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，针对多性状选择的研究数量持续增长，适应度曲面（fitness surfaces）已成为理解多元选择与演化的核心工具。然而，针对不同时间或空间尺度下多元选择曲面的严谨统计比较，长期以来仅局限于对二次回归模型估算的选择系数开展参数化分析。尽管当选择近似呈线性或二次形式时，参数化比较方法具备较高实用价值，但在应对崎岖适应度曲面的复杂特性时，这类方法的适用性存在明显局限。在此，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应度曲面的全新解决方案。通过运用本质上属于高阶主成分分析（principal components analysis）的塔克3张量分解（Tucker3 tensor decomposition），本文展示了如何对适应度曲面的核心特征进行统计比较。结合自助抽样（bootstrap）算法，本文开发了三项统计检验方法，可分别识别：1）非参数化适应度曲面的形状差异；2）不同时间或空间尺度下，各曲面对适应度变异的贡献度差异；3）随时间或空间发生显著变化的曲面特定区域（即性状组合）。本文通过理想化适应度曲面示例，对该张量分解与统计分析流程进行了演示。