Spatial heterogeneity and critical patch size: Area effects via diffusion in closed environments

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22 Scopus citations

Abstract

We describe a class of mathematical models for critical patch size in which the mechanisms inducing area effects are based on source-sink population dynamics arising from dispersal throughout a closed, finite, but spatially heterogeneous environment. Our models are reaction-diffusion equations, but unlike classical KISS models for area effects they do not assume that there is dispersal across the boundary of the environment into a hostile exterior. We observe that simple rescaling has the same effects in our models as in KISS models and hence predicts the same sort of area effects, but that other sorts of rescaling may not predict area effects. The models considered here provide an alternative to the KISS models used in our previous work on species-area relationships in island biogeography.

Original languageEnglish (US)
Pages (from-to)161-171
Number of pages11
JournalJournal of theoretical biology
Volume209
Issue number2
DOIs
StatePublished - Mar 21 2001

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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