Change of Environment in Model Ecosystems: Effect of a Protection Zone in Diffusive Population Models

In this paper, we report some recent theoretical work of Du-Shi, Du-Liang and Du-Peng-Wang that examines the effect of environmental changes in three well-known diffusive population models, each modeling the interaction of two population species in a common habitat. For each model, we consider the situation that one of the two species is endangered and a simple protection zone is created in the habitat for the endangered species. The focus is on the effect of the protection zone on the dynamics of the two species systems. We demonstrate that, though the effects of the protection zone on the dynamical behavior of the three systems are significantly different from each other, they all share one important property, namely, there exists a critical patch size for the protection zone: If the protection zone is below this size, each model behaves similarly to the no-protection zone case, but every model undergoes profound changes in dynamical behavior once the protection zone is above the critical patch size, and in such a case the endangered species is always saved from extinction.