Extinction times in finite metapopulation models with stochastic local dynamics

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A metapopulation model with stochastic local dynamics is developed assuming a small individual migration rate and many local populations. A diffusion approximation for local population dynamics is employed to derive how rates of local extinction and colonization depend on individual migration rate and habitat occupancy in the metapopulation. For a given migration rate, increasing habitat occupancy increases numbers of migrants and the average size of local populations, which together can substantially decrease the rate of local extinction (rescue effect) and increase the rate of colonization (establishment effect). Coupling with local dynamics influences metapopulation dynamics both qualitatively and quantitatively. For some parameters, multiple equilibria may exist for habitat occupancy, with an unstable equilibrium at low habitat occupancy (a type of Allee effect at the metapopulation level) as suggested by Hanski and Gyllenberg. Decreasing local extinction rate and increasing colonization rate with increasing habitat occupancy both increase the mean time to metapopulation extinction. Large underestimates in metapopulation persistence times can result from neglecting rescue and establishment effects.

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