ASTRAL: genome-scale coalescent-based species tree estimation

Because biological processes can result in different loci having different evolutionary histories, species tree estimation requires multiple loci from across multiple genomes. While many processes can result in discord between gene trees and species trees, incomplete lineage sorting (ILS), modeled by the multi-species coalescent, is considered to be a dominant cause for gene tree heterogeneity. Coalescent-based methods have been developed to estimate species trees, many of which operate by combining estimated gene trees, and so are called "summary methods". Because summary methods are generally fast (and much faster than more complicated coalescent-based methods that co-estimate gene trees and species trees), they have become very popular techniques for estimating species trees from multiple loci. However, recent studies have established that summary methods can have reduced accuracy in the presence of gene tree estimation error, and also that many biological datasets have substantial gene tree estimation error, so that summary methods may not be highly accurate in biologically realistic conditions. Mirarab et al. (Science 2014) presented the "statistical binning" technique to improve gene tree estimation in multi-locus analyses, and showed that it improved the accuracy of MP-EST, one of the most popular coalescent-based summary methods. Statistical binning, which uses a simple heuristic to evaluate "combinability" and then uses the larger sets of genes to re-calculate gene trees, has good empirical performance, but using statistical binning within a phylogenomic pipeline does not have the desirable property of being statistically consistent. We show that weighting the re-calculated gene trees by the bin sizes makes statistical binning statistically consistent under the multispecies coalescent, and maintains the good empirical performance. Thus, "weighted statistical binning" enables highly accurate genome-scale species tree estimation, and is also statistically consistent under the multi-species coalescent model. New data used in this study are available at DOI: http://dx.doi.org/10.6084/m9.figshare.1411146, and the software is available at https://github.com/smirarab/binning.

Implementing and testing the multispecies coalescent model: A valuable paradigm for phylogenomics.

BackgroundSpecies tree estimation is frequently based on phylogenomic approaches that use multiple genes from throughout the genome. However, estimating a species tree from a collection of gene trees can be complicated due to the presence of gene tree incongruence resulting from incomplete lineage sorting (ILS), which is modelled by the multi-species coalescent process. Maximum likelihood and Bayesian MCMC methods can potentially result in accurate trees, but they do not scale well to large datasets.ResultsWe present STELAR (Species Tree Estimation by maximizing tripLet AgReement), a new fast and highly accurate statistically consistent coalescent-based method for estimating species trees from a collection of gene trees. We formalized the constrained triplet consensus (CTC) problem and showed that the solution to the CTC problem is a statistically consistent estimate of the species tree under the multi-species coalescent (MSC) model. STELAR is an efficient dynamic programming based solution to the CTC problem which is highly accurate and scalable. We evaluated the accuracy of STELAR in comparison with SuperTriplets, which is an alternate fast and highly accurate triplet-based supertree method, and with MP-EST and ASTRAL – two of the most popular and accurate coalescent-based methods. Experimental results suggest that STELAR matches the accuracy of ASTRAL and improves on MP-EST and SuperTriplets.ConclusionsTheoretical and empirical results (on both simulated and real biological datasets) suggest that STELAR is a valuable technique for species tree estimation from gene tree distributions.

Species tree estimation from multi-locus data is complicated as biological processes can result in different loci having different evolutionary histories. Incomplete lineage sorting (ILS), modeled by the multi-species coalescent (MSC), is considered to be a dominant cause for gene tree incongruence. Various optimization criteria (e.g., quartet score, pseudo-likelihood, etc.) are statistically consistent under the MSC model, meaning that they return the true species tree with high probability given sufficiently large numbers of accurate gene trees. However, the number of genes is limited and estimating highly accurate gene trees is difficult. Therefore, even popular methods, optimizing a particular criterion, may fail to reconstruct highly accurate trees under practical model conditions with limited numbers of genes and in the presence of gene tree estimation error. In this study, we advocate multi-objective optimization to tackle this challenge. Particularly, we present a multi-objective metaheuristic (i.e., SNOGA), a modified version of the popular NSGAII, which combines various optimization criteria to find a suitable search space containing highly accurate species trees.

The estimation of species trees using multiple loci has become increasingly common. Because different loci can have different phylogenetic histories (reflected in different gene tree topologies) for multiple biological causes, new approaches to species tree estimation have been developed that take gene tree heterogeneity into account. Among these multiple causes, incomplete lineage sorting (ILS), modeled by the multi-species coalescent, is potentially the most common cause of gene tree heterogeneity, and much of the focus of the recent literature has been on how to estimate species trees in the presence of ILS. Despite progress in developing statistically consistent techniques for estimating species trees when gene trees can differ due to ILS, there is substantial controversy in the systematics community as to whether to use the new coalescent-based methods or the traditional concatenation methods. One of the key issues that has been raised is understanding the impact of gene tree estimation error on coalescent-based methods that operate by combining gene trees. Here we explore the mathematical guarantees of coalescent-based methods when analyzing estimated rather than true gene trees. Our results provide some insight into the differences between promise of coalescent-based methods in theory and their performance in practice.

During the last decades, gene trees have been often interpreted as species phylogenies. However, the extensive gene tree discordance found in multi‐locus datasets has put into question this interpretation, and a variety of new methods that explicitly consider species trees have been proposed in recent years. Some of these explicitly consider evolutionary processes that can lead to true gene tree discordance, namely incomplete lineage sorting, gene duplication and loss and horizontal gene transfer. Choosing the most appropriate species tree method for the data at hand is not straightforward due to different data prerequisites, model assumptions, analytical strategies and computational implementations.Key Concepts:We could think of at least three different phylogenetic layers corresponding to species trees, locus trees and gene trees. These depict, respectively, the history of the sampled species, loci and genes copies.Traditional phylogenetic inference has focused on the reconstruction of gene trees, assumed to be accurate proxies for species history.True species, locus and gene trees can be incongruent due to the effect of evolutionary processes like incomplete lineage sorting, gene duplication and loss and horizontal gene transfer. This incongruence might appear larger due to estimation error.Extensive gene tree incongruence unveiled in multi‐locus datasets has encouraged the development of methods that explicitly reconstruct species trees. The supermatrix approach combines loci into a super‐alignment and estimates the corresponding supergene tree. Supertree methods combine gene trees to obtain an estimate of the species tree. Other methods co‐estimate gene and species trees in a single step using full probabilistic models.Different species tree methods require distinct data specifications, mainly related with the consideration of paralogs, number of sampled species, missing taxa and number of loci.Rooting and reconstruction uncertainty must be carefully considered before choosing a species tree method.

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.

Rooted species trees are used in several downstream applications of phylogenetics. Most species tree estimation methods produce unrooted trees and additional methods are then used to root these unrooted trees. Recently, Quintet Rooting (QR) (Tabatabaee et al., ISMB and Bioinformatics 2022), a polynomial-time method for rooting an unrooted species tree given unrooted gene trees under the multispecies coalescent, was introduced. QR, which is based on a proof of identifiability of rooted 5-taxon trees in the presence of incomplete lineage sorting, was shown to have good accuracy, improving over other methods for rooting species trees when incomplete lineage sorting was the only cause of gene tree discordance, except when gene tree estimation error was very high. However, the statistical consistency of QR was left as an open question. Here, we present QR-STAR, a polynomial-time variant of QR that has an additional step for determining the rooted shape of each quintet tree. We prove that QR-STAR is statistically consistent under the multispecies coalescent model, and our simulation study shows that QR-STAR matches or improves on the accuracy of QR. QR-STAR is available in open source form at https://github.com/ytabatabaee/Quintet-Rooting.

Gene flow among populations or species and incomplete lineage sorting (ILS) are two evolutionary processes responsible for generating gene tree discordance and therefore hindering species tree estimation. Numerous studies have evaluated the impacts of ILS on species tree inference, yet the ramifications of gene flow on species trees remain less studied. Here, we simulate and analyse multilocus sequence data generated with ILS and gene flow to quantify their impacts on species tree inference. We characterize species tree estimation errors under various models of gene flow, such as the isolation-migration model, the n-island model, and gene flow between non-sister species or involving ancestral species, and species boundaries crossed by a single gene copy (allelic introgression) or by a single migrant individual. These patterns of gene flow are explored on species trees of different sizes (4 vs. 10 species), at different time scales (shallow vs. deep), and with different migration rates. Species trees are estimated with the multispecies coalescent model using Bayesian methods (BEST and *BEAST) and with a summary statistic approach (MPEST) that facilitates phylogenomic-scale analysis. Even in cases where the topology of the species tree is estimated with high accuracy, we find that gene flow can result in overestimates of population sizes (species tree dilation) and underestimates of species divergence times (species tree compression). Signatures of migration events remain present in the distribution of coalescent times for gene trees, and with sufficient data it is possible to identify those loci that have crossed species boundaries. These results highlight the need for careful sampling design in phylogeographic and species delimitation studies as gene flow, introgression, or incorrect sample assignments can bias the estimation of the species tree topology and of parameter estimates such as population sizes and divergence times.

BackgroundIncomplete lineage sorting (ILS), modelled by the multi-species coalescent (MSC), is known to create discordance between gene trees and species trees, and lead to inaccurate species tree estimations unless appropriate methods are used to estimate the species tree. While many statistically consistent methods have been developed to estimate the species tree in the presence of ILS, only ASTRAL-2 and NJst have been shown to have good accuracy on large datasets. Yet, NJst is generally slower and less accurate than ASTRAL-2, and cannot run on some datasets.ResultsWe have redesigned NJst to enable it to run on all datasets, and we have expanded its design space so that it can be used with different distance-based tree estimation methods. The resultant method, ASTRID, is statistically consistent under the MSC model, and has accuracy that is competitive with ASTRAL-2. Furthermore, ASTRID is much faster than ASTRAL-2, completing in minutes on some datasets for which ASTRAL-2 used hours.ConclusionsASTRID is a new coalescent-based method for species tree estimation that is competitive with the best current method in terms of accuracy, while being much faster. ASTRID is available in open source form on github.

Species tree estimation from multilocus data sets is extremely challenging, especially in the presence of gene tree heterogeneity across the genome due to incomplete lineage sorting (ILS). Summary methods have been developed which estimate gene trees and then combine the gene trees to estimate a species tree by optimizing various optimization scores. In this study, we have extended and adapted the concept of phylogenetic terraces to species tree estimation by "summarizing" a set of gene trees, where multiple species trees with distinct topologies may have exactly the same optimality score (i.e., quartet score, extra lineage score, etc.). We particularly investigated the presence and impacts of equally optimal trees in species tree estimation from multilocus data using summary methods by taking ILS into account. We analyzed two of the most popular ILS-aware optimization criteria: maximize quartet consistency (MQC) and minimize deep coalescence (MDC). Methods based on MQC are provably statistically consistent, whereas MDC is not a consistent criterion for species tree estimation. We present a comprehensive comparative study of these two optimality criteria. Our experiments, on a collection of data sets simulated under ILS, indicate that MDC may result in competitive or identical quartet consistency score as MQC, but could be significantly worse than MQC in terms of tree accuracy-demonstrating the presence and impacts of equally optimal species trees. This is the first known study that provides the conditions for the data sets to have equally optimal trees in the context of phylogenomic inference using summary methods. [Gene tree; incomplete lineage sorting; phylogenomic analysis, species tree; summary method.].

Genome sequencing projects routinely generate haploid consensus sequences from diploid genomes, which are effectively chimeric sequences with the phase at heterozygous sites resolved at random. The impact of phasing errors on phylogenomic analyses under the multispecies coalescent (MSC) model is largely unknown. Here, we conduct a computer simulation to evaluate the performance of four phase-resolution strategies (the true phase resolution, the diploid analytical integration algorithm which averages over all phase resolutions, computational phase resolution using the program PHASE, and random resolution) on estimation of the species tree and evolutionary parameters in analysis of multilocus genomic data under the MSC model. We found that species tree estimation is robust to phasing errors when species divergences were much older than average coalescent times but may be affected by phasing errors when the species tree is shallow. Estimation of parameters under the MSC model with and without introgression is affected by phasing errors. In particular, random phase resolution causes serious overestimation of population sizes for modern species and biased estimation of cross-species introgression probability. In general, the impact of phasing errors is greater when the mutation rate is higher, the data include more samples per species, and the species tree is shallower with recent divergences. Use of phased sequences inferred by the PHASE program produced small biases in parameter estimates. We analyze two real data sets, one of East Asian brown frogs and another of Rocky Mountains chipmunks, to demonstrate that heterozygote phase-resolution strategies have similar impacts on practical data analyses. We suggest that genome sequencing projects should produce unphased diploid genotype sequences if fully phased data are too challenging to generate, and avoid haploid consensus sequences, which have heterozygous sites phased at random. In case the analytical integration algorithm is computationally unfeasible, computational phasing prior to population genomic analyses is an acceptable alternative. [BPP; introgression; multispecies coalescent; phase; species tree.]

With the increasing availability of whole genome data, many species trees are being constructed from hundreds to thousands of loci. Although concatenation analysis using maximum likelihood is a standard approach for estimating species trees, it does not account for gene tree heterogeneity, which can occur due to many biological processes, such as incomplete lineage sorting. Coalescent species tree estimation methods, many of which are statistically consistent in the presence of incomplete lineage sorting, include Bayesian methods that coestimate the gene trees and the species tree, summary methods that compute the species tree by combining estimated gene trees, and site-based methods that infer the species tree from site patterns in the alignments of different loci. Due to concerns that poor quality loci will reduce the accuracy of estimated species trees, many recent phylogenomic studies have removed or filtered genes on the basis of phylogenetic signal and/or missing data prior to inferring species trees; little is known about the performance of species tree estimation methods when gene filtering is performed. We examine how incomplete lineage sorting, phylogenetic signal of individual loci, and missing data affect the absolute and the relative accuracy of species tree estimation methods and show how these properties affect methods' responses to gene filtering strategies. In particular, summary methods (ASTRAL-II, ASTRID, and MP-EST), a site-based coalescent method (SVDquartets within PAUP*), and an unpartitioned concatenation analysis using maximum likelihood (RAxML) were evaluated on a heterogeneous collection of simulated multilocus data sets, and the following trends were observed. Filtering genes based on gene tree estimation error improved the accuracy of the summary methods when levels of incomplete lineage sorting were low to moderate but did not benefit the summary methods under higher levels of incomplete lineage sorting, unless gene tree estimation error was also extremely high (a model condition with few replicates). Neither SVDquartets nor concatenation analysis using RAxML benefited from filtering genes on the basis of gene tree estimation error. Finally, filtering genes based on missing data was either neutral (i.e., did not impact accuracy) or else reduced the accuracy of all five methods. By providing insight into the consequences of gene filtering, we offer recommendations for estimating species tree in the presence of incomplete lineage sorting and reconcile seemingly conflicting observations made in prior studies regarding the impact of gene filtering.

The estimation of species trees typically involves the estimation of trees and alignments on many different genes, so that the species tree can be based on many different parts of the genome. This kind of phylogenomic approach to species tree estimation has the potential to produce more accurate species tree estimates, especially when gene trees can differ from the species tree due to processes such as incomplete lineage sorting (ILS), gene duplication and loss, and horizontal gene transfer. Because ILS (also called "deep coalescence") is a frequent problem in systematics, many methods have been developed to estimate species trees from gene trees or alignments that specifically take ILS into consideration. In this paper we consider the problem of estimating species trees from gene trees and alignments for the general case where the gene trees and alignments can be incomplete, which means that not all the genes contain sequences for all the species. We formalize optimization problems for this context and prove theoretical results for these problems. We also present the results of a simulation study evaluating existing methods for estimating species trees from incomplete gene trees. Our simulation study shows that *BEAST, a statistical method for estimating species trees from gene sequence alignments, produces by far the most accurate species trees. However, *BEAST can only be run on small datasets. The second most accurate method, MRP (a standard supertree method), can analyze very large datasets and produces very good trees, making MRP a potentially acceptable alternative to *BEAST for large datasets.

Species tree estimation from genes sampled from throughout the whole genome is complicated due to the gene tree-species tree discordance. Incomplete lineage sorting (ILS) is one of the most frequent causes for this discordance, where alleles can coexist in populations for periods that may span several speciation events. Quartet-based summary methods for estimating species trees from a collection of gene trees are becoming popular due to their high accuracy and statistical guarantee under ILS. Generating quartets with appropriate weights, where weights correspond to the relative importance of quartets, and subsequently amalgamating the weighted quartets to infer a single coherent species tree can allow for a statistically consistent way of estimating species trees. However, handling weighted quartets is challenging. We propose wQFM, a highly accurate method for species tree estimation from multi-locus data, by extending the quartet FM (QFM) algorithm to a weighted setting. wQFM was assessed on a collection of simulated and real biological datasets, including the avian phylogenomic dataset, which is one of the largest phylogenomic datasets to date. We compared wQFM with wQMC, which is the best alternate method for weighted quartet amalgamation, and with ASTRAL, which is one of the most accurate and widely used coalescent-based species tree estimation methods. Our results suggest that wQFM matches or improves upon the accuracy of wQMC and ASTRAL. Datasets studied in this article and wQFM (in open-source form) are available at https://github.com/Mahim1997/wQFM-2020. Supplementary data are available at Bioinformatics online.