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arXiv · 0710.0383

Noise and Correlations in a Spatial Population Model with Cyclic Competition

Tobias Reichenbach·Mauro Mobilia·Erwin Frey
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Abstract

Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al., Nature {\bf 418}, 171 (2002)]. To reach a better theoretical understanding of these phenomena, we consider a paradigmatic spatial model where three species exhibit cyclic dominance. Using an individual-based description, as well as stochastic partial differential and deterministic reaction-diffusion equations, we account for stochastic fluctuations and spatial diffusion at different levels, and show how fascinating patterns of entangled spirals emerge. We rationalize our analysis by computing the spatio-temporal correlation functions and provide analytical expressions for the front velocity and the wavelength of the propagating spiral waves.

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Tobias Reichenbach, Mauro Mobilia, Erwin Frey. 2007-12-08. Noise and Correlations in a Spatial Population Model with Cyclic Competition. https://doi.org/10.1103/physrevlett.99.238105

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