Long-range seed dispersal enables almost stationary patterns in a model for dryland vegetation

Lukas Eigentler (Lead / Corresponding author), Jonathan A. Sherratt

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Abstract

Spatiotemporal patterns of vegetation are a ubiquitous feature of semi-arid ecosystems. On sloped terrain, vegetation patterns occur as stripes perpendicular to the contours. Field studies report contrasting long-term dynamics between different observation sites; some observe slow uphill migration of vegetation bands while some report stationary patterns. In this paper, we show that long-range seed dispersal provides a mechanism that enables the occurrence of both migrating and stationary patterns. We utilise a nonlocal PDE model in which seed dispersal is accounted for by a convolution term. The model represents vegetation patterns as periodic travelling waves and numerical continuation shows that both migrating and almost stationary patterns are stable if seed dispersal distances are sufficiently large. We use a perturbation theory approach to obtain analytical confirmation of the existence of almost stationary patterned solutions and provide a biological interpretation of the phenomenon.
Original languageEnglish
Article number15
Number of pages28
JournalJournal of Mathematical Biology
Volume86
Issue number15
Early online date17 Dec 2022
DOIs
Publication statusPublished - Jan 2023

Keywords

  • Matched asymptotics
  • Nonlocal dispersal
  • Periodic travelling waves
  • Perturbation theory
  • Vegetation patterns
  • Wavetrains

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