Moment-closure Approximations to Levins Metapopulation Model

In this study, we apply the log-normal mixture and beta-binomial) mixture approximations to the stochastic version of the Levins metapopulation model. Mixture approximations arc able to capture the behaviour of the model around the threshold between persistence and extinction of occupied patches. Comparison with simulation results show that mixture approximations are able to predict extinction behaviour but on a shorter time seale than the simulations, describe meta-stable persistence of occupied patches but slightly underestimate the mean and describe quasiequilibrium probabilities.

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