title: Non-local concepts and models in biology.
abstract: 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.
authors.affiliation: Institute of Theoretical Dynamics, University of California, Davis, CA 95616, USA.
authors.forename: C T
authors.initials: CT
authors.lastname: Lee
authors.forename: M F
authors.initials: MF
authors.lastname: Hoopes
authors.forename: J
authors.initials: J
authors.lastname: Diehl
authors.forename: W
authors.initials: W
authors.lastname: Gilliland
authors.forename: G
authors.initials: G
authors.lastname: Huxel
authors.forename: E V
authors.initials: EV
authors.lastname: Leaver
authors.forename: K
authors.initials: K
authors.lastname: McCann
authors.forename: J
authors.initials: J
authors.lastname: Umbanhowar
authors.forename: A
authors.initials: A
authors.lastname: Mogilner
mesh_terms: D000819:Animal Communication; D000818:Animals; D001042:Aphids / Q000502:physiology; D001522:Behavior, Animal; D008433:Mathematics; D008870:Microtubules / Q000502:physiology; D008954:Models, Biological; D009231:Myxococcales / Q000502:physiology; D011156:Population Density; D011157:Population Dynamics; D011323:Primates / Q000502:physiology