Pattern Formation in Mesic Savannas

Denis Patterson, Simon Levin, Ann Carla Staver, Jonathan Touboul

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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. 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.

Original languageEnglish (US)
Article number3
JournalBulletin of Mathematical Biology
Volume86
Issue number1
DOIs
StatePublished - Jan 2024

All Science Journal Classification (ASJC) codes

  • General Environmental Science
  • General Biochemistry, Genetics and Molecular Biology
  • General Neuroscience
  • General Agricultural and Biological Sciences
  • Pharmacology
  • Computational Theory and Mathematics
  • Immunology
  • General Mathematics

Keywords

  • Integro-differential equations
  • Pattern formation
  • Savanna
  • Spatial modeling
  • Vegetation dynamics

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