Stochastic Skellam model

Abstract

We consider the dynamics of a biological population described by the Fisher-Kolmogorov Petrovskii-Piskunov (FKPP) equation in the case where the spatial domain consists of alternating favorable and adverse patches whose sizes are distributed randomly. For the one-dimensional case we define a stochastic analogue of the classical critical patch size We address the Issue of persistence of a population and we show that the fraction of the length of favorable segments to the total length is always smaller in the stochastic case than in a periodic arrangement. In this sense, spatial stochasticity favors viability of a population. (C) 2009 Elsevier B.V. All rights reserved.