Spatial Heterogeneity of Resources Versus Lotka-Volterra Dynamics

The problem is motivated by a consideration of two phenotypes of a species in a strongly heterogenous spatial environment. The phenotypes vary in their diffusion rates and interspecific interactions. The aim is to investigate the relative strengths of the diffusion and reaction effects. The problem is thus of competing species type, but there are many questions which arise which are not covered by standard theory. We investigate, in particular, the stability of the equilibria and the existence of coexistence solutions with emphasis on cases where the spatial variation of the environment becomes large. We discuss briefly the implications of our results for the principle of competitive exclusions and for the question of the evolution of diffusion discussed in Dockery et al. (J. Math. Biol.37 (1998), 61–83).