Assessing the robustness of spatial pattern sequences in a dryland vegetation model

Karna Gowda, Yuxin Chen, Sarah Iams, Mary Silber*

*Corresponding author for this work

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

A particular sequence of patterns, 'gaps → labyrinth → spots', occurs with decreasing precipitation in previously reported numerical simulations of partial differential equation dryland vegetation models. These observations have led to the suggestion that this sequence of patterns can serve as an early indicator of desertification in some ecosystems. Because parameter values in the vegetation models can take on a range of plausible values, it is important to investigate whether the pattern sequence prediction is robust to variation. For a particular model, we find that a quantity calculated via bifurcation-theoretic analysis appears to serve as a proxy for the pattern sequences that occur in numerical simulations across a range of parameter values. We find in further analysis that the quantity takes on values consistent with the standard sequence in an ecologically relevant limit of the model parameter values. This suggests that the standard sequence is a robust prediction of the model, and we conclude by proposing a methodology for assessing the robustness of the standard sequence in other models and formulations.

Original languageEnglish (US)
Article number20150893
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume472
Issue number2187
DOIs
StatePublished - Mar 2016

Keywords

  • Desertification
  • Dryland ecosystems
  • Early-warning signs
  • Models of vegetation pattern formation
  • Pattern formation

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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