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. [ABSTRACT FROM AUTHOR]