Local approximation of a metapopulation’s equilibrium

Abstract

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset Ω of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to q1(z) , the equilibrium occupation probability in Levins’s model, at any point z∈ Ω not too close to the boundary, if the local colonization pressure and extinction rates appro..