Center for Advanced Intelligence Project, RIKEN, Tokyo 103-0027, Japan
Proc Natl Acad Sci U S A. 2020 Sep 29;117(39):24336-24344. doi: 10.1073/pnas.2001548117. Epub 2020 Sep 14.
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 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.
一类特殊的随机游走，即所谓的 Lévy 游走，在从细胞、昆虫、鱼类和鸟类到哺乳动物（包括人类）等各种生物体中都有观察到。尽管 Lévy 游走的普遍性被认为是为了提高搜索效率而进行自然选择的结果，但一些研究结果表明，Lévy 游走也可能是由与环境相互作用而产生的附带现象。因此，为什么它们在生物运动中如此普遍仍然是一个悬而未决的问题。基于一些证据表明 Lévy 游走是在大脑中自发产生的，以及 Lévy 游走中的幂律分布可以在临界点出现的事实，我们假设 Lévy 游走的优势可能会因临界点而增强。然而，对于 Lévy 游走的功能优势，我们还知之甚少。在这里，我们为运动生成建模了非线性系统，并表明在临界点附近出现的 Lévy 游走具有最佳的信息编码动态范围。这一发现表明，Lévy 游走可以根据环境刺激的大小来改变运动轨迹。然后，我们表明 Lévy 游走的高灵活性能够根据外部线索的性质进行开发/探索的切换。最后，我们分析了自由移动幼虫的运动轨迹，并从经验上表明，Lévy 游走可能在临界点附近出现，并且具有较大的动态范围和较高的灵活性。我们的研究结果表明，常见的 Lévy 游走是在临界点附近出现的，可以基于这些功能优势来解释。
