Diverging fluctuations in a spatial five-species cyclic dominance game

TL;DR

This paper investigates a five-species cyclic dominance model on a lattice, revealing diverging fluctuations and neutrality phenomena at specific invasion rates through simulations and mean-field analysis.

Contribution

It introduces a spatial five-species predator-prey model with two invasion rates and uncovers diverging fluctuations and neutrality at critical ratios, extending understanding of cyclic dominance systems.

Findings

Diverging fluctuations occur at a specific invasion rate.

Neutrality emerges between species associations at critical points.

Mean-field analysis predicts zero-frequency oscillations.

Abstract

A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial distribution of species is governed by site exchange and invasion between the neighboring predator-prey pairs, where the cyclic symmetry can be characterized by two different invasion rates. The mean-field analysis has indicated periodic oscillations in the species densities with a frequency becoming zero for a specific ratio of invasion rates. When varying the ratio of invasion rates, the appearance of this zero-eigenvalue mode is accompanied by neutrality between the species associations. Monte Carlo simulations of the spatial system reveal diverging fluctuations at a specific invasion rate, which can be related to the vanishing dominance between all pairs of species associations.