Alonzo and Mangel: Sex-change rules, stock dynamics, and the performance of spawning-per-recruit measures in protogynous stocks 243 



the fishing pattern in relation to size at maturity and 

 size at sex change observed in the population, and a 

 failure to do so can lead to a sudden and unexpected 

 collapse of the fishery — a collapse from which it may 

 be difficult to recover. 



We assume in all cases that the same cues determine 

 both the probability of maturity and the probability of 

 sex change within a species. For example, when sex 

 change was affected by the relative size of individuals 

 at the mating site, we assume that this same cue af- 

 fected the probability of maturing. This assumption has 

 a large effect on the predicted dynamics of the stock. 

 Alternatives exist. For example, the size at which fish 

 mature could be determined by endogenous rather than 

 exogenous factors even in a population where the prob- 

 ability of sex change is affected by external cues. If this 

 were the case, the population can easily be fished into a 

 situation where it cannot compensate for size-selective 

 fishing and is predicted to crash for any fishing pat- 

 tern that targets reproductive individuals. For example, 

 when L,= 30 and r=l, populations with plastic size at 

 maturity and sex change were not predicted to crash 

 independent of fishing mortality. In contrast, simula- 

 tions where populations were assumed to have fixed size 

 at maturity rules (L m =20) but plastic patterns of sex 

 change crashed at most fishing mortalities with L^=30 

 and r=l. Hence, knowledge of the cues determining both 

 maturity and sex change will be important in predict- 

 ing and understanding larval production and the effect 

 of fishing on a population. 



It is possible to argue that a protogynous species with 

 fixed patterns of sex change may have very different 

 dynamics than dioecious stocks, but the compensatory 

 patterns of sex change will be less sensitive to fishing 

 and exhibit dynamics very similar to their dioecious 

 counterparts. However, our results indicate that even 

 stocks with plastic patterns of sex change are predicted 

 to have dynamics distinctly different from otherwise 

 identical dioecious populations. For example, sperm 

 limitation is predicted to occur for all sex change rules, 

 except for the pattern where sex change is determined 

 by expected reproductive success (rule 4). However, 

 even a stock exhibiting the reproductive sucess rule 

 has dynamics that are distinctly different from those 

 of a dioecious species because a change in the size dis- 

 tribution of the population due to size-selective fishing 

 is predicted to have a large effect on the productivity 

 and sex ratio of the protogynous population. Similarly, 

 mating group size is predicted to affect the stock dy- 

 namics in all cases except for the reproductive success 

 rule. Therefore, although knowing the pattern of sex 

 change is predicted to be important in understanding 

 stock dynamics, it is also clear that the pattern of sex 

 change must be considered in the context of the mat- 

 ing system of the stock, as well as in the context of the 

 basic biology of the stock. 



Protogynous stocks are thus predicted to be sensitive 

 to the fishing pattern, and nonlinear stock dynamics 

 are possible when fishing operations target a wide range 

 of fish sizes. However, each stock is also predicted to 



have a unique response to the same fishing pattern 

 (Figs. 4-6) and to have different relationships between 

 traditional spawning-per-recruit measures and changes 

 in mean population size with fishing mortality (Figs. 1, 

 2, and 7). As a result, monitoring changes in spawn- 

 ing stock biomass per recruit or egg production per 

 recruit alone will not make it possible to determine the 

 relationship between these measures and mean popula- 

 tion size or to know whether the population is at risk 

 for large and sudden declines in population size. Our 

 results indicate that although it is important to know 

 whether sex change occurs when managing a stock, 

 it will also be important to know what endogenous or 

 exogenous cues induce sex change and how behavioral 

 patterns and life history strategies affect the demo- 

 graphic rates of the stock. 



Plasticity is not predicted to yield populations that 

 have stock dynamics that are identical to those of di- 

 oecious species, and the performance of spawning-per- 

 recruit measures and the relationship between egg pro- 

 duction and population size differed greatly between all 

 four patterns of sex change, despite the fact that the 

 basic patterns of growth, survival, and fecundity where 

 identical between all the scenarios considered. Because 

 sperm limitation is more common with the fixed and 

 relative size rules of sex change, these situations are 

 predicted to have the greatest difference between clas- 

 sic SPR measures and the production of fertilized eggs. 

 Clearly it is not just whether a population changes sex 

 or not, but also how sex change is induced, that deter- 

 mines the population's predicted response to fishing 

 and the performance of spawning-per-recruit measures 

 in predicting and indicating the effect of fishing on the 

 population. 



Although it is important to know what life history 

 strategy and behavioral patterns are observed in a 

 species, these alone will not always be sufficient to 

 predict expected changes in population size and pro- 

 ductivity under new conditions. Instead, knowledge of 

 the plasticity of behavioral and life history patterns, 

 as well as information about the internal and exter- 

 nal cues that induce phenotypic changes, may also be 

 necessary. Phenotypic plasticity is often expressed as a 

 threshold response (such as sex change) to a continuous 

 endogenous or exogenous cue. Therefore, as predicted by 

 our model, plasticity can generate nonlinear changes in 

 important demographic characters. An understanding 

 of the natural variation in behavior and life history 

 combined with knowledge of fish vital rates and envi- 

 ronmental conditions will lead to a better understand- 

 ing of and ability to predict the response of a stock to 

 fishing mortality, environmental changes, and specific 

 management strategies. 



Acknowledgments 



This research was supported by National Science Foun- 

 dation grant IBN-0110506 to Suzanne Alonzo and the 

 Center for Stock Assessment Research (CSTAR). 



