Effect of mobility in the rock-paper-scissor dynamics with high mortality

TL;DR

This paper investigates how mobility and natural death influence the coexistence and extinction dynamics in a spatial rock-paper-scissor model, revealing complex patterns and scenarios through Monte Carlo simulations.

Contribution

It introduces a detailed simulation study of the combined effects of mortality and mobility in a spatial RPS model, highlighting new coexistence and extinction behaviors.

Findings

Emergence of spiral patterns with diffusion.

Death rate and diffusion jointly affect coexistence.

New scenarios of species extinction and coexistence.

Abstract

In the evolutionary dynamics of a rock-paper-scissor (RPS) model, the effect of natural death plays a major role in determining the fate of the system. Coexistence, being an unstable fixed point of the model becomes very sensitive towards this parameter. In order to study the effect of mobility in such a system which has explicit dependence on mortality, we perform Monte Carlo simulation on a $2$-dimensional lattice having three cyclically-competing species. The spatio-temporal dynamics has been studied along with the two-site correlation function. Spatial distribution exhibits emergence of spiral patterns in the presence of diffusion. It reveals that the joint effect of death rate and diffusion (migration) leads to new coexistence and extinction scenarios.