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

Abstract

Levy 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 Levy walks can be advantageous when searching for randomly and sparsely distributed resources, prompting the suggestion that Levy 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 Levy walks. Nonetheless, Levy 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 Levy walk research. This research has sought to identify biologically plausible mechanisms by which organisms can execute Levy 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 Levy 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 Levy walk search theory.