Labyrinthine clustering in a spatial rock-paper-scissors ecosystem

TL;DR

This paper investigates how spatial structures like labyrinthine clusters in a rock-paper-scissors ecosystem can stabilize biodiversity, especially under slow growth conditions, by analyzing cluster distributions and feedback loops.

Contribution

It introduces a new statistical measure to quantify clustering and explains how labyrinthine configurations slow dynamics and promote stability in the ecosystem.

Findings

Labyrinthine clusters form when one species grows slowly.

Heavy-tailed cluster size distributions are observed.

Clustering stabilizes the ecosystem through spatial feedback loops.

Abstract

The spatial rock-paper-scissors ecosystem, where three species interact cyclically, is a model example of how spatial structure can maintain biodiversity. We here consider such a system for a broad range of interaction rates. When one species grows very slowly, this species and its prey dominate the system by self-organizing into a labyrinthine configuration in which the third species propagates. The cluster size distributions of the two dominating species have heavy tails and the configuration is stabilized through a complex, spatial feedback loop. We introduce a new statistical measure that quantifies the amount of clustering in the spatial system by comparison with its mean field approximation. Hereby, we are able to quantitatively explain how the labyrinthine configuration slows down the dynamics and stabilizes the system.