Noise and Correlations in a Spatial Population Model with Cyclic Competition

TL;DR

This paper investigates how noise and spatial factors influence cyclic competition among three species, revealing the emergence of spiral patterns and providing analytical insights into their dynamics.

Contribution

It introduces a comprehensive spatial model combining stochastic and deterministic approaches to analyze cyclic dominance and pattern formation.

Findings

Spiral wave patterns emerge from stochastic fluctuations and spatial diffusion.

Analytical expressions for front velocity and spiral wavelength are derived.

Correlation functions characterize the spatio-temporal dynamics of the system.

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.