Metastability as a Coexistence Mechanism in a Model for Dryland Vegetation Patterns

Lukas Eigentler, Jonathan A. Sherratt

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction–diffusion model based on the single-species Klausmeier model, to analytically investigate the existence of states in which both species coexist. Ecologically, the study finds that coexistence is supported if there is a small difference in the plant species’ average fitness, measured by the ratio of a species’ capabilities to convert water into new biomass to its mortality rate. Mathematically, coexistence is not a stable solution of the system, but both spatially uniform and patterned coexistence states occur as metastable states. In this context, a metastable solution in which both species coexist corresponds to a long transient (exceeding 10 3 years in dimensional parameters) to a stable one-species state. This behaviour is characterised by the small size of a positive eigenvalue which has the same order of magnitude as the average fitness difference between the two species. Two mechanisms causing the occurrence of metastable solutions are established: a spatially uniform unstable equilibrium and a stable one-species pattern which is unstable to the introduction of a competitor. We further discuss effects of asymmetric interspecific competition (e.g. shading) on the metastability property.

Original languageEnglish
Pages (from-to)2290-2322
Number of pages33
JournalBulletin of Mathematical Biology
Issue number7
Early online date22 Apr 2019
Publication statusPublished - Jul 2019


  • Metastability
  • Pattern formation
  • Reaction–diffusion systems
  • Semi-arid landscapes
  • Species coexistence
  • Vegetation patterns

ASJC Scopus subject areas

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


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