168 



A Monte Carlo demographic analysis 



of the silky shark (Carcharhinus faiciformis): 



implications of gear selectivity 



Lawrence Beerkircher 



Mahmood Shivji 



Guy Harvey Research Institute 



Oceanographic Center 



Nova Southeastern University 



8000 N, Ocean Dnve 



Dania Beach, Flonda 33004 



E mail address (for L Beerkircher) beerkirc@ocean nova edu 



Enric Cortes 



National Marine Fisheries Service 

 3500 Delwood Beach Road 

 Panama City, Florida 32408 



Demographic analysis has recently 

 been used as a tool to approximate the 

 dynamics of shark populations (Cail- 

 liet, 1992; Sminkey and Musick, 1996; 

 Au and Smith, 1997; Cortes, 1999). 

 The widespread use of demographic 

 models for shark species, however, is 

 hampered by a paucity of informa- 

 tion on vital rates, which are required 

 as input parameters for the models. 

 A vital rate of special importance 

 is natural mortality, which remains 

 unknown for most shark species and 

 many other marine taxa. Demographic 

 models thus must often rely on indirect 

 methods of natural mortality estima- 

 tion rather than empirically observed 

 values specific to a given population. 

 Several methods to estimate natural 

 mortality have shown promise for 

 shark demographic analysis (Cortes, 

 1998). Other vital rates such as fecun- 

 dity, although often strongly influenced 

 by size and age, likely also vary inde- 

 pendently of time over the lifespan of 

 individuals within a population. Incor- 

 poration of Monte Carlo simulation in 

 demographic models has been used to 

 account for some of this uncertainty 

 in vital rate estimates and construct 

 confidence intervals for model output 

 (Cortes, 1999:2002). 



One of the most valuable aspects 

 of demographic modeling is the abil- 

 ity to examine how populations might 

 respond to various levels of fishing 



mortality (Au and Smith, 1997; Cortes, 

 1998; Smith et al., 1998; Simpfendor- 

 fer, 1999). To date, most authors have 

 used empirical estimates of fishing 

 mortality (F) and either applied them 

 uniformly to all age groups or have 

 produced various scenarios with F 

 applied starting at a particular age 

 to simulate various fisheries manage- 

 ment schemes (Sminkey and Musick, 

 1996; Au and Smith, 1997; Liu and 

 Chen, 1999). Gear selectivity and its 

 effect on F at various ages, however, 

 has not been incorporated into demo- 

 graphic models even though it is very 

 likely that some selection occurs. Here, 

 we produce a demographic analysis 

 of the silky shark (Carcharhinus fai- 

 ciformis) off the southeastern United 

 States. Monte Carlo methods are used 

 to simulate variability in model input 

 parameters, and multiple scenarios 

 are considered, incorporating natu- 

 ral mortality only, and added fishing 

 mortality components. We include in 

 our analysis scenarios that reflect pos- 

 sible longline gear selectivity for silky 

 sharks, using catch-at-age information 

 estimated from length-frequency data 

 provided by the U.S. pelagic longline 

 observer program for the southeastern 

 U.S. coast. Finally, we compare sce- 

 narios that incorporate the same mean 

 value of fishing mortality, but with dif- 

 ferent assumptions of selectivity pat- 

 terns. The results of the demographic 



analysis are discussed in the context of 

 the robustness of model assumptions. 



Materials and methods 



Life history parameters for the silky 

 shark demography were obtained from 

 the best available literature sources. 

 Von Bertalanffy parameters of L^ = 

 311 cm total length, K = O.lOl/yr, and 

 tg = -2.718 yr were taken from Bonfil 

 et al. (1993). To account for some of 

 the uncertainty in the estimate of 

 age-at-maturity (t^^i) of 12 years given 

 by Bonfil et al. (1993), values for t^^^ 

 were drawn at random from a discrete 

 probability distribution of P = 0.25, 

 0.5, and 0.25 for ages 11, 12, and 13, 

 respectively. Longevity (^„,,,x' ^^^ simi- 

 larly varied by assigning the estimate 

 of Bonfil et al. ( 1993 ) of 22 years a P = 

 0.5 and linearly decreasing P by 50% 

 for each subsequent year. 



Estimates of natural mortality (M) 

 were selected by using three methods: 

 Peterson and Wroblewski ( 1984 ), Chen 

 and Watanabe (1989), and Jensen 

 (1996) (Table 1). For the Peterson and 

 Wroblewski method, weights-at-age 

 were determined by calculating total 

 length-at-age from the von Bertalanffy 

 growth function, and then converting 

 these values to fork length and weight 

 (in grams) by using the relationships 

 given by Kohler et al. (1995) for the 

 silky shark. Wet weight was used 

 instead of dry weight to generate val- 

 ues of M. Annual survival (S,; S=e"'^, 

 .v=age) values were randomly drawn 

 from a distribution in which the three 

 methods of calculating mortality rates 

 had equal probability. 



Fecundity (nij, the number of fe- 

 male pups produced per each year 

 of life, was calculated by combining 

 the data of Fourmanoir (1961), Bane 

 (1966), Gilbert and Schlernitzauer 

 (1966), Branstetter (1987), and Bonfil 

 et al. (1993), which yielded a mean of 

 10.3 (SD=2.213, n = 16) pups per lit- 

 ter Observations in the literature of 

 litter sizes lower than five pups were 

 not included because of the possibil- 

 ity that females might have aborted 

 pups from one uterus during capture 



Manuscript accepted 10 July 2002. 

 Fish. Bull. 101:168-174 (200;!). 



