# Spatial modeling of forest-savanna bistability: impacts of fire dynamics and timescale separation

## TL;DR

This paper explores how fire dynamics and vegetation regrowth influence the coexistence of forests and savannas in tropical ecosystems.

## Contribution

The study introduces a spatial stochastic model that explicitly integrates fire dynamics and vegetation regrowth to explain forest-savanna bistability.

## Key findings

- Bistability arises from periodic fires maintaining low forest cover and dense forests inhibiting fire spread.
- Deterministic mean-field models predict bistability but differ in transient dynamics from spatial models.
- Timescale separation between fire and vegetation processes is critical for ecosystem resilience.

## Abstract

Forest-savanna bistability – the hypothesis that forests and savannas exist as alternative stable states in the tropics – and its implications are key challenges for mathematical modelers and ecologists in the context of ongoing climate change. To generate new insights into this problem, we present a spatial Markov jump process model of savanna forest fires that integrates key ecological processes, including seed dispersal, fire spread, and non-linear vegetation flammability. In contrast to many models of forest-savanna bistability, we explicitly model both fire dynamics and vegetation regrowth in a mathematically tractable framework. This approach bridges the gap between slow-timescale vegetation models and highly resolved fire dynamics, shedding light on the influence of short-term and transient processes on vegetation cover. In our spatial stochastic model, bistability arises from periodic fires that maintain low forest cover, whereas dense forest areas inhibit fire spread and preserve high tree density. The deterministic mean-field approximation of the model similarly predicts bistability, but deviates quantitatively from the fully spatial model, especially in terms of its transient dynamics. These results also underscore the critical role of timescale separation between fire and vegetation processes in shaping ecosystem structure and resilience.