Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model.

A discrete model for a metapopulation consisting of two local populations connected by migration is described and analyzed. It is assumed that the local populations grow according to the logistic law, that both populations have the same emigration rate, and that migrants choose their new habitat patch at random. Mathematically this leads to a coupled system of two logistic equations. A complete characterization of fixed 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 populations have the same growth rate, the analysis is rigorous with complete proofs. In the nonsymmetric case, where the populations grow at different rates, the results are obtained numerically. The results are interpreted biologically. Particular attention is given to the sense in which migration has a stabilizing and synchronizing effect on local dynamics.