Evolutionary dynamics of single species model with Allee effects and aposematism

Abstract

A single species population model subject to additive Allee effects, due to predation satiation is proposed and analyzed by considering a continuous strategy evolutionary game theory (EGT). Moreover, we consider the aposematic behavior of the population. We assume a single trait that affects aposematic behavior and saturation constant, following the Gaussian distribution. First, we analyze our single species deterministic model in global perspective. Then, we consider the aposematism parameter and saturation constant are functions of a mean phenotypic trait subject to evolution and formulate a model that describes the coupled population and mean trait dynamics. We can see that the extinction equilibrium also can be an evolutionary stable strategy (ESS) depending on the evolutionary functional forms. The ratio of variation in aposematic behavior and saturation constant phenotypes has some important role in the equilibria stability and ESS conditions of our evolutionary model. We find the ESS conditions for all equilibria and numerical simulation suggests that our evolutionary model can have multiple ESSs.