ON THE EFFECTS OF SPATIAL HETEROGENEITY ON THE PERSISTENCE OF INTERACTING SPECIES

The dynamics of two interacting theoretical populations inhabiting a h eterogeneous environment are modelled by a system of two weakly couple d reaction-diffusion equations having spatially dependent reaction ter ms. Longterm persistence of both populations is guaranteed by an invas ibility condition, which is itself expressed via the signs of certain eigenvalues of related linear elliptic operators with spatially depend ent lowest order coefficients. The effects of change in these coeffici ents upon the eigenvalues are here exploited to study the effects of s patial 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 environm ent does or does not affect the success of a predator in predator-prey models, while the second concerns cases of competition models in whic h the outcome of competition in a spatially varying environment differ s from that which would be expected in a spatially homogeneous environ ment.