Replicator-dynamics models of sexual conflict.

Evolutionary conflict between the sexes has been studied in various taxa and in various contexts. When the sexes are in conflict over mating rates, natural selection favors both males that induce higher mating rates and females that are more successful at resisting mating attempts. Such sexual conflict may result in an escalating coevolutionary arms race between males and females. In this article, we develop simple replicator-dynamics models of sexual conflict in order to investigate its evolutionary dynamics. Two specific models of the dependence of a female's fitness on her number of matings are considered: in model 1, female fitness decreases linearly with increasing number of matings and in model 2, there is an optimal number of matings that maximizes female fitness. For each of these models, we obtain the conditions for a coevolutionary process to establish costly male and female traits and examine under what circumstances polymorphism is maintained at equilibrium. Then we discuss how assumptions in previous models of sexual conflict are translated to fit to our model framework and compare our results with those of the previous studies. The simplicity of our models allows us to consider sexual conflict in various contexts within a single framework. In addition, we find that our model 2 shows more complicated evolutionary dynamics than model 1. In particular, the population exhibits bistability, where the evolutionary outcome depends on the initial state, only in model 2.