Coexistence in a One-Dimensional Cyclic Dominance Process

TL;DR

This paper analyzes a one-dimensional cyclic dominance model with mutations, revealing how equilibrium and non-equilibrium processes shape the stationary state, with exact descriptions at different mutation rates and validation through simulations.

Contribution

It provides asymptotically exact descriptions of the reactive steady state in a three-species cyclic model with mutations, highlighting the interplay of different processes.

Findings

Exact descriptions of steady states at high and low mutation rates

Comparison of analytical results with stochastic lattice simulations

Insights into non-equilibrium stochastic processes

Abstract

Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium processes in the stationary state. We exploit these insights to obtain asymptotically exact descriptions of the emerging reactive steady state in the regimes of high and low mutation rates. The results are compared to stochastic lattice simulations. Our methods and findings are potentially relevant for the spatio-temporal evolution of other non-equilibrium stochastic processes.