Modeling sexual selection in T\'ungara frog and rationality of mate choice

Abstract

The males of the specie of frogs Engystomops pustulosus produce simple and com- plex calls to lure females, as a way of Intersexual selection. Complex calls lead males to a greater reproductive success than simple calls do. However, the complex calls are also more attractive to the main predator of these amphibians, the bat Trachops cirrhosus. Therefore, as M. Ryan suggests, the complexity of the calls let the frogs keep a trade off between reproductive success and predation. In this paper, we first propose to model the proportion of simple to complex calls as a symmetric game of two strategies. We also propose a model with three strategies (simple callers, complex callers and quiet males), where we assess the effect of a male that keeps quiet and intercepts females, which would play a role of Intrasexual selection. We analyze the stable points of the replicator equations of the models that we propose. Under the assumption that the decision of the males takes into account this trade off between reproductive success and predation, our model reproduces the observed behavior reported in the literature with minimal assumption on the parameters. From the three strategies model, we verify that the quiet strategy could only coexists with the simple and complex strategies as long as the rate at which quiet males intercept females is high. We conclude that the reproductive strategy of the male frog Engystomops pustulosus is rational.