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

• Published in: Bulletin of mathematical biology 2005-07, Vol.67 (4), p.663-682
• Main Authors: Brännström, Å., Sumpter, D.J.T.
• Format: Article
• Language: English
• Subjects: Animals; Bees - parasitology; Ecosystem; MATEMATIK; MATHEMATICS; Mites - growth & development; Models, Biological; Numerical Analysis, Computer-Assisted; Population Dynamics; Stochastic Processes
• ISSN: 0092-8240; 1522-9602; 1522-9602
• DOI: 10.1016/j.bulm.2004.09.006

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.