Metapopulation moments: coupling, stochasticity and persistence.

1. Spatial heterogeneity has long been viewed as a reliable means of increasing persistence. Here, an analytical model is developed to consider the variation and, hence, the persistence of stochastic metapopulations. This model relies on a novel moment closure technique, which is equivalent to assuming log-normal distributions for the population sizes. 2. Single-species models show the greatest persistence when the mixing between subpopulations is large, so spatial heterogeneity is of no benefit. This result is confirmed by stochastic simulation of the full metapopulation. 3. In contrast, natural-enemy models exhibit the greatest persistence for intermediate levels of coupling. When the coupling is too low, there are insufficient rescue effects between the subpopulations to sustain the dynamics, whereas when the coupling is too high all spatial heterogeneity is lost. 4. The difference in behaviour between the one- and two-species models can be attributed to the oscillatory nature of the natural-enemy system.

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