Phylogenetic history of the bread wheat.

<p>(<b>A</b>–<b>C</b>) The three phylogenetic networks that comprise the 95% credible set, (<b>D</b>) and a plausible summary of the three networks that is consistent with the model of phylogenetic history of bread wheat (Fig 3 in [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1006006#pgen.1006006.ref029" target="_blank">29</a>]).</p

The seven moves that the MCMC sampler utilizes can be classified into ones that do not modify the topology of the phylogenetic network (moves 1 and 2), ones that modify the topology but do not change the model’s dimensions (moves 3, 4, and 5), and ones that modify the topology and model’s dimensions (moves 6 and 7).

<p>The current-state phylogenetic network is shown at the center in dark blue, and the resulting next-state phylogenetic network after each moves is show in black lines. Moves 1 and 2 modify branch lengths and inheritance probabilities, respectively. Moves 3–5 relocate one of the children of a tree node, relocate the head of a reticulation edge, and reverse the direction of a reticulation edge, respectively. Moves 6 and 7 add and remove a reticulation edge, respectively. The probabilities <i>κ</i> and <i>ω</i> determine which of the three groups of moves is selected in an iteration. Within each group, an edge is selected and a move is selected uniformly at random among all the ones that are applicable to the selected edge within that group.</p

Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent

<div><p>The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation.</p></div

The multispecies coalescent on trees and networks.

<p>(<b>A</b>) The multispecies coalescent (MSC) links populations by a tree structure and allows for modeling gene genealogies within the branches of a species tree. The gene genealogy indicated by thick lines inside the species tree is incongruent with the species tree due to incomplete lineage sorting (ILS). (<b>B</b>) The multispecies network coalescent (MSNC) links populations by a network structure, thus allowing for reticulations events among populations. The gene genealogy indicated by thick lines inside the species network is involved in reticulation, e.g., hybridization. The gene genealogies in both panels have the same topologies, but have different probabilities under the MSC and MSNC models.</p

The 7 moves that the Metropolis-Hastings algorithm employs.

<p>The 7 moves that the Metropolis-Hastings algorithm employs.</p

PGENETICS-D-15-02479R1-DATA

This directory contains four input files on which PhyloNet can be run to conduct the Bayesian analyses reported in the paper for the four data sets (the wheat data set, the mouse data set, the mosquito autosome data set, and the mosquito X chromosome data set)

Phylogenetic history of the six mosquito genomes.

<p>(<b>A</b>) The single phylogenetic network in the 95% credible set sampled on the X chromosome data. (<b>B</b>) A summary of the three phylogenetic networks in the 95% credible set sampled on the autosome data. The dotted circle indicates the temporal order of the two reticulation events involving R cannot be discerned with confidence from the data.</p

MAF.tar

MAF.ta

The topological distance (pink) between sampled networks and true network, and the Robinson-Foulds distance (orange) between sampled trees and true backbone tree, under different simulation settings and violation in the different assumptions.

<p>In each panel at most one condition is violated. (a) Mean of 1.0 is used for the Poisson prior on the number of reticulations. (b) Mean of 3.0 is used for the Poisson prior on the number of reticulations. (c) Linked loci: 10 sites are generated per gene tree. (d) Linked loci: 100 sites are generated per gene tree. (e) Rate variation across lineages with 0.1 of invariable sites and 3.0 as shape of gamma rate heterogeneity. (f) Rate variation across lineages with 0.2 of invariable sites and 5.0 as shape of gamma rate heterogeneity. (g) Rate variation across markers with 0.1 of invariable sites and 3.0 as shape of gamma rate heterogeneity. (h) Rate variation across markers with 0.2 of invariable sites and 5.0 as shape of gamma rate heterogeneity.</p

Illustrating the “growth” of lineages of a gene tree in a phylogenetic network.

<p>The histories of green and red alleles are shown as solid (green) lines and dashed (red) lines, respectively.</p