# Desertification by Front Propagation?

## TL;DR

This paper investigates desertification in dryland ecosystems, demonstrating through models and numerical analysis that the final transition to bare soil is abrupt, challenging the idea of gradual front propagation as a possible pathway.

## Contribution

The study shows that in two different models, desertification occurs only as an abrupt shift, revealing the mathematical reasons behind this behavior and questioning the occurrence of gradual transitions in nature.

## Key findings

- Final desertification step is always abrupt in the models.
- Disappearance of spot-pattern domains causes the abrupt shift.
- Gradual front propagation desertification is unlikely in these models.

## Abstract

Understanding how desertification takes place in different ecosystems is an important step in attempting to forecast and prevent such transitions. Dryland ecosystems often exhibit patchy vegetation, which has been shown to be an important factor on the possible regime shifts that occur in arid regions in several model studies. In particular, both gradual shifts that occur by front propagation, and abrupt shifts where patches of vegetation vanish at once, are a possibility in dryland ecosystems due to their emergent spatial heterogeneity. However, recent theoretical work has suggested that the final step of desertification - the transition from spotted vegetation to bare soil - occurs only as an abrupt shift, but the generality of this result, and its underlying origin, remain unclear. We investigate two models that detail the dynamics of dryland vegetation using a markedly different functional structure, and find that in both models the final step of desertification can only be abrupt. Using a careful numerical analysis, we show that this behavior is associated with the disappearance of confined spot-pattern domains as stationary states, and identify the mathematical origin of this behavior. Our findings show that a gradual desertification to bare soil due to a front propagation process can not occur in these and similar models, and opens the question of whether these dynamics can take place in nature.