Impulsive Fire Disturbance in a Savanna Model: Tree\u2013Grass Coexistence States, Multiple Stable System States, and Resilience

Alanna Hoyer-Leitzel,Sarah Iams

doi:10.1007/s11538-021-00944-x

Alanna Hoyer-Leitzel, Sarah Iams

Open Access

https://doi.org/10.1007/s11538-021-00944-x

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Abstract

Savanna ecosystems are shaped by the frequency and intensity of regular fires. We model savannas via an ordinary differential equation (ODE) encoding a one-sided inhibitory Lotka–Volterra interaction between trees and grass. By applying fire as a discrete disturbance, we create an impulsive dynamical system that allows us to identify the impact of variation in fire frequency and intensity. The model exhibits three different bistability regimes: between savanna and grassland; two savanna states; and savanna and woodland. The impulsive model reveals rich bifurcation structures in response to changes in fire intensity and frequency—structures that are largely invisible to analogous ODE models with continuous fire. In addition, by using the amount of grass as an example of a socially valued function of the system state, we examine the resilience of the social value to different disturbance regimes. We find that large transitions (“tipping”) in the valued quantity can be triggered by small changes in disturbance regime.

Highlights

Introduction2009; Djeumen et al 2021; Goel et al 2020; Patterson et al 2020; Ratajczak et al 2017; Schertzer et al 2015; Staver et al 2011a; Tamen et al 2016, 2017; Touboul et al 2018; Wuyts et al 2019; Yatat et al 2018)
Given the ecological, economic and cultural value of savannas as well as their precarious ecological role, savanna ecosystems are a frequent target of modeling investigations
In tree–grass–fire interaction models of savanna ecosystems, the impact of fire on tree and grass biomass is often represented as a continuous mortality in ordinary differential equation (ODE) models (Accatino et al 2010; Beckage et al 2009; Djeumen et al 2021; Staver et al 2011a; Touboul et al 2018) and in spatial partial differential equations (PDE) models (Goel et al 2020; Wuyts et al 2019; Yatat et al 2018)

Summary

Introduction

2009; Djeumen et al 2021; Goel et al 2020; Patterson et al 2020; Ratajczak et al 2017; Schertzer et al 2015; Staver et al 2011a; Tamen et al 2016, 2017; Touboul et al 2018; Wuyts et al 2019; Yatat et al 2018). In tree–grass–fire interaction models of savanna ecosystems, the impact of fire on tree and grass biomass is often represented as a continuous mortality in ordinary differential equation (ODE) models (Accatino et al 2010; Beckage et al 2009; Djeumen et al 2021; Staver et al 2011a; Touboul et al 2018) and in spatial partial differential equations (PDE) models (Goel et al 2020; Wuyts et al 2019; Yatat et al 2018). Patterson et al (2020) shows that stochastic loss terms can be used to underpin continuum models, giving a nuanced relationship between the two types of models

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