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演化生物学分支学科而言具有重要意义，涵盖表型可塑性（phenotypic plasticity）、演化发育生物学（evolutionary developmental biology）、形态演化、生理演化、演化生态学以及行为演化等领域。上述领域的研究者通常会处理多变量表型数据。当表型变量数量超过研究对象数量时，这类数据被称为“高维数据”，此时研究者将面临分析层面的挑战。要求观测数与变量数之比足够高的参数检验会让研究者陷入两难困境：一方面，剔除变量可能会降低比较分析的效应量（effect size）；另一方面，检验统计量本身要求观测数多于变量数。针对“多维”表型的数据会加剧这一问题——这类表型的描述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）利用（数量可灵活调整的）大量解剖学地标点的笛卡尔坐标系坐标来描述生物体形态。这类形态变量共同构成了生物体形态的完整描述，但单独分析每个变量几乎无法为解答生物学问题提供有效帮助。本研究提出了一种不受表型变量数量限制的效应量非参数评估方法，并通过利用几何形态测量学数据开展表型变化分析的实例，阐明该方法的应用场景。我们的实例以一种沙漠鱼类为研究对象，对比了其身体形态的不同表征方式，用于测量并比较两个种群间的两性异形（sexual dimorphism）。研究结果表明，纳入更多表型变量可提升效应量，进而得出说服力更强的推论。