Metastability as a coexistence mechanism in a model for dryland vegetation patterns

TL;DR

This paper investigates how vegetation species coexist in water-scarce environments through a reaction-diffusion model, revealing metastable states that allow long-term coexistence despite instability.

Contribution

It introduces a two-species reaction-diffusion model extending the Klausmeier model to analyze metastable coexistence states in dryland vegetation.

Findings

Coexistence supported by small fitness differences.

Metastable states last over 1000 years.

Two mechanisms for metastability identified.

Abstract

Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model based on the single-species Klausmeier model, to analytically investigate the existence of states in which both species coexist. Ecologically, the study finds that coexistence is supported if there is a small difference in the plant species' average fitness, measured by the ratio of a species' capabilities to convert water into new biomass to its mortality rate. Mathematically, coexistence is not a stable solution of the system, but both spatially uniform and patterned coexistence states occur as metastable states. In this context, a metastable solution in which both species coexist corresponds to a long transient (exceeding $10^3$ years in dimensional parameters) to a stable one-species state. This behaviour is characterised by the small size of a positive eigenvalue which has the same order of magnitude as the average fitness difference between the two species. Two mechanisms causing the occurrence of metastable solutions are established: a spatially uniform unstable equilibrium and a stable one-species pattern which is unstable to the introduction of a competitor. We further discuss effects of asymmetric interspecific competition (e.g. shading) on the metastability property.