Non-local concepts and models in biology

C. T. Lee, M. F. Hoopes, J. Diehl, W. Gilliland, G. Huxel, E. V. Leaver, K. Mccann, J. Umbanhowar, A. Mogilner

Research output: Contribution to journalArticlepeer-review


In this paper, we consider local and non-local spatially explicit mathematical models for biological phenomena. We show that, when rate differences between fast and slow local dynamics are great enough, non-local models are adequate simplifications of local models. Non-local models thus avoid describing fast processes in mechanistic detail, instead describing the effects of fast processes on slower ones. As a consequence, non-local models are helpful 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.

Original languageEnglish (US)
Pages (from-to)201-219
Number of pages19
JournalJournal of Theoretical Biology
Issue number2
StatePublished - May 21 2001

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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