Circles and spirals

population persistence in a spatially explicit predator-prey model

William Gurney, A.R. Veitch, I. Cruickshank, G. McGeachin

Research output: Contribution to journalArticle

68 Citations (Scopus)

Abstract

The primary aim of the work reported in this paper is to elucidate the relationship between discrete and continuous deterministic representations of spatial population processes. Our experimental vehicle is a spatially explicit version of the Rosenzweig-McArthur model with immobile prey and a diffusively dispersing predator. We find that careful formulation of the discrete representation leads to essentially complete behavioral concordance between the two representations. We examine the invasions that follow localized introduction of predators into such a system and show that the biological realism of the model predictions can be greatly enhanced by preventing in situ regrowth of predator populations from densities that should be interpreted as representing local extinction. We exploit the close concordance of behavior between continuous and discrete representations by using the discrete version to perform a wide range of numerical experiments on one-dimensional and two-dimensional systems, while turning to the continous version to provide approximate analytic results for the natural time and space scales of the predicted population patterns. We conclude by discussing the implications of our findings for the experimental and theoretical study of spatial population dynamics.
Original languageEnglish
Pages (from-to)2516-2530
Number of pages14
JournalEcology
Volume79
Issue number7
DOIs
Publication statusPublished - Oct 1998

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persistence
predator
predators
local extinction
regrowth
theoretical study
space and time
population dynamics
extinction
experimental study
prediction
experiment
in situ
vehicle
biological models

Keywords

  • population persistence
  • spatially explicit
  • predator-prey model
  • spatial population models
  • discrete spatial models
  • persistence of spatial populations
  • reaction diffusion models
  • scale of spatial patterns

Cite this

Gurney, William ; Veitch, A.R. ; Cruickshank, I. ; McGeachin, G. / Circles and spirals : population persistence in a spatially explicit predator-prey model. In: Ecology. 1998 ; Vol. 79, No. 7. pp. 2516-2530.
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abstract = "The primary aim of the work reported in this paper is to elucidate the relationship between discrete and continuous deterministic representations of spatial population processes. Our experimental vehicle is a spatially explicit version of the Rosenzweig-McArthur model with immobile prey and a diffusively dispersing predator. We find that careful formulation of the discrete representation leads to essentially complete behavioral concordance between the two representations. We examine the invasions that follow localized introduction of predators into such a system and show that the biological realism of the model predictions can be greatly enhanced by preventing in situ regrowth of predator populations from densities that should be interpreted as representing local extinction. We exploit the close concordance of behavior between continuous and discrete representations by using the discrete version to perform a wide range of numerical experiments on one-dimensional and two-dimensional systems, while turning to the continous version to provide approximate analytic results for the natural time and space scales of the predicted population patterns. We conclude by discussing the implications of our findings for the experimental and theoretical study of spatial population dynamics.",
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Circles and spirals : population persistence in a spatially explicit predator-prey model. / Gurney, William; Veitch, A.R.; Cruickshank, I.; McGeachin, G.

In: Ecology, Vol. 79, No. 7, 10.1998, p. 2516-2530.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Circles and spirals

T2 - population persistence in a spatially explicit predator-prey model

AU - Gurney, William

AU - Veitch, A.R.

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KW - predator-prey model

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KW - discrete spatial models

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KW - reaction diffusion models

KW - scale of spatial patterns

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