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.

xiphophorus_genetree_pairwiseDistances Pairwise distances obtained from RAxML gene trees, averaged across genes after normalization to a median branch length of 1 within each tree. xiphophorus_morphology_Cui_etal_2013 Reduced data from Cui et al (2013). xiphophorus_networks_calibrated Calibrated networks for h=0,1,3. xiphophorus_snaq_h0 Network (h=0) obtained with SNaQ with branch lengths in coalescent units. xiphophorus_snaq_h1 Network (h=1) obtained with SNaQ with branch lengths in coalescent units. xiphophorus_snaq_h3 Network (h=3) obtained with SNaQ with branch lengths in coalescent units. xiphophorus_PCM_analysis (ipynb) Contains the Julia commands for the PCM analyses in the manuscript. Executable IJulia notebook. xiphophorus_PCM_analysis.ipynb xiphophorus_PCM_analysis (html) Contains the julia commands for the PCM analyses in the manuscript. Executed version of the ipynb file. xiphophorus_PCM_analysis.html xiphophorus_networks_calibration (ipynb) Code to calibrate the SNaQ networks, with comments. Executable IJulia notebook. xiphophorus_networks_calibration.ipynb xiphophorus_networks_calibration (html) Code to calibrate the SNaQ networks, with comments. Executed version of the ipynb file. xiphophorus_networks_calibration.html The .tre files in this repository represent networks, and are written in an extended newick format. Please refer to the companion article for a description of those networks, and to the companion scripts for instruction on how to open them using the Julia Package PhyloNetworks.

Files History: v2 File xiphophorus_PCM_analysis is updated to (1) correct an implementation error regarding power computations in an empirical case and (2) make it compatible with Julia version 1.4.1. See header of this file for more information. v1 Initial release along with the original article.