Noise and Correlations in a Spatial Population Model with Cyclic Competition

Tobias Reichenbach, Mauro Mobilia, and Erwin Frey
Phys. Rev. Lett. 99, 238105 – Published 7 December 2007
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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 (London) 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 spatiotemporal correlation functions and provide analytical expressions for the front velocity and the wavelength of the propagating spiral waves.

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  • Received 19 July 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.238105

©2007 American Physical Society

Authors & Affiliations

Tobias Reichenbach, Mauro Mobilia*, and Erwin Frey

  • Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany

  • *Current address: Mathematics Institute & Complexity Complex, The University of Warwick, Coventry CV4 7AL, United Kingdom.

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Issue

Vol. 99, Iss. 23 — 7 December 2007

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