Data from: Inference of adaptive shifts for multivariate correlated traits

To study the evolution of several quantitative traits, the classical phylogenetic comparative framework consists of a multivariate random process running along the branches of a phylogenetic tree. The Ornstein-Uhlenbeck (OU) process is sometimes preferred to the simple Brownian Motion (BM) as it models stabilizing selection toward an optimum. The optimum for each trait is likely to be changing over the long periods of time spanned by large modern phylogenies. Our goal is to automatically detect the position of these shifts on a phylogenetic tree, while accounting for correlations between traits, which might exist because of structural or evolutionary constraints. We show that, in the presence shifts, phylogenetic Principal Component Analysis (pPCA) fails to decorrelate traits efficiently, so that any method aiming at finding shift needs to deal with correlation simultaneously. We introduce here a simplification of the full multivariate OU model, named scalar OU (scOU), which allows for noncausal correlations and is still computationally tractable. We extend the equivalence between the OU and a BM on a re-scaled tree to our multivariate framework. We describe an Expectation Maximization algorithm that allows for a maximum likelihood estimation of the shift positions, associated with a new model selection criterion, accounting for the identifiability issues for the shift localization on the tree. The method, freely available as an R-package (PhylogeneticEM) is fast, and can deal with missing values. We demonstrate its efficiency and accuracy compared to another state-of-the-art method (l1ou) on a wide range of simulated scenarios, and use this new framework to re-analyze recently gathered datasets on New World Monkeys and Anolis lizards.

为探究多个数量性状的进化规律，经典的系统发育比较框架依托于在系统发育树各分支上运行的多元随机过程。相较于简单的布朗运动（Brownian Motion, BM），奥恩斯坦-乌伦贝克（Ornstein-Uhlenbeck, OU）过程常更受青睐，因其可模拟向最优值的稳定选择。在大型现代系统发育所覆盖的漫长时间尺度中，各性状的最优值大概率会发生变化。我们的研究目标是，在考虑性状间可能因结构或进化约束而存在的相关性的前提下，自动检测这些最优值漂移在系统发育树上的位点。研究表明，当存在此类漂移时，系统发育主成分分析（phylogenetic Principal Component Analysis, pPCA）无法有效去除性状间的相关性，因此任何旨在检测漂移的方法都需同时处理相关性问题。本文提出一种针对完整多元OU模型的简化版本，命名为标量OU（scalar OU, scOU）模型，该模型可容纳非因果相关性，且仍具备计算可处理性。我们将重标度树上OU过程与布朗运动的等价关系推广至多元分析框架中。本文描述了一种期望最大化（Expectation Maximization, EM）算法，该算法可实现漂移位点的最大似然估计，并配套提出新的模型选择准则，同时考虑了树上游移定位的可识别性问题。该方法已以R包（PhylogeneticEM）的形式免费公开，运行速度快且支持缺失值处理。我们在大量模拟场景中验证了该方法相较于另一项当前最先进的方法（l1ou）的效率与准确性，并利用这一新框架重新分析了近期采集的新世界猴与安乐蜥属蜥蜴相关数据集。