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



per recruit (SSBR). We also kept track of the 

 total fecundity (egg production per recruit I, 

 fertility (sperm production per recruit), and 

 eggs fertilized per recruit. 



Marine reserves 



^=150 (about 60 females) 



OS- 



'S 0.6 



■s 0.4 



02 



We examined the effect of no-take marine 

 reserves on the predicted stock dynamics by 

 comparing the stock dynamics in the presence 

 and absence of reserves. Without a reserve, 

 individuals at all mating sites are subject to 

 fishing. In the presence of a no-take marine 

 reserve, we "protect" a percentage of the 

 mating sites (and thus the population) from 

 fishing. We examined cases in which 09c, 10%, 

 20%, and 30% of mating sites were protected 

 from fishing. We assumed that the population 

 is completely open among mating sites. Thus, 

 eggs produced from all mating sites enter one 

 larval pool and recruitment occurs randomly 

 between mating sites. Clearly other possibili- 

 ties exist and could be considered in future analyses, but 

 this case represents a reasonable baseline situation to con- 

 sider because many marine fish have pelagic larval phases. 

 We also recognize that these analyses ignore the effect of 

 interactions between species within the reserve on stock 

 dynamics. We examined two situations. In the first case, 

 reduced fishing effort occurs when mean fishing mortality 

 is decreased in the presence of reserves because fishing 

 mortality (F) at the unprotected sites remains the same as 

 before the reserve. In the second case, the redistribution of 

 fishing effort occurs when mean fishing mortality across all 

 sites remains the same because fishing mortality increases 

 at the unprotected sites. 



Comparison of sex-changing stocks and dioecious stocks 



Ideally, we would like to distinguish the effects of sex change 

 in isolation from the confounding effects of mating pattern, 

 sex ratio, survival, growth, and population fecundity on 

 stock dynamics. To differentiate whether sex change in iso- 

 lation or other aspects of the mating system determine the 

 predicted stock dynamics, we also examined a version of the 

 model described above for a population where sex is fixed 

 at birth. In this dioecious population, we keep all aspects 

 of the stock constant except for the pattern of sex determi- 

 nation (whether the species changes sex or is dioecious). 

 One would generally expect a dioecious population with 

 no differences between the sexes in mortality to exhibit a 

 50:50 sex ratio ( Fisher, 1930; Trivers, 1972; Charnov, 1982 ). 

 However, we wanted to control for all differences between 

 the dioecious and protogynous stocks other than the sex- 

 determination pattern. Therefore, we considered the same 

 sex ratio at maturity (0.67=the proportion of adults that 

 are female) as found in the sex-changing population in the 

 absence of fishing. Assuming no sex-specific differences in 

 survival to maturity, this is the same as assuming a 0.67 

 sex ratio at birth. In this model, individuals remain one sex 

 (determined randomly at birth) throughout their lifetime. 



K m =1750 (about 700 females) 



K>750 (about 300 females) 



5.000 



10.000 



1 5.000 



20,000 



Sperm number (S) 

 (in millions, about 1 to 100 males) 



Figure 2 



Fertilization rate as a function of the number of eggs and sperm per mating 

 site. The saturation parameter K m =\E+x is taken from Equation 9. 



Fishing is size but not sex selective. We assumed that males 

 mature at the same size as females. 



Parameter values 



We used previous research on California sheephead (Lab- 

 ridae, Semicossyphus pulcher), a commercially important 

 sex-changing fish, to provide evolutionarily and ecologi- 

 cally reasonable parameters for the model. Although the 

 growth, survival, and reproduction of this species have 

 been studied, less is known about the factors that induce 

 sex change and mating behavior. In this species, sex change 

 occurs at approximately 30 cm although the exact pattern 

 varies among populations (Warner, 1975; Cowen, 1990). It 

 is not known whether sex change is fixed or socially medi- 

 ated. Because nothing is known about fertilization rates in 

 the California sheephead, we generated k and y <Eq. 9) by 

 fitting a line through the estimated values of K m for small 

 and large bluehead wrasse females as a function of their 

 mean egg production (see Table 1 and Fig. 2; Warner et 

 al., 1995; Petersen et al., 2001). For parameter values and 

 sensitivity analyses see Table 1. 



Results 



We present the average across 20 simulations of the mean 

 population measures of the last 50 years for each simula- 

 tion. The variation around the mean in all measures con- 

 sidered was very low (hundredths of a percent of the mean 

 or less). For the spawning per recruit (SPR) measures we 

 give the mean value across the first 50 years of fishing to 

 ensure that the entire cohort had died before the end of the 

 simulation. When the ratio of sperm to eggs is 10 4 to 10 6 , 

 a single male can fertilize all of the eggs in the population. 

 When the ratio of sperm to eggs is 10 2 , sperm limitation 

 occurs even in the absence of fishing. Therefore, we present 

 results for the case where the ratio of sperm to eggs is 10 3 



