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Background Evolutionary histories can be discordant across the genome, and such discordances need to be considered in reconstructing the species phylogeny. ASTRAL is one of the leading methods for inferring species trees from gene trees while accounting for gene tree discordance. ASTRAL uses dynamic programming to search for the tree that shares the maximum number of quartet topologies with input gene trees, restricting itself to a predefined set of bipartitions. Results We introduce ASTRAL-III, which substantially improves the running time of ASTRAL-II and guarantees polynomial running time as a function of both the number of species ( n ) and the number of genes ( k ). ASTRAL-III limits the bipartition constraint set ( X ) to grow at most linearly with n and k . Moreover, it handles polytomies more efficiently than ASTRAL-II, exploits similarities between gene trees better, and uses several techniques to avoid searching parts of the search space that are mathematically guaranteed not to include the optimal tree. The asymptotic running time of ASTRAL-III in the presence of polytomies is O ( nk ) 1.726 D where D = O ( nk ) is the sum of degrees of all unique nodes in input trees. The running time improvements enable us to test whether contracting low support branches in gene trees improves the accuracy by reducing noise. In extensive simulations, we show that removing branches with very low support (e.g., below 10%) improves accuracy while overly aggressive filtering is harmful. We observe on a biological avian phylogenomic dataset of 14K genes that contracting low support branches greatly improve results. Conclusions ASTRAL-III is a faster version of the ASTRAL method for phylogenetic reconstruction and can scale up to 10,000 species. With ASTRAL-III, low support branches can be removed, resulting in improved accuracy.

Gene tree discordance in large genomic data sets can be caused by evolutionary processes such as incomplete lineage sorting and hybridization, as well as model violation, and errors in data processing, orthology inference, and gene tree estimation. Species tree methods that identify and accommodate all sources of conflict are not available, but a combination of multiple approaches can help tease apart alternative sources of conflict. Here, using a phylotranscriptomic analysis in combination with reference genomes, we test a hypothesis of ancient hybridization events within the plant family Amaranthaceae s.l. thatwas previously supported bymorphological, ecological, and Sanger-based molecular data. The data set included seven genomes and 88 transcriptomes, 17 generated for this study. We examined gene-tree discordance using coalescent-based species trees and network inference, gene tree discordance analyses, site pattern tests of introgression, topology tests, synteny analyses, and simulations. We found that a combination of processes might have generated the high levels of gene tree discordance in the backbone of Amaranthaceae s.l. Furthermore, we found evidence that three consecutive short internal branches produce anomalous trees contributing to the discordance. Overall, our results suggest that Amaranthaceae s.l. might be a product of an ancient and rapid lineage diversification, and remains, and probably will remain, unresolved. This work highlights the potential problems of identifiability associated with the sources of gene tree discordance including, in particular, phylogenetic network methods. Our results also demonstrate the importance of thoroughly testing for multiple sources of conflict in phylogenomic analyses, especially in the context of ancient, rapid radiations. We provide several recommendations for exploring conflicting signals in such situations.

Species tree reconstruction is complicated by effects of incomplete lineage sorting, commonly modeled by the multi-species coalescent model (MSC). While there has been substantial progress in developing methods that estimate a species tree given a collection of gene trees, less attention has been paid to fast and accurate methods of quantifying support. In this article, we propose a fast algorithm to compute quartet-based support for each branch of a given species tree with regard to a given set of gene trees. We then show how the quartet support can be used in the context of the MSC to compute (1) the local posterior probability (PP) that the branch is in the species tree and (2) the length of the branch in coalescent units. We evaluate the precision and recall of the local PP on a wide set of simulated and biological datasets, and show that it has very high precision and improved recall compared with multi-locus bootstrapping. The estimated branch lengths are highly accurate when gene tree estimation error is low, but are underestimated when gene tree estimation error increases. Computation of both the branch length and local PP is implemented as new features in ASTRAL.

Phylogenetic inference from genome-wide data (phylogenomics) has revolutionized the study of evolution because it enables accounting for discordance among evolutionary histories across the genome. To this end, summary methods have been developed to allow accurate and scalable inference of species trees from gene trees. However, most of these methods, including the widely used ASTRAL, can only handle single-copy gene trees and do not attempt to model gene duplication and gene loss. As a result, most phylogenomic studies have focused on single-copy genes and have discarded large parts of the data. Here, we first propose a measure of quartet similarity between single-copy and multicopy trees that accounts for orthology and paralogy. We then introduce a method called ASTRAL-Pro (ASTRAL for PaRalogs and Orthologs) to find the species tree that optimizes our quartet similarity measure using dynamic programing. By studying its performance on an extensive collection of simulated data sets and on real data sets, we show that ASTRAL-Pro is more accurate than alternative methods.

Reticulate species evolution, such as hybridization or introgression, is relatively common in nature. In the presence of reticulation, species relationships can be captured by a rooted phylogenetic network, and orthologous gene evolution can be modeled as bifurcating gene trees embedded in the species network. We present a Bayesian approach to jointly infer species networks and gene trees from multilocus sequence data. A novel birth-hybridization process is used as the prior for the species network, and we assume a multispecies network coalescent prior for the embedded gene trees. We verify the ability of our method to correctly sample from the posterior distribution, and thus to infer a species network, through simulations. To quantify the power of our method, we reanalyze two large data sets of genes from spruces and yeasts. For the three closely related spruces, we verify the previously suggested homoploid hybridization event in this clade; for the yeast data, we find extensive hybridization events. Our method is available within the BEAST 2 add-on SpeciesNetwork, and thus provides an extensible framework for Bayesian inference of reticulate evolution.

PhyloNet was released in 2008 as a software package for representing and analyzing phylogenetic networks. At the time of its release, the main functionalities in PhyloNet consisted of measures for comparing network topologies and a single heuristic for reconciling gene trees with a species tree. Since then, PhyloNet has grown significantly. The software package now includes a wide array of methods for inferring phylogenetic networks from data sets of unlinked loci while accounting for both reticulation (e.g., hybridization) and incomplete lineage sorting. In particular, PhyloNet now allows for maximum parsimony, maximum likelihood, and Bayesian inference of phylogenetic networks from gene tree estimates. Furthermore, Bayesian inference directly from sequence data (sequence alignments or biallelic markers) is implemented. Maximum parsimony is based on an extension of the “minimizing deep coalescences” criterion to phylogenetic networks, whereas maximum likelihood and Bayesian inference are based on the multispecies network coalescent. All methods allow for multiple individuals per species. As computing the likelihood of a phylogenetic network is computationally hard, PhyloNet allows for evaluation and inference of networks using a pseudolikelihood measure. PhyloNet summarizes the results of the various analyzes and generates phylogenetic networks in the extended Newick format that is readily viewable by existing visualization software.

Fully Bayesian multispecies coalescent (MSC) methods like *BEAST estimate species trees from multiple sequence alignments. Today thousands of genes can be sequenced for a given study, but using that many genes with *BEAST is intractably slow. An alternative is to use heuristic methods which compromise accuracy or completeness in return for speed. A common heuristic is concatenation, which assumes that the evolutionary history of each gene tree is identical to the species tree. This is an inconsistent estimator of species tree topology, a worse estimator of divergence times, and induces spurious substitution rate variation when incomplete lineage sorting is present. Another class of heuristics directly motivated by the MSC avoids many of the pitfalls of concatenation but cannot be used to estimate divergence times. To enable fuller use of available data and more accurate inference of species tree topologies, divergence times, and substitution rates, we have developed a new version of *BEAST called StarBEAST2. To improve convergence rates we add analytical integration of population sizes, novel MCMC operators and other optimizations. Computational performance improved by 13.5× and 13.8× respectively when analyzing two empirical data sets, and an average of 33.1× across 30 simulated data sets. To enable accurate estimates of per-species substitution rates, we introduce species tree relaxed clocks, and show that StarBEAST2 is a more powerful and robust estimator of rate variation than concatenation. StarBEAST2 is available through the BEAUTi package manager in BEAST 2.4 and above.

Abstract The relative importance of introgression for diversification has long been a highly disputed topic in speciation research and remains an open question despite the great attention it has received over the past decade. Gene flow leaves traces in the genome similar to those created by incomplete lineage sorting (ILS), and identification and quantification of gene flow in the presence of ILS is challenging and requires knowledge about the true phylogenetic relationship among the species. We use whole nuclear, plastid, and organellar genomes from 12 species in the rapidly radiated, ecologically diverse, actively hybridizing genus of peatmoss (Sphagnum) to reconstruct the species phylogeny and quantify introgression using a suite of phylogenomic methods. We found extensive phylogenetic discordance among nuclear and organellar phylogenies, as well as across the nuclear genome and the nodes in the species tree, best explained by extensive ILS following the rapid radiation of the genus rather than by postspeciation introgression. Our analyses support the idea of ancient introgression among the ancestral lineages followed by ILS, whereas recent gene flow among the species is highly restricted despite widespread interspecific hybridization known in the group. Our results contribute to phylogenomic understanding of how speciation proceeds in rapidly radiated, actively hybridizing species groups, and demonstrate that employing a combination of diverse phylogenomic methods can facilitate untangling complex phylogenetic patterns created by ILS and introgression.

When multiple speciation events occur rapidly in succession, discordant genealogies due to incomplete lineage sorting (ILS) can complicate the detection of introgression. A variety of methods, including the D-statistic (a.k.a. the \"ABBABABA test\"), have been proposed to infer introgression in the presence of ILS for a four-taxon clade. However, no integrated method exists to detect introgression using allelic patterns for more complex phylogenies. Here we explore the issues associated with previous systems of applying D-statistics to a larger tree topology, and propose new DFOIL tests as an integrated framework to infer both the taxa involved in and the direction of introgression for a symmetric five-taxon phylogeny. Using theory and simulations, we show that the DFOIL statistics correctly identify the introgression donor and recipient lineages, even at low rates of introgression. DFOIL is also shown to have extremely low false-positive rates. The DFOIL tests are computationally inexpensive to calculate and can easily be applied to phylogenomic data sets, both genome-wide and in windows of the genome. In addition, we explore both the principles and problems of introgression detection in even more complex phylogenies.

We introduce the concept of topology weighting, a method for quantifying relationships between taxa that are not necessarily monophyletic, and visualizing how these relationships change across the genome. A given set of taxa can be related in a limited number of ways, but if each taxon is represented by multiple sequences, the number of possible topologies becomes very large. Topology weighting reduces this complexity by quantifying the contribution of each taxon topology to the full tree. We describe our method for topology weighting by iterative sampling of subtrees (Twisst), and test it on both simulated and real genomic data. Overall, we show that this is an informative and versatile approach, suitable for exploring relationships in almost any genomic dataset. Scripts to implement the method described are available at http://github.com/simonhmartin/twisst.