How multiple weak species jeopardise biodiversity in spatial rock-paper-scissors models

TL;DR

This study investigates how multiple weak species in spatial rock-paper-scissors models affect biodiversity, revealing that spatial arrangement and species positioning influence stability and coexistence.

Contribution

It introduces a detailed analysis of multi-species weak interactions in spatial models, highlighting the impact of species positioning on biodiversity stability.

Findings

Spatial organisation determines cyclic game stability.

Adjacent weak species increase biodiversity loss.

Distribution unevenness affects territorial dominance.

Abstract

We study generalised rock-paper-scissors models with an arbitrary odd number N \geq 5 of species, among which n are weak, with 2 \leq n \leq (N-1)/2. Because of the species' weakness, the probability of individuals conquering territory in the cyclic spatial game is low. Running stochastic simulations, we study the role of unevenness in the rock-paper-scissors game in spatial patterns and population dynamics, considering diverse models where the weak species are in different positions in the cyclic game order. Studying systems with five and seven species, we discover that the individuals' spatial organisation arising from the pattern formation process determines the stability of the cyclic game with multiple weak species. Our outcomes show that the presence of species unbalances the spatial distribution of organisms of the same species bringing consequences on territorial dominance, with the predominant species being determined by the position in the cyclic game order. Our simulations elucidate that, in general, the further apart the regions inhabited by different weak species are, the less the coexistence between the species is jeopardised. We show that if multiple weak species occupy adjacent spatial domains, the unevenness in the cyclic game is reinforced, maximising the chances of biodiversity loss. Our discoveries may also be helpful to biologists in comprehending systems where weak species unbalance biodiversity stability.