Researchers using geometric morphometric methods can be confronted with a need to combine separate landmark configurations from the same research subjects as a more holistic description of organismal morphology. Combining configurations might be valid if single configurations represent separate anatomical structures that can change position with respect to each other or have been shown to be phenotypically integrated, and researchers would prefer to recognize these structures as one set, rather than multiple sets. However, generalized Procrustes analysis (GPA) scales separate configurations to unit size, meaning that in combination, some attempt to relativize the size of configurations should be made. A few recent studies have calculated the relative size of separate configurations in different ways but there has been no formal consideration for the implications of a priori judgments for how configuration sizes should be weighted, before the synthesis presented here. We offer a general solution for weighting separate configuration centroid sizes when combining them, which captures the intention of different methods thus far proposed. We also demonstrate that under various conditions, weighting via normalized centroid size is fraught with problems, and should be avoided. By contrast, an unweighted approach that seeks to maintain landmark densities in separate configurations provides reliable results. Nevertheless, researchers should realize that combining configurations creates new configurations with landmark covariances that are arbitrary with respect to any real anatomical features. As such, combining landmark configurations should not be a haphazard enterprise under any circumstances.

中文翻译：

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在几何形态计量学数据中组合地标配置的首尾

使用几何形态计量学方法的研究人员可能需要将来自同一研究主题的独立界标配置组合在一起，以更全面地描述生物形态。如果单个配置代表可以彼此相对改变位置的单独解剖结构，或者已被证明是表型整合的，则组合配置可能是有效的，并且研​​究人员希望将这些结构识别为一组，而不是多组。但是，广义Procrustes分析（GPA）将单独的配置按比例缩放到单位大小，这意味着在组合使用时，应该做出一些使配置大小相对化的尝试。最近的一些研究以不同的方式计算了单独构型的相对大小，但是在这里提出的综合之前，尚未正式考虑先验判断对应如何加权构型大小的影响。当组合它们时，我们为加权单独的配置质心大小提供了一种通用的解决方案，该解决方案抓住了迄今为止提出的不同方法的意图。我们还证明，在各种条件下，通过归一化质心大小进行加权会遇到很多问题，应避免使用。相比之下，试图在单独的配置中保持界标密度的未加权方法提供了可靠的结果。不过，研究人员应该认识到，组合构型会创建具有界标协方差的新构型，而这些协方差对于任何实际解剖特征都是任意的。因此，在任何情况下，组合地标配置都不应该是偶然的企业。