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arXiv · 2601.06681

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

Maciej Tadej·Ricardo Martinez-Garcia·Michael Hecht
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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.

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Maciej Tadej, Ricardo Martinez-Garcia, Michael Hecht. 2026-01-25. Extinction and persistence criteria in non-local Klausmeier model of vegetation dynamics on flat landscapes. https://arxiv.org/abs/2601.06681

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