Models for predator-prey systems at multiple scales

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20 Scopus citations


Spatially explicit models are constructed for predator dispersal, predator-prey interactions, and prey dispersal and population dynamics in a system where the appropriate spatial and temporal scales for the predator are different from those for the prey. The models are based on the hypotheses that the predator experiences the environment as a collection of patches and disperses among the patches by immigration and emigration on a time scale much shorter than its reproductive interval, while the prey experiences each patch as a continuum on which it disperses by diffusion while reproducing logistically. The models are motivated by a natural system in which ladybird beetles aggregate at and feed upon colonies of aphids which grow on patches of host plants. Structurally the models are a hybrid of patch models and reaction-diffusion (i.e., KISS) models. The models are studied at equilibrium or pseudoequilibrium via methods derived from reaction-diffusion theory. The behavior of the models under variations in patch size is analyzed, and it is shown that in some cases they predict smaller prey densities on larger patches, or even maximum as well as minimum patch sizes which can sustain a prey population. This last prediction is in contrast with the predictions of reaction-diffusion (KISS) models for the prey alone, in which there is typically a minimum patch size which will sustain a prey population and the prey density increases toward carrying capacity as patch size increases.

Original languageEnglish (US)
Pages (from-to)256-286
Number of pages31
JournalSIAM Review
Issue number2
StatePublished - Jun 1996


  • Patch models
  • Predator-prey
  • Reaction-diffusion
  • Spatial scales
  • Temporal scales

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics


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