A model of seasonal savanna dynamics

TL;DR

This paper develops a mathematical model for savanna vegetation that incorporates seasonal changes and stochastic fire disturbances, providing insights into the long-term dynamics of mixed woodland and grassland ecosystems.

Contribution

It introduces a novel piecewise deterministic Markov process model that accounts for seasonal effects and stochastic fires in savanna ecosystems, extending traditional ecological models.

Findings

Model captures seasonal vegetation dynamics.

Analyzes long-term behavior of savanna ecosystems.

Incorporates stochastic fire disturbances.

Abstract

We introduce a mathematical model of savanna vegetation dynamics. The usual approach of nonequilibrium ecology is extended by including the impact of wet and dry seasons. We present and rigorously analyze a model describing a mixed woodland-grassland ecosystem with stochastic environmental noise in the form of vegetation biomass losses manifesting fires. Both, the probability of ignition and the strength of these losses depend on the current season (as well as vegetation growth rates etc.). Formally it requires an introduction and analysis of a system that is a piecewise deterministic Markov process with parameters switching between given constant periods of time. We study the long time behavior of time averages for such processes.