Alonzo and Mangel: The effects of size-selective fisheries on the stock dynamics of and sperm limitation in sex-changing fish 9 



escape fishing and thus increases the pro- 

 duction of fertilized eggs at the population 

 level. However, yield decreased proportion- 

 ally to the percentage of sites protected by 

 the reserve unless fishing effort is redis- 

 tributed among the remaining sites. We as- 

 sumed that fish do not move between sites 

 after the larval stage, and thus larger and 

 older individuals do not leave the reserve 

 and become exposed to fishing. Although this 

 assumption is clearly appropriate for some 

 species, it is important to realize that the dy- 

 namics and predictions would differ for more 

 closed populations or migratory species. For 

 the fishing pattern and biological scenario 

 examined in this study, marine reserves are 

 not predicted to increase biomass available 

 to the fishery (Figs. 7B and 8B). 



Dynamics of dioecious versus protogynous 

 stocks 



In the dioecious stock with a single ran- 

 domly mating aggregation, both male and 

 female biomass per recruit and fecundity 

 or fertility per recruit are predicted to 

 decrease as fishing mortality increases ( Fig. 

 6). Because both egg production and sperm 

 production decrease with increased fishing 

 pressure in the dioecious stock, the number 

 of eggs fertilized per recruit did not differ 

 much from the other SPR measures. Thus, 

 SSBR and eggs per recruit also indicated the 

 impact of fishing on the stock in dioecious 

 stocks with large mating aggregations. The 

 percent drop in population size and fertil- 

 ized egg production is predicted to be much 

 greater in dioecious species and occurred 

 more quickly than in the sex-changing 

 stock because of a reduction in overall 

 population fecundity even in the absence of 

 decreased fertilization rates. However, dioe- 

 cious stocks are predicted to exhibit larger 

 mean population size for the same fishing 

 mortality and to support a larger fishery 

 because of the additional egg production of 

 large fecund females. At very small mating 

 aggregations, sperm limitation is predicted 

 even in the dioecious stock and fertilized 

 eggs per recruit become a better indicator 

 of stock dynamics in the presence of fishing. 

 Dioecious stocks are also predicted to benefit 

 from marine no-take reserves through the 

 protection of large fecund females ( Fig. 7 ). 



Discussion 



In this study we developed a general frame- 

 work that examines the consequences to 



0.95 



0.9 



0.85 



Egg production 

 (per recruit) 



Fertilized eggs 

 (per recruit) 



Mean population 

 size 



Figure 5 



Mating aggregation size affects the response to fishing. Large (one large 

 mating aggregation ) and small ( 10 smaller mating aggregations I situations 

 are compared. Percent change in the presence of fishing (from F=0 to F=l> 

 in egg production per recruit, mean fertilized egg production per recruit, and 

 mean population size are given. Total population fecundity and mean body 

 size are lower for the smaller mating aggregations. 



PROTOGYNOUS POPULATION 



600 650 700 750 800 850 900 950 



Mean population size 



Figure 6 



Spawning-per-recruit (SPR) measures in a protogynous (squares) and dioe- 

 cious (triangles) stock: Mean egg production per recruit (filled) and mean 

 fertilized eggs per recruit (open) are shown for a randomly mating popula- 

 tion with one large mating group. Error bars indicate the standard error of 

 the mean. For the dioecious population, the two SPR measures overlap. 



