Extinction and persistence criteria in non-local Klausmeier model of vegetation dynamics on flat landscapes

TL;DR

This study analyzes how non-local plant dispersal influences vegetation survival in water-limited ecosystems, revealing critical habitat sizes and biomass thresholds that determine persistence or extinction, with implications for ecosystem resilience.

Contribution

It introduces a generalized non-local Klausmeier model, establishing well-posedness and deriving new criteria for vegetation persistence and extinction based on habitat size and biomass density.

Findings

Non-local dispersal with fat-tailed kernels enhances resilience.

Critical habitat size determines extinction or survival.

Stable biomass distributions can emerge under certain conditions.

Abstract

This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a finite habitat. We establish the well-posedness of the system and provide a rigorous analysis of the conditions required for vegetation survival. Our results identify a critical patch size governed by the trade-off between local growth and boundary losses; habitats smaller than this threshold lead to inevitable extinction. Furthermore, we derive a critical maximal biomass density below which the population collapses to a desert state, regardless of the domain size. We determine stability criteria for stationary solutions and describe the emergence of stable, non-trivial biomass distributions. Numerical experiments comparing sub-Gaussian and super-Gaussian kernels confirm that non-local dispersal mechanisms, particularly those with fat tails, enhance ecosystem resilience by allowing vegetation to persist in smaller, fragmented habitats than predicted by classical local diffusion models.