Model of two competing populations in two habitats with migration: Application to optimal marine protected area size

The standard model of a single population fragmented into two patches connected by migration, was first introduced in the 1970s by Freedman and Waltman, since generating long-term research interest, though its full analysis for arbitrary values of migration rate has only been completed relatively recently. Here, we present a model of two competing species in a two-patch habitat with migrations between patches. We derive equilibrium solutions of this model for three cases of migration rate resulting in isolated, well-mixed and semi-isolated habitats. We evaluate the full range of effects of habitat, life-history and migration parameters on population sizes. Finally, we add harvesting mortality and define conditions under which introduction of a no-harvesting (protected) area may lead to increased maximum sustainable yield. The results have applications in mixed fishery management and the design of wildlife protection zones, including marine protected areas (MPAs). •We consider a system of two competing populations with asymmetric migrations between two habitats.•We obtain equilibrium population sizes for zero, sufficiently small and infinite migration rates.•The coexistence condition for two competing species in a perfectly mixed habitat is derived.•Harvest mortality is added to the system and the maximum sustainable yield (MSY) is calculated.•The conditions under which a no-harvesting zone (e.g., marine protected area) can increase MSY are evaluated.