Data from: Phylogenetic comparative methods on phylogenetic networks with reticulations

The goal of Phylogenetic Comparative Methods (PCMs) is to study the distribution of quantitative traits among related species. The observed traits are often seen as the result of a Brownian Motion (BM) along the branches of a phylogenetic tree. Reticulation events such as hybridization, gene flow or horizontal gene transfer, can substantially affect a species' traits, but are not modeled by a tree. Phylogenetic networks have been designed to represent reticulate evolution. As they become available for downstream analyses, new models of trait evolution are needed, applicable to networks. One natural extension of the BM is to use a weighted average model for the trait of a hybrid, at a reticulation point. We develop here an efficient recursive algorithm to compute the phylogenetic variance matrix of a trait on a network, in only one preorder traversal of the network. We then extend the standard PCM tools to this new framework, including phylogenetic regression with covariates (or phylogenetic ANOVA), ancestral trait reconstruction, and Pagel's λ test of phylogenetic signal. The trait of a hybrid is sometimes outside of the range of its two parents, for instance because of hybrid vigor or hybrid depression. These two phenomena are rather commonly observed in present-day hybrids. Transgressive evolution can be modeled as a shift in the trait value following a reticulation point. We develop a general framework to handle such shifts, and take advantage of the phylogenetic regression view of the problem to design statistical tests for ancestral transgressive evolution in the evolutionary history of a group of species. We study the power of these tests in several scenarios, and show that recent events have indeed the strongest impact on the trait distribution of present-day taxa. We apply those methods to a dataset of Xiphophorus fishes, to confirm and complete previous analysis in this group. All the methods developed here are available in the Julia package PhyloNetworks.系统发育比较方法（Phylogenetic Comparative Methods, PCMs）的核心目标是探究近缘物种间数量性状的分布规律。观测所得的性状通常被视作沿系统发育树分支开展的布朗运动（Brownian Motion, BM）的产物。然而，杂交、基因流或水平基因转移等网状演化事件会显著改变物种性状，但传统系统发育树无法对这类事件进行建模。系统发育网络（Phylogenetic networks）正是为表征网状演化而设计的分析工具。随着其在下游分析中的应用愈发普及，亟需适配网络结构的全新性状演化模型。 布朗运动模型的一项自然拓展，是在网状事件节点处为杂种性状采用加权平均模型。本文提出一种高效的递归算法，仅需对系统发育网络进行一次前序遍历（preorder traversal），即可计算得到性状在网络上的系统发育方差矩阵。随后，我们将标准系统发育比较方法工具拓展至该新框架中，涵盖带协变量的系统发育回归（即系统发育方差分析（phylogenetic ANOVA））、祖先性状重建（ancestral trait reconstruction），以及Pagel’s λ系统发育信号检验（Pagel's λ test of phylogenetic signal）。 部分杂种的性状会超出其双亲的性状范围，例如由杂种优势（hybrid vigor）或杂种衰退（hybrid depression）引发的情况，这类现象在现生杂种中较为常见。 超亲演化（transgressive evolution）可被建模为网状事件发生后出现的性状值偏移。我们构建了一套通用框架以处理此类偏移，并借助系统发育回归的研究视角，设计了用于检测物种类群演化历史中祖先超亲演化的统计检验方法。 我们在多种场景下评估了上述检验的效能，结果显示近期发生的网状事件对现生类群的性状分布影响最为显著。 我们将所提方法应用于剑尾鱼属（Xiphophorus）鱼类的数据集，验证并完善了该类群此前的相关研究。 本文开发的所有方法均已在Julia语言的PhyloNetworks工具包中实现。