Marine Ecosystems and Aquaculture Division, Pacific Biological Station, Fisheries and Oceans, Canada, Nanaimo, British Columbia, Canada.
PLoS One. 2012;7(10):e45174. doi: 10.1371/journal.pone.0045174. Epub 2012 Oct 5.
Ecologists are collecting extensive data concerning movements of animals in marine ecosystems. Such data need to be analysed with valid statistical methods to yield meaningful conclusions.
We demonstrate methodological issues in two recent studies that reached similar conclusions concerning movements of marine animals (Nature 451:1098; Science 332:1551). The first study analysed vertical movement data to conclude that diverse marine predators (Atlantic cod, basking sharks, bigeye tuna, leatherback turtles and Magellanic penguins) exhibited "Lévy-walk-like behaviour", close to a hypothesised optimal foraging strategy. By reproducing the original results for the bigeye tuna data, we show that the likelihood of tested models was calculated from residuals of regression fits (an incorrect method), rather than from the likelihood equations of the actual probability distributions being tested. This resulted in erroneous Akaike Information Criteria, and the testing of models that do not correspond to valid probability distributions. We demonstrate how this led to overwhelming support for a model that has no biological justification and that is statistically spurious because its probability density function goes negative. Re-analysis of the bigeye tuna data, using standard likelihood methods, overturns the original result and conclusion for that data set. The second study observed Lévy walk movement patterns by mussels. We demonstrate several issues concerning the likelihood calculations (including the aforementioned residuals issue). Re-analysis of the data rejects the original Lévy walk conclusion.
We consequently question the claimed existence of scaling laws of the search behaviour of marine predators and mussels, since such conclusions were reached using incorrect methods. We discourage the suggested potential use of "Lévy-like walks" when modelling consequences of fishing and climate change, and caution that any resulting advice to managers of marine ecosystems would be problematic. For reproducibility and future work we provide R source code for all calculations.
生态学家正在收集有关海洋生态系统中动物运动的大量数据。为了得出有意义的结论，这些数据需要使用有效的统计方法进行分析。
我们在最近的两项研究中展示了方法学问题，这两项研究得出了关于海洋动物运动的相似结论（《自然》451：1098；《科学》332：1551）。第一项研究分析了垂直运动数据，得出了多种海洋捕食者（大西洋鳕鱼、姥鲨、大眼金枪鱼、棱皮龟和麦哲伦企鹅）表现出“莱维漫步样行为”，接近假设的最佳觅食策略。通过再现大眼金枪鱼数据的原始结果，我们表明，所测试模型的可能性是从回归拟合的残差计算得出的（一种不正确的方法），而不是从正在测试的实际概率分布的似然方程计算得出的。这导致了错误的 Akaike 信息准则，以及对不符合有效概率分布的模型的测试。我们展示了这如何导致对一个没有生物学依据且在统计上是虚假的模型的压倒性支持，因为其概率密度函数为负。使用标准似然方法重新分析大眼金枪鱼数据，推翻了该数据集的原始结果和结论。第二项研究通过贻贝观察到莱维漫步运动模式。我们展示了似然计算的几个问题（包括上述残差问题）。对数据的重新分析拒绝了原始的莱维漫步结论。
因此，我们对海洋捕食者和贻贝搜索行为的标度律的存在提出质疑，因为这些结论是使用不正确的方法得出的。我们不鼓励在模拟渔业和气候变化的后果时建议使用“莱维样漫步”，并警告说，这将给海洋生态系统管理者带来问题。为了可重复性和未来的工作，我们提供了所有计算的 R 源代码。
