Brewster-Geisz and Miller: Management of Carcharhinus ptumbeus 



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0.35 

 0.30 

 0.25 



g 0.20 



Hi 



« 



S 0.15 



0.10 



0.05 t- 



0.00 



Neonate 



Juvenile 



Subadult Pregnant adult Resting adult 



I Fecundity ^f) M Growth from stage (G, ) D Stage residence (P, ) 



Figure 7 



The proportional sensitivities (elasticity) of each stage to fecundity, growth, and stage residence if 

 only juveniles are protected lF,,=0; F,=0.10; F, ^ -=0.20 >. 



They suggested that the use of turtle excluder devices 

 would protect juvenile sea turtles and aid in conserva- 

 tion and recovei7 of this species. Additionally, Heppell 

 et al. (1996) indicated that population enhancement 

 by means of hatchery production of sea turtles would 

 likely not be successful. In contrast, marine mam- 

 mals show a different pattern of sensitivity. For these 

 taxa, population gi-owth appears most sensitive to 

 events occurring during the adult stages (Heppell et 

 al., 1999). Studies indicate that maiine fish may also 

 show a different pattern of sensitivity, where there is 

 increased sensitivity to events in the early life history 

 (Heppell et al. 1999; Quinlan and Crowder, 1999). 



Three features of our approach require one to use 

 caution in interpreting our conclusions. First, there 

 are problems in using stage-based models, or demo- 

 graphic models of all types, with highly migratory 

 animals such as sharks. For instance, most demo- 

 graphic models assume that the population is closed. 

 In the case of the sandbar shark this assumption 

 may not hold true. Tagging studies show that a 

 small percentage of sandbar sharks tagged in U.S. 

 waters are caught in Mexican waters. Because it is 

 currently unknown if there are nursery grounds in 

 Mexican waters, this migration to Mexico may rep- 

 resent an additional source of loss to the population 

 that may not be replaced. The model does not con- 

 sider this loss. If a significant number of sandbar 

 sharks are found to migrate to Mexican waters, cur- 

 rent estimates oiF may be underestimates. If this is 



the case, even greater reductions in F may be neces- 

 sary to help the stock recover. 



Second, we have presented a deterministic model 

 of sandbar shark population dynamics. Thus, we 

 have ignored uncertainty of and plasticity in vital 

 rates such as growth and fecundity. Tuljapurkar 

 ( 1997 ) and Nations and Boyce ( 1997 ) have discussed 

 the potential biases that may result from basing har- 

 vest strategies on results from a deterministic model, 

 particularly when juvenile survival is closely tied to 

 environmental conditions. In addition to potential 

 biases in the results, a deterministic model yields 

 only a point estimate of population growth rate. 

 Cortes (1999) included a stochastic term for fecun- 

 dity in his model for sandbar sharks. Subsequently, 

 he used Monte Carlo simulations to generate distri- 

 butions of predicted population gi'owth rates when 

 fecundity varies stochastically. His results indicate 

 that predicted population growth rates may vary by 

 2-3*^ when fecundity is allowed to vary. The impact 

 of stochasticity in survival and growth on the pre- 

 dicted population growth rates is unknown. How- 

 ever, given the sensitivity of the model to transition 

 involving growth and survival for juvenile and sub- 

 adult animals, its impact may be substantial. 



Finally, unlike many traditional fishery models, our 

 demographic model does not take into account den- 

 sity dependence or compensation. However, given the 

 longevity and age to maturity of sandbar sharks, and 

 sharks in general, compensation may not be as signif- 



