Intrinsic Lévy behaviour in organisms – searching for a mechanism: Comment on “Liberating Lévy walk research from the shackles of optimal foraging” by A.M. Reynolds

Abstract

The seminal papers by Viswanathan and colleagues in the late 1990s [1] and [2] proposed not only that scale-free, superdiffusive Lévy walks can describe the free-ranging movement patterns observed in animals such as the albatross [1], but that the Lévy walk was optimal for searching for sparsely and randomly distributed resource targets [2]. This distinct advantage, now shown to be present over a much broader set of conditions than originally theorised [3], implied that the Lévy walk is a search strategy that should be found very widely in organisms [4]. In the years since there have been several influential empirical studies showing that Lévy walks can indeed be detected in the movement patterns of a very broad range of taxa, from jellyfish, insects, fish, reptiles, seabirds, humans [5], [6], [7], [8], [9] and [10], and even in the fossilised trails of extinct invertebrates [11]. The broad optimality and apparent deep evolutionary origin of movement (search) patterns that are well approximated by Lévy walks led to the development of the Lévy flight foraging (LFF) hypothesis [12], which states that “since Lévy flights and walks can optimize search efficiencies, therefore natural selection should have led to adaptations for Lévy flight foraging”.

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