Pacific Biological Station, Fisheries and Oceans Canada, 3190 Hammond Bay Road, Nanaimo, British Columbia V9T 6N7, Canada.
Ecology. 2011 Jun;92(6):1247-57. doi: 10.1890/10-1182.1.
A surprisingly diverse variety of foragers have previously been concluded to exhibit movement patterns known as Lévy flights, a special type of random walk. These foragers range in size from microzooplankton in experiments to fishermen in the Pacific Ocean and the North Sea. The Lévy flight conclusion implies that all the foragers have similar scale-free movement patterns that can be described by a single dimensionless parameter, the exponent micro of a power-law (Pareto) distribution. However, the previous conclusions have been made using methods that have since been shown to be problematic: inaccurate techniques were used to estimate micro, and the power-law distribution was usually assumed to hold without testing any alternative hypotheses. Therefore, I address the open question of whether the previous data still support the Lévy flight hypothesis, and thus determine whether Lévy flights really are so ubiquitous in ecology. I present a comprehensive reanalysis of 17 data sets from seven previous studies for which Lévy flight behavior had been concluded, covering marine, terrestrial, and experimental systems from four continents. I use the modern likelihood and Akaike weights approach to test whether simple alternative models are more supported by the data than Lévy flights. The previously estimated values of the power-law exponent micro do not match those calculated here using the accurate likelihood approach, and almost all of them lie outside of the likelihood-based 95% confidence intervals. Furthermore, the original power-law Lévy flight model is overwhelmingly rejected for 16 out of the 17 data sets when tested against three other simple models. For one data set, the data are consistent with coming from a bounded power-law distribution (a truncated Lévy flight). For three other data sets, an exponential distribution corresponding to a simple Poisson process is suitable. Thus, Lévy flight movement patterns are not the common phenomena that was once thought, and are not suitable for use as ecosystem indicators for fisheries management, as has been proposed.
以前的研究得出结论，各种各样的觅食者表现出一种称为 Lévy 飞行的特殊随机漫步模式。这些觅食者的大小范围从实验中的微型浮游动物到太平洋和北海的渔民。 Lévy 飞行的结论意味着所有的觅食者都有类似的无标度运动模式，可以用单个无维参数来描述，即幂律（帕累托）分布的指数微。然而，以前的结论是使用有问题的方法得出的：用来估计微的技术不准确，而且通常假设幂律分布成立，而没有测试任何替代假设。因此，我解决了以前的数据是否仍然支持 Lévy 飞行假说的开放性问题，从而确定 Lévy 飞行在生态学中是否真的如此普遍。我对以前的七个研究中得出 Lévy 飞行行为的 17 个数据集进行了全面的重新分析，这些研究涵盖了来自四大洲的海洋、陆地和实验系统。我使用现代似然和 Akaike 权重方法来检验简单的替代模型是否比 Lévy 飞行更受数据支持。以前估计的幂律指数微值与使用准确似然方法计算的值不匹配，几乎所有值都在基于似然的 95%置信区间之外。此外，当针对三个其他简单模型对 17 个数据集的原始幂律 Lévy 飞行模型进行测试时，有 16 个数据集被压倒性地拒绝。对于一个数据集，数据与来自有界幂律分布（截断 Lévy 飞行）的情况一致。对于另外三个数据集，对应于简单泊松过程的指数分布是合适的。因此，Lévy 飞行的运动模式并不是以前认为的普遍现象，也不适合作为渔业管理的生态系统指标，正如已经提出的那样。
