Non-local concepts and models in biology

In this paper, we consider local and non-local spatially explicit mathemati cal models for biological phenomena. We show that, when rate differences be tween fast and slow local dynamics are great enough, non-local models are a dequate simplifications of local models. Non-local models thus avoid descri bing fast processes in mechanistic detail, instead describing the effects o f fast processes on slower ones. As a consequence, non-local models are hel pful to biologists because they describe biological systems on scales that are convenient to observation, data collection, and insight. We illustrate these arguments by comparing local and non-local models for the aggregation of hypothetical organisms, and we support theoretical ideas with concrete examples from cell biology and animal behavior. (C) 2001 Academic Press.