Limits of large metapopulations with patch dependent extinction probabilities

We propose a model for the presence/absence of a population in a collection of habitat patches. This model assumes that colonisation and extinction of the patches occur as distinct phases. Importantly, the local extinction probabilities are allowed to vary between patches. This permits an investigation of the effect of habitat degradation on the persistence of the population. The limiting behaviour of the model is examined as the number of habitat patches increases to infinity. This is done in the case where the number of patches and the initial number of occupied patches increase at the same rate and for the case where the initial number of occupied patches remains fixed.