Using moment equations to understand stochastically driven spatial pattern formation in ecological systems

Benjamin Bolker, Stephen Wilson Pacala

Research output: Contribution to journalArticle

296 Scopus citations

Abstract

Spatial patterns in biological populations and the effect of spatial patterns 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 s new approach to modeling spatial interactions by deriving approximations for the time evolution of the moments (mean end spatial covariance) of ensembles of distributions of organisms; the analysis is made possible by 'moment closure,' neglecting higher-order spatial structure in the population. We use the growth and competition of plants in an explicitly spatial environment as a starting point for exploring the properties of second-order moment equations 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-covariance model provides a useful and analytically tractable approximation to the stochastic spatial model, and combines useful features of stochastic models and traditional reaction-diffusion-like models.

Original languageEnglish (US)
Pages (from-to)179-197
Number of pages19
JournalTheoretical Population Biology
Volume52
Issue number3
DOIs
StatePublished - Jan 1 1997

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics

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