Evolution of Conditional Dispersal: ESS in Spatial Models

Adrian Lam
Mathematical Biosciences Institute, The Ohio State University

(November 29, 2012 10:20 AM - 11:15 AM)

Evolution of Conditional Dispersal: ESS in Spatial Models

Abstract

We consider a two-species reaction-diffusion-advection competition model in which the species have the same population dynamics but different dispersal strategies. Regarding the advection coefficients as movement strategies of species, we investigate their course of evolution in the game-theoretical setting. By applying invasion analysis we find that if the spatial environmental variation is less than a critical value, there is a unique evolutionarily singular strategy, which is also evolutionarily stable. If the spatial environmental variation exceeds the critical value, there can be at least three evolutionarily singular strategies, one of which is not evolutionarily stable. Our results suggest that the evolution of directed movement of organisms depends upon the spatial heterogeneity of the environment in a subtle way.