Self-organisation, scale and stability in a spatial predator-prey interaction

William Gurney, A.R. Veitch

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

Simple predator-prey models often predict extreme instability in interactions where the prey are depressed well below their carrying capacity. Although the behaviour of some laboratory systems conforms to this pattern, field and mesocosm studies generally show prolonged co-existence of prey and predator. Prominent among the possible causes of this discrepancy are the effects of spatial heterogeneity. In this paper we show that both discrete and continuous representations of the spatial Rosenzweig-McArthur model with immobile prey can be stabilized by self-organized prey heterogeneity. This concordance of behaviour closely parallels that which we have previously established in the context of invasion waves. We use the continuous model variant to calculate the characteristic spatial scales of the self-organized structures. The discrete variant forms the basis of a simulation study demonstrating the variety of stable structures and elucidating their relation to the history of the system. We note that all stable prey distributions take the form of a network of occupied patches separated by prey-free regions, and liken the process which generates such assemblages to the formation of a landscape mozaic.
LanguageEnglish
Article numberbulm.1999.0130
Pages61-86
Number of pages25
JournalBulletin of Mathematical Biology
Volume62
Issue number1
DOIs
Publication statusPublished - 2000

Fingerprint

Predator-prey
self organization
predator-prey interaction
predator-prey relationships
Conservation of Natural Resources
Self-organization
Prey
History
Interaction
predator
predators
mesocosm
carrying capacity
coexistence
Spatial Heterogeneity
history
Carrying Capacity
Concordance
Predator-prey Model
Invasion

Keywords

  • Simple predator-prey models
  • self-organisation
  • spatial predator-prey interaction
  • spatial Rosenzweig-McArthur model

Cite this

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Self-organisation, scale and stability in a spatial predator-prey interaction. / Gurney, William; Veitch, A.R.

In: Bulletin of Mathematical Biology, Vol. 62, No. 1, bulm.1999.0130 , 2000, p. 61-86.

Research output: Contribution to journalArticle

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