A metapopulation model with local competitions

A metapopulation model with explicit local dynamics is studied.Unlike many patch-based metapopulation models which assume thatthe 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 havespecies 1 only, species 2 only, or both species. For patcheswith both species, the Lotka-Volterra type of competition isassumed. It is shown that when the local dynamics is coupledwith the metapopulation dynamics the model outcomes can be verydifferent comparing with metapopulation models that do notexplicitly include local population dynamics. The analysis ofthe coupled system is carried out by using techniques in singularperturbation theory.