Fishery Bulletin 102(1) 



fecundity, and male sperm production — all of which can 

 affect stock dynamics. Thus, we cannot treat sex change as 

 an isolated aspect of a species. Instead, we must consider 

 sex change within the context of the mating system and 

 the life history of the species to make general predictions. 

 Behaviorally appropriate models are required to gener- 

 ate constructive qualitative and quantitative theory. Past 

 theory has indicated that sex-changing populations exhibit 

 stock dynamics that often differ from those of dioecious 

 populations (Bannerot et al., 1987; Huntsman and Schaaf, 

 1994; Armsworth, 2001; Fu et al, 2001 ). Furthermore, pro- 

 togynous stocks are predicted to be sensitive to fishing pat- 

 tern and may exhibit nonlinear dynamics that could lead 

 to population crashes (Armsworth, 2001). However, it is not 

 known which aspects of the mating behavior and life his- 

 tory pattern of sex-changing stocks drive these differences. 

 Here we focus on comparing a protogynous stock with an 

 otherwise identical dioecious population to determine the 

 effect of mating aggregation size, fertilization rates, and 

 life history pattern on stock dynamics. 



Size-selective (or age-selective) fisheries can impact a 

 species through a decrease in spawning stock biomass, in 

 general and through the removal of highly fecund larger 

 and older individuals, in particular (Sadovy, 2001). How- 

 ever, in protogynous species, fisheries that preferentially 

 remove large males can also change the population sex 

 ratio; however, the exact effect of fishing pressure on stock 

 dynamics in a protogynous species is complex. At one 

 extreme, the complete removal of males from the popula- 

 tion would cause a stock to crash, potentially making sex- 

 changing species more vulnerable than dioecious species 

 in the face of high fishing pressures. At the other extreme, 

 sex-changing species may be less affected by size-selective 

 fisheries if female fecundity limits recruitment and males 

 are not removed in such numbers as to reduce mating 

 or fertilization rates. Currently, there is no theory that 

 predicts the potential for sperm limitation in protogynous 

 stocks as a function of gamete production, fertilization 

 rates, and mating pattern. 



It has been suggested that marine reserves may be a vi- 

 able management option for species where highly fecund 

 older individuals are critical to reproduction (Levin and 

 Grimes, 2002). However, no theory exists that can predict 

 the impact of marine reserves on stock dynamics in sex- 

 changing species. We consider the impact of a no-take 

 marine reserve on the stock dynamics. We compare the 

 effect of setting aside 0-30% of the spawning population 

 in a reserve. We assume that larval production is exported 

 from within the reserve to the rest of the population and 

 determine whether the reserve can mediate some of the ef- 

 fects of fishing outside the reserve because this represents 

 the optimal scenario for marine reserves. We also compare 

 mean catch rates in the presence and absence of a reserve 

 as a function of fishing mortality. 



Spawning-per-recruit (SPR) measures are often used to 

 estimate the impact of fishing on a stock (Parkes, 2000; 

 Jennings et al., 2001). Ideally, a spawning-per-recruit mea- 

 sure would keep track of per-recruit production of larvae 

 or eggs (Jennings et al., 2001). However, spawning stock 

 biomass per recruit (SSBR) is commonly used to estimate 



the reproductive output per recruit at different intensities 

 of fishing. One assumes that the biomass of mature fish is 

 linearly related to reproductive output, which may be the 

 case when egg production limits biomass and fecundity in- 

 creases linearly with biomass. In protogynous stocks, over- 

 fishing of males alone may decrease fertilization rates and 

 hence reproductive output without affecting either female 

 biomass or egg production. Thus, in protogynous stocks or 

 sex-selective fisheries, classic measures of spawning per re- 

 cruit may misrepresent the impact of fishing on the stock's 

 reproduction and hence population stability (Punt et al., 

 1993). We examine a variety of per-recruit measures and 

 determine their ability to predict changes due to exploita- 

 tion in mean population size. 



In this study, we describe a general approach using sex- 

 and size-dependent individual-based simulation models 

 that predict reproduction, size distribution, and sex ratio 

 in fished populations as a function of mating system and 

 sex-change pattern. We examine the case where sex change 

 occurs at a specific size threshold. We recognize that plastic 

 and socially mediated sex-change patterns have been ob- 

 served, and our results will apply only to species with fixed 

 sex change. We explore the impact of mating aggregation 

 size, sperm production, and asymptotic fertilization rates 

 on the predicted stock dynamics in the presence of exploita- 

 tion. We make predictions regarding the effects of fishing 

 on population size, reproduction, sex ratio, size distribu- 

 tion, and fertilization rates. We also compare our results 

 to previous work and discuss future directions. 



Methods 



We used an individual-based simulation to predict the size 

 distribution, individual and population fecundity, popula- 

 tion sex ratio, fertilization rate, and population size as a 

 function of fishing mortality (Fig. 1). Individuals vary in 

 age, size, sex, and mating site. Population size varies as a 

 function of baseline survival, fishing mortality, reproduc- 

 tion, and larval recruitment. Reproduction depends on the 

 pattern of sex change, mating system, sex ratio, mating site, 

 and fecundity (or fertility) of individual males and females. 

 For each annual time period, we determined individual 

 survival, the size and age of these individuals in the next 

 time period, and the total production of surviving offspring 

 by those individuals. Initial analyses showed that a station- 

 ary size, sex, and age distribution is found within approxi- 

 mately 50 time periods and is independent of the initial 

 population conditions. Thus, we simulated 100 time periods 

 prior to examining the impact of fishing on stock dynamics 

 to ensure that the population had already reached the sta- 

 tionary size and sex distribution for that scenario and set 

 of parameters. We then examined the model for 100 repro- 

 ductive seasons in the presence of fishing with a constant 

 mean fishing mortality. Because a number of elements of 

 the model were stochastic, we examined 20 simulations for 

 each scenario and set of parameter values. Initial analyses 

 indicated that 20 simulations were more than sufficient to 

 lead to low variability in the key measures of interest. We 

 assumed that reproduction occurs at the level of the mating 



