Etherington Thomas R
Manaaki Whenua-Landcare Research, Lincoln, New Zealand.
PeerJ. 2019 Apr 2;7:e6678. doi: 10.7717/peerj.6678. eCollection 2019.
The Mahalanobis distance is a statistical technique that can be used to measure how distant a point is from the centre of a multivariate normal distribution. By measuring Mahalanobis distances in environmental space ecologists have also used the technique to model: ecological niches, habitat suitability, species distributions, and resource selection functions. Unfortunately, the original description of the Mahalanobis distance technique for ecological modelling contained an error describing how Mahalanobis distances could be converted into probabilities using a chi-squared distribution. This error has been repeated in the literature, and is present in popular modelling software. In the hope of correcting this error to maximise the potential application of the Mahalanobis distance technique within the ecological modelling community, I explain how Mahalanobis distances are calculated, and through a virtual ecology experiment demonstrate how to correctly produce probabilities and discuss the implications of the error for previous Mahalanobis distance studies.
马氏距离是一种统计技术，可用于衡量一个点与多元正态分布中心的距离。通过测量环境空间中的马氏距离，生态学家还使用该技术对生态位、栖息地适宜性、物种分布和资源选择函数进行建模。不幸的是，用于生态建模的马氏距离技术的原始描述中存在一个错误，该错误描述了如何使用卡方分布将马氏距离转换为概率。这个错误在文献中反复出现，并且存在于流行的建模软件中。为了纠正这个错误，以最大限度地发挥马氏距离技术在生态建模领域的潜在应用，我解释了马氏距离是如何计算的，并通过一个虚拟生态实验演示了如何正确地生成概率，并讨论了该错误对以往马氏距离研究的影响。
