USING MOMENT EQUATIONS TO UNDERSTAND STOCHASTICALLY DRIVEN SPATIAL PATTERN-FORMATION IN ECOLOGICAL-SYSTEMS

Spatial patterns in biological populations and the effect of spatial p atterns on ecological interactions are central topics in mathematical ecology. Various approaches to modeling have been developed to enable us to understand spatial patterns ranging from plant distributions to plankton aggregation. We present a new approach to modeling spatial in teractions by deriving approximations for the time evolution of the mo ments (mean and spatial covariance) of ensembles of distributions of o rganisms; the analysis is made possible by ''moment closure,'' neglect ing higher-order spatial structure in the population. We use the growt h and competition of plants in an explicitly spatial environment as a starting point for exploring the properties of second-order moment equ ations and comparing them to realizations of spatial stochastic models . We find that for a wide range of effective neighborhood sizes (each plant interacting with several to dozens of neighbors), the mean-covar iance model provides a useful and analytically tractable approximation to the stochastic spatial model. and combines useful features of stoc hastic models and traditional reaction-diffusion-like models. (C) 1997 Academic Press.