Evaluating the impacts of fishing on sex-changing fish: a game-theoretic approach

Abstract

Abstract Sex change has been widely documented in many commercially and recreationally important fish species, yet the implications of this life history trait are not considered in most stock assessments. This omission can lead to poor estimates of parameters vital to understanding the health of sequentially hermaphroditic stocks. Here, we present a game theoretic approach to model the sex changing behaviour of a stock of protogynous (female first) hermaphroditic fish and produce estimates of maximum sustainable yield (MSY), equilibrium biomass at MSY (BMSY) and sex ratio, then compare these reference points to those from an otherwise identical gonochoristic (non-sex changing) stock. We tested each stock at varying levels of exploitation and with a range of assumptions about how sex ratio impacts fertilization rate. We show that a protogynous hermaphroditic stock with flexible timing of sex change produces similar MSY and slightly higher BMSY than a gonochoristic stock with otherwise identical vital rates. Sex changing stocks were also able to maintain a higher proportion of males in the population than did non-sex changing stocks as exploitation increased. Although sex changing stocks were able to maintain their sex ratio, the age at which females changed sex decreased with increased exploitation, suggesting smaller body size, and presumably lower fecundity, for females in heavily exploited sex changing stocks. Our game theoretic approach to evaluating hermaphroditic stocks can accommodate a wide variety of sex changing cues and behaviours and allows a flexible model for understanding the effects of exploitation on hermaphroditic stocks.