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1 Application of Life-History Theory and Population Model Analysis to Turtle Conservation Author(s): Selina S. Heppell Source: Copeia, Vol. 1998, No. 2 (May 1, 1998), pp Published by: American Society of Ichthyologists and Herpetologists (ASIH) Stable URL: Accessed: :36 UTC REFERENCES Linked references are available on JSTOR for this article: You may need to log in to JSTOR to access the linked references. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at American Society of Ichthyologists and Herpetologists (ASIH) is collaborating with JSTOR to digitize, preserve and extend access to Copeia

2 Copeia, 1998(2), pp Application of Life-History Theory and Population Model Analysis to Turtle Conservation SELINA S. HEPPELL As more reptiles find their way onto endangered species lists, it is increasingly important to identify management alternatives that can be applied across taxa. I have compared life tables from several turtle populations using elasticity analysis, a method that calculates the proportional contribution of each vital rate (age-specific survival and fecundity) to the annual population multiplication rate, k [In (X) = r, the intrinsic rate of increase]. Most freshwater turtles share similar elasticity patterns across age classes, in spite of large variations in mean annual fecundity, annual survival, and age at maturity. High adult survival elasticity and low fecundity elasticity in these species suggests that conservation efforts that reduce mortality of adults are likely to stabilize declining populations. Desert tortoises and sea turtles had different elasticity patterns, with relatively higher juvenile elasticities when summed across age classes. Three different life tables for painted turtles also showed variation in elasticity patterns. Approximate elasticities can be generated for age-based matrices without a complete life table for each species, requiring only age at maturity, adult female annual survival, and population multiplication rate. This approximation may help identify sensitive life stages for poorly known species, thereby guiding research and management efforts and furthering our understanding of lifehistory patterns. THIRTY-THREE species of reptiles were federally listed as threatened or endangered phibians tend to be less well studied than mamin, 1988; Iverson, 1991a). Also, reptiles and am- in the United States in 1994, and six additional mals and birds, and many reptiles have generation times that far exceed the average research species were listed as vulnerable or rare in the IUCN Red Data Book. Unfortunately, there isfunding cycle. How then can we make prelimi- recovery plans with such limited biological little demographic data available for many ofnary information? these species, making it difficult to develop population models that can guide management One obvious solution is to model potential plans. Although management alternatives that management impacts on similar, well-studied will increase habitat and/or survival rates mayspecies (Van Buskirk and Crowder, 1994; Heppell et al., 1996a). However, it is unclear wheth- be easy to visualize, the potential impacts of various alternatives may not be obvious. When timeer phylogenetic relationship, morphological similarity, or similarity in some life-history characteristic is likely to be the most important fac- and resources are limited, it may be desirable to rank management plans according to their tor in matching data from well-studied species potential benefit for species recovery and cost to those of conservation concern. For example, effectiveness (Heppell et al., 1996a). Analytical is it best to test possible management scenarios methods for calculating the proportional effects for poorly known Berlandier's tortoises (Gopherus berlandieri) on a model population of conge- of changes in particular vital rates (fecundity, growth, survival) have been used to evaluateneric gopher tortoises (Gopherus polyphemus) or population models and the effectiveness of yellow mud turtles (Kinosternon flavescens), management plans for freshwater turtles (Wil-whicbur, 1975; Congdon et al., 1993; Cunningtonand lifespan (Iverson, 1991b)? This paper will have a similar age at maturity, clutch size, and Brooks, 1996), tortoises (Doak et al., 1994), develop a method for predicting similarities in and sea turtles (Crouse et al., 1987; Heppell etlife table characteristics across species, thereby al., 1996a, 1996b). These analyses involve rela-givintively simple life tables and population matricesfects of a particular management plan on the managers a way to predict the relative ef- but still require age-specific annual survivalpopulation growth rate for poorly known species. rates, fecundities, and growth probabilities. This may be particularly problematic for reptiles and MATERIALS AND METHODS amphibians, which have multiple life-history stages that occupy a variety of habitats and niches (Harless and Morlock, 1979; Wilbur and Morcific survival and fecundity. By making the Life tables are simple descriptions of age-spe- crit-? 1998 by the American Society of Ichthyologists and Herpetologists

3 368 COPEIA, 1998, NO. 2 ical assumption that annual vital rates are relatively where Fx is the number of one-y constant for each age class, we can use the offspring produced by a female life table to calculate the proportion of the population annual fecundity X first-year surv that is in each age class, the average l), Gx is annual survival probabili number of mature female offspring producedxmax is the maximum age provi by each female (RO), mean generation time, and table. This is a prebreeding census model, the asymptotic growth rate of the populationwhere individuals are "counted" just prior to (the intrinsic rate of increase, r). A life table can the breeding season (Caswell 1989). The actual be converted into a two-dimensional matrix, maximum lifespan is unknown for most turtles, providing analytical methods for quickly calculating and several of the life tables had a maximum population characteristics, including the age set at the point where less than.1 effect of small changes in model parameters adult turtles remained in the population (Caswell, 1989). though many turtles exhibit an increas A useful calculation for qualitative evaluation clutch size with female body size (Wilbur a of management proposals is an elasticity analysis Morin, 1988; Congdon and Gibbons, 199; V of a deterministic matrix model, which gives the Buskirk and Crowder, 1994), most of the lif proportional change in the annual population bles gave an average fecundity for all adults multiplication rate [X, where loge(k) = r] given all had a constant annual survival rate for a proportional change in age- or stage-specific adults. To simplify my matrices and eli survival, growth, or fecundity. This analysis allows us to compare the relative effects of pro- the arbitrary maximum age, I lumped adults into a single age class, represented portional change in one or more life-history final column of the matrix: stages. For example, an elasticity analysis can reveal whether a 2% increase in hatchling survival will have the same population-level impact as a 5% increase in adult survival. I compared the elasticity values from life tables of a variety of turtle species in search of predictable patterns across taxa. I examined a number of life tables from the GI M2=... O F G2.. O G,_1 P (2) literature and technical reports (Table 1). Life where P is the mean annual survival rate for tables present the proportion of individuals remaining in a cohort after each year (survivorship, I4) and the number of female offspring tion growth rates and elasticity values were adult females and a is age at maturity. Pop produced by females in each age class each tually yearidentical between matrices with and w (fecundity, mx). This fecundity term is an out annual the lumped adult age class; the resu average that includes an interbreeding interval present here are for model type M2 [equat for those species that do not nest every year. (2)]. In some cases, more than one life table was To presented for a particular species or population program Mathcad? to determine the stable age calculate elasticities, I used the software (e.g., Frazer et al., 199), and in others, distribution agespecific survival and fecundity rates were values given (vx), which are the right and left eigen- (wx) and age-specific reproductive without a complete life table (e.g., Mitchell, vectors associated with the dominant eigenvalue, X. The elasticity matrix (Ex,), which shows 1988). Some of the life tables include preliminary survival estimates or those derived the by proportional assuming the population is at stationary equilibtional change in each matrix parameter (M2,), change in X given a proporrium (r =.). I did not attempt to judge is given the by: accuracy of each life table, but the results shown should be robust to minor changes in annuala log k M2xy v, X wy (3) fecundity or age-specific annual survival. Y a a log log M2xy M2,,y x X (v w) (vlw) I converted the life tables into age-based Leslie models (Leslie, 1945), with each row and where column representing a single year in a turtle's tors, life: or I(vx X wx) (de Kroon et al., 1986; Cas- (vlw) is the inner product of the two vecwell, 1989). Elasticities of matrix elements sum Fl F2... Fxmax- Fxmax to 1.; thus, the elasticities can be interpreted G1 as proportional contributions of each matrix parameter to the population multiplication rate, k M1= G2 (1) '*. (de Kroon et al., 1986). Elasticities differ from sensitivities, which are simply the change in k Gxma- given a change in a matrix parameter (BX/

4 HEPPELL-TURTLE MODELS AND MANAGEMENT 369 TABLE 1. SOURCES AND MEAN VITAL RATES USED TO COMPARE TURTLE LIFE HISTORIES. Age at Mean annual matur- fecundity Population ity (female multiplication Common name Scientific name Source (yr) eggs/female)a rate (X) Common mud Kinosternon subrubrum Frazer et al., 4.86,.96,1.7b.89,.962,1.74 turtle 1991 Slider turtle Trachemys scripta Frazer et al., ,1.28, 1.62b.777,.867, Yellow mud turtle Kinosternon flavescens Iverson, 1991b Blanding's turtle Emydoidea blandingii Congdon et al., Snapping turtle A Chelydra serpentina Cunnington and Brooks, 1996 Snapping turtle B Chelydra serpentina Congdon et al., Desert tortoise Gopherus agassizi Turner et al., Loggerhead sea Caretta caretta Crowder et al., turtle (U.S.) 1994 Loggerhead sea Caretta caretta Heppell et al., turtle (Australia) 1996b Painted turtle Chrysemys picta Wilbur, Tinkle et al., Within-population elasticities.-the qualitative Life-table elasticities.-the elasticities for most patterns generated by elasticity analysis can be freshwater turtles were very similar, in spite robust of for a given population, even when vital differences in age at maturity (Fig. 1). Adult survival had the greatest influence on k for all ferent life from those in another set (Fig. 3). rates from one set of data are considerably dif- Bea Assumes 5:5 sex ratio. Mitchell, bthree values represent best, average, and worstcase scenarios (respectively) presented by the auth M2x,y). By calculating the tables, proportional whereas fecundity change elasticity was always in X, we can compare the effects very low. of The proportional summed juvenile and subadult changes in fecundity and annual survival elasticities survival, varied, which depending on the are on different scales (Caswell, number of 1989). years spent in each stage. In all cases, In general, management plans adult survival impact elasticity a was lifehistory stage rather than a cundity/first particular year survival age group elasticity. far greater than fe- (e.g., reducing incidental trawling In the desert mortality tortoise and sea in turtle models, sea turtles increases survival juvenile probabilities and subadult survival forelasticities were large juveniles, subadults and relatively adults, much spanning higher, and outranked adult a number of age classes; Crowder survival elasticities et al., in 1994). the two loggerhead populations effects (Fig. 2). of Unlike increas- the freshwater species, To compare the proportional ing annual survival in different a large proportion life of stages, the sea turtle I populations summed the elasticities for occurs those in the years juvenile designated by stages denoted juveniles, ment impacts were subadults, predicted to result in a 5% stages. Thus, if manage- and adults. Many of the life increase tables in annual I analyzed survival for did a particular sea not designate the number turtle of years stage, it spent would be as best juveniles versus subadults, which should be based that enhanced survival of subadults (U.S. log- to invest in plans on size or habitat preference. I arbitrarily sep-gerheadsarated juveniles from subadults based on surviv- rather than adults. The results for desert tor- or juveniles (Australian loggerheads) al probabilities; subadults were those animalstoises are different; adult survival still has the that experienced higher and/or more consis-highestent annual survival probabilities (Table 2). a large proportional effect on population elasticity, but subadult survival also has growth. RESULTS

5 37 COPEIA, 1998, NO. 2 TABLE 2. STAGE LENGTHS AND ANNUAL SURVIVAL RATES DERIVED FROM TURTLE POPULATION STUDIES CITED IN TABLE 1. Common mud turtle: Hatchlingsa Juvenilesb Subadults Adults Mean Mean Mean Mean Age annual Age annual Age annual annual (yr) survival (yr) survival (yr) survival survival Worst case Average case Best case Slider: Worst case (1) (2-3) Average case (1) (2-3) Best case Painted turtle: Wilbur (1975) Tinkle et al. (1981) Mitchell (1988) Yellow mud turtle Blanding's turtle Snapping turtle A Snapping turtle B Desert tortoise Loggerhead sea turtle (U.S.) Loggerhead sea turtle (Australia) a Includes egg survival and survival to age one. b Stage lengths for juveniles and subadults set arbitrarily : annual survival based >.8. on annual survival cause of uncertainty in their venile and survival subadult elasticities and fecundity rates, Frazer et al. (199, update of 1991) Wilbur's presented life table provided new fe combined. An three different life tables for common mud and cundity and nest survival rates (Tinkle et a slider turtles, representing "best," "worst," 1981). and The updated life table predicted a ra "average" scenarios (Tables 1-2). Both populations showed qualitatively similar elasticities relative contribution of survival in the preadu idly increasing population, which increased t across the three scenarios, in spite of large age differences in annual survival probabilities. Adult central Virginia (Mitchell, 1988) showed elast classes. In contrast, painted turtles fro survival had the highest elasticity for all three ity patterns similar to other freshwater turtl cases; and although juvenile and subadult Thus, survival elasticities increased from worst to best sce- ities, and we need some way to estimate a there is no guaranteed pattern of elast narios, the same general pattern could be inferred from all three models. tory data. compare them even when we have poor life-h Between-population elasticities.-two life tables New for method: elasticity approximation.-as discussed Cun- by Caswell (1989), in an age-based ma- snapping turtles (Congdon et al., 1994; nington and Brooks, 1996) showed qualitatively trix, all prereproductive age-class survival elasticities adult are identical and are equal to the fecun- similar elasticity patterns with very high annual survival elasticity (Fig. 1). However, dity the elasticity summed across all adult age class- elasticity patterns generated by three life tables in a Leslie model, type M1 [equation (1)]. In for painted turtles were different due to an large age-based model with adults grouped into a differences in vital rates (Fig. 4). In a population from southeastern Michigan (Wilbur, elasticity and each juvenile survival elasticity are single stage [M2, equation (2)], the fecundity 1975), adult survival elasticity was lower than equal. ju- This is because population growth is de-

6 A l HEPPELL-TURTLE MODELS AND MANAGEMENT *Fecundity * Juvenile [ Subadult ladult c> ',.7-1 _.-.6- o.5 - -? EIv.1 I - 4 Common Slider Yellow Blandings Snapping Snapping Mud Mud Turtle A Turtle B m?.- m.7-, o. Wo E? E.3- ci, u ---*- I_ I I ' I- 1 I worst average best Common Mud Turtle worst average best Slider Turtle F- Fig. 1. Elasticities from Fig. freshwater 3. Elasticities for worst, turtle average, and population models. Elasticity = best case scenarios proportional expressed in life contribution tables for common mud o fecundity or annual survival turtles and to slider X, turtles the (Frazer population et al., 199, 1991). mu tiplication rate. Age-specific Each life elasticities table included lowest, were average, and summe highest within life-history stages (juvenile, subadult, adult survival and fecundity rates measured for each species Life table sources, stage (Table lengths, 1 and 2). and vital rates liste in Tables 1 and 2. Fecundity includes survival to ag one (prebreeding census model). Snapping turtle A = Cunnington and Brooks, 1996; snapping turtle B = Congdon et al., O ec E= Ef pendent on net reproductive rate (Ro) and sur *-. vivorship to maturity (la). A proportional change in the annual survival O O O rate (Ef/c)-, 1 of any prer eproductive age class will equally affect X, du to the commutative property of multiplication (5) For example, a 5% increase in age-i survival ha where a is age at maturity and Efre is the elasticity the same effect on survivorship to maturity as of fecundity. Because matrix elasticities sum to 5% increase in age-2 survival: 1., all the elasticities of an M2-type matrix can lo = l X GI X G2X G3 be X reconstructed.. Ga_ if EfC is known. By examining the eigenvectors of matrix A42, I found that: l, X (GI X 1.5) X G2 X G3 X... G._- P- X = lx G X (G2 1.5)X G3X... Ga_, Ee" - ( - 1)P - atx (6) = 1l X 1.5 (4) In other words, if age at maturity (a), adult survival (P), and annual population multiplication Thus, the elasticities of an age-based rate (X) can be estimated from mark-recapture form M2 [equation (2)] always look lik.8.9 -r Fecundity *Juvenile CSubadult ElAdult Painted turtle (Chrysemys picta) ( *Fecundity mjuvenile rsubadult -ladult _ o ~~~~~~~~~~~~._ o. r O, I -] u Co o o E.3- =.S.2- U- J J- ^ J - -'!. I_ > CD Desert Tortoise Loggerhead Loggerhead (U.S.) (Aus.) _._. n ll Wilbur (1975) Tinkle et al. (1981) Mitchell (1988) Fig. 2. Elasticities from Fig. desert 4. Elasticities tortoise for three painted and turtle logge life head sea turtle models. bles. Loggerhead Tinkle et al. (1981) is an models updated life table ge ated from populations Wilbur's at Little (1975) population Cumberland in southeastern Michig Isla Georgia (U.S.) and Heron Mitchell Reef, (1988) is for Australia a population in central (Aus.). Virgin

7 372 COPEIA, 1998, NO. 2 TABLE 3. ELASTICITIES FROM LESLIE MATRIX MODEL with age. Although age-specific elasticities d DERIVED FROM COMPLETE LIFE TABLES (SUMMED OVER cline after first reproduction, once they RELEVANT AGES) AND APPROXIMATED FROM EQUATION pooled into a single "stage" there is very litt (6) FOR DESERT TORTOISES (TURNER ET AL., 1987; difference X = between the age-based matrix elast 1.1), BLANDING'S TURTLES (CONGDON ET AL., ities 1993; and those generated by equation (6). T X = 1.), AND SNAPPING TURTLES (CONGDON ET AL., poorest approximation was for the snappi 1994; K = 1.). turtle life table, which had low fecundity val for subadults aged 11 and 12 to account for e Juvenile Subadult Adult Model Fecundity survival survival survival ly-maturing individuals. Desert tortoise To demonstrate the usefulness of the appro imation technique, I predicted the stage-speci Leslie matrix elasticities for a number of turtles compared Equation (6) a recent paper by Shine and Iverson (1995; T Blanding's turtle ble 4). I assumed stable populations for th Leslie matrix analysis (K = 1.) and summed Efe across a Equation (6) preadult age classes. Species with high adult Snapping turtle B nual survival (>.9) also had very high ad Leslie matrix survival elasticities. However, juvenile elastici outranked adult elasticity for some species w Equation (6) late maturity, such as Gopherus polyphemus. Th is in part due to the large proportion of a p ulation in the preadult age classes for spec and long-term census data, the proportional effect of changing fecundity or any age-specific change in the juvenile survival rate may affec that take many years to reach maturity. Thus survival rate can be approximated without much a larger proportion of the population th complete life table. Note that this approximation is only useful when the adult age classes vided that the change affects all preadult ag a similar change in adult annual survival, pr can be treated as a single stage with mean annual survival and fecundity, as is often done for classes. turtles in life-table analyses (e.g., Congdon et DISCUSSION al., 1993). I used arithmetic mean values for adult survival and annual fecundity of desert tortoises, ties of life-history characteristics across species Many researchers have explored the similari- Blanding's turtles, and Congdon et al.'s phylogenetic snapping turtles to compare the elasticities ined approx- correlations between characters such as fe- groups, and body sizes and examimated by equation (6) with those pooled cundity from and age at maturity, age at maturity an a complete Leslie matrix (type M1; Table adult 3). lifespan, and so on (Stearns, 1992). Wi The complete life tables for these three bur species and Morin (1988), Iverson (1991a), and include an increase in survival and/or fecundity Congdon and Gibbons (199) concluded that TABLE 4. HATCHLING, JUVENILE, AND ADULT SURVIVAL ELASTICITIES CALCULATED FROM TURTLE LIFE HISTORIE COMPILED BY SHINE AND IVERSON (1995; TABLE 1) USING EQUATION (6) AND ASSUMING A STABLE POPULATION ( = 1.). Hatchling Juvenile Adult (age ) (preadult) Adult Age at annual survival survival survival Species maturity survival elasticity elasticity elasticity Podocnemis voglii Chelodina longicollis Kinosternon sonoriense Terrapene ornata Terrapene ornata Mauremys leprosa Gopherus polyphemus Geochelone gigantea Testudo graeca Psammobates geometricus

8 HEPPELL-TURTLE MODELS AND MANAGEMENT 373 turtles share common features of low annual fe- cause the elasticities themselves will increase or cundity, low and variable egg and hatchling decrease survival, and long lifespan due to high adult sur-it is important to remember that elasticities depending on the model parameters. vival rates. However, Iverson (1991a), Shine represent and the effects of proportional changes in Iverson (1995), and Cunnington and Brooks age- or stage-specific survival or fecundity. This (1996) also suggested that differences may exist does not invoke a value on individuals; in fact, between freshwater, terrestrial, and marine because adults have the highest reproductive turtle life histories because of variation in body value and are often a small proportion of a population, conservation efforts that save a few in- size, growth rates, and annual fecundity. Age maturity is highly correlated with adult annual dividual adults may have a very large proportional impact on stage-specific annual survival. survival across taxa (Shine and Iverson, 1995). My analysis shows that age-specific elasticities Thus, in addition to calculating elasticities, are dependent on these two life-history variables. of various management alternatives must be some analysis of the potential costs and benefits Van Buskirk and Crowder (1994) found some considered (Green and Hirons, 1991; Heppell similarities in the reproductive characteristics et ofal., 1996a). related sea turtle species but also found considerable variability within species. Because of analysis has been that the life-history stage with One criticism of the usefulness of elasticity strong differences in the reproductive traits greatest of elasticity may be inaccessible to management (Green and Hirons, 1991). But a high different populations, these authors cautioned against a "general" sea turtle population model. I found that elasticity patterns can be quite sible anthropogenic mortality sources that affect elasticity value should focus research into pos- different for congeneric species and perhaps that stage and should indicate a high potential even populations of the same species (e.g., for population extinction should a new source painted turtles) due to differences in estimates of mortality affect that stage. Examples of this of age at maturity and adult survival rate. As include proposed harvest of adult snapping turtles in Ontario (Brooks et al., 1991) and sargas- initial management and research guides, models should be applied to species with similar lifehistory characteristics. (Crowder et al., 1994). Congdon et al. (1993) sum harvest affecting small juvenile sea turtles Calculating elasticities allows us to comparesuggested that turtle life histories make them the effects of a proportional increase in a lifehistory stage. In practice, management options adults suffer increased mortality, primarily be- particularly prone to overexploitation when will have different levels of impact. For example, although adult survival of a particular popcess each year demands extreme iteroparity. My cause the low probability of reproductive suculation may only be increased by 5% (Plan A), elasticity results for freshwater turtles support it may be possible to increase juvenile survival these hypotheses and predict a similar trend for by 25% (Plan B). The elasticities give a rough all species that have very high adult survival measure of how each management optionrates. could be ranked according to its potential impact on population growth: to determine which management proposals Perhaps the best use for elasticity analysi unlikely to work, based on their impact on lo Proportional increase in Xh Proportional increase in term population recovery. The "headstarting survival X Elasticity (7) program for Kemp's ridley sea turtles is For this example, assume that the current such population is declining at a rate of 5% per year were (k hatched and reared in individual contain- an example (Heppell et al., 1996a). Turt =.95). If adult survival elasticity is.6 and ers for juvenile survival elasticity is.2, the increase additional in X conservation efforts that reduced nine months and then released. Without for Plan A would be approximately.5 X large.6 juvenile and adult mortality (Turtle Excluder Devices that reduce incidental drownin =.3 (3% increase, X =.95 X 1.3 =.9785), whereas Plan B would generate an in increase of approximately.25 X.2 =.5 such (5% a program could ever impact the popula- shrimp trawls), there was little chance tha increase, X =.95 X 1.5 =.9975). In spite tion, given of the low elasticity of first-year surviv the much greater elasticity of adult survival, in long-lived species. Even if headstarting resul management Plan B would be the better in option overall hatchling survival increases of 1- according to the population model. However, 2%, such a program would probably have lit the effects of large proportional changes tle in effect annual survival rates may not be adequately with pre-age- survival elasticties of less than.5 on the growth rate of a population dicted by elasticity analysis in this manner, Most be- important, increasing age- survival can

9 374 COPEIA, 1998, NO. 2 not compensate for high adult mortality (Heppell et al., 1996a). However, successful captivelife stages have the greatest influence on pop- to compare life histories and determine which rearing programs can produce large cohorts to ulation growth. Elasticity analysis can suggest "boost" a recovering population once its principle source of decline has been identified andresearch. Once a set of management alterna which demographic variables need the greatest reduced. tives has been evaluated and initiated, additional data are necessary to produce predictive I have compared and approximated elasticities of simple age-based models with adults models and to monitor the impacts of human grouped into a single stage. The models are intervention. deterministic and assume that the populations are at a stable age distribution, where the proportion of individuals in each age class is constant ACKNOWLEDGMENTS over time. Naturally, this assumption is not This met research was supported in part by the in most populations, and elasticities should National be Oceanic and Atmospheric Administration, rep- National Marine Fisheries Service and the compared with caution. Because elasticities resent relative contributions to X, large perturbations in annual survival may not translate (R/MER-21 di- and NOAA/NMFS NA9AA-D- University of North Carolina Sea Grant rectly into proportional changes in population S6847), and a National Science Foundation Pregrowth [equation (7)]. Finally, variable growth Doctoral Fellowship. J. Iverson, L. Crowder, N. rates and stage-specific habitats suggest that Frazer, turtles, like other poikilotherms, should be classi- helpful comments on earlier drafts. and an anonymous reviewer provided fied by size rather than age. However, the agespecific methods described here could be applied to stage-based models that have been con- LITERATURE CITED verted to age, as described by Cochran and Ellner (1992) Effects of a sudden increase in natural mor- BROOKS, R. J., G. P. BROWN, AND D. A. GALBRAITH. Age-specific elasticities can be approximated tality of adults on a population of the common algebraically if adult annual survival, age at snapping maturity, and population growth rate can be 69: esti- turtle (Chelydra serpentina). Can. J. Zool. mated. This information may still be difficult CASWELL, to H Matrix population models. Sinauer Associates, Sunderland, MA. attain for many species, but a range of possibilities could be plotted to predict which life COCHRAN, stages M. E., AND S. ELLNER Simple methods for calculating age-based life history parameters are most critical to population recovery. Particularly problematic may be the population mul- for stage-structured populations. Ecol. Monogr. 62: tiplication rate, which is often calculated from CONGDON, J. D., AND A. E. DUNHAM Contributions of long-term life history studies to conser- the life table itself. However, long-term censusing may give a general idea of whether a population is increasing or decreasing, and many vation biology. G. K. Meffe and C. R. Carroll (eds.). vation biology, p In: Principles of conser- life-history analyses assume that vital rates Sinauer reflect stable populations. The approximation, AND J. W. GIBBONS The evolution of Associates, Sunderland, MA. method should be regarded as a way to guide turtle life histories, p In: Life history and initial research and management efforts before ecology of the slider turtle. J. W. Gibbons (ed.). Smithsonian Institution Press, Washington, DC. more complete demographic data are available., A. E. DUNHAM, AND R. C. VAN LOBEN SELS. Future research and monitoring of adaptive Delayed sexual maturity and demographics management programs will help resolve whether simple, deterministic models can adequately cations for conservation and management of long- of Blanding's turtles (Emydoidea blandingii): impli- predict population responses to conservation lived efforts and perturbations., AND Demographics of organisms. Conserv. Biol. 7: Long-term field studies are critical to effective common snapping turtles (Chelydra serpentina): implications or for conservation and management of management and recovery of endangered threatened species (Congdon and Dunham, long-lived organisms. Am. Zool. 34: CROUSE, D. T., L. B. CROWDER, AND H. CASWELL ). Models that produce quantitative population projections, probabilities of persistence, A stage-based population model for loggerhead sea turtles and implications for conservation. Ecology and the impact of variability on population 68: size and structure ultimately are needed for proper CROWDER, L. B., D. T. CROUSE, S. S. HEPPELL, AND T. management (Soule, 1987; Shaffer, 199; Meffe H. MARTIN Predicting the impact of turtle and Carroll, 1994). Until complete data are excluder devices on loggerhead sea turtle populations. way Ecol. Applic. available, the equations I present provide a 4:

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