Uneven rock-paper-scissors models: Patterns and coexistence

¹ Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte - Caixa Postal 1524, 59072-970, Natal, RN, Brazil
² Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam - Science Park 904, 1098 XH Amsterdam, The Netherlands
³ Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte 59078-970, Natal, RN, Brazil

Received: 11 March 2019
Accepted: 12 April 2019

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.