In many animals, males employ coercive mating strategies to help them maximize their expected number of offspring. In such systems, selection will favor behavioral adaptations in females that help them mitigate harassment costs and maximize their reproductive fitness. Previously, Bokides et al. [1] presented a model showing how male harassment strategies can co-evolve with female habitat preferences in a mating game. Their results indicated that if females dispersed freely between habitats where males were present and where males were excluded, selection could favor males who strategically harassed at high (or low) levels, depending on the proximity of their phenotype to a threshold level h∗h∗. This article is a continuation of that work addressing the questions of stability at equilibria where males harass at the threshold level (i.e., h∗h∗). We show these states are both locally and globally asymptotically stable. Further, we argue based on these results that h∗h∗ is an evolutionary stable male harassment level at which females will be ideally distributed to match the resource quality and social environments of their alternative habitats.
