Transport and anisotropic diffusion models for movement in oriented habitats

Thomas Hillen*, Kevin J. Painter

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

43 Citations (Scopus)


A common feature of many living organisms is the ability to move and navigate in heterogeneous environments. While models for spatial spread of populations are often based on the diffusion equation, here we aim to advertise the use of transport models; in particular in cases where data from individual tracking are available. Rather than developing a full general theory of transport models, we focus on the specific case of animal movement in oriented habitats. The orientations can be given by magnetic cues, elevation profiles, food sources, or disturbances such as seismic lines or roads. In this case we are able to present and contrast the three most common scaling limits, (i) the parabolic scaling, (ii) the hyperbolic scaling, and (iii) the moment closure method. We clearly state the underlying assumptions and guide the reader to an understanding of which scaling method is used in what kind of situations. One interesting result is that the macroscopic drift velocity is given by the mean direction of the underlying linear features, and the diffusion is given by the variance-covariance matrix of the underlying oriented habitat. We illustrate our findings with specific applications to wolf movement in habitats with seismic lines.

Original languageEnglish
Title of host publicationDispersal, Individual Movement and Spatial Ecology
Subtitle of host publicationA Mathematical Perspective
Number of pages46
ISBN (Electronic)978-3-642-35497-7
Publication statusPublished - 2013

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434

ASJC Scopus subject areas

  • Algebra and Number Theory


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