Spatially Heterogeneous Systems: Islands and Patchy Regions

Abstract

Perhaps the single greatest discrepancy between traditional mathematical models of population dynamics and populations in the real world is the customary neglect of spatial heterogeneity in the models. Levin (1979) has remarked that, while the statistical description of spatial pattern in ecosystems is relatively well developed (s. especially Pielou, 1977), the description of the dynamics giving rise to such spatial patterns is not. All ecological systems exist on landscapes (or seascapes) of varying complexity, and the dynamics of populations and processes cannot be divorced from these spatial contexts, but mathematical models of spatially extended ecosystems are difficult and the numerical evaluation of the behavior of even only moderately realistic models is far beyond the capabilities of the fastest computers.