Evolutionary game in an androdioecious population: Coupling of outcrossing and male production

Androdioecy, the coexistence of hermaphrodites and males, is very rare in vertebrates but occurs in mangrove killifish living in ephemeral or unstable habitats. Hermaphrodites reproduce both by outcrossing with males and by selfing. Outbreeding is advantageous because of inbreeding depression, but it requires encounters with males. The advantages of a propensity for outcrossing among hermaphrodites and the production of males affect each other very strongly. To study the evolutionary coupling of these two aspects, we here analyze a simple evolutionary game for a population composed of three phenotypes: outcrossing-oriented hermaphrodites, selfing-oriented hermaphrodites, and males. Outcrossing-oriented hermaphrodites first attempt to search for males and perform outcrossing if they encounter males. If they fail to encounter males, they reproduce via selfing. Selfing-oriented hermaphrodites simply reproduce by selfing. The replicator dynamics may show bistability, in which both the androdioecious population (with outcrossing-oriented hermaphrodites and males) and the pure hermaphroditic population are locally stable. The model shows the fraction of males is either zero or relatively high (more than 25%), which is not consistent with the observed low fraction of males (less than 5%). To explain this discrepancy, we studied several models including immigration and enforced copulation. We concluded that the observed pattern can be most likely explained by a population dominated by selfing-oriented hermaphrodites receiving immigration of males.