sharks of the open ocean || intrinsic rates of increase in pelagic elasmobranchs

Chapter 25

Intrinsic Rates of Increase in Pelagic Elasmobranchs

Susan E. Smith, David W. Au and Christina Show

Abstract

Elasmobranch demography is briefl y reviewed and intrinsic rebound rates are calculated for 11 selected pelagic species. These rates are compared to those of 22 other shark species calculated by the same method. Rates of population increase for most pelagic species fall within the middle range of the shark productivity spectrum, but some lie near the limits of the entire range, from a low of 1–2% per year for basking shark (Cetorhinus maximus) to a high of 6–10% per year for pelagic stingray (Pteroplatytrygon violacea). All calculated elasmobranch values are low compared to those of most teleosts, especially if a total mor-tality equaling 1.5 times the instantaneous natural mortality is considered to be the most appropriate for producing maximum sustainable yield in sharks.

Key words: demographic analysis, intrinsic rates of increase, population growth rate.

Introduction

Demography, developed originally to forecast human population growth, combines age- or stage-specifi c mortality and natality rates to produce estimates of net reproductive rate, generation time, and per capita instantaneous rate of increase of a population (r). The method is useful for sharks because surplus production modeling or other age-structured analyses are often not feasible for many species for which catch-rate and age data are lacking. Our purpose is to briefl y review shark demography and compare rebound poten-tials of pelagic versus nonpelagic shark species, with rebound ability being a proxy for sensitivity to fi shery exploitation.

All demographic models used for elasmobranchs are based on the equation developed by Euler (1760) and rediscovered by Lotka (1907). It demonstrates that when age-specifi c rates of survivorship and fecundity remain constant with time, an age distribution eventu-ally forms where the proportion of the population in each age interval remains constant, and the population then increases at an intrinsic rate r. It is the basic equation of popula-tion dynamics; most statistics of population analyses are derived from it.

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

Intrinsic Rates of Increase in Pelagic Elasmobranchs 289

This equation may be written (e.g., Stearns, 1992)

l e mxrx

xx

w�

�

�1α

∑

where age at maturity (α), age at last reproduction (w), probability of survival to a given age class (lx), and number of offspring produced by a given age class (mx) are related to the rate of growth (r) of the population. The stable-aged condition is assumed, in which the population grows smoothly and exponentially, and when not growing it is in a stationary condition (r � 0). The resulting rate (r) is considered the maximum potential growth rate for a given survival–fecundity schedule. The rate usually (though not always) represents the rate achieved in the absence of crowding, resource competition, or any other built-in compensatory response related to population density. The model is a useful conceptual construct, especially for wide-ranging pelagic sharks that are diffi cult to sample. A major drawback is the diffi culty of obtaining empirical estimates or suitable proxies for the prob-ability of survival to age x. Survival schedules are lacking for most elasmobranchs, thus mortality is usually estimated indirectly and broadly applied, with assumptions made for various age classes or stages. These assumptions usually differ among studies, making comparison of results diffi cult.

Traditional demographic methods of varying complexity have been used to estimate rates of increase for nonpelagic sharks such as spiny dogfi sh (Squalus acanthias, Squalidae; Jones and Geen, 1977), angel shark (Squatina californica, Squatinidae; Cailliet et al., 1992; Heppell et al., 1999), bonnethead (Sphyrna tiburo, Sphyrnidae; Cortés and Parsons, 1996; Cortés, 1998), and the following carcharhinid sharks: lemon (Negaprion brevirostris; Hoenig and Gruber, 1990; Cortés, 1998), sandbar (Carcharhinus plumbeus; Hoff, 1990; Sminkey and Musick, 1996; Cortés, 1999; Brewster-Geisz and Miller, 2000), blacktip (C. limbatus; Cortés, 1998), dusky (C. obscurus; Cortés, 1998; Simpfendorfer, 1999a), leopard (Triakis semifasciata; Cailliet, 1992; Heppell et al., 1999), Atlantic sharpnose (Rhizo prionodon ter-raenovae; Cortés, 1995, 1998), and Australian sharpnose (R. taylori; Simpfendorfer, 1999b). In this volume, Cortés (2008) estimates potential rates of increase for eight pelagic sharks under various vital rate scenarios using an age-based probabilistic model that allows assess-ment of the sensitivity of population growth to proportional mortality increases in young-of-the-year, juvenile, and adult life stages.

A nontraditional method has also been used to compare and rank rates of increase in an array of pelagic and nonpelagic sharks hypothetically exposed to a maximum sustainable level of harvest (Au and Smith, 1997; Smith et al., 1998; Show, 2000; Au et al., 2008). Like traditional methods, it uses the Euler–Lotka equation as its base, but also incorpo-rates concepts of sustainability and population compensation to circumvent the survival schedule problem and other data limitations, and to compare species. The method is used here to estimate the rebound rates of 11 pelagic elasmobranch species. Unlike standard demographic analyses, this method approximates each species’ growth potential for sus-taining a given level of harvest, which becomes its potential to increase once fi shing is removed.

290 Sharks of the Open Ocean

Methods

The approach of Au and Smith (1997) and Smith et al. (1998) is used to determine the intrinsic rebound potential rZ(MSY) at a total mortality level chosen for maximum sustain-able yield. Unlike traditional r values, this method estimates population growth rates for each species at the same population level – about half the virgin population size (Fig. 25.1). A density-dependent feature allows the modeled population to respond to imposed fi shing mortality and enables estimation of net juvenile survival.

Estimating the intrinsic rate of increase rZ(MSY) or rebound potential

As in Au and Smith (1997) and Smith et al. (1998, Equation 3), rZ(MSY) is estimated using age at maturity α, maximum reproductive age w, adult instantaneous natural mortality M, average number of female pups per adult female b, and survival to age at maturity lα. Juvenile survival lα replaces survival to a given age class lx up to age α and is determined by assuming that the total adult mortality Z to be applied is sustainable, and that juvenile survival compensates for any reduced reproductive output resulting from this imposed mortality. The value of rZ(MSY) is then determined by removing fi shing mortality and allowing the population to rebound in an unfi shed state with juvenile survival remaining at the “enhanced” compensatory level. Previously (Smith et al., 1998) the traditional mor-tality level of ZMSY � 2.0M was applied, but here we use it as a comparative upper value. The level ZMSY � 1.5M as proposed by Au et al. (2008) is now considered to be the more appropriate maximum estimate for sharks using our method (see also Cortés, 2008). The value of M (or Z in the unfi shed state) is estimated from maximum age as described by Hoenig (1983; ln M � 1.44 � 0.982 ln w). Among indirect methods, Hoenig produced the most realistic estimate for R. taylori in a study comparing seven indirect methods for esti-mating M with an empirical method based on catch curve analysis (Simpfendorfer, 1999b). The value of M can also be estimated from body size (Peterson and Wroblewski, 1984). Smith et al. (1998) discussed various caveats in estimating rZ(MSY) using this method.

Species A

Net production

Species B

Species C

0.0 0.5

Population size (fraction carrying capacity K)

K

Intr

insi

c ra

te o

f p

op

ula

tio

n in

crea

se

Z(MSY)

Fig. 25.1 Schematic representing r as a decreasing function of population density, with points representing intrinsic rates of increase for species of varying productivities (A being most productive; C being least productive) measured at 0.5 of carrying capacity K.


Choosing and applying life-history parameters

Parameters were obtained from the literature and expert sources for 10 pelagic shark stocks and one pelagic stingray as cited in Table 25.1 and as described by Smith et al. (1998). Values of b account for reproductive cycles of more than 1 year. The fecundity adjustment described in Smith et al. (1998) is not applied here. Rebound rates based on parameters from Smith et al. (1998) are presented for 22 other shark species/stocks for comparison: sevengill (Notorynchus cepedianus, Hexanchidae); spiny dogfi sh (Northeast Pacifi c and Northwest Atlantic stocks); angel shark; sand tiger (Carcharias taurus, Odontaspididae); white shark (Carcharodon carcharias, Lamnidae); the triakid sharks, school (Galeorhinus galeus), gray smoothhound (Mustelus californicus), brown smoothhound (M. henlei), and leopard; the carcharhinid sharks, gray reef (Carcharhinus amblyrhynchos), Galapagos

Table 25.1 Intrinsic rebound potential estimates for selected pelagic elasmobranch species, listed in order of most productive to least, calculated for ZMSY � 1.5M and ZMSY � 2.0M.

Species/parametersa

α (year) w (year) b M (year�1) r1.5M (year�1) CV (r1.5M) r2.0M (year�1) CV (r2.0M) Referencesb

Pelagic stingray (Pteroplatytrygon violacea, Dasyatidae, northeastern Pacifi c) 3 8 3.0 0.548 0.062 0.091 0.104 0.089 1

Oceanic whitetip (Carcharhinus longimanus, Carcharhinidae, North and South Pacifi c) 5 22 3.0 0.203 0.039 0.070 0.067 0.070 2

Common thresher (Alopias vulpinus, Alopiidae, northeastern Pacifi c) 5 25 2.0 0.179 0.037 0.068 0.065 0.068 3

Shortfi n mako (Isurus oxyrinchus, Lamnidae, northwestern Atlantic) 6 15 3.1 0.295 0.036 0.092 0.062 0.088 4

Blue shark (Prionace glauca, Carcharhinidae, North Pacifi c and North Atlantic) 6 20 11.6 0.223 0.035 0.076 0.061 0.076 5, 6, 7

Porbeagle (Lamna nasus, Lamnidae, southwestern Pacifi c) 8 30 1.9 0.150 0.026 0.072 0.046 0.073 8, 9, 10

Salmon shark (L. ditropis, Lamnidae, northwestern Pacifi c) 9 25 2.3 0.179 0.024 0.083 0.043 0.082 11, 12

Silky shark (C. falciformis, Carcharhinidae, western Atlantic) 9 25 2.6 0.179 0.025 0.084 0.043 0.082 13

Pelagic thresher (A. pelagicus, Alopiidae, northwestern Pacifi c) 9 29 1.0 0.155 0.024 0.076 0.043 0.077 14

Bigeye thresher (A. superciliosus, Alopiidae, northwestern Pacifi c and northeastern Atlantic) 13 20 1.0 0.223 0.016 0.233 0.028 0.203 15, 16, 17

Basking shark (Cetorhinus maximus, Cetorhinidae, Atlantic) 18 50 1.5 0.091 0.012 0.118 0.018 0.125 18, 19

aα: female age at maturity; w: maximum reproductive age; b: average number of female pups per adult female annually; M: natural mortality rate; r: intrinsic rebound potential at Z � 1.5M, Z � 2.0M; CV: coeffi cient of variation for r1.5M and r2.0M.bOther than cited in Smith et al. (1998), as follows: 1: Henry F. Mollet, September 1999, personal communi-cation, Monterey Bay Aquarium, Monterey, CA; 2: Seki et al. (1998); 3: Smith et al. (2008); 4: Mollet et al. (2000); 5: Cailliet et al. (1983); 6: Tanaka et al. (1990); 7: Nakano and Seki (2002); 8: Aasen (1963); 9: Francis and Stevens (2000); 10: Francis et al. (2008); 11: Tanaka (1980); 12: Goldman and Human (2005); 13: Bonfi l et al. (1993); 14: Liu et al. (1999); 15: Moreno and Morón (1992); 16: Chen et al. (1997); 17: Liu et al. (1998); 18: Pauly (1978); 19: Pauly (2002).


(C. galapagensis), bull (C. leucas), blacktip, dusky, sandbar, tiger (Galeocerdo cuvier), lemon, Atlantic sharpnose, and whitetip reef (Triaenodon obesus); and the sphyrnid sharks, scalloped hammerhead (Sphyrna lewini) and bonnethead.

Precision

We carried out Monte Carlo simulations (n � 10,000) of rZ to determine the distribution and coeffi cient of variation (CV) of each species’ productivity estimates, given combinations of age at maturity α and maximum age w values, adjusting natural mortality M inversely as w varied. Both α and w were presumed to vary 20% about their mean or estimated values, a reasonably conservative estimate of variation in these parameters, which represent aver-age values over the long term. The probability distributions of α and w were assumed to be normal with 20% representing two standard deviations (i.e., CV � 10%). Fecundity was held constant. Confi dence intervals are calculable from CV and rZ(MSY) (mean) values.

Results

Rebound rates among the pelagic sharks examined ranged from a high of 6–10% per year for pelagic stingray to a low of 1–2% per year for basking shark (Table 25.1). All oth-ers fell between 2–4% (Z � 1.5M) or 3–7% (Z � 2.0M) per year. Precision of estimated rZ(MSY) is indicated by listed CVs, which ranged between 0.068 and 0.233 with distribu-tions approximately normal.

The basking and bigeye thresher (Alopias superciliosus, Alopiidae) sharks are among the least productive of the 33 elasmobranchs considered, similar to many slow-growing, late-maturing large coastal sharks (Fig. 25.2). The pelagic stingray was among the most productive, similar to small inshore coastal sharks, which are all relatively fast-growing and early to mature. The more productive species had a greater rZ(MSY) range than the less productive species, with rates differing widely under the Z � 1.5M and Z � 2M mortality conditions, indicating a higher sensitivity to imposed mortality. Differences under the two mortality assumptions ranged from 0.01 (Z � 1.5M) to 0.017 (Z � 2M) for the least pro-ductive spiny dogfi sh, to 0.079 (Z � 1.5M) to 0.139 (Z � 2M) for the most productive gray smoothhound. For the pelagic elasmobranchs, the r1.5M values averaged 58% lower than the r2.0M values.

Discussion

Most pelagic elasmobranchs are in the midrange of shark productivity, but the range is broader than previously thought. Basking and bigeye thresher sharks rank among the least productive examined to date with this method; both have low reproductive rates and advanced ages at fi rst maturity. Cortés (2008) has also obtained low r values for bigeye thresher using a different demographic method. This late-maturing, long-lived strategy is similar to that of medium to large coastal shark species, and indeed both sharks seem to diverge from the epipelagic shark ecotype with their particular habitat and trophic


0.0 0.02 0.04 0.06 0.08 0.10 0.12

0.0 0.02 0.04 0.06 0.08 0.10 0.12

Productivity comparisonamong elasmobranchs

MSY mortalitylevel (Z )

1.5 M 2.0 M

Spiny dogfish (NW Atlantic)

Spiny dogfish (B.C.)Dusky sharkBasking sharkSevengill sharkBull sharkScalloped hammerheadSandbar sharkBigeye thresherLeopard sharkSchool/soupfin shark

Lemon sharkAngel sharkWhite sharkTiger shark

Silky sharkSalmon sharkPorbeagle (S. Pacific)Galapagos sharkWhitetip reef sharkSand tiger shark (Atlantic)Gray reef sharkBlacktip sharkBlue sharkShortfin mako sharkCommon thresherOceanic whitetip

Atlantic sharpnoseBonnethead sharkPelagic stingrayBrown smoothhoundGray smoothhound

Pelagic thresher

MSY

Fig. 25.2 Productivity comparison of pelagic elasmobranchs (in bold) with other shark species. Values for non-pelagic species are taken from Smith et al. (1998) and Au et al. (2008).

specializations. The basking shark is a sluggish, primarily coastal, fi lter-feeding species (Compagno, 1984). The bigeye thresher can occur near the surface, but generally ranges deeper than other threshers, although it may also enter coastal and even shallow waters (Gruber and Compagno, 1981). According to cited references, parameters for the basking shark are preliminary, but those of the bigeye thresher appear more reliable, except per-haps w may be underestimated. The low w in relation to high α likely caused the relatively high CV value (0.19) for bigeye, but even increasing w to 30 years would have little effect on productivity, which is primarily driven by α. Inexact estimates of w also directly affect estimates of M, a drawback of using Hoenig’s (1983) method, although long-lived species appear least affected by inaccuracies in M (Au et al., 2008).


The pelagic stingray is one of the most productive elasmobranchs we examined, but its parameters are also preliminary. Little is known of the reproductive periodicity and fecun-dity of the viviparous rays, such as P. violacea (Neer, 2008). Captive young specimens have been observed to grow rapidly and reach sexual maturity within a few years (H. F. Mollet, personal communication). Results of recent biological studies on this species are provided by Neer (2008), who found that maximum age in the wild may extend to 10 years (or more) based on banding patterns.

Pelagic sharks with midrange productivities appear to invest early in somatic growth, delaying sexual maturity and living longer than the more productive small neritic sharks, while being faster-growing, shorter-lived, and earlier to mature than the least productive coastal sharks. Because of their higher productivity, vast ranges, and greater likelihood of seeding from unfi shed areas, epipelagic sharks may be more resilient to fi shing than the slow-growing, late-maturing coastal sharks. But they are also vulnerable to oceanic fi sh-eries, and early life stages of some may be vulnerable to inshore fi sheries as well (Smith et al., 1998).

Elasmobranch productivity is low compared to that of many teleosts, being more comparable to the productivity of marine mammals (Smith et al., 1998; Au et al., 2008). Additionally, if ZMSY � 1.5M is the more appropriate maximum MSY level for determining the intrinsic rebound potential of elasmobranchs (Au et al., 2008), it is considerably lower and the range narrower than previously estimated using this method. Low-productivity species are particularly vulnerable as represented by the fl attest yield curve in Fig. 25.1. Even a slight reduction from their production peak can lead to a dangerously depleted condition. The more productive species may be less sensitive to incremental increases in fi shing effort, but their faster turnover rates make them more sensitive to changes in total mortality and to factors affecting their vital rates. Although empirical evidence is still needed to determine how much different species and life stages can adjust their sur-vival under different population conditions, demographic analyses can help approximate the productivity potential of elasmobranchs under mortality conditions observed or hypo-thetically imposed.

Acknowledgments

We thank Enric Cortés, Gregor M. Cailliet, Henry F. Mollet, and Malcolm P. Francis for helpful comments and suggestions, and Henry Mollet for providing pelagic stingray input parameters.

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