A general structured model of a hermaphrodite population

Both empirical and theoretical studies, have dealt with the question how to best optimize reproductive fitness for hermaphrodites, using models such as game theory or complicated energetic costs and benefits of mating displays. However, hermaphrodites exhibit a broad spectrum of sexual behaviors like simultaneous, sequential or lifetime gonochorist that cannot be explained using a unique formalism. A possible explanation of this diversity relies on the way these species maximize their fitness: Does the individual hermaphrodite split its time between strategies maximizing its instantaneous reproductive fitness or its evolutionary fitness? Here, we compare these two points of view and extend a game theoretical formalism to a sex allocation model that underlies all sexual behaviors as a result of a dynamic game whose payoff depends on the costs and benefits of sexual reproduction. Using this formalism, we prove that a simultaneous hermaphrodites strategy is stable even for high values of sex changing costs. Moreover, we prove that the stability of a sequential hermaphrodite is linked to the average energy allocated to the pure female strategy.