Data from: Exploring variation in fitness surfaces over time or space

As the number of studies estimating selection on multiple traits has increased in recent years, fitness surfaces have become a fundamental tool for understanding multivariate selection and evolution. However, rigorous statistical comparisons of multivariate selection surfaces over time or space have been limited to parametric analyses of selection coefficients estimated using a quadratic regression model. Although parametric comparisons are useful when selection is approximately linear or quadratic in nature, they are limited when confronting the complex nature of rugged fitness surfaces. Here, I present a novel solution to comparing non-parametric fitness surfaces over time or space. Using a Tucker3 tensor decomposition, which is essentially a higher-order principal components analysis, I show how major features of fitness surfaces can be compared statistically. Combined with a bootstrap algorithm, I develop three statistical tests that identify 1) Differences in the shape of non-parametric fitness surfaces, 2) Differences in the contribution of each surface to variation in fitness across time or space, and 3) Specific areas of the surfaces (trait combinations) that vary significantly over time or space. I illustrate the tensor decomposition and statistical analyses using idealized fitness surfaces.

近年来，针对多性状选择的评估研究数量持续增长，适合度曲面（fitness surfaces）已成为理解多变量选择与生物演化的核心工具。然而，长期以来针对不同时间或空间尺度下多变量选择曲面的严谨统计比较，仅局限于对通过二次回归模型估算得到的选择系数开展参数化分析。尽管当选择本质上近似线性或二次形式时，参数化比较具备应用价值，但当面对崎岖型适合度曲面的复杂特性时，这类方法便存在局限。为此，本文提出一种可用于比较不同时间或空间尺度下非参数化适合度曲面的全新解决方案。本文采用本质上属于高阶主成分分析的Tucker3张量分解（Tucker3 tensor decomposition）方法，阐明了如何对适合度曲面的核心特征开展统计比较。结合Bootstrap算法（bootstrap algorithm），本文构建了三类统计检验，可分别实现：1）非参数化适合度曲面的形态差异识别；2）不同曲面对不同时间或空间尺度下适合度变异的贡献度差异识别；3）曲面中随时间或空间发生显著变化的特定区域（即性状组合）识别。本文通过理想化适合度曲面示例，对张量分解与统计分析流程进行了演示说明。