Alonzo and Mangel: Sex-change rules, stock dynamics, and the performance of spawning-per-recruit measures in protogynous stocks 237 



fishery is centered below the mean size at sex change 

 (L^=25, r=l), the stock was predicted to crash at high 

 fishing mortality (F>1, Fig. 4A). Furthermore, when 

 the selectivity pattern was not steep (L,= 30, r=0.1), the 

 population was always predicted to crash even at low 

 fishing mortality (and thus this case is not shown in 

 Figs. 4A-6A). When the steepness of the fishery's selec- 

 tivity changes, the size range over which fish are targeted 

 also changes. Thus, smaller and younger fish are removed 

 by the fishery when r=0.1 and hence a greater number 

 of age classes are affected by fishing. At an extreme, 

 fishing mortality could be high enough that all of the 

 individuals in any size classes targeted by the fishery 

 are removed. As a result, although the steepness of the 

 selectivity function only affects the spread of the function 

 mathematically, it has the biological effect of decreasing 

 the size at which fish experience fishing mortality and 

 can have a large effect on the size and age distribution 

 of the population. In contrast, when the fishery's selectiv- 

 ity is steep (r=l) and only fish at or above the mean size 

 at sex change (L^&30) are targeted, the effect of fishing 

 on the population is predicted to be much less (Fig. 4A). 

 Independent of the selectivity pattern, the population 

 sex ratio is predicted to be more female-biased in the 

 presence of fishing than in the absence of fishing. The 

 lower the mean size removed by the fishery, the greater 

 the predicted change in population sex ratio as a result 

 of fishing (Fig. 5A). For situations in which the stock is 

 not predicted to crash (i.e., L^30 and r=l), yield is pre- 

 dicted to increase with diminishing returns with fishing 

 mortality (Fig. 6A), catch is not predicted to decline with 

 increased fishing mortality (at least up to F=3), and steep 

 size-selective fishing patterns with lower size thresholds 

 are predicted to lead to more yield (Fig. 6A). 



Rule 2 When sex change is determined by the mean 

 size of individuals in the mating site and the size-selec- 



tivity is weak (r=0.1), the population is predicted to 

 crash when F^l.67 (Fig. 4B). This crash occurs because 

 individuals do not escape fishing mortality even at small 

 sizes. However, unlike when sex change is fixed (Fig. 4A), 

 the population is predicted not to crash when the size 

 selected by the fishery is less than the mean size at sex 

 change in the absence of fishing (L,=25, Fig. 4B). The 

 larger the mean size selected by the fishery, the smaller 

 the predicted effect of fishing on the mean population 

 size and the population sex ratio (Figs. 4B and 5B). 

 Although catch is predicted to increase with diminishing 

 returns as fishing mortality increases from zero to three, 

 the difference between the size-selectivity patterns is 

 predicted to decrease and yield will be greater annually 

 if larger fish are targeted (Fig. 6B). 



Rule 3 As above, when the probability of sex change 

 depends on the relative frequency of smaller mature 

 individuals, the population is predicted to crash when- 

 ever size-selectivity is weak because fish do not escape 

 fishing even when small (r=0.1, Fig. 4C). Although the 

 population is predicted not to crash when the size tar- 

 geted by the fishery is less than the mean size at sex 

 change in the absence of fishing (L / =25, Fig. 4C), this 

 fishing pattern is predicted to lead to a large decrease 

 in mean population size and a marked decrease in popu- 

 lation sex ratio (Figs. 4C and 5C). In contrast fishing 

 selectivity that is centered at or above the mean size of 

 sex change in the absence of fishing (L,— 30 and L^35) 

 is predicted to lead to a weaker effect on mean popula- 

 tion size and to almost no effect on the population sex 

 ratio (Figs. 4C and 5C). However, in contrast to the two 

 scenarios described above this pattern of sex change 

 leads to the prediction that targeting fish at or larger 

 than the normal mean size of sex change (Zy=30 and 

 r=l) will lead to the greatest annual yield over time for 

 most fishing mortalities (Fig. 6C). 



