Instability of spatial patterns and its ambiguous impact on species diversity

TL;DR

This paper studies how spatial pattern instability near a bifurcation point affects species diversity, revealing that medium mobility can cause extinction, while low mobility promotes diversity, analyzed through a complex Ginzburg-Landau framework.

Contribution

It provides a quantitative analysis of pattern formation and stability near a bifurcation point in ecological systems with cyclic dominance, highlighting the impact on species diversity.

Findings

Medium mobility leads to rapid species extinction.

Low mobility promotes species diversity.

High mobility renders spatial patterns irrelevant.

Abstract

Self-arrangement of individuals into spatial patterns often accompanies and promotes species diversity in ecological systems. Here, we investigate pattern formation arising from cyclic dominance of three species, operating near a bifurcation point. In its vicinity, an Eckhaus instability occurs, leading to convectively unstable "blurred" patterns. At the bifurcation point, stochastic effects dominate and induce counterintuitive effects on diversity: Large patterns, emerging for medium values of individuals' mobility, lead to rapid species extinction, while small patterns (low mobility) promote diversity, and high mobilities render spatial structures irrelevant. We provide a quantitative analysis of these phenomena, employing a complex Ginzburg-Landau equation.