Stochastic evolution of four species in cyclic competition

Abstract

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios, from single species domination to coexistence between non-interacting species. Using exact results and numerical simulations we discuss the temporal evolution of the system for different values of $N$, for different values of the reaction rates, as well as for different initial conditions. As expected, the stochastic evolution is found to closely follow the mean-field result for large $N$, with notable deviations appearing in proximity of extinction events. Different ways of characterizing and predicting extinction events are discussed.

19 pages, 6 figures, submitted to J. Stat. Mech

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Cited by in corpus (12)

• Stochastic population dynamics in spatially extended predator-prey systems
• Coexistence and Survival in Conservative Lotka-Volterra Networks
• Cyclic competition of four species: domains and interfaces
• Interplay between partnership formation and competition in generalized May-Leonard games
• Coarsening with non-trivial in-domain dynamics: correlations and interface fluctuations
• Extinction in four species cyclic competition
• Mobility-Dependent Selection of Competing Strategy Associations
• Spirals and coarsening patterns in the competition of many species: A complex Ginzburg-Landau approach
• Rock-paper-scissors played within competing domains in predator-prey games
• Fixation probabilities for the Moran process in evolutionary games with two strategies: graph shapes and large population asymptotics
• Environmental vs demographic variability in stochastic predator-prey models
• Travelling waves and heteroclinic networks in models of spatially-extended cyclic competition