Functional advantages of Levy walks emerging near a critical point

A special class of random walks, so-called Levy 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 Levy 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 Levy walks are spontaneously generated in the brain and the fact that power-law distributions in Levy walks can emerge at a critical point, we hypothesized that the advantages of Levy walks might be enhanced by criticality. However, the functional advantages of Levy walks are poorly understood. Here, we modeled nonlinear systems for the generation of locomotion and showed that Levy walks emerging near a critical point had optimal dynamic ranges for coding information. This discovery suggested that Levy walks could change movement trajectories based on the magnitude of environmental stimuli. We then showed that the high flexibility of Levy 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 Levy walks may emerge near a critical point and have large dynamic range and high flexibility. Our results suggest that the commonly observed Levy walks emerge near a critical point and could be explained on the basis of these functional advantages.