A metapopulation model with local competitions

A metapopulation model with explicit local dynamics is studied. Unlike many patch-based metapopulation models which assume that the local population within each patch is at its equilibrium, our model incorporates population changes in local patches that interact with metapopulation dynamics. The model keeps track of the fractions of patches that have species 1 only, species 2 only, or both species. For patches with both species, the Lotka-Volterra type of competition is assumed. It is shown that when the local dynamics is coupled with the metapopulation dynamics the model outcomes can be very different comparing with metapopulation models that do not explicitly include local population dynamics. The analysis of the coupled system is carried out by using techniques in singular perturbation theory.