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



the percentage of mature individuals that are female) also 

 increases as fishing mortality increases (Fig. 4B) and the 

 mean size of adults in the population decreases. These pat- 

 terns depend on fishing being size selective, which causes a 

 disproportional take of males. If the size-selectivity of the 

 fishery targeted smaller size classes (L<L C ), a decline in 

 annual biomass removed by the fishery is predicted with 

 increasing F and the stock is predicted to crash at a rela- 

 tively low fishing mortality (Fig. 4C). If the fishery is less 

 selective (r=0.1, L,=L C ), the population is also predicted 

 to crash for most fishing mortalities. Thus, allowing some 

 proportion of mature males to consistently escape fishing 

 is critical even at low fishing mortality. As fishing mortality 

 increases, the predicted biomass removed by the fishery 

 increases with diminishing returns ( Fig. 4C ). When Lf=L c , 

 the biomass removed by the fishery does not continue to 

 increase with F because all males above the size at sex 

 change are being removed by the fishery. In this case, the 

 males in the population are essentially breeding only once 

 before they are taken by the fishery. For the range of fish- 

 ing mortality considered, we did not observe a decline in 

 biomass taken with increasing F unless L<L t . or r=0.1. If 

 more size classes are allowed to escape fishing (L f >L c ), the 

 general patterns remain the same, but for the same fishing 

 mortality (.F), the effect of fishing on the population is less 

 (Fig. 4). Female biomass does not decrease much with fish- 

 ing mortality when L f =L c even though some females are 

 removed by the fishery because the probability of a female 

 changing sex is the probability of it being fished. Therefore, 

 female loss due to the fishery affects male biomass rather 

 than female biomass in the population. 



Sperm limitation and production 



The removal of large males from the population is pre- 

 dicted to cause sperm limitation and decreased fertiliza- 

 tion rates (Fig. 3, A and C), leading to a decrease in mean 

 population size (Fig. 4A). The degree to which the fertiliza- 

 tion rate and thus the population size decreases depends 

 to a great extent on the pattern of sperm production 

 and fertilization. We assumed that only a few males are 

 needed to fertilize the eggs of many females (Fig. 2). We 

 also assumed that per-capita reproduction and recruitment 

 are high even at a low population size (Barrowman and 

 Myers, 2000). Thus, protogynous populations with lower 

 sperm production or fertilization rates would experience 

 greater effects from fishing than predicted in the present 

 study. Similarly, populations with lower production or sur- 

 vival would experience larger decreases in population size 

 even with the same level of sperm limitation and fishing. 

 In general, however, the removal of males alone from a pro- 

 togynous population with a fixed sex change is predicted to 

 cause decreased fertilization rates and lower mean popula- 

 tion size even when the fertilization rate function is asymp- 

 totic and individual male sperm production is high. 



Mating aggregation size 



As mating aggregation size decreased and fishing mortality 

 and effort remained constant, the effect of fishing on the pop- 



Eggs produced 



1 1.5 2 



Fishing mortality (F) 



Figure 3 



Spawning-per-recruit measures. Results are presented for 

 the sex-changing stock with one mating site when L^= L c 

 and r=l. Means across 20 simulations are given. For details 

 see the general text. 



ulation increased. As described above, we assumed that fish- 

 ing effort would not be concentrated on the few large mating 

 aggregations and thus increase total fishing mortality. The 

 sex ratio, mean size, mean fecundity, and mean fertility all 

 remained the same across different mating aggregation 

 sizes with constant fishing mortality. However, the mean 

 fertilization rate and number of fertilized eggs per recruit 

 decreased with mating group size ( Fig. 5 ) even though male 

 biomass and SSBR remained the same. Both predicted 

 mean population size and biomass taken decreased as fish- 

 ing mortality increased (Fig. 5). This pattern was generated 

 by sperm limitation in small mating groups. Smaller groups 

 have higher probabilities that sperm production within the 

 group will not be sufficient to fertilize the eggs produced 

 within the mating group. Small mating aggregations may 

 not only be sperm limited but also be male limited and fail 

 to reproduce completely; populations with small group sizes 

 (50 individuals or less) were predicted to become extinct in 



