Bridging the gulf between correlated random walks and Lévy walks: autocorrelation as a source of Lévy walk movement patterns.

Journal of the Royal Society, Interface
Andy Reynolds

Abstract

For many years, the dominant conceptual framework for describing non-oriented animal movement patterns has been the correlated random walk (CRW) model in which an individual's trajectory through space is represented by a sequence of distinct, independent randomly oriented 'moves'. It has long been recognized that the transformation of an animal's continuous movement path into a broken line is necessarily arbitrary and that probability distributions of move lengths and turning angles are model artefacts. Continuous-time analogues of CRWs that overcome this inherent shortcoming have appeared in the literature and are gaining prominence. In these models, velocities evolve as a Markovian process and have exponential autocorrelation. Integration of the velocity process gives the position process. Here, through a simple scaling argument and through an exact analytical analysis, it is shown that autocorrelation inevitably leads to Lévy walk (LW) movement patterns on timescales less than the autocorrelation timescale. This is significant because over recent years there has been an accumulation of evidence from a variety of experimental and theoretical studies that many organisms have movement patterns that can be approximated by LWs, a...Continue Reading

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Citations

Jun 3, 2011·Journal of the Royal Society, Interface·Alex JamesAndrew M Edwards
May 5, 2011·PloS One·Yelena Y GrinbergRichard P Kraig
Jan 26, 2011·Attention, Perception & Psychophysics·Damian G Stephen, Jason Anastas
May 21, 2011·Attention, Perception & Psychophysics·Damian G Stephen, Alen Hajnal
Dec 25, 2013·Proceedings of the National Academy of Sciences of the United States of America·David A RaichlenHerman Pontzer
Jan 29, 2014·Proceedings of the National Academy of Sciences of the United States of America·Laurent Seuront, H Eugene Stanley
Aug 8, 2014·Journal of the Royal Society, Interface·Andy M Reynolds
Jun 15, 2011·The American Naturalist·Eliezer Gurarie, Otso Ovaskainen
Jun 18, 2014·Ecology·Marie Auger-MéthéEdward A Codling
Jul 19, 2012·The European Journal of Neuroscience·John G Milton
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Sep 26, 2015·Nature Communications·Gil ArielAvraham Be'er
Apr 4, 2015·Physics of Life Reviews·Andy Reynolds
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Jan 13, 2018·Biology Open·Andy M Reynolds
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Sep 19, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R M TromerG M Viswanathan

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