Finite metapopulation models with density–dependent migration and stochastic local dynamics

Bernt-Erik Sæther, Steinar Engen, Russell Lande

Abstract

The effects of small density–dependent migration on the dynamics of a metapopulation are studied in a model with stochastic local dynamics. We use a diffusion approximation to study how changes in the migration rate and habitat occupancy affect the rates of local colonization and extinction. If the emigration rate increases or if the immigration rate decreases with local population size, a positive expected rate of change in habitat occupancy is found for a greater range of habitat occupancies than when the migration is density–independent. In contrast, the reverse patterns of density dependence in respective emigration and immigration reduce the range of habitat occupancies where the metapopulation will be viable. This occurs because density–dependent migration strongly influences both the establishment and rescue effects in the local dynamics of metapopulations.