 

and Xliez2 for juvenile hawksbiis on Mona Island, Puerto 

Th& age-length and length-weight relationships are 

remabhg ddakns are age-dependent. All fishery data 

age frm length and weight records using equations 1 

Van Dam, R, and C. E. Diez. 1994. Foraging ecology and population dynami 

(&e&ocheZys imbricata) at Mona Island, Puerto Rico. Nat. Mar. Fish. 

Nat Resour., unpublished rep., 26 pp. 
Figam 4. van, Bertalanffy growth curve used 

liangth- Lengths at age 1 and 2 are t3rorn captive 

points and an estimate of maximum length of 100 

LENGTH AT AGE 2 

0 5 10 15 20 25 30 35 40 

Table 2. Straight Carapace Length and Proportion 

Class Us& iri the Doi et al. (1992) Analysis of the C 

- C 6 < 49.9 

7 54.7 

8 59.1 

9 63 .O 

10 66.6 

11 69.8 

12 72.7 

13 75.3 
&om nesting meys are used to estirnat 

&males, Bmuse each fde lays more than one nes 

every the following relationship must be used 

0: 

f=[ mean eggs / nest x mean nests / breeding 

mean remigration interval 

where man remigration interval is the number of years between breed 

probab'Wy of hatch. Doi et al. (1992) use 130 eggsfnest, 2.3 nests/bre 

remigrittian interval, and 75% hatch to get an annual fecundity of 86 eg 

Annual hrvi~al Rale and Availability: In a lo 

critical Ear pmdictin$: population size. DQW calculates 

hawk&iilla at each age (Br) with a series of 

above. Tb biomass wes can be pro 

size, assunzing that recruitment to age 1 

Bt = R( 8,'" w,) . 

fiom the age at full avdablity to the first age class represe 

DOW d&a&ines the availability of each age class by so 

iteratively fi3r Qt-~: 

where Ct is the capture frequency at age t, obtained from harvest 

assumes that availability, recruitment, and survival rates are const 

Boptda4ka @&e aigd Sustainable Yield: D 

statiantq @&bcium. Catch per effort, bas 

cdd&d for the yeas 1979-89 @&o As 

apparent @end in catch per vessel over that 

constant *ld assumption is critical, becaus 

sustainable. 

The number of 1-year-olds in the p 

by caleg tatcchabb biomass (P). Cat 

exploit-a2ion rate (E). Because yield is assumed to be cons 

and the 6s&g ,mortality coefficient (F) 

the esfmtd catchable biomass is high. 

mi et d. (1992) use the equilibrium population assumption to argue that cat&able 

biomass is a oonstant proportion of total biomass. Thus, P can be used to calculateth 

number of individuals in each age class using weight, survival, and availability e9fWs. The 

number of 1-ydar-old turtles (R) is then the only unknown in the following equation: 

P = zbiomass of catchable turtles = R(Q,w,) + R[ 

where wt islweight at age t. Once R has been estimated, th 

class is ~dwlated using the survival and availability es 

the sum efdl age classes multiplied by the proportion 

A &pb segmented stock-recruit curve was used to c 

6). Accolndingr to a subroutine in DOIRAP, recruitment of 1-y 

and the nu~bw of adults defined the inflection point of the cu 

inflection point, the stock-recruit curve is flat; consequently, 

increams the number of adults, has no effect on the number 

sect yield or population size, as P is dependent on yield an 
mbe of eggs laid per year. The ratio of recruits to adults is the prod 

which is at maximum at the curve's inflection point. 

Sust&able yield curves can be generated 

(f;) wh& hor,$&ng recruitment constant for F value 

Changs hp alter the expected catch-at-age curves 

cdwiM by weight, decreasing fishing mortality c 

numb& qf h#m~st;tc;d turtles decreases (Fig. 8). If F is to 

ptpWbn beforre they reach an optimal size. If F is too 

m~E;t#iy befbre: they can be harvested. DOW's calculat 

give 'hf!wfition about the status of the population, because 

) be censtmt and sustainable. 
Figyrs; 7. Ezpected catch-&age curves for different fishing mo 

hmvltSibw model. Total yield is the area under each curve. 

I I 

12 
~ 1 I I 

111 ' 

To estimate the impact of merit fishing on the population, DQ~ et at. (am) \ 

calculated the ratio of adult bvtles in the present population with that &om a hygo&e:dcal , 

virgin, or unhanestted population. The number of adult turtles in the virgin popdlq60n was , 

estimated by mmhg DOW with F = 0.0 and the number of recruits held cotastant, thus 

assuming tzo effect of cumt harvest on recruitment. 

Modd Mod$f2utionr and Results: DOIRAP is dependent on the age-length r~la#io&$p, , ' 

I I which applies to catch-at-age frequencies. We did not receive all of the cat&at+im& 

frscueticty data thst wtu usad in the oriw DOIRAP analysis. Thuq we uqcd te* , , , I;, , ff equ$liw recads provided at the 1992 meeting, which sparmed the years 1985 (&FQT!fiq$, , {, 

to 1990. Any model runs that included a change the age-length relationshib E+&~ ,&nm, 

cakdiuiian of catch-at-age and percent mature-at-age. When applied to the PR~S~, k& 

used in cZie Cuban andysiq our catch eequencies were lower than, but wmpadbk to, thore I: 

used h the ariginal andysis (Fig. 9). With the new catch-length records, If-yea-dd ;turtle8 

wefe the 682 class most frequently captured; hence, the age at fbll availability was shifted 

&om 10. yws to 8 years. , I 
I 

I I I ,I 

me new catch-length records (1985-90) affected the fishing survival rate (8, 

exploitation r&e (4 and sustainable yield. In the original analysis, Doi et al. repd&s $ = > 

0.782, E 0.1246, and a maximum sustainable yield of 245 t, or 5,500 turtles. when we I 

DOIRAP e& the same growth equation but 1985-90 catch-length records, we obhed s = 

calculated the total instantsneous mortatity rate Q using the descending 

at-age We (frequencies in transformed, Hilbom and Walters, 1992). The 

were 2 = -0.235 @ 0.016), S * 0.79. For consistency, we used DOIRAP's 

far all modd comparisons. The results of Doi et al. (1992) and our DOW mn 

that wi* du: hent harvest of 243.7 t, the present adult population is at 39% 

sto~L, below the "opthal"leveI of 50% poi et al. 1992). In their report, Doi 

sqgested th8t the current size limit of 50 cm. straight carapace length is too 

the limit should be raised to 70 cm SCL to increase the adult population size and attab a 

]nigher yi@ld. I 

Model V4[dc~on: Doi et al. (1992) attempt to validate their results by cornpathi 11 predioted mhber of adult turtles from the model results with an estimate derived fiom1+ack 

surveys. A pieliminary count of 3 nests on 18 km of beach is translated into 1 nebt ger $,b 

of mitable nesting beach poi et al., 1992). Using an 

nest at the same rate throughout the year, Doi et al. (1992) 

df 34SW6lan x 365 days = 20,988 nests per year. According $he 1 

in DOW (source unknown), iffemales lay 2.3 times per year evq 1.6 

Id) an estimated 23,730 adult females and 29,660 adult turtles (sek &$'b * #&/"p" 

DO~~AP population analysis calculates a total of 24,l Od ad& tiid&, 

new catch-length records gave 28,700 adults. Doi et al. (1992) 

sug$est tliat the model result is very close to the empirical estimate. However, a $yearll 

tagging &#dY :at Jumby Bay, Antigua, indicates that hawksbilis there have a ne&#'sq&n , 

that spans 5-6; months with peak activity in August and September (Hoyle and ~i'~l$rdkcp'. 

Thus, it my be unreasonable to assume continuous reproduction throughout the ieiit. 

Jumby Bay hawksbill 

ehavior of add female 

Island, Antigua, W.I. 1987-199 

14 
Sensitivity Analysis 

Sensftivjty of Model Parameters: We studied 

se&viq'&laly&s: catchable biomass 0, numb 

~~iet yield @BY). Me DOW contains over 

ard witted pig. 3); thus, we focused on 6 key paramet 

seasidvity of a model parameter @) by comparing th 

MSY) with each parameter increased anb de 

I 11, 'It OI ') 'JIJ 1 

For mple, a 9% change in the fishing mortality coefficjent O made halfthat total I(,7Il cwfi,,, 

in P ~'aMe 3). A direct effect of change in a model parameter on a model red& produces a ,, sensitivity of 1.0. Changes in yield had such an effect because catchable biom~9, md h$nce I 

I popd%rdon size, is yield I exploitation rate (YIE). Of the six parameters studi&, tb)wi~, , :j) anrP mot# smsitive to changes in the natural survival rate. Note that for the numbs ~f;~qd!~~~,,,,~ 

r. in us pme(a had a sensitivity 13 times greater tban the dbwt eft!& of $asj \, { ) ),, bl 'Ihc model was less sensitive to changes in growth 'we steepae:~,~ f&$ g ,j 

modq @ 'Ihe len&th-w&& coefficient only afEected adult population ste;' w/$q F, , I I t ,), 

mifo aad fecundity had no effect on any ofthe model reds. This is because popdatiqn $ppl _ ;, ( 

in the it~adbl is determined by constant yield rather than reproduction. i 1 I l\\it~l II 

Changes in Early Growth Rate: At the 1992 meeting, several sea turtle biologists 

expressed concern over the high growth rate used in the Cuban analysis (Bekko Association, 

1992). Recapture studies on wild hawksbills have generally predicted a much slower growth 

rate, particularly in older turtles. We modifiied the age-length key in DOIRAP by reducing 

growth &om age 0 to 1 (9 cm SCL) and age 1 to 2 (8 cm SCL) by 5, 10, and 25%. The 

effect was a drop in the steepness of the von Bert- growth we (Fig. 10). We used 

the new growth rates to reassign catch-at-age, using the catch-length records of 1985-90. 

For each growth rate decrease, DOIRAP calculated a new fishing survival rate based on the 

number of turtles caught in each age class (Table 4). Percent mature-at-age was calculated 

by translating the maturation curve from age back to length (see previous section on 

Maturation Rate, Sex Ratio and Fecundity). 
I 

Table 3. ~endtivity analysis of DOIRAP. 

Parameter Catchable population 

size (biomass) 

steepnos8 (k) 

Length-wei& 

coeBcierrt 

Yield 

Fishing mortality 

CO@BGW (3) 

Natural modty (SO) I 13.157 

Pipre 10, von Bertaianffy age-at-length curves with 
I 1 I 

,I 

I ,I 

I I 111 J,~,JJ 

D&asing the growth rate flattens the biomass curve and inawes the ~ge )'I// 

rmndmum biomass (Eq. 4). Because DOIRAP is a stationaq equilibrium model wiQ 90- 

yield, dmges in biomass and fishing survival rate have a direct impact on popda&n,,&s b#,(: tmxirmm yield, but not sustainabiity. In our model runs, the catchable biomass incrqqflt+s 

body grow& rate decreased (Table 4). Although the maximum yield calculated by Rpi $,M. , (1992) was very close to the current yield of 243.7 t, DOIRAP runs with the 1985-99 catch, , 

records Mcated that current fishing mortality is above optimal (Fig. 8). ~odkf re&, , , , , indicate tii&t if the eady growth rate is 5-25% lower than observed in captive Ma, higher 

yields (in terms of kilograms of hawksb'i per year) could be obtained with reduced fishing , 

presswe (Table 5). 

Table 4. Model results after reduction of early growth rate. 

0% 0.812 2,623.63 28,698 

5% 0.797 2,241.17 25,263 

10% 0.806 2,456.01 29,213 

25% 0.826 3,120.45 39,078 

Table 3. Sustainable yield results with reduction in early growth rate. 

Current Optimal Current Optimal yiel 
One way to validate the results obtained with DOIRAP is to compare mod4 output 

with survey data We compared the number of adult turtles calculated for each model nm 

with the estimated nubnber of adults fiom Cuban beach surveys (see previous section on 

Model Validation). Using Cuban estimates of nest frequency (2.3 nestdyear), remigration 

interval (2.6 year breeding cycle), and sex ratio (80% female), the estimated number of adults 

is 29,700. Growth rates that are 5, 10, and 25% lower than originally calculated predict an 

adult population size of 25,000-39,000 (Table 4). Variation in the estimated adult population 

size given by D~IRAP compare favorably with the Cuban population estimate @om bwh 

surveys (Eg. 11). We also calculated an adult population size estimate using nest da+,d& 

Antigua where females lay 4.52 nests per year on average (4.0-4.8 mean nests per &el R= 

176 nestin$ turtles) and return to breed every 2.53 years (2-4 years, N= 60 turtles &om the 

first two years of the study) (Hoyle and ~ichardson)). This reduces the mean adult 

population estimate to 14,700 turtles, considerably lower than the model result at any growth 

rate. 
DOIRAP Results Using Data 

We used mark-recapture data fiom several 

Australia to calculate new growth curves (Tab1 

recaptures greater than one year &om the origin 

(k) for each turtle was calculated using size at cap 

between captures (inf) and the asymptotic length ascribed 

We used the mean of all Ks in each study to calculate a von Bertal- curve. Growth mtgs 

varied substantially in St. Thomas and the Bahamas, although these populations also had the 

smallest number of recaptures (Figure 12). For the Bahamas data, one turtle out of five 

recaptures showed an abnormally high growth rate (k = 0.15). We ran ROW Mce for 

the Bahamas population, once with the mean of all five turtles (k = 0.115, model Bahamas A) 

and once with the outlier removed (k = 0.08, model Bahamas B). The mean growth rate fir 

Mona bland was so low (k = 0.03 1) that DOIRAP could not calculate a reasonable fishing 

survival rate (i.e., fishing survival > natural swival~ for our comparative analysis, we used 

the maximum growth rate observed in the Mona Island population (k = 0.05 1). The size at 

hatch (f .= 0) in the original model for Cuban hawksbills was too large (10 = 8.12 cm.), a result 

of the curve fit. In the new growth curve equations, we decreased size at hatch to 5 cm as 

reported for several hawksbi populations worldwide (Van Buskirk and Crowder, 1994). 

The von Bertale curves fiom each population show a wide range of qges at 

critical sizes, with a threefold increase in age at the mean adult size of 80 cm pig. 13). We 

ran simulations with growth rates fkom the Bahamas (A and B) with a natural survival rate of 

0.9 as used in the original Cuban analysis. The populations with growth rates &om St. 

Thomas, Australia and Mona Island received fishing survival rate estimates of 0.886,0.894 

and 0.928, respectively, and were run with a natural survival rate of 0.95. This increase in 

natural survival rate greatly increased the biomass of turtles in older age classes because 

DOW assigns the same natural survival rate to all turtles age 1 and older. 

As with the sensitivity analysis, we entered catch-length record 

calculate catch-at-age specified by each growth curve. The new 

affected percent mature-at-age. No other changes were made to 

each model run. 
Table 6. Growth and supivd estimates for hawksbill sea turtles. S 

growth rate coefficients (k) are shown in parentheses. 

(1 992) 

Hoyle and Antigua 

Richardson 

(1 993) 

Bjorndal and Great Inagua, 0.1 15 (5) 14 

Bolten Bahamas 

(1 98 8) 

Boulon St. Thomas, 0.071 (9) 22 

(1994) Virgin Islands 

Van Dam Mona Island, 0.036 (1 5) 43 

and Diez Puerto Rico (max=O.OSl) (31) 

deis using the original C 
Growth rate survival Catchable No. of 

origin 

~uba' 

20,719 . 0.3196 

(w/o cbutlier) 

Mona 1s1. * 0.928 10,794.60 118,627 

natural SUNival rate = 0.9 

*natural survival rate = 0.95 

Table 8. Sustainable yield results from DOIRAP using growth rat 

hawksbjEfl populations. 

ch success x sex ratio. Hatch success = 0.82 
The first stage in the matrix models represented pelagic hatchlings and juveniles; 5-30 

cm in length. These turtles live far out to sea and are rarely seen; thus, there is no estimate for 

annual shval in stage 1, and growth rates fiom older turtles (except in the Cuban growth 

estimate) must be extrapolated to these first years. We assumed that unharvested populations 

are stable (A= 1.0, r = 0.0, population neither increasing nor decreasing each year) and solved 

for pelagic juvenile annual survival as a single unknown (Crouse et al., 1987; Crowder et al, 

1994). Each of the five hawksbill models had two estimates for pelagic juvenile survival, one 

for model populations with the Doi et al. (1992) parameters and the other for models with 

AntigwlAustralia parameters (Table 10). Pelagic juvenile survival was higher in the models 

with survival and fecundity rates fiom Doi et al. in order to achieve a stable population, 

primarily because of the lower fecundity. When we added Doi et al.'s harvest rate to the 

models, we held pelagic juvenile su~val constant and calculated the rate of decline for each 

population under conditions of no density dependence and constant environment. 
Table 10. Stage durations and pelagic juvenile survival for matrix 

growtb rates calculated for Caribbean and Australian populations. 

The probability of surviving and remaining in a stage (PI) in the adult ad 

benthic juvenile size classes showed the fi&est elasticities in both the unharvested wd 

harvested population models (Fig. 17A-D). For the pelagic juvenile stage, elasticities for the 

probaMity of sdving and growing into the next stage (Gt) were higher than P elastittities in 

the Cuba BWan, and St. Thomas growth rate models but were lower in the Awttdim 

and Mona J[sZagd models. In the models with harvest pigwe 17B, D), the relative 

cantn:bu%im ofearly matwing and My nature stages to population growth was re& &om 

elasticities obitabed in the unharvested models. The probability of surviving and rermhingh 

a stage atways had a higher elasticity than fecundity (Ft) (fed~y elasticity =juvenile G 

elasticities). Tkrese results are similar to those obtained by Crouse et al. (1987) for ioggahd 

sea turtles, Caretfa carreffa. We observed an increase in the juvede survival elastidies in 

models with harvest. When adult survival rates decreased, the relative impact of juvenile 

mmivd on population growth increased, primarily because of the small proportion sf Wes 

that suwive to older stages. In harvested populations, a proportional change in juvenile 

survival sects a larger proportion of the population than the same proportional change in an 

unharvested population. 

Figure: 3% Ebticities, or proportional sensit 

growth P&W fmm 6ve hawksbill populations. 

iigure: hwa &&cities for stage-specific transitio 

surd* ad remaining in a stage (A and B), while 

growing int~o the next stage (C and D). Results are shown 

Anti~Au~a survival and fecundity estimates. A and 

1.0 for all mdels). B and D = harvested popul 
A. Unharvested P Elasticities 

0.6 

0.5 

0.4 a ST. THOMAS 

0.3 6 AUSTRALIA 

0.2 

0.1 

0 

PELAGIC BENTHIC EARLY LATE FULLY 

JUVENILE JUVENILE MATURING MATURING MATURE 

B. Harvest P Elasticities 

0.5 

PELAGIC BENTHIC EARLY LATE FULLY 

JUVENILE JUVENILE MATURING MATURING MATURE 

C. Unharvested G Elasticities 

0.1 

0 

PELAGIC BENTHIC EARLY LATE 

JUVENILE JUVENlLE MATURING MATURING 

D. Harvest G Elasticities 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

PELAGIC BENTHIC EARLY LATE 

JUVENILE JUVENILE MATURING MATURING 
Stage--specific survival contriiute 

elasticitieii jnmased in the early matu 

In models without harvest (Fig, 18 

elastidty in the fully mature stage, 

individuals. With harvest (Fig. 18B), maximum su 

shifted to Ohe early maturing stage. 

maturing dult stages had the highest 

due to %he mxd number of individuals in the later 

models. r93tbough the reproductive 

much as 10 times benthic juvenile reproductive 

of the total population. 

Figure 18. $Itagc+specific survival elasticiti 

rates from fwe hawbbm populations. Results are shown for model 

AntigudAusttalia survival and fecundity e 

all models). B = harvested populations (harvest su~val rate = 0.782). 

I 

A. UNHARVESTED I 

BAHAMAS Dl ST. THOMAS 

O AUSTRALIA B MONA ISL. 

PELAGIC BENTHIC EARLY LATE FULLY 

JUVENILE JUVENILE MATURING MATURING MATURE 
Discussion 

Age-length Key: Clearly, a mark-recapture study is needed to calculate a growth curve for 

wild Cubm hawksbills. The average growth rate coefficient for Mona Island, Puerto Rico, is 

less than half of that calculated using captive growth rates. However, there is considerable 

individual variability in the Mona Island growth rates (Fig. 19). It is unlikely that individuals 

remain on the same growth trajectory through life; effort should be made to determine if the 

growth parameter changes for individuals in different size classes. In addition, the Australian 

mark-recapture data revealed considerable variability in size at maturity. Assigning 

maturation rates to size, and particularly age, classes is probably inappropriate for hawksb'is 

and other long-lived species. Until a method is established for ve-g age in sea turtles, 

growth rate c&ulations will be highly speculative. 

TWO ather types of growth curve are built into the 

growth and logistic growth. A von Bertal- curve gave 

of kg($: juvenile and subadult loggerhead turtles (Frazer 

h 0th~ sea We growth studies. However, growth rat 

year my not be described by a von Bertal- curve, 

unknow11. 

'IJsing a growth curve to assign ages to lengths has been criticized in fisheries literature 

(Bartoo and Parker, 1983). In an annual model, age is defined as a discrete variable while 

length is continuous. The length to age conversion results in a "piling up" of lengths at each 

age (Fig. 20). At later ages, the number of size classes within an age may increase or decrm 

depending on how age is rounded oE This variability was a particular problem for calculating 

age-at-c;%pture frequencies. Problems with length-to-age conversion, variability in growth 

rates, and an inability to age sea turtles suggests that hture models should be based on size as 

Sustainable Yield: DOIRAP assumes that the current yield of 243.7 t is constant and 

sustainable. Unlike many fisheries models (Hilborn and Walters, 1992), catch per unit of 

effort is not included as a variable. The number of turtles in the population is estimated from 

the constant yield and exploitation rate, and is thus assumed to be independent of fecundity or 

sex ratio. When we ran DOIRAP with slower (and perhaps more realistic) growth rates, the 

model assumption that effort and yield are stable led to overestimates of population size. The 

current stock-recruit curve is defined by the number of adults and recruits obtained by the 

model itse& thus, the production rate (recruitdadults) under the current harvest regime is 

assumecl to be at maximum, with recruitment held constant for any increase in adult survival. 

While this may be a "conse~ative" estimate of density-dependent reproduction poi et al., 

1992; El&o Association, 1992), it is not possible to detect a decline in population numbers 

with the current model. OverJishing can only be inferred through the ratio of current adult 

population to preharvest adult population (which is assumed to have the same recruitment 

rate). The sustainable yield curves calculated for the current Cuban growth rate estimate, as 

well as c~everal other growth rates, suggest that the harvest level is too high to attain maximum 

yield, bca does not indicate population growth or decline. In this species, which is currently at 

low 1eve:ls in Cuba poi et al., 1992), it is imperative to devise a model which can relax the 

assumption that recruitment will be constant with decreased fishing pressure, and preferable to 

generate a non-equilibrium model which can calculate changes in population size over time. 

Maximurn sustainable yield does not change substant 

rate, but k does increase when natural survival is increased 

when growth rates are low is much higher than census est 

growth rate for Cuban hawksb'is, the model's assumptio 

equilibrium may be invalid, and serious overfishing may 
Migrations The msumption that Cuba' 

qvestioned at nwe%bgs sponsored by the 

Bdcb bissca~tion, 1992). An extensive 

underway. Cbdy, migration could 

Migration of hamestable-size 

decline, p~idly if 

Life History Considerations for Management: Even at the high growth rates estimated for 

Cuba and d~e Bahamas, hawksbills take several years to reach maturity. The high survival rate 

observed in adult females nesting in Antigua (Hoyle and ~ichardson~) suggests a Life history 

with a long natural life span that compensates for high mortality in early life through 

iteropariiy and high fecundity. Our matrix models for unharvested populations showed high 

elasticities fbr adult survival rates and low elasticities for fecundity and pelagic juvenile 

survival rates. Decreasing survival in adult stages through harvest had a strong impact on 

population growth, as suggested by declines in exploited hawksbill populations worldwide. 

Conservation efforts associated with nesting-beach protection must be maintained, particularly 

for those beaches which attract large numbers of hawksbii females. However, nesting-beach 

protection done is unlikely to prevent population decline in harvested populations (Crowe et 

al. 1987). Minimizing the impact of harvest on the most sensitive stages could help sustain 

the Cuban population, but strict monitoring and constant updates of model parameters should 

Headstarting, or raising hatchling turtles in captivity to a certain age before release 

into.the wild, is one of several management tools suggested to offset losses due to harvest. 

By raising turtles in a protected environment through their most vulnerable year of life, their 

survivorship could be increased dramatically. However, even if headstarted turtles have no 

reduction in survival or growth after release, hawlcsbiis take so long to mature that very few 

headstarted turtles would reach a harvestable size of 70 ern SCL. As a management tool for 

conserving I~awksbiill populations, headstarting focuses on survival in the first year, part of the 

life stage least critical to population growth (see Fig. 18A). To compensate for low survival 

in the adult stages of models depicting harvested populations, pelagic juvenile survival would 

have to increase by as much as 80% (Table 11). Considering that the population may contain 

tens of thousands of pelagic juveniles, it is unlikely that a headstarting program could be large 

enough to support a heavy harvest. Headstarting of long-lived, slow-growing turtles has been 

debated extt:nsively (Taubes, 1992; Frazer, 1992; Congdon et al., 1993; Heppell et al., in 

press) and is generally considered to be an unfeasible management option with little chance of 

populations. 
Table 111. Increase in pelagic juvenile survival need 

mortality in matrix model populations of hawksbill s 

given in 'Tables 5.1 and 5.2, Compensation occurs when p 

Pelagic juvenile Pelagic juvenile 

Growth rate origin 

Cuba 0.086 0.154 

3-1 

St. Thonw 0.180 0.280 

Aumaiizu 0.407 0.520 

Mom I&. 

Final Analysis of DOIRAP: There are three reasons why DOIRAP is not an appropriate 

model for management at this time: 1) the model is very complex but the data available for 

parametakation are extremely limited, 2) there is no uncertainty associated with any of the 

parameters, making the model entirely deterministic, and 3) when growth data fiom Australian 

and nearby Caribbean populations were used, the model results changed dramatically. Several 

parameters in the model are oversimplified or outright speculation, such as annual survival 

rate, and many equations are overlaid or nested within other equations that are based on 

equilibrium assumptions. The age-length key, which is critical to all equations and results in 

the model, is derived &om a point estimate of growth in captive-reared hatchlings. The model 

calculates population size &om pooled catch-length records, assumes that current yield is 

constant and sustainable, and assumes that recruitment of 1-year-olds will be independent of 

any decrease in fishing mortality. These assumptions, with a lack of supporting data from the 

wild Cuban population, make the current model and analysis unacceptable for hawksbill 

- 

Future models should incorporate population dynamics through variation in annual 

yield and catch per unit effort (e.g., delay diierence models, see Hilborn and Walters (1992)). 

The models could be size-based and incorporate variation in growth rates. Size-specific 

survival and exploitation rates should be added. A genetic analysis should determine whether 

the Cuban population is isolated from the rest of the Caribbean; if not, the approximate rates 

of migration should be calculated and used in the model. Recruitment to the nesting 

population can be determined through a long-term tagging study and should be used to 

monitor changes in preadult population size. Finally, estimates of vital rates should be 

obtained from wild hawksbiils whenever possible, and changes in these rates should be 

monitored so harvest quotas can be continuously updated. 
Acknowledgments 

This pr~ject was supported by Grant #NFEH 20003000 17 fiom the National Mahe , 

Rshefies S&ma NOAA, working through the U.S. Fish and Wildwe Service, Coopmdve \ 

Extension # H& Carom State University (RWO #30). We ate. indebted to our @0jeictt 

leader, Phil Wfiarns, for his support, and to Joe Hightower of the USNBS Coopmdve , 

Extqnai~1. $bere thanks to Takeyuld Doi and the Japanese Bekko Associadon fax tdk&qgi 

DUW md it# docwnentation. Geofge Balazs provided us with a diskette of D@&W\ ae3d ,, war, imtzwm$ in obtaining information about the program and data presented at the: T~ky(ir 

meethgs. 

Thanks to Karen Bjorndal, Debby Crouse, Colin Limpus, Richard Byles, and Jack 

Woody for their support and encouragement. Jim Richardson, Robert VanDam, Carlos Diez, 

and Colin Limpus provided data vital to our analysis. Special thanks to the Jumby Bay Club 

and its members for providing important data on reproduction and survival of nesting 

hawksbills and the continuing support of their project in Antigua. Several anonymous 

reviewers gave us helpfbl comments which improved the manuscript; thanks to Barbara 

Schroeder and Pam Plotkin for handling the review process. Thanks to Scott Heppell for his 

help with figures and editing. Selina Heppell was supported by an NSF Predoctoral 
Age at fd availability: The age at which all turtles 

proportion of turtles in each age class below 

e&er because they are avoided by the fishery 

Age-lmgth key: See von Bertalw growth curve. 

Avail&ittI%y (Q): The proportion of turtles in an age 

cklculated from catch records. Maximum Q 

Biomass-atgage: The weight of all turtles in an age class. Dep 

wte of each age group and body growth rate. 

Catch-&age frequencies: The number 

v~an Baal- curve) from length fi-equencies obs 

Catch-per-wit-enort (CPUE): Catch (in 

&ort, such as hours of netting. 

par wgsel per year 

C&tcIt&M& biomass (P): The total weight of all turtles susc , 

Equillbuiurn model: A model whieh as 

&ual and body growth 

cr.dt$ fn a equilibrium popul 

ojlags every year. See also stationary equiXib 

Expl~itatbh, rate (23): The proportion of total mortality caused by fishing. 

FecunilEQ: @I matrix models) The mean number of female eggs produced 

sw$ult female turtle. 

Fishing ~azottt&Iity coefficient (F): 

daqe in the number of turtles in each age class c 

Fishing ~sarvival rate (S): The proportion of turtles in eac 

that survive each year, as determined by the sum of fi 

maopt&ty. 

Growth rate: 1) Increase in strai 

rate). 2) Change in populatio 

~QW rate). This may be expres I 

I ) 38 , 
Cpopuiation at stable equilibrium when r = 0.0) or A, the domin 

pupufation matrix (r = In (A)). 

Matum$i@a level: The proportion of turtles in an age class that is s 

d~tennjned by gonad analysis. 

Md.mrt~%~ swstainable yield (MSY) or Optimal yield: A 

bIrmus af catch. Dependent on the natural mortality 

pwth rate. 

Natural ~~Wfty rate (M): The instantaneous r&te (i.e. compound-' 

ia tihe number of turtles in each age class due-to non-fishery re1 

Natud su~ival rate (SO): The proportion of turtles in each age class that su 

in 1b absence of harvest. 

Reerui@@at (&: The number of turtles that reach one year of age. 

Remigltr~&n interval: The number of years between breedings. No 

intl$r-~stin&; interval, the number of days or weeks between ea 

bteadhg year. 

\ 

Reprad#Ytive vdue (v): A measure of fbture reproductive pot 

&&&g expeeted for an average individual in an agebr'ur~e8 the probability of surviving to realize hture repr 

The I& eigenvwtor of a transition matrix. 

SeaditiWyt The change in a model result (e.g., catchable b 

fdowkg a change in a model parameter (e.g., natur I 

Stable stage dktfibution (w): A vector giving the proportion 

om@ the population has reached equilibrium. The right 

mat&. 

Straight clrrapace length (SCL): The length of a turtle's shell measured by 

Stationary equ-Hibrium: An equilibrium population which does not inc 

&ora year to year (r = 0.0, h = 1.0). By assuming constant yield, 

that population numbers are constant. 

Tots1 moo*l:diq ((23: The instantaneous rate (i.e., compound-interes 

mr~1es above the age at full recruitment (2 = M + F). Obtain 

deqcending slope of the In transformed catch frequencies. 
1111 

I Ill I1 11111/1 

I 1 (s ~I~I~~~IIIIJ Tranridon matrk A population model consisting of an equal number of row$ W ~91~ 

each wpresentiag a stage in a turtles We. Numbers in the body of the -1~4

fecundity (F - top row of the matrix) or probabilities of turtles swviving &ld r lt $ 2 { l/~~~ 

in a stage (P) and surviving and growing to the next stage (G). , 

I 

Virgin gop'ulation: An estimate of the stationary equilibrium popul 

haswest. 

von Bertaiaiim growth curve: An asymptotic curve 

(on &e body growth rate (k) and maximum le 
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Bjorndal, K. A, and A B. Bolton. 1988. Growth rates of immature 

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Mds., 328 p. 

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loggerhead sea turtles and implications for conservation. Ecology 68: 14 

rowder, L. B.,' D. T. Crouse, S. S. Heppek and T. H. Martin. 1994. Pr 

of blrtle excluder devices on loggerhead sea turtle populations. E 

4:437445. 

Doi, T., R Marquez, H. Kimoto, and N. Azeno. 1992. Diagnosis and conservation ~f %e 

lxiwbbill turtle population in the Cuban Archipelago. Tech. Rep., The Be.lcko Indust*, 

Jpn. 3 1 ,pp. 

Frazet, N.B. 1992. Sea turtle conse~ation and "half-way technology". Cons 

Bibbg~ 6:179-184. 

Frazer, N. B., md L. M. Ehrhart. 1985. Preliminary growth models for green (Chelonia 

my&) and loggerhead (Caretta careffa) turtles in the wild. Copeia 198973-79. 

Heppell, 5. S., I,. B. Crowder, and D. T. Crouse. 1996. Models to evaluate headst 

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Hilbom, R., tuld C. J. Walters. 1992. Quantitative Fisheries Stock Assessment. Chapman 
Limpus, C. i 1992. The HawWi turtle, ErebnocheZys irn 

plopulation structure within a southern Great Barrier 

P~s. '19:489-506. 

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Fkt. &cad. Press, Wash., D.C., 259 p. 

Ogren, L,. kditor). 1989. Proceedings of the Second Western 

11. S. Dep. Cornmer., NOAA Tech. Memo. WS-SEF 

Taubes, G. 1992. A dubious battle to save the Kemp's ridley sea turtle. 

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C:opeia 1994:66-8 1. 

SCL' winter 

1985 

90 2 

91 0 

92 0 

93 0 

94 0 

95 0 

% 0 

97 0 

98 0 

Totals 129 
Total turtles by 

size class 

30-39 cm SCL 

4049 cm SCL 

50-59 cm SCL 

60-69 cm SCL 

70-79 cm SCL 

80-89 cm SCL 

90-99 cm SCL 

ToGil>90cm 

Total 380 cm 

Total >70 cm 

Minimum 

Ii&Ximurn 

Mean length 

Proportions 

30-39 cm SCL 

4049 cm SCL 

50-59 cm SCt 

60-69 cm SCL 

70-79 SCL 

80-89 cm SCL 

90-99 ~m SCL 

SCL = Wght apace length in centimeten 

Remaining 1985 catch data incomplete 

45 

I 
Appe~diir 2,. Annual total catch and catch per v 

Cuba, Pkaw data presented at the Hawksbii Turtle 

Worlcshc~p, Tokyo, Japan, 25 Mar. 1993. 

Zone A 

Year Catch (t) No. of vessels CatcWvessel 

1979 138.8 21 6.61 

1980 195.4 21 9.30 

1981 164.7 18 9.15 

1982 177.3 18 9.85 

1983 135 16 8.44 

1984 184 20 9.20 

1985 207 16 12.94 

1986 171 16 10.69 ' 

1987 194 13 14.92 

1988 112 11 10.18 

1989 136 11 12.36 

Zone 3 

Year Catch (t) No. of vessels Catch/vessel 

1979 192.9 15 12.86 

1980 213 13 16.38 

1981 200 14 14.29 

1982 243.2 13 18.71 

1983 224.8 12 18.73 

1984 157 10 15.70 

1985 107 10 10.70 

1986 115 10 11.50 

1987 137 10 13.70 

1988 98 10 9.80 

1989 136 10 13.60 
Zone C 

Year Catch (t) No. of vessels Catcldvessel 

1979 246.8 24 10.28 

Zone: D 

Year Catch (t) No. of vessels Catcldvessel 

1979 183.7 32 5.74 

Total 

Year Catch (t) No. of vessels Catch/vessel 

1979 762.2 92 8.28 
Total weight of catch per year 

Year Catch (t) 

1976 204.9 

1977 202.2 

1978 202.5 

1979 202.9 

1980 263 .O 

1981 262.8 

1982 283.2 

Mean 240.5