Effects of Environmental Heterogeneity in a Host-Parasite Coevolutionary Chase

Species-species interactions are ubiquitous and it is thought that selection is very strong in many of these interactions, resulting in reciprocal evolution by natural selection. In antagonistic coevolution, one species benefits at the cost of another, resulting in a system where selection favors the strengthening of the interaction in one species, and acts to reduce the interaction in the other species. Previous theoretical work in homogeneous systems has identified a wide range of possible behaviors (including limit cycles, heteroclinic cycles, and equilibria) as well as explored how parameters effect local adaptation in species. Here we explore how heterogeneous systems and spatial structure affect the dynamics behavior and local adaptation.