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response and intracellular delay
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.