Metapopulation moments: coupling, stochasticity and persistence

1. Spatial heterogeneity has long been viewed as a reliable means of increa sing persistence. Here, an analytical model is developed to consider the va riation and, hence, the persistence of stochastic metapopulations. This mod el relies on a novel moment closure technique, which is equivalent to assum ing log-normal distributions for the population sizes. 2. Single-species models show the greatest persistence when the mixing betw een subpopulations is large, so spatial heterogeneity is of no benefit. Thi s result is confirmed by stochastic simulation of the full metapopulation. 3. In contrast, natural-enemy models exhibit the greatest persistence for i ntermediate levels of coupling. When the coupling is too low, there are ins ufficient 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.