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，针对多性状选择效应的研究数量持续增长，适应度曲面（fitness surface）已成为理解多变量选择与演化过程的核心工具。然而，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，长期以来仅局限于基于二次回归模型估算的选择系数所开展的参数化分析。尽管当选择效应近似呈线性或二次形式时，参数化比较方法具备一定应用价值，但在处理崎岖型适应度曲面（rugged fitness surface）的复杂特征时，这类方法的适用性会受到极大限制。为此，本文提出了一种可用于比较不同时间或空间尺度下非参数化适应度曲面的全新解决方案。本文借助本质上属于高阶主成分分析的Tucker3张量分解（Tucker3 tensor decomposition）方法，阐明了如何通过统计手段对适应度曲面的核心特征进行比较。结合bootstrap算法（bootstrap），本文构建了三类统计检验方法，可分别实现以下目标：1）识别非参数化适应度曲面的形态差异；2）比较不同曲面在不同时间或空间尺度下对适应度变异的贡献程度；3）检测曲面中随时间或空间发生显著变化的特定区域（即性状组合区域）。本文通过理想化适应度曲面示例，对上述张量分解与统计分析流程进行了演示说明。