DOES MIGRATION STABILIZE LOCAL-POPULATION DYNAMICS - ANALYSIS OF A DISCRETE METAPOPULATION MODEL

A discrete model for a metapopulation consisting of two local populati ons connected by migration is described and analyzed. It is assumed th at the local populations grow according to the logistic law, that both populations have the same emigration rate, and that migrants choose t heir new habitat patch at random. Mathematically this leads to a coupl ed system of two logistic equations. A complete characterization of fi xed point and two-periodic orbits is given, and a bifurcation analysis is performed. The region in the parameter plane where the diagonal is a global attractor is determined. In the symmetric case, where both p opulations have the same growth rate, the analysis is rigorous with co mplete proofs. In the nonsymmetric case, where the populations grow at different rates, the results are obtained numerically. The results ar e interpreted biologically. Particular attention is given to the sense in which migration has a stabilizing and synchronizing effect on loca l dynamics.