229 



Abstract— Predicting and under- 

 standing the dynamics of a popula- 

 tion requires knowledge of vital rates 

 such as survival, growth, and repro- 

 duction. However, these variables are 

 influenced by individual behavior, 

 and when managing exploited popu- 

 lations, it is now generally realized 

 that knowledge of a species' behav- 

 ior and life history strategies is 

 required. However, predicting and 

 understanding a response to novel 

 conditions — such as increased fish- 

 ing-induced mortality, changes in 

 environmental conditions, or specific 

 management strategies — also require 

 knowing the endogenous or exogenous 

 cues that induce phenotypic changes 

 and knowing whether these behaviors 

 and life history patterns are plastic. 

 Although a wide variety of patterns of 

 sex change have been observed in the 

 wild, it is not known how the specific 

 sex-change rule and cues that induce 

 sex change affect stock dynamics. 

 Using an individual based model, we 

 examined the effect of the sex-change 

 rule on the predicted stock dynamics, 

 the effect of mating group size, and 

 the performance of traditional spawn- 

 ing-per-recruit (SPR) measures in a 

 protogynous stock. We considered four 

 different patterns of sex change in 

 which the probability of sex change is 

 determined by 1) the absolute size of 

 the individual, 2) the relative length 

 of individuals at the mating site, 3) 

 the frequency of smaller individuals 

 at the mating site, and 4) expected 

 reproductive success. All four pat- 

 terns of sex change have distinct 

 stock dynamics. Although each sex- 

 change rule leads to the prediction 

 that the stock will be sensitive to the 

 size-selective fishing pattern and may 

 crash if too many reproductive size 

 classes are fished, the performance of 

 traditional spawning-per-recruit mea- 

 sures, the fishing pattern that leads 

 to the greatest yield, and the effect of 

 mating group size all differ distinctly 

 for the four sex-change rules. These 

 results indicate that the management 

 of individual species requires knowl- 

 edge of whether sex change occurs, 

 as well as an understanding of the 

 endogenous or exogenous cues that 

 induce sex change. 



Manuscript submitted 22 September 2003 

 to the Scientific Editor's Office. 



Manuscript approved for publication 



20 December 2004 by the Scientific Editor. 



Fish. Bull. 103:229-245 (2005). 



Sex-change rules, stock dynamics, 



and the performance of spawning-per-recruit 



measures in protogynous stocks 



Suzanne H. Alonzo 



Institute ol Marine Sciences and the Center for Stock Assessment Research (CSTAR) 



University of California Santa Cruz 



1156 High Street 



Santa Cruz. California 95064 



Present address: Department of Ecology and Evolutionary Biology 



Yale University 



165 Prospect St., OML 427 



New Haven, Connecticut 06511 

 Email address Suzanne Alonzoia'yaleedu 



Marc Mangel 



Department of Applied Mathematics and Statistics 



Jack Baskm School of Engineering and the Center for Stock Assessment Research (CSTAR) 



University of California Santa Cruz 



1156 High Street 



Santa Cruz California 95064 



Growth, survival, and reproduction 

 all affect the dynamics of a population 

 and its response to fishing and man- 

 agement (Quinn and Deriso, 1999; 

 Haddon, 2001). However, these three 

 key variables are influenced by many 

 aspects of a species' biology, environ- 

 ment, and evolutionary history. There 

 is an increasing realization that the 

 management of populations requires 

 an understanding of their behavior, 

 life history strategies, and repro- 

 ductive patterns (Sutherland, 1990; 

 Huntsman and Schaaf, 1994; Col- 

 lins et al„ 1996; Greene et al„ 1998; 

 Sutherland, 1998; Beets and Fried- 

 lander, 1999; Coleman et al., 1999; 

 Fulton et al., 1999; Kruuk et al., 

 1999; Constable et al., 2000; Cowen 

 et al., 2000; Koeller et al„ 2000; Fu 

 et al., 2001; Apostolaki et al., 2002; 

 Levin and Grimes, 2002). Although it 

 is important to document the normal 

 patterns of behavior and reproduction 

 within a population, predicting and 

 understanding a stock's response to 

 novel conditions also requires knowl- 

 edge of the degree of plasticity in 

 behaviors that affect growth, survival, 

 and reproduction, and the cues that 

 induce phenotypic changes. Numer- 

 ous examples exist of context- and 

 condition-dependent behavior in fish 



(e.g., Metcalfe et al., 1989; Snyder and 

 Dingle, 1990; Schultz and Warner, 

 1991; Wainwright et al., 1991; Mit- 

 telbach et al., 1992; Nishibori and 

 Kawata, 1993; Ridgeway and Shuter, 

 1994; Breden et al., 1995), and this 

 kind of plasticity has the potential 

 to affect the dynamics of a stock. For 

 example, many commercially impor- 

 tant species of fish change sex from 

 female to male. Researchers have 

 argued that this life history pat- 

 tern will lead to different population 

 dynamics and responses to fishing and 

 management strategies than will the 

 life history pattern of dioecious (sep- 

 arate-sex) species (e.g., Snyder and 

 Dingle, 1990; Schultz and Warner, 

 1991; Wainwright et al., 1991; Nishi- 

 bori and Kawata, 1993; Ridgeway and 

 Shuter, 1994; Alonzo and Mangel, 

 2004). However, it is important to 

 consider not only whether sex change 

 occurs, but also how it occurs; whether 

 plasticity in sex change exists and 

 what cues determine sex change in 

 an individual species. 



A variety of patterns of sex change 

 have been observed in the wild (War- 

 ner and Lejeune, 1985; Charnov, 

 1986; Shapiro, 1987; Charnov and 

 Bull, 1989; Iwasa, 1990; Warner and 

 Swearer, 1991; Lutnesky, 1994, 1996; 



