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.
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Brännström, Å., Sumpter, D.J.T. Coupled map lattice approximations for spatially explicit individual-based models of ecology. Bull. Math. Biol. 67, 663–682 (2005). https://doi.org/10.1016/j.bulm.2004.09.006
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DOI: https://doi.org/10.1016/j.bulm.2004.09.006