The Effects of the Size and Shape of Landscape Features on the Formation of Traveling Waves in Cyclic Populations

J. A. Sherratt, Xavier Lambin, T. N. Sherratt

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

Recent field data indicate that in a number of cyclic populations, the cycles are organized spatially with the form of a periodic traveling wave. One way in which this type of wave is generated is when dispersing individuals encounter landscape features that impede movement in certain directions. In this article, we investigate the dependence of such periodic waves on ecological parameters and on the form of the landscape feature. Using a standard predator-prey model as a prototype for a cyclic population, we calculate the speed and amplitude of waves generated by a large landscape feature. This enables us to determine parameters for which the waves are stable; in other cases, they evolve into irregular oscillations. We then undertake for the first time a detailed study of the effects of the size and shape of a landscape feature on the waves that it generates. We show that size rather than shape is the key waveforming property, with smaller obstacles generating waves with longer wavelength and waves from larger landscape features dominating those from smaller ones. Our results suggest that periodic traveling waves may be much more common than has previously been assumed in real ecological systems, and they enable quantitative predictions on the properties of these waves for particular cases.

Original languageEnglish
Pages (from-to)503-513
Number of pages10
JournalThe American Naturalist
Volume162
Issue number4
DOIs
Publication statusPublished - Oct 2003

Keywords

  • traveling waves
  • population cycles
  • mathematical modeling
  • PREDATOR-PREY SYSTEMS
  • SPATIAL ASYNCHRONY
  • FOREST BIRDS
  • DYNAMICS
  • SYNCHRONY
  • CHAOS
  • VOLES
  • OSCILLATORS
  • BEHAVIOR
  • PATTERNS

Cite this

The Effects of the Size and Shape of Landscape Features on the Formation of Traveling Waves in Cyclic Populations. / Sherratt, J. A.; Lambin, Xavier; Sherratt, T. N.

In: The American Naturalist, Vol. 162, No. 4, 10.2003, p. 503-513.

Research output: Contribution to journalArticle

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