A model for random fire induced tree-grass coexistence in savannas

TL;DR

This paper introduces a stochastic model for tree-grass coexistence in savannas, emphasizing the role of unpredictable fire events and providing a rigorous mathematical analysis of the system's long-term behavior.

Contribution

It presents a minimalistic stochastic model of fire-induced tree-grass dynamics and applies linear semigroup theory for detailed mathematical analysis.

Findings

Existence of a unique stationary distribution of biomasses

Model captures the impact of stochastic fire on coexistence

Provides a rigorous mathematical framework for savanna dynamics

Abstract

Tree-grass coexistence in savanna ecosystems depends strongly on environmental disturbances out of which crucial is fire. Most modeling attempts in the literature lack stochastic approach to fire occurrences which is essential to reflect their unpredictability. Existing models that actually include stochasticity of fire are usually analyzed only numerically. We introduce new minimalistic model of tree-grass coexistence where fires occur according to stochastic process. We use the tools of linear semigroup theory to provide more careful mathematical analysis of the model. Essentially we show that there exists a unique stationary distribution of tree and grass biomasses.