At the edge of chaos--error tolerance and the maintenance of Lévy statistics in animal movement: Comment on "Liberating Lévy walk research from the shackles of optimal foraging" by A.M. Reynolds.

Fractal patterns abound in nature [1] and began to capture the imaginations of ecologists and animal behaviorists a little over three decades ago [2–4]. One field of study in which interest in fractal patterns has grown substantially over this time is animal movement ecology, where three basic approaches have been employed [reviewed in [5]]. Among these are (i) spatial [4,6,7] and (ii) temporal [8,9] fractal dimension estimation of animal movements, and (iii) studies testing or otherwise relating to the Lévy Flight Foraging hypothesis, which has garnered by far the most interest [10–16]. A.M. Reynolds [14] thus offers a timely, and extensive, overview of the current state of research in this field, showing that it can no longer be denied that multiscale movement patterns are often well characterized by Lévy statistics. Reynolds [14] also argues, however, that the theoretical underpinnings of the ‘Lévy paradigm’ – which state that Lévy movements reflect an evolved strategy to optimize foraging success in heterogeneous resource fields – should now be modified in light of recent research showing that various seemingly ‘innocuous’ and ‘banal’ interactions between an animal and its environment can also lead to the emergence of Lévy patterns. Indeed, among the major criticisms of the Lévy Flight Foraging hypothesis has been the question, and to some the implausibility, of generative mechanisms [17,18]. Reynolds [14] offers a large list of generative mechanisms that indeed have little if anything to do with search optimization, but at the same time there is little evidence to suggest that these are the sole generative mechanisms at play. Behavior patterns measured at any scale but in particular measured across large numbers of scales simultaneously represent the product of complex, often nonlinear interactions between veritably innumerable intrinsic