Department of Anthropology, University of Alaska Fairbanks, P.O. Box 757720, Fairbanks, AK 99775-7720, USA.
Am J Hum Biol. 2010 May-Jun;22(3):378-95. doi: 10.1002/ajhb.21010.
The mean measure of divergence (MMD) distance statistic has been used by researchers for nearly 50 years to assess inter-sample phenetic affinity. Its widespread and often successful use is well documented, especially in the study of cranial and dental nonmetric traits. However, the statistic has accumulated some undesired mathematical baggage through the years from various workers in their attempts to improve or alter its performance. Others may not fully understand how to apply the MMD or interpret its output, whereas some described a number of perceived shortcomings. As a result, the statistic and its sometimes flawed application(s) have taken several well-aimed hits; a few researchers even argued that it should no longer be utilized or, at least, that its use be reevaluated. The objective of this report is to support the MMD, and in the process: (1) provide a brief history of the statistic, (2) review its attributes and applicability relative to the often-used Mahalanobis D(2) statistic for nonmetric traits, (3) compare results from MMD and D(2) model-free analyses of previously-recorded sub-Saharan African dental samples, and (4) investigate its utility for model-bound analyses. In the latter instance, the ability of the D(2) and other squared Euclidean-based statistics to approximate a genetic relationship matrix and Sewall Wright's fixation index using phenotypic data, and the inability of the MMD to do so, is addressed. Three methods for obtaining such results with nonlinear MMD distances, as well as an assessment of the fit of the isolation-by-distance model, are presented.
均值差异（MMD）距离统计量已被研究人员使用近 50 年，用于评估样本间的表型亲缘关系。其广泛而成功的应用得到了很好的记录，特别是在颅面和牙齿非测量特征的研究中。然而，该统计量多年来通过不同研究人员的改进和修改，积累了一些不受欢迎的数学包袱。其他人可能不完全理解如何应用 MMD 或解释其输出，而有些描述了一些被认为的缺点。因此，该统计量及其有时有缺陷的应用受到了几次有针对性的打击；一些研究人员甚至认为它不应该再被使用，或者至少应该重新评估它的使用。本报告的目的是支持 MMD，并在这个过程中：（1）提供该统计量的简要历史；（2）相对于非测量特征常用的马氏距离（D(2)）统计量，审查其属性和适用性；（3）比较 MMD 和 D(2)非模型分析以前记录的撒哈拉以南非洲牙科样本的结果；（4）研究其在模型受限分析中的实用性。在后一种情况下，解决了 D(2)和其他基于平方欧几里得的统计量使用表型数据近似遗传关系矩阵和 Sewall Wright 的固定指数的能力，以及 MMD 不能这样做的问题。提出了三种用非线性 MMD 距离获得这些结果的方法，以及对隔离距离模型拟合的评估。
