Coupled map lattice approximations for spatially explicit individual-based models of ecology

Authored by DJT Sumpter, A Brannstrom

Date Published: 2005

DOI: 10.1016/j.bulm.2004.09.006

Sponsors: No sponsors listed

Platforms: Swarm MATLAB

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

Spatially explicit individual-based models are widely used in ecology but they are often difficult to treat analytically. Despite their intractability they often exhibit clear temporal and spatial patterning. We demonstrate how a spatially explicit individual-based model of scramble competition with local dispersal can be approximated by a stochastic coupled map lattice. The approximation disentangles the deterministic and stochastic element of local interaction and dispersal. We are thus able to understand the individual-based model through a simplified set of equations. In particular, we demonstrate that demographic noise leads to increased stability in the dynamics of locally dispersing single-species populations. The coupled map lattice approximation has general application to a range of spatially explicit individual-based models. It provides a new alternative to current approximation techniques, such as the method of moments and reaction-diffusion approximation, that captures both stochastic effects and large-scale patterning arising in individual-based models. \© 2004 Society for Mathematical Biology. Published by Elsevier Ltd. All rights reserved.

Tags

Competition Simulation Evolution Dispersal Chaos Epidemic Population-dynamics Intermediate-scale Determinism Densities