Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games

TL;DR

This paper investigates how mobility affects biodiversity in rock-paper-scissors ecological models, revealing a critical threshold beyond which species coexistence is lost, impacting ecological stability and pattern formation.

Contribution

It demonstrates that mobility can both promote and jeopardize biodiversity, identifying a critical mobility threshold affecting species coexistence in cyclic competition models.

Findings

Biodiversity is maintained below a critical mobility threshold.

Exceeding this threshold leads to loss of species diversity.

Traveling spiral wave patterns emerge in the coexistence regime.

Abstract

Biodiversity is essential to the viability of ecological systems. Species diversity in ecosystems is promoted by cyclic, non-hierarchical interactions among competing populations. Such non-transitive relations lead to an evolution with central features represented by the `rock-paper-scissors' game, where rock crushes scissors, scissors cut paper, and paper wraps rock. In combination with spatial dispersal of static populations, this type of competition results in the stable coexistence of all species and the long-term maintenance of biodiversity. However, population mobility is a central feature of real ecosystems: animals migrate, bacteria run and tumble. Here, we observe a critical influence of mobility on species diversity. When mobility exceeds a certain value, biodiversity is jeopardized and lost. In contrast, below this critical threshold all subpopulations coexist and an entanglement of travelling spiral waves forms in the course of temporal evolution. We establish that this phenomenon is robust, it does not depend on the details of cyclic competition or spatial environment. These findings have important implications for maintenance and evolution of ecological systems and are relevant for the formation and propagation of patterns in excitable media, such as chemical kinetics or epidemic outbreaks.