How many animals really do the Lévy walk? Comment.
How many animals really do the Lévy walk? Comment.
复制标题
莱维到底行走了多少只动物？
作者：
A. Reynolds
空间生态学的两个主要挑战是理解景观异质性对运动的影响，并将小空间和时间尺度上的观察转化为更大尺度上的预期模式（Morales和Ellner 2002）。相关随机游走（CRW）模型来自于对实验中获得的短尺度运动数据的分析，这些实验通常持续不到一个小时，并且在延伸不超过几米的竞技场中进行（Kareiva和Shigesada 1983，Bovet和Benhamou 1988，Turchin 1991）。在更大的空间尺度和/或更长的时间尺度上对动物运动的分析产生了Lévy步行模型（LW，通常称为Lévy飞行模型; Viswanathan et al. 1996，1999，Atkinson et al. 2002）。然而，最近，Edwards等人（2007）质疑了由Viswanathan等人（1996）首次报道的流浪信天翁中Lévy飞行行为的说法。Edwards等人（2007年）还发现了其他一些数据集（Viswanathan等人，1999年），其中的分析无法明确区分是否存在Lévy航班。Bartumeus等人（2005）认为，CRW可以被解释为局部扫描机制的副产品，而LW具有基本属性（超扩散性和尺度不变性），可以在随机搜索场景中实现更高的搜索效率。这促使他们提出，一些动物可能已经进化出在面对不确定性时执行LW的能力。在最近的一份生态学报告中，Benhamou（2007）丰富了这一争论。他强调了两点：（1）LW在斑块环境中看起来像觅食模式，但在这样的环境中，LW远不是最佳搜索策略;以及（2）使用通常的方法，很容易在复合布朗随机游动运动（以下根据标准术语称为复合CRW运动）中找到明显的LW。在这里，我指出，Benhamou（2007）的复合CRW模型实际上可以被解释为自适应LW模型，因此，他已经证明，自适应LW比非自适应LW在斑块环境中搜索时更好。然后，我概括Benhamou的第二点表明，重尾分布的移动长度，LW的标志，几乎是不可避免的，当整理在观测尺度上获得的运动数据，包括异质性。这阐明了观察的尺度影响模式描述的概念（Levin 1992）。然而，平方反比幂律尾部的出现确实需要局部运动和异质性模式的特殊组合。这与在各种环境中移动的各种动物中这种结垢的普遍性不同（Atkinson等人，2002年; Bartumeus等人，2003年; Reynolds，2007年a、B; Reynolds和Frye，2007年）。最后，我证明了内在的LW特性是相当强大的二次采样，因此，报告LW源于分析的基础上移动任意位置之间的修复仍然是安全的。
Two major challenges in spatial ecology are understanding the effects of landscape heterogeneity on movement, and translating observations taken at small spatial and temporal scales into expected patterns at greater scales (Morales and Ellner 2002). Correlated random walk (CRW) models emerged from the analysis of short-scaled movement data acquired in experiments usually lasting less than an hour and performed in arenas extending over no more than several meters (Kareiva and Shigesada 1983, Bovet and Benhamou 1988, Turchin 1991). Analysis of animal movements over much larger spatial scales and/or longer temporal scales has given rise to Lévy walk models (LW, often referred to as Lévy flight models; Viswanathan et al. 1996, 1999, Atkinson et al. 2002). Recently, however, Edwards et al. (2007) questioned the claim of Lévy flight behavior in the Wandering Albatross, first reported by Viswanathan et al. (1996). Edwards et al. (2007) also identified some other data sets (Viswanathan et al. 1999) in which the analysis was unable to definitively discriminate the presence of Lévy flights. Bartumeus et al. (2005) argued that CRW can be interpreted as being the by-product of local scanning mechanisms, whereas LW have fundamental properties (super-diffusivity and scale invariance) that allow for higher search efficiencies in random search scenarios. This prompted them to propose that some animals may have evolved the ability to perform LW when confronted with uncertainty. In a recent Ecology report, Benhamou (2007) enriched the debate. He stressed two points: (1) that LW can look like foraging patterns in patchy environments, but in such an environment LW are far from being an optimal searching strategy; and (2) with the usual methodology it is easy to find apparent LW in composite Brownian random walks movements (hereafter referred to as composite CRW movements in accordance with standard terminology). Here I point out that Benhamou’s (2007) composite CRW model can, in fact, be interpreted as being an adaptive LW model and that, as a consequence, he has demonstrated that adaptive LW are better than nonadaptive LW when searching in patchy environments. I then generalize Benhamou’s second point by showing that heavy-tailed distributions of move lengths, a hallmark of LW, are almost inevitable when collating movement data acquired at observational scales that encompass heterogeneity. This elucidates the notion that the scale of observation influences the description of the pattern (Levin 1992). The emergence of an inverse-square power-law tail does, however, require rather special combinations of local movements and patterns of heterogeneity. This is at variance with the prevalence of such scaling in a diverse range of animals moving within a diverse range of environments (Atkinson et al. 2002, Bartumeus et al. 2003, Reynolds 2007a, b, Reynolds and Frye 2007). Finally, I demonstrate that intrinsic LW characteristics are quite robust with respect to subsampling and that, as a consequence, reports on LW stemming from analyses based on moves between arbitrary location fixes remain secure.