Abstract: Many species of teleost fish live in coral reefs and change sex depending on their social status; some even demonstrate sex change in both directions. Typically, in the absence of a more dominant competitive individual, the fish functions as a male; however, when a more competitively superior individual arrives, the focal fish becomes a female. Among these bidirectional sex changers, there are species that retain the gonads of the currently nonfunctional sex, i.e., a male retains female reproductive tissues or a female retains male reproductive tissues. We construct a game-theoretic model and examine the conditions under which gonads of both the functional and the nonfunctional sex would be kept. We observe that a focal fish always retains both gonads when the social conditions change frequently in either direction, while it retains only the gonads of the currently functional sex when there is an infrequent change of social conditions. However, in order to explain the observed patterns of a monogamous goby Paragobiodon echinocephalus that undergoes a complete reconstruction of the entire gonad during sex change and a polygynous goby Trimma okinawae that retains the gonad of the nonfunctional sex, we need to assume that the cost of a male retaining the female gonad is much less than that of a female retaining a male gonad. We argue that this assumption is plausible given structural differences in male and female fitness payoffs. Significance Statement: Among coral fish that exhibit bidirectional sex change, some retain the gonad of the nonfunctional sex as well as the current sex, while others exhibit the gonad of the current sex only. A game-theoretic model was developed to investigate under what conditions we might expect a bidirectional sex changer should keep the gonad of the nonfunctional sex. The frequency of sex change opportunity, the time required to reconstruct the gonad, and the maintenance cost all affect the evolution of gonad retention. A quantitative parameterization of the model for well-studied species concluded that the cost for a male to keep a female gonad must be much smaller than the cost for a female to retain a male gonad. The results demonstrated the importance of combining physiological and morphological aspects in the evolutionary ecology of sex changing fish.
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