Pattern Formation in Mesic Savannas

TL;DR

This paper investigates pattern formation in forest-savanna dynamics using a spatially extended nonlinear model, revealing conditions for bifurcations, the impact of resource limitations, and the presence of multistability.

Contribution

It introduces a spatially extended model for savanna dynamics, analyzes pattern-forming bifurcations, and explores the effects of resource limitations through numerical simulations.

Findings

Homogeneous solutions dominate the standard model.

Resource limitations can lead to pattern formation.

Multistability occurs in realistic parameter regimes.

Abstract

We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations. Analytically, we show that homogeneous solutions dominate the dynamics of the standard forest-savanna model, regardless of the length scales of the various spatial processes considered. However, several different pattern-forming scenarios are possible upon including spatial resource limitation, such as competition for water, soil nutrients, or herbivory effects. Using numerical simulations and continuation, we study the nature of the resulting patterns as a function of system parameters and length scales, uncovering subcritical pattern-forming bifurcations and observing significant regions of multistability for realistic parameter regimes. Finally, we discuss our results in the context of extant savanna-forest modeling efforts and highlight ongoing challenges in building a unifying mathematical model for savannas across different rainfall levels.