Mobility and asymmetry effects in one-dimensional rock-paper-scissors games

TL;DR

This paper investigates how mobility and asymmetry influence species coexistence and dominance in one-dimensional rock-paper-scissors games, revealing complex phase behaviors and differences from nonspatial models.

Contribution

It introduces a detailed analysis of spatial rock-paper-scissors games with species-dependent rates, highlighting the effects of mobility and asymmetry on species coexistence and dominance.

Findings

Enhanced swapping rates promote coexistence in symmetric cases.

Asymmetry leads to eventual dominance by a single species.

Spatial effects can alter species dominance compared to nonspatial models.

Abstract

As the behavior of a system composed of cyclically competing species is strongly influenced by the presence of fluctuations, it is of interest to study cyclic dominance in low dimensions where these effects are the most prominent. We here discuss rock-paper-scissors games on a one-dimensional lattice where the interaction rates and the mobility can be species dependent. Allowing only single site occupation, we realize mobility by exchanging individuals of different species. When the interaction and swapping rates are symmetric, a strongly enhanced swapping rate yields an increased mixing of the species, leading to a mean-field like coexistence even in one-dimensional systems. This coexistence is transient when the rates are asymmetric, and eventually only one species will survive. Interestingly, in our spatial games the dominating species can differ from the species that would dominate in the corresponding nonspatial model. We identify different regimes in the parameter space and construct the corresponding dynamical phase diagram.