On the effects of spatial heterogeneity on the persistence of interacting species

The dynamics of two interacting theoretical populations inhabiting a heterogeneous environment are modelled by a system of two weakly coupled reaction-diffusion equations having spatially dependent reaction terms. Longterm persistence of both populations is guaranteed by an invasibility condition, which is itself expressed via the signs of certain eigenvalues of related linear elliptic operators with spatially dependent lowest order coefficients. The effects of change in these coefficients upon the eigenvalues are here exploited to study the effects of spatial heterogeneity on the persistence of interacting species through two particular ecological topics of interest. The first concerns when the location of favorable hunting grounds within the overall environment does or does not affect the success of a predator in predator-prey models, while the second concerns cases of competition models in which the outcome of competition in a spatially varying environment differs from that which would be expected in a spatially homogeneous environment.