Diffusion about the mean drift location in a biased random walk.

Abstract:

:Random walks are used to model movement in a wide variety of contexts: from the movement of cells undergoing chemotaxis to the migration of animals. In a two-dimensional biased random walk, the diffusion about the mean drift position is entirely dependent on the moments of the angular distribution used to determine the movement direction at each step. Here we consider biased random walks using several different angular distributions and derive expressions for the diffusion coefficients in each direction based on either a fixed or variable movement speed, and we use these to generate a probability density function for the long-time spatial distribution. We demonstrate how diffusion is typically anisotropic around the mean drift position and illustrate these theoretical results using computer simulations. We relate these results to earlier studies of swimming microorganisms and explain how the results can be generalized to other types of animal movement.

journal_name

Ecology

journal_title

Ecology

authors

Codling EA,Bearon RN,Thorn GJ

doi

10.1890/09-1729.1

subject

Has Abstract

pub_date

2010-10-01 00:00:00

pages

3106-13

issue

10

eissn

0012-9658

issn

1939-9170

journal_volume

91

pub_type

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