Assessing the robustness of spatial pattern sequences in a dryland vegetation model

TL;DR

This paper investigates the robustness of a specific pattern sequence in dryland vegetation models, demonstrating that a bifurcation-theoretic quantity can predict pattern transitions across parameter variations, supporting its use as an early desertification indicator.

Contribution

It introduces a bifurcation-based approach to assess the robustness of pattern sequences in vegetation models, providing a methodology applicable to various formulations.

Findings

The pattern sequence is robust across a range of parameters.

A bifurcation-theoretic quantity correlates with pattern transitions.

The approach can evaluate early desertification indicators.

Abstract

A particular sequence of patterns, "$\text{gaps} \to \text{labyrinth} \to \text{spots}$," occurs with decreasing precipitation in previously reported numerical simulations of PDE dryland vegetation models. These observations have led to the suggestion that this sequence of patterns can serve as an early indicator of desertification in some ecosystems. Since parameter values can take on a range of plausible values in the vegetation models, it is important to investigate whether the pattern sequence prediction is robust to variation. For a particular model, we find that a quantity calculated via bifurcation-theoretic analysis appears to serve as a proxy for the pattern sequences that occur in numerical simulations across a range of parameter values. We find in further analysis that the quantity takes on values consistent with the standard sequence in an ecologically relevant limit of the model parameter values. This suggests that the standard sequence is a robust prediction of the model, and we conclude by proposing a methodology for assessing the robustness of the standard sequence in other models and formulations.