skip to main content

Title: Probabilistic Species Tree Distances: Implementing the Multispecies Coalescent to Compare Species Trees Within the Same Model-Based Framework Used to Estimate Them
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 more » 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. « less
; ;
Award ID(s):
Publication Date:
Journal Name:
Systematic Biology
Page Range or eLocation-ID:
194 to 207
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract Stochastic models of character trait evolution have become a cornerstone of evolutionary biology in an array of contexts. While probabilistic models have been used extensively for statistical inference, they have largely been ignored for the purpose of measuring distances between phylogeny-aware models. Recent contributions to the problem of phylogenetic distance computation have highlighted the importance of explicitly considering evolutionary model parameters and their impacts on molecular sequence data when quantifying dissimilarity between trees. By comparing two phylogenies in terms of their induced probability distributions that are functions of many model parameters, these distances can be more informative than traditional approaches that rely strictly on differences in topology or branch lengths alone. Currently, however, these approaches are designed for comparing models of nucleotide substitution and gene tree distributions, and thus, are unable to address other classes of traits and associated models that may be of interest to evolutionary biologists. Here we expand the principles of probabilistic phylogenetic distances to compute tree distances under models of continuous trait evolution along a phylogeny. By explicitly considering both the degree of relatedness among species and the evolutionary processes that collectively give rise to character traits, these distances provide a foundation for comparing modelsmore »and their predictions, and for quantifying the impacts of assuming one phylogenetic background over another while studying the evolution of a particular trait. We demonstrate the properties of these approaches using theory, simulations, and several empirical datasets that highlight potential uses of probabilistic distances in many scenarios. We also introduce an open-source R package named PRDATR for easy application by the scientific community for computing phylogenetic distances under models of character trait evolution.« less
  2. 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-basedmore »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.]

    « less
  3. Abstract Species tree inference from multilocus data has emerged as a powerful paradigm in the postgenomic era, both in terms of the accuracy of the species tree it produces as well as in terms of elucidating the processes that shaped the evolutionary history. Bayesian methods for species tree inference are desirable in this area as they have been shown not only to yield accurate estimates, but also to naturally provide measures of confidence in those estimates. However, the heavy computational requirements of Bayesian inference have limited the applicability of such methods to very small data sets. In this article, we show that the computational efficiency of Bayesian inference under the multispecies coalescent can be improved in practice by restricting the space of the gene trees explored during the random walk, without sacrificing accuracy as measured by various metrics. The idea is to first infer constraints on the trees of the individual loci in the form of unresolved gene trees, and then to restrict the sampler to consider only resolutions of the constrained trees. We demonstrate the improvements gained by such an approach on both simulated and biological data.
  4. Abstract

    Contamination of a genetic sample with DNA from one or more nontarget species is a continuing concern of molecular phylogenetic studies, both Sanger sequencing studies and next-generation sequencing studies. We developed an automated pipeline for identifying and excluding likely cross-contaminated loci based on the detection of bimodal distributions of patristic distances across gene trees. When contamination occurs between samples within a data set, a comparison between a contaminated sample and its contaminant taxon will yield bimodal distributions with one peak close to zero patristic distance. This new method does not rely on a priori knowledge of taxon relatedness nor does it determine the causes(s) of the contamination. Exclusion of putatively contaminated loci from a data set generated for the insect family Cicadidae showed that these sequences were affecting some topological patterns and branch supports, although the effects were sometimes subtle, with some contamination-influenced relationships exhibiting strong bootstrap support. Long tip branches and outlier values for one anchored phylogenomic pipeline statistic (AvgNHomologs) were correlated with the presence of contamination. While the anchored hybrid enrichment markers used here, which target hemipteroid taxa, proved effective in resolving deep and shallow level Cicadidae relationships in aggregate, individual markers contained inadequate phylogenetic signal, inmore »part probably due to short length. The cleaned data set, consisting of 429 loci, from 90 genera representing 44 of 56 current Cicadidae tribes, supported three of the four sampled Cicadidae subfamilies in concatenated-matrix maximum likelihood (ML) and multispecies coalescent-based species tree analyses, with the fourth subfamily weakly supported in the ML trees. No well-supported patterns from previous family-level Sanger sequencing studies of Cicadidae phylogeny were contradicted. One taxon (Aragualna plenalinea) did not fall with its current subfamily in the genetic tree, and this genus and its tribe Aragualnini is reclassified to Tibicininae following morphological re-examination. Only subtle differences were observed in trees after the removal of loci for which divergent base frequencies were detected. Greater success may be achieved by increased taxon sampling and developing a probe set targeting a more recent common ancestor and longer loci. Searches for contamination are an essential step in phylogenomic analyses of all kinds and our pipeline is an effective solution. [Auchenorrhyncha; base-composition bias; Cicadidae; Cicadoidea; Hemiptera; phylogenetic conflict.]

    « less
  5. Abstract Motivation

    Phylogenomics faces a dilemma: on the one hand, most accurate species and gene tree estimation methods are those that co-estimate them; on the other hand, these co-estimation methods do not scale to moderately large numbers of species. The summary-based methods, which first infer gene trees independently and then combine them, are much more scalable but are prone to gene tree estimation error, which is inevitable when inferring trees from limited-length data. Gene tree estimation error is not just random noise and can create biases such as long-branch attraction.


    We introduce a scalable likelihood-based approach to co-estimation under the multi-species coalescent model. The method, called quartet co-estimation (QuCo), takes as input independently inferred distributions over gene trees and computes the most likely species tree topology and internal branch length for each quartet, marginalizing over gene tree topologies and ignoring branch lengths by making several simplifying assumptions. It then updates the gene tree posterior probabilities based on the species tree. The focus on gene tree topologies and the heuristic division to quartets enables fast likelihood calculations. We benchmark our method with extensive simulations for quartet trees in zones known to produce biased species trees and further with larger trees. We alsomore »run QuCo on a biological dataset of bees. Our results show better accuracy than the summary-based approach ASTRAL run on estimated gene trees.

    Availability and implementation

    QuCo is available on

    Supplementary information

    Supplementary data are available at Bioinformatics online.

    « less