Uneven rock-paper-scissors models: patterns and coexistence

Abstract

We study a class of the stochastic May-Leonard models, with three species dominating each other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. We introduce an unevenness in the system, by considering that one of the species is weaker because of a lower selection probability. The simulation results show that the pattern formation is drastically affected by the presence of the weaker species, with no spiral waves arising immediately from random initial conditions. Instead, single-species spatial domains cyclically dominate the entire territory until a region occupied by the weaker species is sufficiently narrow to be crossed by individuals without being selected. This leads to the appearance of spatial patterns responsible for the species coexistence. We verify that the asymmetry in the selection probabilities leads to different spatial autocorrelation function and average relative species abundances. Finally, we investigate the coexistence probability and show that the surviving species depends on the level of unevenness of the model and the mobility of individuals.

6 pages, 7 figures

References in corpus (8)

• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Cyclic dominance in evolutionary games: A review
• Self-Organization of Mobile Populations in Cyclic Competition
• Stochastic population dynamics in spatially extended predator-prey systems
• Spatial Rock-Paper-Scissors Models with Inhomogeneous Reaction Rates
• Junctions and spiral patterns in Rock-Paper-Scissors type models
• Phase transitions induced by variation of invasion rates in spatial cyclic predator-prey models with four or six species
• The LHC Inverse Problem, Supersymmetry, and the ILC