Vegetation pattern formation induced by local growth outpacing susceptibility to non-local competition

TL;DR

This paper introduces a general framework for vegetation pattern formation in arid ecosystems, identifying two mechanisms, including a novel one, that lead to self-organized spatial patterns through Turing instabilities.

Contribution

It presents a unified analytical framework revealing two distinct mechanisms for vegetation pattern formation, including a newly identified one driven by local growth outpacing competition susceptibility.

Findings

Two mechanisms for Turing instabilities identified

Numerical simulations show stable vegetation patterns

A supercritical bifurcation leads to pattern formation

Abstract

In this work, we present and analyze a general framework for vegetation dynamics in arid and semi-arid ecosystems in which non-local interactions are purely competitive. The generality of the formulation enables a systematic search for ecological mechanisms that may lead to self-organized patterns. We identify two distinct mechanisms generating Turing instabilities across a broad class of models. The first mechanism arises from intensified competition in the areas between vegetated patches due to the cumulative pressure from their surroundings, and is well-documented in the literature. The second mechanism is novel and occurs when local growth outpaces competitive susceptibility near the uniform equilibrium. The analytical findings are complemented by numerical simulations of two benchmark models, both exhibiting a supercritical Turing bifurcation that leads to the formation of stable and robust vegetation patterns.