Should a park be an island?

The object of this article is to study the interaction of interspecies competition and environmental heterogeneity in the context of refuge or preserve design. Specifically, situations in which the primary preserve is surrounded by partially disrupted secondary successional environments are compared to those in which the surroundings of the preserve are completely disrupted and hence inhospitable to both primary and secondary biomes. The somewhat surprising conclusion is reached (suggested in the ecological literature) that in some cases complete disruption of surroundings is preferable to partial disruption if the partially disrupted `buffer zones' benefit some species more than their competitors. The modelling approach is based on reaction-diffusion equations with variable coefficients, and the analysis relies on finding criteria for coexistence or extinction in terms of elliptic eigenvalue problems and then estimating the eigenvalues in terms of environmental parameters.