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Beyond Optimal Searching: Recent Developments in the Modelling of Animal Movement Patterns as Lévy Walks

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Dispersal, Individual Movement and Spatial Ecology

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2071))

Abstract

Lévy walks first entered the biological literature when Shlesinger and Klafter (Growth and Form, Martinus Nijhof Publishers, Amsterdam, 1986, pp 279–283) proposed that they can be observed in the movement patterns of foraging ants. The fractal and superdiffusive properties of Lévy walks can be advantageous when searching for randomly and sparsely distributed resources, prompting the suggestion that Lévy walks represent an evolutionary optimal searching strategy. The suggestion is supported by a plethora of empirical studies which have revealed that many organisms (a diverse range of marine predator, honeybees, Escherichia coli) have movement patterns that can approximated by Lévy walks. Nonetheless, Lévy walks with their strange fractal geometry appear alien to biology and their relevance to biology has been hotly debated. Here I describe some of my own recent contributions to Lévy walk research. This research has sought to identify biologically plausible mechanisms by which organisms can execute Lévy walks and to demonstrate that these movement patterns have a utility beyond the understanding and prediction of optimal searching patterns. This work has made apparent that Lévy walks do not stand outside of the now well-established correlated random walk paradigm but are instead natural consequences of it. I also describe some recent advances in Lévy walk search theory.

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Acknowledgements

Rothamsted Research receives grant aided support from the Biotechnology and Biological Sciences Research Council. I am indebted to Don Reynolds and Chris Rhodes for their support and encouragement.

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    Andy Reynolds

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  1. Mathematical & Statistical Sciences, University of Alberta, Central Academic Building 632, Edmonton, T6G 2G1, Alberta, Canada

    Mark A. Lewis

  2. Mathematical Institute, Centre for Mathematical Biology, University of Oxford, St. Giles Street 24-29, Oxford, OX1 3LB, United Kingdom

    Philip K. Maini

  3. Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

    Sergei V. Petrovskii

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Reynolds, A. (2013). Beyond Optimal Searching: Recent Developments in the Modelling of Animal Movement Patterns as Lévy Walks. In: Lewis, M., Maini, P., Petrovskii, S. (eds) Dispersal, Individual Movement and Spatial Ecology. Lecture Notes in Mathematics(), vol 2071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35497-7_3

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