sharks of the open ocean || comparative life history and demography of pelagic sharks

Chapter 27

Comparative Life History and Demography of Pelagic Sharks

Enric Cortés

Abstract

Pelagic shark species exhibit differences in life-history traits related to body size, repro-duction, age, and growth. These differences are ultimately refl ected in their population statistics and dynamics, and the capacity of each individual species to withstand exploita-tion. Uncertainty associated with age at maturity, longevity, fertility, and natural mortality was incorporated through Monte Carlo simulation to estimate population growth rates (λ) and generation times (T) for eight species of pelagic sharks for which all that information was available. Age-based matrix elasticities (proportional sensitivities) were calculated to help identify the most vulnerable life stages for these species. By determining the relative position of the infl ection point of population growth curves (R), it is postulated that the pelagic shark species analyzed reach maximum sustainable yield at or above 50% of their carrying capacity (K). A principal component analysis of fi ve life-history traits yielded groupings that corresponded well with species having similar population growth rates, thus providing a good initial indication of their relative ability to compensate for exploita-tion. The blue shark (Prionace glauca) is the most productive species, with high fecundity and an infl ection point near 50% of K, whereas two of the three Alopias species and the shortfi n mako (Isurus oxyrinchus) are the least productive pelagic sharks, with very low fecundity and infl ection points that are probably very near K. Elasticity analysis indicated that in all species juvenile survival elasticity was the highest, followed by adult survival elasticity, whereas fertility or age-0 elasticity was low. Although caution should be exer-cised when making conservation and management recommendations based only on this approach, results indicate that protection should focus mainly on juveniles and also adults rather than age-0 individuals. Given the biology of these pelagic species, it is hardly sur-prising that recovery to preexploitation levels after intensive fi shing will be very slow.

Key words: demographic models, density dependence, elasticity analysis, matrix popu-lation models, maximum sustainable yield, pelagic sharks.

Introduction

Little is known of the demography and dynamics of populations of pelagic shark species. Demographic analyses of shark populations typically have used deterministic life tables and limited sensitivity analyses to estimate intrinsic rates of increase and to assess exploitation Sharks of the Open Ocean: Biology, Fisheries and Conservation. Edited by M. D. Camhi, E. K. Pikitch and E. A. Babcock

© 2008 Blackwell Publishing Ltd. ISBN: 978-0632-05995-9

310 Sharks of the Open Ocean

potential. Using a modifi ed demographic technique based on density dependence consider-ations, Smith et al. (1998) estimated intrinsic rebound potentials for a number of shark species, and Smith et al. (2008a) calculated the potentials of 10 pelagic sharks and the pelagic stingray and compared these with 22 other shark species. Mollet and Cailliet (2002) applied a stage-based matrix population model to the pelagic thresher (Alopias pelagicus, Alopiidae). Uncertainty in vital rates has not been incorporated into demographic population models of sharks in general, except for Cortés (1999, 2002), who used Monte Carlo simula-tion in a stage-based analysis of the sandbar shark (Carcharhinus plumbeus, Carcharhinidae) and in age-based population models for 41 shark populations – including the pelagic spe-cies analyzed here. Elasticities (proportional sensitivities; De Kroon et al., 1986) for pelagic sharks were only calculated in the studies by Cortés (2002) and Mollet and Cailliet (2002).

One problem associated with the use of deterministic life tables, mean-matrix projec-tions, and deterministic matrix element elasticities is that these approaches do not take account of the full range of natural variability or address the uncertainty in estimates of vital rates for a particular species. Uncritical use of conclusions derived from deterministic pop-ulation models is potentially dangerous because it can lead to inappropriate conservation measures and management actions (Benton and Grant, 1999). Randomization procedures, such as stage simulation analysis (Wisdom et al., 2000), have been proposed to circumvent the shortcomings of deterministic approaches. With randomization – a form of Monte Carlo simulation – population growth rates (λ), elasticities, and other population parameters of interest can be evaluated across a wide range of vital rates.

The relative position of the infl ection point of population growth curves or the corre-sponding peak in production curves, that is, the fraction of the carrying capacity (K) at which the maximum production occurs, is known to vary along a continuum across animal species (Fowler, 1981a, 1988). Very productive commercial fi sh species are thought to reach the infl ection point at a low fraction of K, whereas some large mammals are believed to reach the infl ection point at population levels well above 0.5K (Fowler, 1981b, 1987). No studies have investigated this aspect of population dynamics in sharks.

In view of the dearth of information on comparative life-history traits and demography of pelagic sharks, the need for incorporating uncertainty in estimates of vital rates into population models, and the lack of information on the position of the infl ection point of population growth curves of sharks, this chapter answers the following questions relative to pelagic shark species: (1) Do pelagic shark species exhibit differences in life-history traits that may be ultimately refl ected in their population dynamics and capacity to withstand exploitation? (2) How does uncertainty in demographic traits applied consistently to all species affect esti-mates of population growth rates and generation times on a relative scale? (3) What vital rates exhibit the highest elasticities? and (4) At what fraction of their theoretical carrying capacity are pelagic shark species estimated to reach the maximum sustainable yield (MSY)?

Methods

Analysis of differences in life-history traits among species

A principal component analysis (PCA) of three observed (maximum adult female body length, offspring length, mean annual fecundity) and two estimated (growth coeffi cient

Comparative Life History and Demography of Pelagic Sharks 311

from the von Bertalanffy growth function, k, and empirical maximum age) life-history traits was used to analyze differences among eight species of pelagic sharks. The following popu-lations, for which information on all fi ve traits was available from published sources at the time of this writing, were used in the analysis: pelagic thresher and bigeye thresher (Alopias superciliosus) from the northwestern Pacifi c, thresher shark (A. vulpinus) from the north-eastern Pacifi c, porbeagle (Lamna nasus, Lamnidae) from the northwestern Atlantic, silky shark (Carcharhinus falciformis, Carcharhinidae) from the southern Gulf of Mexico, oce-anic whitetip shark (C. longimanus, Carcharhinidae) from the central and western Pacifi c supplemented with data from the southwestern equatorial Atlantic, blue shark (Prionace glauca, Carcharhinidae) from the North Atlantic, and shortfi n mako (Isurus oxyrinchus, Lamnidae) from the northwestern Atlantic (Table 27.1). To further examine similarities among species, the scores of the fi rst three components of the PCA were used in a hierar-chical cluster analysis with a Euclidean distance metric and single linkage method (Unistat Statistical Package v. 4.53, Unistat Ltd., London, UK).

Estimation of population parameters and elasticities

Age-structured life tables and Leslie matrices based on a life cycle with reproduction fi rst and then survival (Ebert, 1999, p. 83) for a yearly time-step applied only to females were used to model the demography of the eight species of pelagic sharks. Monte Carlo simulation was used to incorporate uncertainty in demographic parameters and generate estimates of population growth rates, generation times, and elasticities for a large set of life tables/Leslie matrices that spanned a wide range of possible values. Age at maturity, maximum age, and age-specifi c fecundity and survivorship were randomly selected from statistical distributions assumed to describe these demographic parameters.

Age at maturity was represented by a triangular distribution (Table 27.1; and see Fig. 1 in Cortés, 2002). Generally a single value (obtained by back-transforming the length at which a female fi rst becomes mature, or in other cases, the length at which 50% of the population matures, into age through a von Bertalanffy growth function) was reported in the literature and set as the likeliest value, with the lower and upper bounds obtained using �1 year as an approximation; if a range of ages was reported, the midpoint was used as the likeliest value and the range was used to bound the distribution. Age at fi rst reproduction was set to 1 year after age at maturity. Maximum age was represented by a linearly decreasing distribution scaled to a total relative probability of 1. The likeliest value used was the highest empiri-cal value of longevity reported in the literature, while the unlikeliest value was obtained by arbitrarily adding 30% to that value.

The probability of survival at age was estimated through six indirect life-history methods that have been described extensively elsewhere (Cortés, 2002, and references therein). Four of these methods rely largely on parameter estimates derived from the von Bertalanffy growth function, one on knowledge of longevity, and one on weight informa-tion to estimate natural mortality. The lower and higher estimates from the six methods were used to bound a linearly increasing distribution scaled to a total relative probabil-ity of 1. The likeliest value in this distribution was assigned to the highest estimate of survival, while the unlikeliest value was the lowest estimate of survival. For the bigeye thresher, this approach yielded negative values of r. Thus, the probability of survival at age was fi xed to the maximum estimate.

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Table 27.1 Values of life-history traits used in a principal component analysis, and statistical distributions and values of demographic traits used in Monte Carlo simulation of popu-lation statistics for eight species of pelagic sharks.a

Population Maximum Age at maturityc kd Life spane Fecundityf Offspring Survivalg (year�1) Reference sizeb (years) (year�1) (years) (pups per litter) size (cm TL) (cm TL)

Carcharhinus falciformis 308 Tri (11, 12, 13) 0.091 22 (29) N2 (10.2; 1.3; 6–14) 76 0.85–0.90 (0.77–0.91) Bonfi l et al. (1993); Castro (1983)

Carcharhinus longimanus 272 Tri (5, 6.5, 8) 0.099 17 (22) N2 (6.2; 2.9; 1–14) 70 0.78–0.89 (0.81–0.92) Seki et al. (1998); Lessa et al. (1999)

Prionace glauca 327 Tri (4, 5, 6) 0.13 16 (21) N2 (37; 14.6; 4–75) 45 0.30–0.86 (0.60–0.91) Castro and Mejuto (1995); Pratt (1979); Skomal and

Natanson (2003)Isurus oxyrinchus 375 Tri (17, 18, 19) 0.087 32 (42) N3 (12.7; 3.0; 9–18) 75 0.35–0.92 (0.80–0.93) Mollet et al. (2000);

Natanson et al. (2006)Lamna nasus 360 Tri (12, 13, 14) 0.061 25 (31) Tri1 (3.9; 2–5) 70 0.85–0.93 (0.83–0.91) Aasen (1963); Campana

et al. (2002); Natanson et al. (2002)

Alopias pelagicus 375 Tri (7, 8.5, 10) 0.085 16 (21) –1 (2) 174 0.77–0.89 (0.85–0.90) Liu et al. (1999)Alopias superciliosus 422 Tri (11, 12.8, 14) 0.092 20 (26) –1 (2) 137 0.81–0.90 (0.82–0.91) Chen et al. (1997); Liu

et al. (1998)Alopias vulpinus 630 Tri (2, 3.5, 5) 0.158 15 (20) Tri1 (4; 2–4) 136 0.35–0.83 (0.83–0.93) Cailliet et al. (1983)

aSee text for information on the populations used for this analysis.bTL is cm total length.cValues in parentheses are low, likeliest, and high from a triangular distribution (Tri).dk is the growth coeffi cient from the von Bertalanffy growth function.eMaximum empirical age; values in parentheses are �30% of the fi rst value.fValues in parentheses after the distribution name are mean, standard deviation, and range (normal distribution, N) or likeliest value and range (triangular distribution, Tri). All values extracted from these distributions were divided by two to account for an assumed 1:1 male-to-female embryo ratio and then by one, two, or three to account for the length of the reproductive cycle in years, which is indicated by a superscript after the distribution name.gRange of annual survivorship values obtained from six indirect life-history methods; values in parentheses show the range of age-specifi c estimates obtained through the weight-based method (see text for an explanation).


Fecundity-at-age was generally represented by a normal distribution with the mean and standard deviation obtained or calculated from the literature and the reported range in lit-ter size used to bound the distribution (Table 27.1). If the mode was reported instead of the mean, a triangular distribution was assumed with the range used to bound the dis-tribution. A constant value of two pups per litter was assumed for the pelagic and big-eye threshers (Table 27.1). A 1:1 male-to-female ratio was assumed in all cases and also that 100% of females were reproductively active 1 year after reaching maturity. Annual reproductive cycles were assumed for the porbeagle and the three thresher species, a bien-nial cycle for the three carcharhinid species, and a triennial cycle for the shortfi n mako. Annual fecundity was thus expressed as the number of female offspring at birth divided by the length of the reproductive cycle in years.

Annual population growth rates (λ � er) were obtained from per capita rates of pop-ulation increase (r) calculated through the discrete form of the Euler–Lotka equation as described in Cortés (2002). Generation time (here called T) was calculated as the mean age of mothers of newborn sharks when the population is in a stable age distribution (Caswell, 2001, p. 129). The reproductive value distribution (vx) and stable age distribu-tion (cx) were also calculated as described in Cortés (2002). In matrix formulation, λ was calculated as the dominant eigenvalue of a Leslie matrix. The reproductive value (v) and stable age (w) distribution vectors were obtained as the left and right eigenvectors, respec-tively, associated with the dominant eigenvalue of the Leslie matrix. Elasticities (propor-tional sensitivities) of matrix elements (eij) were calculated as described in Caswell (2001). Elasticities for age-0 survival or fertility, juvenile survival, and adult survival were calcu-lated by summation of matrix element elasticities across relevant age classes. The sum of all matrix element elasticities is 1. Formulas and more details are given in Cortés (2002).

The simulation and projection process

A set of values for age-specifi c survival, age-specifi c fertility, age at fi rst reproduction, and life span was randomly selected from the probability distribution describing each individual life-history trait. That set of variables was then used to construct a life table and an age-based matrix population model and elasticity matrix, from which the popu-lation statistics of interest (λ, T, and fertility, juvenile survival, and adult survival elas-ticities) were estimated at each iteration. Medians and frequency distributions for those parameter estimates were obtained after 10,000 iterations of the life table and population matrix model for each population analyzed. Confi dence intervals for the population statis-tics were obtained as the 2.5th and 97.5th percentiles of each distribution. All simulations were implemented using Microsoft Excel spreadsheet software equipped with proprietary add-in risk assessment (Crystal Ball 2000, Decisioneering Inc., Denver, CO) and matrix function (MatriXL v. 4.5, MathTools Ltd., Ft. Washington, PA) software, and Microsoft Visual Basic. (Reference to trade names does not imply endorsement by the National Marine Fisheries Service, NOAA.)

The position of the infl ection point of population growth curves (R) was estimated by solv-ing the linear equation derived by Fowler (1988) based on data for various animal species:

R � 0.633 � 0.187(ln(rT ))


where rT is the dimensionless rate of increase per generation, calculated here using the median values of r and T obtained from Monte Carlo simulation.

Results

Differences in life-history traits among pelagic shark species

The PCA revealed that the fi rst three components explained about 94% of the variance in life-history traits (Table 27.2). The fi rst factor explained 45% of the variance in the fi ve vari-ables and correlated positively with adult body size, offspring size, and k, and negatively with longevity. The second and third factors explained 35% and 15% of the variance, respec-tively. The second factor mainly correlated positively with fecundity and k, and negatively with offspring size, whereas the third factor mainly correlated positively with longevity and adult body size. The second factor helps to isolate the pelagic and bigeye threshers because of low fecundity and large offspring size, and the blue shark for its high fecundity and small offspring. The fi rst factor explains the positioning of the thresher shark by virtue of its large adult size and relatively fast growth completion rate (high k) and short life span. The short-fi n mako/porbeagle and oceanic whitetip/silky shark are very close to each other because of their life-history similarities. The two lamnids share similar adult and offspring size, annual fecundity, low k, and relatively high longevity, whereas the two carcharhinids share similar characteristics (Fig. 27.1(a)). The third factor helps in separating the shortfi n mako/porbea-gle and silky/oceanic whitetip shark as a result of the higher longevity of the shortfi n mako and silky shark, respectively. Cluster analysis confi rmed the positioning of species in the plot of components 1 and 2 (Fig. 27.1(a)) by placing very closely the shortfi n mako and por-beagle, the pelagic and bigeye threshers, and the oceanic whitetip and silky sharks, whereas the blue and thresher sharks were more separated from the rest (Fig. 27.1(b)).

Simulation of population parameters and elasticities, and position of the infl ection point of population growth curves

Population growth rates for the species of pelagic sharks analyzed varied widely, ranging from high values for the blue shark to values very close to zero for the shortfi n mako and

Table 27.2 Results of a PCA of fi ve life-history traits for eight species of pelagic sharks.*

Life-history trait Component 1 Component 2 Component 3

Adult body length 0.56 �0.13 0.59Annual fecundity �0.06 0.71 0.02Offspring length 0.45 �0.49 �0.27Growth coeffi cient (k) 0.51 0.42 0.26Longevity �0.47 �0.25 0.72

Percentage of total variance 44.5 35.1 14.7

*Values shown are the loadings (eigenvectors) of the fi rst three components and the per-centage of the total variance explained by each component.


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Fig. 27.1 (a) Plot of the component scores of the fi rst and second factors from a PCA of fi ve life-history traits of eight species of pelagic sharks. (b) Dendrogram (Euclidean measure, single linkage method) from a hierarchi-cal cluster analysis of the scores of the fi rst three factors obtained in the PCA. The groupings show similarities in life-history traits among species. Species codes are: gla: Prionace glauca; oxy: Isurus oxyrinchus; vul: Alopias vulpinus; pel: A. pelagicus; sup: A. superciliosus; nas: Lamna nasus; fal: Carcharhinus falciformis; lon: C. longimanus.

pelagic and bigeye threshers (Table 27.3). Generation times ranged from about 7 years in the thresher shark to about 25 years in the shortfi n mako. The values of λ obtained from simulation corresponded fairly well with the positioning of species in the PCA plot (Fig. 27.1(a)) in that those species with lower λ tended to be located toward the bottom of the


PCA plot, which was mostly associated with low fecundity, large offspring size, and low k, whereas the species with the highest λ, the blue shark, was located at the top of the PCA plot, which was associated mostly with high fecundity and small offspring size. Species with intermediate values of λ, such as the two carcharhinids and the thresher shark, were located toward the middle of the PCA plot.

Juvenile and adult survival elasticities were always higher than fertility (age-0 sur-vival) elasticities, indicating that the juvenile and adult stages exert the greatest infl uence on λ. Median fertility elasticities ranged from 3.9% in the shortfi n mako to 11.6% in the thresher shark; median juvenile survival elasticities ranged from 46.7% in the thresher shark to 77.3% in the silky shark; and median adult survival elasticities ranged from 16.2% in the silky shark to 41.7% in the thresher shark (Table 27.3). Juvenile survival elasticities were the highest in all species, and adult survival elasticity was of similar magnitude only for the thresher shark.

The position of the infl ection point of population growth curves (R) varied from about 0.5K in the blue shark to very near 1.0K in the shortfi n mako and pelagic and bigeye threshers (Fig. 27.2). Values of R for the oceanic whitetip, silky, porbeagle, and thresher sharks were intermediate (0.63–0.71). Median population growth rates (λ) for the eight species were negatively correlated with R (R2 � 0.92, n � 8; Fig. 27.2).

Discussion

Links between life-history traits and population statistics of pelagic sharks: conservation and management implications

The eight species of sharks analyzed display different sets of life-history traits that are ultimately refl ected in differing population statistics, dynamics, and resilience to exploita-tion. The blue shark’s early age at maturity and high litter size translate into high rates of

Table 27.3 Population growth rates (λ), generation times (T), and elasticities (summed across relevant age classes) for eight species of pelagic sharks obtained from Monte Carlo simulation.*

Population λ (year�1) T (years) Elasticity

Fertility Juvenile survival Adult survival

Prionace glauca 1.254 (1.151–1.373) 8.4 (7.2–9.7) 10.7 (9.3–12.1) 58.6 (52.7–63.7) 30.7 (25.6–36.8)Carcharhinus 1.076 (1.057–1.091) 14.3 (13.7–15.3) 6.5 (6.1–6.8) 77.3 (74.9–79.4) 16.2 (13.8–18.9) falciformisLamna nasus 1.051 (1.039–1.064) 18.5 (17.5–19.8) 5.1 (4.8–5.4) 69.1 (67.1–71.2) 25.8 (23.6–27.9)Isurus oxyrinchus 1.008 (0.978–1.028) 24.8 (23.5–26.3) 3.9 (3.6–4.1) 71.8 (68.0–75.0) 24.3 (21.1–28.1)Carcharhinus 1.069 (1.029–1.119) 11.1 (9.4–13.0) 8.2 (7.5–9.7) 57.9 (53.0–64.2) 33.9 (29.5–40.6) longimanusAlopias pelagicus 1.013 (0.995–1.034) 12.7 (11.6–14.3) 7.3 (6.5–7.9) 65.5 (62.3–68.0) 27.2 (25.1–30.1)Alopias vulpinus 1.090 (0.986–1.206) 7.5 (5.9–9.4) 11.6 (9.6–14.5) 46.7 (39.0–53.1) 41.7 (36.1–48.0)Alopias 1.009 (0.990–1.028) 17.2 (15.9–18.6) 5.6 (5.1–5.9) 71.4 (66.6–76.8) 23.0 (17.7–27.9) superciliosus

*Values shown are medians with 95% confi dence intervals.


increase for this species, despite its smaller offspring, which are likely to be subjected to higher mortality rates than those from the other species. The thresher shark, silky shark, oceanic whitetip shark, and porbeagle exhibit more moderate rates of increase. Of these four species, the thresher shark has dissimilar life-history traits, but the other three share offspring of similar size (70–76 cm total length, TL), similar annual fecundities (3–5 pups per year), slow growth completion rates (k � 0.06–0.10), and moderate life span (17–25 years). The shortfi n mako and two of the Alopias species (pelagic and bigeye threshers) had very low population growth rates. These three species share large adult size (375–422 cm TL), low annual fecundity (2–4), and low k values (0.08–0.09). The species groupings obtained in the PCA, based on a collection of available life-history characteristics, thus provided a good initial indication of the population growth rates of these species and their likely response to exploitation. Although the life-history information has changed notably for some of the populations analyzed by Cortés (2000), that study also found similarities in the life-history traits of pelagic shark species in a PCA and cluster analysis of 41 popula-tions of sharks.

Population growth rates of pelagic shark species were more sensitive to survival of the juvenile and adult stages than to survival of age-0 individuals or fecundity. This is in agree-ment with the general elasticity patterns found by Cortés (2002) for sharks and with fi nd-ings for other long-lived marine species (Heppell et al., 1999) and mammals (Heppell et al., 2000). From a conservation perspective, it suggests that management actions should focus on protection of juveniles and adults rather than age-0 individuals. From a management perspective, minimum size limits and protection of reproductive females could be the most effective measures, as they would enhance juvenile and adult survival directly and reproduc-tive output indirectly. However, conservation and management efforts should not be guided exclusively by elasticity analysis, as it is still unclear how actions directed at one particu-lar stage may affect the dynamics of other life stages (Heppell et al., 2000). Furthermore, the use of regression (Wisdom and Mills, 1997) or correlation analysis (Cortés, 2002) in

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Fig. 27.2 Position of the infl ection point of population growth curves (R) in relation to the mean population growth rate (λ) obtained through Monte Carlo simulation for eight pelagic shark species (see Fig. 27.1 for species codes). The line illustrates a nonlinear regression fi tted to the data.


tandem with stochastic elasticity analysis has been advocated as a way to get a more com-plete picture of the life stages and vital rates that exert the greatest effect on population growth rates and their variance.

Interpretation of rates of increase and the position of the infl ection point of population growth curves

In addition to portraying the demography of the eight species analyzed, one of the main objectives was to provide a relative scale for interspecifi c comparison by consistently applying the same assumptions to specify the statistical distributions describing demo-graphic traits. The values of λ obtained should thus be regarded as relative indices rather than predictors of absolute population growth through time.

Among the factors that may have affected results are the theoretical framework used, that is, the implicit model assumptions about density independence versus den-sity dependence, and the demographic traits used. Life tables/matrix population models project observed vital rates into the future assuming density independence and time invari-ability, and predict that the population will grow exponentially at a rate r and reach a stable age distribution. In contrast, a traditional interpretation of fi sheries models is that unexploited populations have reached carrying capacity (K) and are therefore at equilib-rium (r � 0), thus allowing for positive growth rates only after a population or stock has been exploited and it recovers through logistic growth as a result of a compensatory, posi-tive density-dependent response. Density dependence can also be incorporated into life tables or matrix population models either explicitly, by adding a term for density depen-dence in the model (Grant and Benton, 2000), or implicitly, by assuming that it is built into the vital rates used in the projection of population growth rates. In the present anal-ysis, the latter approach was taken by using statistical distributions that favored higher values of survivorship at age to try to incorporate a potential compensatory density-dependent response to exploitation. The resulting population growth rates should thus be regarded as approximating the maximum biologically possible limit at low population densities.

Regardless of whether these models incorporate density independence or density depend-ence, the lack of a time-dependent abundance vector in studies of shark populations implies that they do not capture the dynamics of the population, and should thus be viewed as static age-structured models. In using this type of model it is therefore important to consider when the vital rate information was collected relative to the duration and extent of harvesting of each population, because the onset and magnitude of potential compensatory density-dependent responses may vary accordingly (Smith et al., 1998).

The eight populations analyzed are all exploited to different degrees, and it is possible that some of the vital rates used in the analyses may have changed as a result of density dependence and that the predicted population growth rates do not refl ect what would be expected from projecting present vital rates. The rapidness and magnitude of a potential density-dependent response are also likely related to the life-history strategy and elasticity profi le of each population. For a given level of exploitation, those populations with both low values of λ and high ratios of juvenile survival to fertility elasticity and adult survival to fertility elasticity (Cortés, 2002), such as the pelagic and bigeye threshers, probably


take longer to show comparatively smaller compensatory changes than populations with high values of λ and low elasticity ratios, such as the blue shark.

Using incorrect life-history traits can also obviously lead to inaccurate interpretations of population parameters. While only populations with published life-history information were included in the analysis, some of the demographic traits used may still have been incor-rect. For example, age has only been validated through direct methods in the porbeagle (Natanson et al., 2002) and shortfi n mako (Natanson et al., 2006). Data on age, growth, and sexual maturity of the thresher shark in the northeastern Pacifi c have just been revised (Smith et al., 2008b). Use of these revised data would likely have resulted in a more pessi-mistic assessment of the capacity of the thresher shark to withstand exploitation. Although the use of Monte Carlo simulation was intended to compensate in part for this problem by including a wide range of variation in the estimates of vital rates and statistical distributions thought to capture the biology of each population to minimize the occurrence of unrealistic combinations of vital rates, the type of distribution used and the range of variation in its values, and covariance among demographic traits, are other potential sources of variability that must be investigated.

The population growth rates and generation times obtained with life tables/matrix popu-lation models for the eight species of pelagic sharks examined resulted in the prediction from Fowler’s regression equation that the populations would reach MSY at or well above 0.5K. This is consistent with predictions from Fowler (1988) and Restrepo et al. (1998), but there are views advocating that slow-growing fi shes such as sharks would reach MSY at 0.30–0.40K (Thompson, 1992; Au et al., 2008) based on stock–recruitment consider ations. One of the main implications resulting from reaching MSY at population sizes above 0.5K is that depleted stocks (low population sizes) will take longer to recover because the pro-duction curve is no longer parabolic, but instead is maximized at stock sizes �0.5K.

The fi ndings obtained through Fowler’s regression equation must be interpreted cau-tiously. That equation may be biased because it was based on a limited number of species showing strong K- or r-selected tendencies for which estimates of both the rate of increase per generation and the position of the infl ection point (fraction of carrying capacity, R) in population growth curves were available from the literature. However, the lack of informa-tion on R for shark populations precluded testing independently whether this parameter is correlated with population statistics such as λ or the rate of increase per generation. Despite its shortcomings, Fowler’s proposed equation is useful because it allows us to place the spe-cies compared along a gradient of R values. Ultimately, it has heuristic value, underscoring the need for further studies and analyses to gain insight into the poorly known population dynamics of sharks in general.

There is mounting concern about the status of shark populations worldwide. While there is little doubt that many populations – especially those of pelagic species – have decreased substantially from their levels prior to the development of modern mech-anized fi shing fl eets, the extent of the declines is the subject of intense debate (Baum et al., 2003, 2005; Baum and Myers, 2004; Burgess et al., 2005a, b). On the basis of our present knowledge of the biology of pelagic shark species, there is a gradient in the level of exploitation that different species can sustain. It is clear, however, that recovery time for most species whose stocks are heavily depleted will be long based on the position of the infl ection point of their population growth curves as found in the present analysis.


Acknowledgments

I thank Merry Camhi, Ellen Pikitch, Beth Babcock, and the Ocean Wildlife Campaign for supporting my travel to the International Pelagic Shark Workshop and for organizing the publication of this volume. The views expressed in this chapter are those of the author and do not necessarily refl ect the view of NOAA or any of its subagencies.

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