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Diffusion about the mean drift location in a biased random walk
Author(s) -
Codling Edward A.,
Bearon Rachel N.,
Thorn Graeme J.
Publication year - 2010
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.1890/09-1729.1
Subject(s) - random walk , statistical physics , diffusion , position (finance) , lévy flight , probability density function , movement (music) , anisotropy , mathematics , physics , statistics , mathematical analysis , optics , quantum mechanics , finance , acoustics , economics
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.