Multiplicative moments and measures of persistence in ecology

Ecologists and epidemiologists have begun focusing on demographic stochasti city and spatial heterogeneity as important biological factors. With high-p owered computers simulation of such systems is a common modelling technique ; however we lack a detailed understanding of the processes involved. Momen t closure approximations provide a simple method which can be used to captu re the main features of a wide variety of stochastic models and to gain a m ore intuitive understanding. In this paper we give an alternative variation based on multiplicative moments which is equivalent to taking a novel thir d-order cumulant approximation. The differential equations for these multip licative moments are far more robust than their additive counterparts. We u se this technique to consider the behaviour and persistence of finite metap opulations for two common ecological systems. (C) 2000 Academic Press.