Cyclic competition of four species: mean field theory and stochastic evolution

Abstract

Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous model, the four form alliance pairs which resemble partnership in the game of Bridge. In a finite system with discrete stochastic dynamics, all but 4 of the absorbing states consist of coexistence of a partner-pair. From a master equation, we derive a set of mean field equations of evolution. This approach predicts complex time dependence of the system and that the surviving partner-pair is the one with the larger product of their strengths (rates of consumption). Simulations typically confirm these scenarios. Beyond that, much richer behavior is revealed, including complicated extinction probabilities and non-trivial distributions of the population ratio in the surviving pair. These discoveries naturally raise a number of intriguing questions, which in turn suggests a variety of future avenues of research, especially for more realistic models of multispecies competition in nature.

arXiv comment6 pages, 4 figures, to appear in EPL

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Cited by in corpus (18)

• Cyclic dominance in evolutionary games: A review
• Stochastic population dynamics in spatially extended predator-prey systems
• Extinction in neutrally stable stochastic Lotka-Volterra models
• Coexistence and Survival in Conservative Lotka-Volterra Networks
• Effects of competition on pattern formation in the rock-paper-scissors game
• Cyclic competition of four species: domains and interfaces
• Intransitivity and coexistence in four species cyclic games
• Interplay between partnership formation and competition in generalized May-Leonard games
• Saddles, Arrows, and Spirals: Deterministic Trajectories in Cyclic Competition of Four Species
• Globally synchronized oscillations in complex cyclic games
• Stochastic evolution of four species in cyclic competition
• Extinction in four species cyclic competition
• Coarsening with non-trivial in-domain dynamics: correlations and interface fluctuations
• Mobility-Dependent Selection of Competing Strategy Associations
• Range Expansion of Heterogeneous Populations
• Synchronization and extinction in cyclic games with mixed strategies
• Rock-paper-scissors played within competing domains in predator-prey games
• Environmental vs demographic variability in stochastic predator-prey models