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Tropical tree cover in a heterogeneous environment: A reaction-diffusion model.

Authors
  • Wuyts, Bert1, 2, 3
  • Champneys, Alan R3
  • Verschueren, Nicolas1, 3
  • House, Jo I4
  • 1 College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom. , (United Kingdom)
  • 2 Bristol Centre for Complexity Sciences, University of Bristol, Bristol, United Kingdom. , (United Kingdom)
  • 3 Applied Nonlinear Mathematics, University of Bristol, Bristol, United Kingdom. , (United Kingdom)
  • 4 School of Geography, University of Bristol, Bristol, United Kingdom. , (United Kingdom)
Type
Published Article
Journal
PLoS ONE
Publisher
Public Library of Science
Publication Date
Jan 01, 2019
Volume
14
Issue
6
Identifiers
DOI: 10.1371/journal.pone.0218151
PMID: 31246968
Source
Medline
Language
English
License
Unknown

Abstract

Observed bimodal tree cover distributions at particular environmental conditions and theoretical models indicate that some areas in the tropics can be in either of the alternative stable vegetation states forest or savanna. However, when including spatial interaction in nonspatial differential equation models of a bistable quantity, only the state with the lowest potential energy remains stable. Our recent reaction-diffusion model of Amazonian tree cover confirmed this and was able to reproduce the observed spatial distribution of forest versus savanna satisfactorily when forced by heterogeneous environmental and anthropogenic variables, even though bistability was underestimated. These conclusions were solely based on simulation results for one set of parameters. Here, we perform an analytical and numerical analysis of the model. We derive the Maxwell point (MP) of the homogeneous reaction-diffusion equation without savanna trees as a function of rainfall and human impact and show that the front between forest and nonforest settles at this point as long as savanna tree cover near the front remains sufficiently low. For parameters resulting in higher savanna tree cover near the front, we also find irregular forest-savanna cycles and woodland-savanna bistability, which can both explain the remaining observed bimodality.

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