The logic of ecological patchiness.

Most ecological interactions occur in environments that are spatially and temporally heterogeneous-'patchy'-across a wide range of scales. In contrast, most theoretical models of ecological interactions, especially large-scale models applied to societal issues such as climate change, resource management and human health, are based on 'mean field' approaches in which the underlying patchiness of interacting consumers and resources is intentionally averaged out. Mean field ecological models typically have the advantages of tractability, few parameters and clear interpretation; more technically complex spatially explicit models, which resolve ecological patchiness at some (or all relevant) scales, generally lack these advantages. This report presents a heuristic analysis that incorporates important elements of consumer-resource patchiness with minimal technical complexity. The analysis uses scaling arguments to establish conditions under which key mechanisms-movement, reproduction and consumption-strongly affect consumer-resource interactions in patchy environments. By very general arguments, the relative magnitudes of these three mechanisms are quantified by three non-dimensional ecological indices: the Frost, Strathmann and Lessard numbers. Qualitative analysis based on these ecological indices provides a basis for conjectures concerning the expected characteristics of organisms, species interactions and ecosystems in patchy environments.