A discrete Markov metapopulation model for persistence and extinction of species. (7th September 2016) - Thompson, Colin J.; Shtilerman, Elad; Stone, Lewi
Abstract: A simple discrete generation Markov metapopulation model is formulated for studying the persistence and extinction dynamics of a species in a given region which is divided into a large number of sites or patches. Assuming a linear site occupancy probability from one generation to the next we obtain exact expressions for the time evolution of the expected number of occupied sites and the mean-time to extinction (MTE). Under quite general conditions we show that the MTE, to leading order, is proportional to the logarithm of the initial number of occupied sites and in precise agreement with similar expressions for continuous time-dependent stochastic models. Our key contribution is a novel application of generating function techniques and simple asymptotic methods to obtain a second order asymptotic expression for the MTE which is extremely accurate over the entire range of model parameter values. Abstract : Highlights: A new model of metapopulation dynamics is formulated. Conditions for species persistence and extinction are obtained. A generating function approach is employed to calculate the mean time to extinction. Predicted mean extinction time is improved using a second order asymptotic expansion. Results of the parallel deterministic process carry over to the stochastic process.