Species Diversity in Rock-Paper-Scissors Game Coupling with Levy Flight

TL;DR

This study explores how long-range Levy flight interactions influence species coexistence and biodiversity in a spatial rock-paper-scissors game, revealing critical conditions and pattern formations.

Contribution

It introduces the effect of Levy flight-based long-range interactions into the RPS model, extending previous nearest-neighbor studies and analyzing their impact on biodiversity.

Findings

Long-range Levy flights affect species coexistence conditions.

Critical curves for stable coexistence are identified.

Levy flights significantly influence spatiotemporal patterns.

Abstract

Rock-paper-scissors (RPS) game is a nice model to study the biodiversity in ecosystem. However, the previous studies only consider the nearest- neighbor- interaction among the species. In this paper, taking the long range migration into account, the effects of the interplay between nearest-neighbor-interaction and long-range-interaction of Levy flight obey the power law distance distribution with the exponent h (-0.3<h<-0.1) in spatial RPS game is investigated. Taking the probability of long range Levy flight and the power exponent as parameters, the coexistence conditions of three species are found. The critical curves for stable coexistence of three species in the parameters space are presented. It is also found that long-range-interaction with Levy flight has interesting effects on the final spatiotemporal pattern of the system. The results reveal that the long-range-interaction of Levy flight exhibit pronounced effects on biodiversity of ecosystem.