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 d ynamics arising from dispersal throughout a closed, finite, but spatially h eterogeneous 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 exterio r. We observe that simple rescaling has the same effects in our models as i n KISS models and hence predicts the same sort of area effects, but that ot her 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. (C) 2001 Academic Press .