Rock-paper-scissors models with a preferred mobility direction

¹ Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto Rua do Campo Alegre s/n, 4169-007 Porto, Portugal
² Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP Rua das Estrelas, 4150-762 Porto, Portugal
³ School of Physics and Astronomy, University of Birmingham - Birmingham B15 2TT, UK
⁴ Departamento de Física, Universidade Estadual de Maringá - 87020-900 Maringá, PR, Brazil

Received: 22 September 2020
Accepted: 28 October 2020

Abstract

We investigate a modified spatial stochastic Lotka-Volterra formulation of the rock-paper-scissors model using off-lattice stochastic simulations. In this model one of the species moves preferentially in a specific direction —the level of preference being controlled by a noise strength parameter ( and corresponding to total preference and no preference, respectively)— while the other two species have no preferred direction of motion. We study the behaviour of the system starting from random initial conditions, showing that the species with asymmetric mobility has always an advantage over its predator. We also determine the optimal value of the noise strength parameter which gives the maximum advantage to that species. Finally, we find that the critical number of individuals, below which the probability of extinction becomes significant, decreases as the noise level increases, thus showing that the addition of a preferred mobility direction studied in the present letter does not favour coexistence.