Functional advantages of Lévy walks emerging near a critical point

Abstract

A special class of random walks, so-called Lévy walks, has been observed in a variety of organisms ranging from cells, insects, fishes, and birds to mammals, including humans. Although their prevalence is considered to be a consequence of natural selection for higher search efficiency, some findings suggest that Lévy walks might also be epiphenomena that arise from interactions with the environment. Therefore, why they are common in biological movements remains an open question. Based on some evidence that Lévy walks are spontaneously generated in the brain and the fact that power-law distributions in Lévy walks can emerge at a critical point, we hypothesized that the advantages of Lévy walks might be enhanced by criticality. However, the functional advantages of Lévy walks are poorly understood. Here, we modeled nonlinear systems for the generation of locomotion and showed that Lévy walks emerging near a critical point had optimal dynamic ranges for coding information. This discovery suggested that Lévy walks could change movement trajectories based on the magnitude of environmental stimuli. We then showed that the high flexibility of Lévy walks enabled switching exploitation/exploration based on the nature of external cues. Finally, we analyzed the movement trajectories of freely moving Drosophila larvae and showed empirically that the Lévy walks may emerge near a critical point and have large dynamic range and high flexibility. Our results suggest that the commonly observed Lévy walks emerge near a critical point and could be explained on the basis of these functional advantages.

Scale-free behavioral dynamics directly linked with scale-free cortical dynamics

“…What are the functional implications of this close relationship between scale-free behavior and brain activity? In previous work, scale-free neural activity has been associated with multiple functional benefits for sensory information processing (26,(37)(38)(39) and scale-free behavior has been associated with benefits for foraging, search, and decision making (3)(4)(5)(6)(7)(8)(9). Our results suggest that these two lists of functional benefits, previously considered separately, may in fact be a single unified list that occurs together.…”

“…The complexity of such movements is often organized with fractal structure, scale-free fluctuations spanning multiple spatiotemporal orders of magnitude (Anteneodo and Chialvo, 2009;Proekt et al, 2012;Sims et al, 2008;Viswanathan et al, 1999). Such behavioral complexity may be beneficial for foraging (Garg and Kello, 2021;Sims et al, 2008;Viswanathan et al, 1999;Wosniack et al, 2017), visual search (Viswanathan et al, 1999), decision making based on priority (Barabási, 2005;Sorribes et al, 2011), flexible switching of behavior (Abe, 2020), and perhaps more. Similarly, fluctuations of ongoing neural activity in cerebral cortex can exhibit fractal, scale-free fluctuations like the spatiotemporal cascades sometimes referred to as 'neuronal avalanches' (Beggs and Plenz, 2003;Bellay et al, 2015;Ma et al, 2019;Priesemann et al, 2014;Scott et al, 2014;Shew et al, 2015;Shriki et al, 2013;Tagliazucchi et al, 2012;Yu et al, 2017) and long-range temporal correlations (Hardstone et al, 2012;Kello et al, 2010;Palva et al, 2013;Smit et al, 2013).…”

“…The complexity of such movements is often organized with fractal structure, scale-free fluctuations spanning multiple spatiotemporal orders of magnitude (1-4). Such behavioral complexity may be beneficial for foraging (3)(4)(5)(6), visual search (4), decision making based on priority (7,8), flexible switching of behavior (9), and perhaps more. Similarly, fluctuations of ongoing neural activity in cerebral cortex can exhibit fractal, scale-free fluctuations like the spatiotemporal cascades sometimes referred to as 'neuronal avalanches' (10)(11)(12)(13)(14)(15)(16)(17)(18) and long-range temporal correlations (19)(20)(21).…”

Lévy walk dynamics explain gamma burst patterns in primate cerebral cortex

“…Lévy walks arising from criticality have been mainly found in models of low-dimensional dynamical systems. For example, one recent study 48 showed Lévy walks can by generated by coupled chaotic oscillators near the transition between synchronous and asynchronous states. In ref.…”

Intrinsic bursts facilitate learning of Lévy flight movements in recurrent neural network models

“…Here, we show the benefits of bursting activity in learning sequences generated by a special class of random walks observed in various animal behaviors. We investigate whether and how bursting neurons improve the ability of neural network models to learn the dynamical trajectories of Lévy flight, which is a random walk with step sizes obeying a heavy-tailed distribution 17 – 19 . As a consequence, Lévy flight consists of many short steps and rare long-distance jumps.…”