Data from: A method for analysis of phenotypic change for phenotypes described by high-dimensional data

The analysis of phenotypic change is important for several evolutionary biology disciplines, including phenotypic plasticity, evolutionary developmental biology, morphological evolution, physiological evolution, evolutionary ecology and behavioral evolution. It is common for researchers in these disciplines to work with multivariate phenotypic data. When phenotypic variables exceed the number of research subjects—data called ‘high-dimensional data’—researchers are confronted with analytical challenges. Parametric tests that require high observation to variable ratios present a paradox for researchers, as eliminating variables potentially reduces effect sizes for comparative analyses, yet test statistics require more observations than variables. This problem is exacerbated with data that describe ‘multidimensional’ phenotypes, whereby a description of phenotype requires high-dimensional data. For example, landmark-based geometric morphometric data use the Cartesian coordinates of (potentially) many anatomical landmarks to describe organismal shape. Collectively such shape variables describe organism shape, although the analysis of each variable, independently, offers little benefit for addressing biological questions. Here we present a nonparametric method of evaluating effect size that is not constrained by the number of phenotypic variables, and motivate its use with example analyses of phenotypic change using geometric morphometric data. Our examples contrast different characterizations of body shape for a desert fish species, associated with measuring and comparing sexual dimorphism between two populations. We demonstrate that using more phenotypic variables can increase effect sizes, and allow for stronger inferences.

表型变化分析对于多个进化生物学分支学科而言至关重要，涵盖表型可塑性（phenotypic plasticity）、进化发育生物学（evolutionary developmental biology）、形态演化、生理演化、进化生态学以及行为演化等领域。上述学科的研究者通常会接触多变量表型数据。当表型变量数量超出研究对象数量时，这类数据被称为‘高维数据’，此时研究者将面临诸多分析层面的挑战。要求高观测值与变量比值的参数检验会令研究者陷入两难困境：剔除变量可能会降低比较分析的效应量，但检验统计量本身又要求观测值数量多于变量数量。当面对用于描述‘多维表型’的数据集时，这一问题会进一步恶化——此类表型的表征本身就依赖高维数据。例如，基于地标点的几何形态测量学数据（landmark-based geometric morphometric data）通过（数量可能较多的）解剖学地标（anatomical landmarks）的笛卡尔坐标（Cartesian coordinates）来描述生物体形态。此类形态变量整体可表征生物体形态，但单独分析单个变量几乎无法为解答生物学问题提供有效价值。在此，我们提出一种不受表型变量数量限制的效应量评估非参数方法，并借助基于几何形态测量学数据的表型变化示例分析来阐明该方法的应用合理性。我们的示例对比了某沙漠鱼类物种的两种不同身体形状表征方案，该方案与测量并比较两个种群间的性二态性（sexual dimorphism）直接相关。研究结果证实，引入更多表型变量可提升效应量，从而支持更具说服力的生物学推断。