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Understanding the dynamics of metapopulations close to extinction is of vitalimportance for management. Levins-like models, in which local patches aretreated as either occupied or empty, have been used extensively for thispurpose, but they ignore the important role of local population dynamics. Inthis paper, we consider a stochastic metapopulation model where localpopulations follow a Ricker dynamics, and use this framework to investigate thebehaviour of the metapopulation at the brink of extinction. As long asdispersal rates are not too large, the system is shown to have a time evolutionconsistent with Levins' dynamics. We derive analytical expressions for thecolonisation and extinction rates (c and e) in Levins-type models in terms ofreproduction, survival, and dispersal parameters of the local populations,providing an avenue to parameterising Levins-like models from the type ofinformation on local demography that is available for a number of species. Tofacilitate applying our results, we provide a numerical implementation forcomputing c and e.

How Levins' dynamics emerges from a Ricker metapopulation model on the brink of extinction