skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 10:00 PM ET on Friday, December 8 until 2:00 AM ET on Saturday, December 9 due to maintenance. We apologize for the inconvenience.

Title: Phylogenomic branch length estimation using quartets
Abstract Motivation

Branch lengths and topology of a species tree are essential in most downstream analyses, including estimation of diversification dates, characterization of selection, understanding adaptation, and comparative genomics. Modern phylogenomic analyses often use methods that account for the heterogeneity of evolutionary histories across the genome due to processes such as incomplete lineage sorting. However, these methods typically do not generate branch lengths in units that are usable by downstream applications, forcing phylogenomic analyses to resort to alternative shortcuts such as estimating branch lengths by concatenating gene alignments into a supermatrix. Yet, concatenation and other available approaches for estimating branch lengths fail to address heterogeneity across the genome.


In this article, we derive expected values of gene tree branch lengths in substitution units under an extension of the multispecies coalescent (MSC) model that allows substitutions with varying rates across the species tree. We present CASTLES, a new technique for estimating branch lengths on the species tree from estimated gene trees that uses these expected values, and our study shows that CASTLES improves on the most accurate prior methods with respect to both speed and accuracy.

Availability and implementation

CASTLES is available at

more » « less
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Page Range / eLocation ID:
p. i185-i193
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    A potential shortcoming of concatenation methods for species tree estimation is their failure to account for incomplete lineage sorting. Coalescent methods address this problem but make various assumptions that, if violated, can result in worse performance than concatenation. Given the challenges of analyzing DNA sequences with both concatenation and coalescent methods, retroelement insertions (RIs) have emerged as powerful phylogenomic markers for species tree estimation. Here, we show that two recently proposed quartet-based methods, SDPquartets and ASTRAL_BP, are statistically consistent estimators of the unrooted species tree topology under the coalescent when RIs follow a neutral infinite-sites model of mutation and the expected number of new RIs per generation is constant across the species tree. The accuracy of these (and other) methods for inferring species trees from RIs has yet to be assessed on simulated data sets, where the true species tree topology is known. Therefore, we evaluated eight methods given RIs simulated from four model species trees, all of which have short branches and at least three of which are in the anomaly zone. In our simulation study, ASTRAL_BP and SDPquartets always recovered the correct species tree topology when given a sufficiently large number of RIs, as predicted. A distance-based method (ASTRID_BP) and Dollo parsimony also performed well in recovering the species tree topology. In contrast, unordered, polymorphism, and Camin–Sokal parsimony (as well as an approach based on MDC) typically fail to recover the correct species tree topology in anomaly zone situations with more than four ingroup taxa. Of the methods studied, only ASTRAL_BP automatically estimates internal branch lengths (in coalescent units) and support values (i.e., local posterior probabilities). We examined the accuracy of branch length estimation, finding that estimated lengths were accurate for short branches but upwardly biased otherwise. This led us to derive the maximum likelihood (branch length) estimate for when RIs are given as input instead of binary gene trees; this corrected formula produced accurate estimates of branch lengths in our simulation study provided that a sufficiently large number of RIs were given as input. Lastly, we evaluated the impact of data quantity on species tree estimation by repeating the above experiments with input sizes varying from 100 to 100,000 parsimony-informative RIs. We found that, when given just 1000 parsimony-informative RIs as input, ASTRAL_BP successfully reconstructed major clades (i.e., clades separated by branches $>0.3$ coalescent units) with high support and identified rapid radiations (i.e., shorter connected branches), although not their precise branching order. The local posterior probability was effective for controlling false positive branches in these scenarios. [Coalescence; incomplete lineage sorting; Laurasiatheria; Palaeognathae; parsimony; polymorphism parsimony; retroelement insertions; species trees; transposon.]

    more » « less
  2. Abstract

    Gene‐tree‐inference error can cause species‐tree‐inference artefacts in summary phylogenomic coalescent analyses. Here we integrate two ways of accommodating these inference errors: collapsing arbitrarily or dubiously resolved gene‐tree branches, and subsampling gene trees based on their pairwise congruence. We tested the effect of collapsing gene‐tree branches with 0% approximate‐likelihood‐ratio‐test (SH‐like aLRT) support in likelihood analyses and strict consensus trees for parsimony, and then subsampled those partially resolved trees based on congruence measures that do not penalize polytomies. For this purpose we developed a new TNT script for congruence sorting (congsort), and used it to calculate topological incongruence for eight phylogenomic datasets using three distance measures: standard Robinson–Foulds (RF) distances; overall success of resolution (OSR), which is based on counting both matching and contradicting clades; and RF contradictions, which only counts contradictory clades. As expected, we found that gene‐tree incongruence was often concentrated in clades that are arbitrarily or dubiously resolved and that there was greater congruence between the partially collapsed gene trees and the coalescent and concatenation topologies inferred from those genes. Coalescent branch lengths typically increased as the most incongruent gene trees were excluded, although branch supports typically did not. We investigated two successful and complementary approaches to prioritizing genes for investigation of alignment or homology errors. Coalescent‐tree clades that contradicted concatenation‐tree clades were generally less robust to gene‐tree subsampling than congruent clades. Our preferred approach to collapsing likelihood gene‐tree clades (0% SH‐like aLRT support) and subsampling those trees (OSR) generally outperformed competing approaches for a large fungal dataset with respect to branch lengths, support and congruence. We recommend widespread application of this approach (and strict consensus trees for parsimony‐based analyses) for improving quantification of gene‐tree congruence/conflict, estimating coalescent branch lengths, testing robustness of coalescent analyses to gene‐tree‐estimation error, and improving topological robustness of summary coalescent analyses. This approach is quick and easy to implement, even for huge datasets.

    more » « less
  3. Abstract

    To examine phylogenetic heterogeneity in turtle evolution, we collected thousands of high-confidence single-copy orthologs from 19 genome assemblies representative of extant turtle diversity and estimated a phylogeny with multispecies coalescent and concatenated partitioned methods. We also collected next-generation sequences from 26 turtle species and assembled millions of biallelic markers to reconstruct phylogenies based on annotated regions from the western painted turtle (Chrysemys picta bellii) genome (coding regions, introns, untranslated regions, intergenic, and others). We then measured gene tree-species tree discordance, as well as gene and site heterogeneity at each node in the inferred trees, and tested for temporal patterns in phylogenomic conflict across turtle evolution. We found strong and consistent support for all bifurcations in the inferred turtle species phylogenies. However, a number of genes, sites, and genomic features supported alternate relationships between turtle taxa. Our results suggest that gene tree-species tree discordance in these data sets is likely driven by population-level processes such as incomplete lineage sorting. We found very little effect of substitutional saturation on species tree topologies, and no clear phylogenetic patterns in codon usage bias and compositional heterogeneity. There was no correlation between gene and site concordance, node age, and DNA substitution rate across most annotated genomic regions. Our study demonstrates that heterogeneity is to be expected even in well-resolved clades such as turtles, and that future phylogenomic studies should aim to sample as much of the genome as possible in order to obtain accurate phylogenies for assessing conservation priorities in turtles. [Discordance; genomes; phylogeny; turtles.]

    more » « less
  4. Abstract Despite the ubiquitous use of statistical models for phylogenomic and population genomic inferences, this model-based rigor is rarely applied to post hoc comparison of trees. In a recent study, Garba et al. derived new methods for measuring the distance between two gene trees computed as the difference in their site pattern probability distributions. Unlike traditional metrics that compare trees solely in terms of geometry, these measures consider gene trees and associated parameters as probabilistic models that can be compared using standard information theoretic approaches. Consequently, probabilistic measures of phylogenetic tree distance can be far more informative than simply comparisons of topology and/or branch lengths alone. However, in their current form, these distance measures are not suitable for the comparison of species tree models in the presence of gene tree heterogeneity. Here, we demonstrate an approach for how the theory of Garba et al. (2018), which is based on gene tree distances, can be extended naturally to the comparison of species tree models. Multispecies coalescent (MSC) models parameterize the discrete probability distribution of gene trees conditioned upon a species tree with a particular topology and set of divergence times (in coalescent units), and thus provide a framework for measuring distances between species tree models in terms of their corresponding gene tree topology probabilities. We describe the computation of probabilistic species tree distances in the context of standard MSC models, which assume complete genetic isolation postspeciation, as well as recent theoretical extensions to the MSC in the form of network-based MSC models that relax this assumption and permit hybridization among taxa. We demonstrate these metrics using simulations and empirical species tree estimates and discuss both the benefits and limitations of these approaches. We make our species tree distance approach available as an R package called pSTDistanceR, for open use by the community. 
    more » « less
  5. It has long been appreciated that analyses of genomic data (e.g., whole genome sequencing or sequence capture) have the potential to reveal the tree of life, but it remains challenging to move from sequence data to a clear understanding of evolutionary history, in part due to the computational challenges of phylogenetic estimation using genome-scale data. Supertree methods solve that challenge because they facilitate a divide-and-conquer approach for large-scale phylogeny inference by integrating smaller subtrees in a computationally efficient manner. Here, we combined information from sequence capture and whole-genome phylogenies using supertree methods. However, the available phylogenomic trees had limited overlap so we used taxon-rich (but not phylogenomic) megaphylogenies to weave them together. This allowed us to construct a phylogenomic supertree, with support values, that included 707 bird species (~7% of avian species diversity). We estimated branch lengths using mitochondrial sequence data and we used these branch lengths to estimate divergence times. Our time-calibrated supertree supports radiation of all three major avian clades (Palaeognathae, Galloanseres, and Neoaves) near the Cretaceous-Paleogene (K-Pg) boundary. The approach we used will permit the continued addition of taxa to this supertree as new phylogenomic data are published, and it could be applied to other taxa as well. 
    more » « less