Abstract: M. Abe (2020)

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

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Functional advantages of Lévy walks emerging near a critical point