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Homogenization of Large-Scale Movement Models in Ecology

Bulletin of Mathematical Biology

By:
, , , and
https://doi.org/10.1007/s11538-010-9612-6

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Abstract

A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion and apply it to a simple model for chronic wasting disease in mule deer. Homogenization allows us to determine the impact of small scale (10-100 m) habitat variability on large scale (10-100 km) movement. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. The simplicity of this homogenization procedure is striking when compared to the multi-dimensional homogenization procedure for Fickian diffusion,and the method will be equally straightforward for more complex models. ?? 2010 Society for Mathematical Biology.

Additional publication details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Homogenization of Large-Scale Movement Models in Ecology
Series title:
Bulletin of Mathematical Biology
DOI:
10.1007/s11538-010-9612-6
Volume:
73
Issue:
9
Year Published:
2011
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Bulletin of Mathematical Biology
First page:
2088
Last page:
2108