The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games

TL;DR

This paper investigates how varying mobility rates affect the formation and stability of spiral wave patterns in a spatial rock-paper-scissors game model, revealing finite mobility ranges for pattern persistence.

Contribution

It introduces an individual-based metapopulation model to analyze the impact of mobility, mutations, and dominance-replacement on spiral wave emergence and stability.

Findings

Spiral waves occur only within a finite mobility range in lattice simulations.

Low mobility leads to convective instability and pattern breakup.

Deterministic equations predict spiral waves, but stochastic effects limit their appearance.

Abstract

We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance (dominance-removal and dominance-replacement), mutations, and pair-exchange of neighboring individuals. Here, we study the influence of mobility on the emerging patterns and investigate when the pair-exchange rate is responsible for spiral waves to become elusive in stochastic lattice simulations. In particular, we show that the spiral waves predicted by the system's deterministic partial equations are found in lattice simulations only within a finite range of the mobility rate. We also report that in the absence of mutations and dominance-replacement, the resulting spiraling patterns are subject to convective instability and far-field breakup at low mobility rate. Possible applications of these resolution and far-field breakup phenomena are discussed.