Department of Genetics, North Carolina State University, Raleigh, NC, USA.
Evolution. 2012 Apr;66(4):1126-37. doi: 10.1111/j.1558-5646.2011.01503.x. Epub 2011 Nov 27.
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 nonparametric 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 nonparametric 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，随着估计多个性状选择的研究数量的增加，适应度表面已成为理解多变量选择和进化的基本工具。然而，对随时间或空间变化的多变量选择表面进行严格的统计比较，仅限于使用二次回归模型估计选择系数的参数分析。虽然当选择本质上是线性或二次时，参数比较是有用的，但当面对崎岖不平的适应度表面的复杂性质时，它们是有限的。在这里，我提出了一种比较随时间或空间变化的非参数适应度表面的新方法。使用 Tucker3 张量分解，它本质上是一种高阶主成分分析，我展示了如何在统计上比较适应度表面的主要特征。结合自举算法，我开发了三个统计检验，用于识别（1）非参数适应度表面形状的差异，（2）每个表面在跨时间或空间的适应度变化中的贡献差异，以及（3）表面的特定区域（性状组合）随时间或空间的显著变化。我使用理想化的适应度表面来说明张量分解和统计分析。
