Data from: Evaluating modularity in morphometric data: challenges with the RV coefficient and a new test measure

1: Modularity describes the case where patterns of trait covariation are unevenly dispersed across traits. Specifically, trait correlations are high and concentrated within subsets of variables (modules), but the correlations between traits across modules are relatively weaker. For morphometric datasets, hypotheses of modularity are commonly evaluated using the RV coefficient, an association statistic used in a wide variety of fields. 2: In this article I explore the properties of the RV coefficient using simulated data sets. Using data drawn from a normal distribution where the data were neither modular nor integrated in structure, I show that the RV coefficient is adversely affected by attributes of the data (sample size and the number of variables) that do not characterize the covariance structure between sets of variables. Thus, with the RV coefficient, patterns of modularity or integration in data are confounded with trends generated by sample size and the number of variables, which limits biological interpretations and renders comparisons of RV coefficients across datasets uninformative. 3: As an alternative I propose the covariance ratio (CR) for quantifying modular structure, and show that it is unaffected by sample size or the number of variables. Further, statistical tests based on the CR exhibit appropriate type I error rates, and display higher statistical power relative to the RV coefficient when evaluating modular data. 4: Overall, these findings demonstrate that the RV coefficient does not display statistical characteristics suitable for reliable assessment of hypotheses of modular or integrated structure, and therefore should not be used to evaluate these patterns in morphological datasets. By contrast, the covariance ratio meets these criteria and provides a useful alternative method for assessing the degree of modular structure in morphological data.

1: 模块化（modularity）描述的是性状协变模式在不同性状间分布不均的情况。具体而言，性状间的相关性较高且集中于变量子集（模块，modules）内，但跨模块的性状间相关性相对较弱。针对形态计量数据集（morphometric datasets），模块化假说通常通过RV系数（RV coefficient）进行检验，该关联统计量已被广泛应用于诸多研究领域。2: 本文基于模拟数据集探究了RV系数的统计特性。本文采用来自正态分布、既无模块化结构也无整合结构的数据集开展研究，结果表明，RV系数会受到数据本身属性（样本量与变量数量）的不利影响，而这些属性并不能反映变量组间的协方差结构。由此可见，采用RV系数时，数据中的模块化或整合模式会与样本量、变量数量所产生的趋势相混淆，这限制了其生物学解释性，且使得不同数据集间的RV系数比较失去参考价值。3: 为此，本文提出协方差比（covariance ratio，CR）以量化模块化结构，并证明该统计量不受样本量与变量数量的影响。进一步研究表明，基于协方差比的统计检验具备合适的一类错误（type I error）率，且在评估模块化数据时，相较RV系数拥有更高的统计效力。4: 综上，本研究结果表明，RV系数并不具备可靠评估模块化或整合结构假说所需的统计特性，因此不应被用于形态计量数据中的此类模式检验。相较而言，协方差比满足上述标准，可为量化形态计量数据中的模块化结构程度提供一种可靠的替代方法。