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We formulate a single—species model to study the dynamics of a metapopulation that is composed of several subpopulations spread among distinct patches. In the case where extinction rates within a patch are a decreasing function of population size, and all disasters lead to extinction of the local population, we determine the equilibrium distribution of numbers within patches. We show that any equilibrium is stable. This model is also applicable to some systems of mutualists, such as some plant—pollinator systems, where the focus is on the dynamics of the plant species. Unlike models for obligate mutualism that do not incorporate spatial structure, our patch model always has a stable equilibrium.
Hastings et al. (Sun,) studied this question.