Spatial Heterogeneity and Critical Patch Size: Area Effects via Diffusion in Closed Environments

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...

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Bibliographic Details
Published in:Journal of theoretical biology 2001-03, Vol.209 (2), p.161-171
Main Authors: CANTRELL, R.S., COSNER, CHRIS
Format: Article
Language:English
Subjects:
Animals
Environment
Models, Biological
Models, Statistical
Population Dynamics
population sinks
population sources
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Summary: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.
ISSN:0022-5193
1095-8541
DOI:10.1006/jtbi.2000.2246