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Updated: Oct 13, 2025

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Model of two competing populations in two habitats with migration: Application to optimal marine protected area size
Alexander Sadykov1, Keith D Farnsworth2
1School of Biological Sciences, Queen's University Belfast, Belfast, UK; The Centre for Ecological and Evolutionary Synthesis, University of Oslo, Oslo, Norway.
Abstract:
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).
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