242 



Fishery Bulletin 103(2) 



Rule 1; Fixed 



0.9 



Q. 0.7 



o 06 



05 



0.4 



650 700 750 



Mean population size 



900 



950 



Figure 7 



Spawning-per-recruit (SPR) measures for all four patterns of sex change and an otherwise 

 identical dioecious stock: mean egg production per recruit (filled) and mean fertilized 

 eggs per recruit (open) are shown for a population with one large mating group when 

 Zy=30 and r=l. The same basic patterns are predicted for multiple mating sites. Each 

 line represents the same range of fishing mortalities, and each point represents fishing 

 mortality increasing from to 3 in increments of 1/3 moving from the right to the left. For 

 the fourth rule (expected reproductive success), the two lines (eggs produced per recruit 

 and eggs fertilized per recruit) overlap. 



whereas sex change based on relative size or the relative 

 frequency of individuals in a mating site is predicted 

 to have similar dynamics to those for the fixed pat- 

 tern of sex change. Thus, it is not possible to say that 

 sex-changing stocks tend to be more or less resilient to 

 fishing than are dioecious populations. However, the 

 sex change rule clearly affects the predicted relation- 

 ship between fishing mortality and the response of the 

 stock to fishing. 



Discussion 



We apply a general approach using individual-based 

 simulation models to determine the predicted effect of 

 the pattern of sex change on the stock dynamics of a 

 protogynous species. Although the model structure and 

 parameter values considered will not apply to all com- 

 mercially important protogynous species, it is important 

 to realize that all the scenarios considered are identical 

 except for the pattern of sex change. As a result, any 

 predicted differences that arise between these situa- 

 tions are a result of the sex-change rule and indicate 



that knowing simply that a species exhibits sex change 

 but not what the behavioral rule of sex change is will 

 lead to an incomplete ability to understand and predict 

 the dynamics of the stock and its response to fishing or 

 management strategies. 



Independent of the sex-change rule, the protogy- 

 nous stocks are always predicted to be sensitive to the 

 size-selective fishing pattern. Mean population size 

 is always predicted to decrease as fishing mortality 

 increases, despite the fact that we have assumed that 

 recruitment is strongly density dependent and that 

 the species is very productive. Stocks are predicted 

 to crash even at low fishing mortality when the size- 

 selective fishing pattern targets all reproductive size 

 classes and for the fixed sex change rule whenever all 

 male sizes sizes are targeted by the fishery. It will 

 be necessary but not sufficient to avoid overfishing at 

 spawning aggregations. Our results indicate that it will 

 also be important to allow smaller and nonreproductive 

 individuals to escape fishing as well. These results 

 indicate that independent of the exact pattern of sex 

 change, management strategies for all protogynous 

 stocks need to be sensitive to the size-selectivity of 



