Noise and correlations in a spatial population model with cyclic competition

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 , 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.