Reynolds Andy, Santini Giacomo, Chelazzi Guido, Focardi Stefano
Rothamsted Research, Harpenden AL5 2JQ, UK.
Dipartimento di Biologia, Università di Firenze, Via Madonna del Piano, 6, 50019 Sesto Fiorentino, Italy.
R Soc Open Sci. 2017 Jun 7;4(6):160941. doi: 10.1098/rsos.160941. eCollection 2017 Jun.
Weierstrassian Lévy walks are the archetypical form of random walk that do not satisfy the central limit theorem and are instead characterized by scale invariance. They were originally regarded as a mathematical abstraction but subsequent theoretical studies showed that they can, in principle, at least, be generated by chaos. Recently, Weierstrassian Lévy walks have been found to provide accurate representations of the movement patterns of mussels () and mud snails () recorded in the laboratory under controlled conditions. Here, we tested whether Weierstrassian Lévy walks and chaos are present under natural conditions in intertidal limpets and and found that both characteristics are pervasive. We thereby show that Weierstrassian Lévy walks may be fundamental to how molluscs experience and interact with the world across a wide range of ecological contexts. We also show in an easily accessible way how chaos can produce a wide variety of Weierstrassian Lévy walk movement patterns. Our findings support the Lévy flight foraging hypothesis that posits that because Lévy walks can optimize search efficiencies, natural selection should have led to adaptations for Lévy walks.
魏尔斯特拉斯式 Lévy 游走是不满足中心极限定理的典型随机游走形式，其特征是尺度不变性。它们最初被视为一种数学抽象，但随后的理论研究表明，至少在原则上，它们可以由混沌产生。最近，人们发现魏尔斯特拉斯式 Lévy 游走能够准确描述在受控条件下实验室中记录的贻贝（ ）和泥螺（ ）的运动模式。在此，我们测试了在潮间带帽贝（ ）和（ ）的自然条件下是否存在魏尔斯特拉斯式 Lévy 游走和混沌现象，结果发现这两种特征普遍存在。由此我们表明，魏尔斯特拉斯式 Lévy 游走可能是软体动物在广泛生态环境中体验世界并与之相互作用的基本方式。我们还以一种易于理解的方式展示了混沌如何产生各种各样的魏尔斯特拉斯式 Lévy 游走运动模式。我们的研究结果支持 Lévy 飞行觅食假说，该假说认为，由于 Lévy 游走可以优化搜索效率，自然选择应该导致了对 Lévy 游走的适应性。
