TY - JOUR
T1 - Non-local concepts and models in biology
AU - Lee, C. T.
AU - Hoopes, M. F.
AU - Diehl, J.
AU - Gilliland, W.
AU - Huxel, G.
AU - Leaver, E. V.
AU - Mccann, K.
AU - Umbanhowar, J.
AU - Mogilner, A.
N1 - Funding Information:
This paper is a result of a research and training project of a multidisciplinary group concerned with understanding the role of non-locality in nonlinear biological dynamics. The corresponding activities were made possible by the support from RTG NSF Grant DBI-9602226 &&Nonlinear dynamics in biology’’. The grant is administered through the Institute for Theoretical Dynamics at the University of California at Davis. We are grateful for long and fruitful discussions with M. Lewis, M. Kot, B. Ermen-trout and E. Holmes that helped us to formulate the ideas of the present work. We also thank A. Amezcua and G. Takimoto for their help at early stages of this project.
PY - 2001/5/21
Y1 - 2001/5/21
N2 - 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.
AB - 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.
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U2 - 10.1006/jtbi.2000.2287
DO - 10.1006/jtbi.2000.2287
M3 - Article
C2 - 11371175
AN - SCOPUS:0035926431
SN - 0022-5193
VL - 210
SP - 201
EP - 219
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
IS - 2
ER -