STELAR: a statistically consistent coalescent-based species tree estimation method by maximizing triplet consistency

wQFM-TREE: highly accurate and scalable quartet-based species tree inference from gene trees

Motivation

methods are becoming increasingly popular for species tree estimation from multi-locus data in the presence of gene tree discordance. Accurate Species TRee Algorithm (ASTRAL), a leading method in this class, solves the Maximum Quartet Support Species Tree problem within a constrained solution space, while heuristics like Weighted Quartet Fiduccia-Mattheyses (wQFM) and Weighted Quartet MaxCut (wQMC) use weighted quartets and a divide-and-conquer strategy. Recent studies showed wQFM to be more accurate than ASTRAL and wQMC, though its scalability is hindered by the computational demands of explicitly generating and weighting Θ ( n 4 ) quartets. Here, we introduce wQFM-TREE, a novel summary method that enhances wQFM by avoiding explicit quartet generation and weighting, enabling its application to large datasets.

Results

Extensive simulations under diverse and challenging model conditions, with hundreds or thousands of taxa and genes, consistently demonstrate that wQFM-TREE matches or improves upon the accuracy of ASTRAL. It outperformed ASTRAL in 25 of 27 model conditions (statistically significant in 20) involving 200-1000 taxa. Moreover, applying wQFM-TREE to re-analyze the green plant dataset from the One Thousand Plant Transcriptomes Initiative produced a tree highly congruent with established evolutionary relationships of plants. wQFM-TREE's remarkable accuracy and scalability make it a strong competitor to leading methods. Its algorithmic and combinatorial innovations also enhance quartet-based computations, advancing phylogenetic estimation.

Availability and implementation

wQFM-TREE is freely available in open source form at https://github.com/abdur-rafi/wQFM-TREE.

wQFM-DISCO: DISCO-enabled wQFM improves phylogenomic analyses despite the presence of paralogs

Motivation

Gene trees often differ from the species trees that contain them due to various factors, including incomplete lineage sorting (ILS) and gene duplication and loss (GDL). Several highly accurate species tree estimation methods have been introduced to explicitly address ILS, including ASTRAL, a widely used statistically consistent method, and wQFM, a quartet amalgamation approach experimentally shown to be more accurate than ASTRAL. Two recent advancements, ASTRAL-Pro and DISCO, have emerged in phylogenomics to consider GDL. ASTRAL-Pro introduces a refined quartet similarity measure, accounting for orthology and paralogy. On the other hand, DISCO offers a general strategy to decompose multi-copy gene trees into a collection of single-copy trees, allowing the utilization of methods previously designed for species tree inference in the context of single-copy gene trees.

Results

In this study, we first introduce some variants of DISCO to examine its underlying hypotheses and present analytical results on the statistical guarantees of DISCO. In particular, we introduce DISCO-R, a variant of DISCO with a refined and improved pruning strategy that provides more accurate and robust results. We then demonstrate with extensive evaluation studies on a collection of simulated and real data sets that wQFM paired with DISCO variants consistently matches or outperforms ASTRAL-Pro and other competing methods.

Availability and implementation

DISCO-R and other variants are freely available at https://github.com/skhakim/DISCO-variants.

Terraces in species tree inference from gene trees

A terrace in a phylogenetic tree space is a region where all trees contain the same set of subtrees, due to certain patterns of missing data among the taxa sampled, resulting in an identical optimality score for a given data set. This was first investigated in the context of phylogenetic tree estimation from sequence alignments using maximum likelihood (ML) and maximum parsimony (MP). It was later extended to the species tree inference problem from a collection of gene trees, where a set of equally optimal species trees was referred to as a "pseudo" species tree terrace which does not consider the topological proximity of the trees in terms of the induced subtrees resulting from certain patterns of missing data. In this study, we mathematically characterize species tree terraces and investigate the mathematical properties and conditions that lead multiple species trees to induce/display an identical set of locus-specific subtrees owing to missing data. We report that species tree terraces are agnostic to gene tree heterogeneity. Therefore, we introduce and characterize a special type of gene tree topology-aware terrace which we call "peak terrace". Moreover, we empirically investigated various challenges and opportunities related to species tree terraces through extensive empirical studies using simulated and real biological data. We demonstrate the prevalence of species tree terraces and the resulting ambiguity created for tree search algorithms. Remarkably, our findings indicate that the identification of terraces could potentially lead to advances that enhance the accuracy of summary methods and provide reasonably accurate branch support.

Dollo-CDP: a polynomial-time algorithm for the clade-constrained large Dollo parsimony problem

The last decade of phylogenetics has seen the development of many methods that leverage constraints plus dynamic programming. The goal of this algorithmic technique is to produce a phylogeny that is optimal with respect to some objective function and that lies within a constrained version of tree space. The popular species tree estimation method ASTRAL, for example, returns a tree that (1) maximizes the quartet score computed with respect to the input gene trees and that (2) draws its branches (bipartitions) from the input constraint set. This technique has yet to be used for parsimony problems where the input are binary characters, sometimes with missing values. Here, we introduce the clade-constrained character parsimony problem and present an algorithm that solves this problem for the Dollo criterion score in [Formula: see text] time, where n is the number of leaves, k is the number of characters, and [Formula: see text] is the set of clades used as constraints. Dollo parsimony, which requires traits/mutations to be gained at most once but allows them to be lost any number of times, is widely used for tumor phylogenetics as well as species phylogenetics, for example analyses of low-homoplasy retroelement insertions across the vertebrate tree of life. This motivated us to implement our algorithm in a software package, called Dollo-CDP, and evaluate its utility for analyzing retroelement insertion presence / absence patterns for bats, birds, toothed whales as well as simulated data. Our results show that Dollo-CDP can improve upon heuristic search from a single starting tree, often recovering a better scoring tree. Moreover, Dollo-CDP scales to data sets with much larger numbers of taxa than branch-and-bound while still having an optimality guarantee, albeit a more restricted one. Lastly, we show that our algorithm for Dollo parsimony can easily be adapted to Camin-Sokal parsimony but not Fitch parsimony.

OrthoMaM v12: a database of curated single-copy ortholog alignments and trees to study mammalian evolutionary genomics

To date, the databases built to gather information on gene orthology do not provide end-users with descriptors of the molecular evolution information and phylogenetic pattern of these orthologues. In this context, we developed OrthoMaM, a database of ORTHOlogous MAmmalian Markers describing the evolutionary dynamics of coding sequences in mammalian genomes. OrthoMaM version 12 includes 15,868 alignments of orthologous coding sequences (CDS) from the 190 complete mammalian genomes currently available. All annotations and 1-to-1 orthology assignments are based on NCBI. Orthologous CDS can be mined for potential informative markers at the different taxonomic levels of the mammalian tree. To this end, several evolutionary descriptors of DNA sequences are provided for querying purposes (e.g. base composition and relative substitution rate). The graphical web interface allows the user to easily browse and sort the results of combined queries. The corresponding multiple sequence alignments and ML trees, inferred using state-of-the art approaches, are available for download both at the nucleotide and amino acid levels. OrthoMaM v12 can be used by researchers interested either in reconstructing the phylogenetic relationships of mammalian taxa or in understanding the evolutionary dynamics of coding sequences in their genomes. OrthoMaM is available for browsing, querying and complete or filtered download at https://orthomam.mbb.cnrs.fr/.

Quartets enable statistically consistent estimation of cell lineage trees under an unbiased error and missingness model

Cancer progression and treatment can be informed by reconstructing its evolutionary history from tumor cells. Although many methods exist to estimate evolutionary trees (called phylogenies) from molecular sequences, traditional approaches assume the input data are error-free and the output tree is fully resolved. These assumptions are challenged in tumor phylogenetics because single-cell sequencing produces sparse, error-ridden data and because tumors evolve clonally. Here, we study the theoretical utility of methods based on quartets (four-leaf, unrooted phylogenetic trees) in light of these barriers. We consider a popular tumor phylogenetics model, in which mutations arise on a (highly unresolved) tree and then (unbiased) errors and missing values are introduced. Quartets are then implied by mutations present in two cells and absent from two cells. Our main result is that the most probable quartet identifies the unrooted model tree on four cells. This motivates seeking a tree such that the number of quartets shared between it and the input mutations is maximized. We prove an optimal solution to this problem is a consistent estimator of the unrooted cell lineage tree; this guarantee includes the case where the model tree is highly unresolved, with error defined as the number of false negative branches. Lastly, we outline how quartet-based methods might be employed when there are copy number aberrations and other challenges specific to tumor phylogenetics.

TreeTerminus -creating transcript trees using inferential replicate counts

A certain degree of uncertainty is always associated with the transcript abundance estimates. The uncertainty may make many downstream analyses, such as differential testing, difficult for certain transcripts. Conversely, gene-level analysis, though less ambiguous, is often too coarse-grained. We introduce TreeTerminus, a data-driven approach for grouping transcripts into a tree structure where leaves represent individual transcripts and internal nodes represent an aggregation of a transcript set. TreeTerminus constructs trees such that, on average, the inferential uncertainty decreases as we ascend the tree topology. The tree provides the flexibility to analyze data at nodes that are at different levels of resolution in the tree and can be tuned depending on the analysis of interest. We evaluated TreeTerminus on two simulated and two experimental datasets and observed an improved performance compared to transcripts (leaves) and other methods under several different metrics.

Quartet Based Gene Tree Imputation Using Deep Learning Improves Phylogenomic Analyses Despite Missing Data

Species tree estimation is frequently based on phylogenomic approaches that use multiple genes from throughout the genome. However, for a combination of reasons (ranging from sampling biases to more biological causes, as in gene birth and loss), gene trees are often incomplete, meaning that not all species of interest have a common set of genes. Incomplete gene trees can potentially impact the accuracy of phylogenomic inference. We, for the first time, introduce the problem of imputing the quartet distribution induced by a set of incomplete gene trees, which involves adding the missing quartets back to the quartet distribution. We present Quartet based Gene tree Imputation using Deep Learning (QT-GILD), an automated and specially tailored unsupervised deep learning technique, accompanied by cues from natural language processing, which learns the quartet distribution in a given set of incomplete gene trees and generates a complete set of quartets accordingly. QT-GILD is a general-purpose technique needing no explicit modeling of the subject system or reasons for missing data or gene tree heterogeneity. Experimental studies on a collection of simulated and empirical datasets suggest that QT-GILD can effectively impute the quartet distribution, which results in a dramatic improvement in the species tree accuracy. Remarkably, QT-GILD not only imputes the missing quartets but can also account for gene tree estimation error. Therefore, QT-GILD advances the state-of-the-art in species tree estimation from gene trees in the face of missing data.

Trying Out a Million Genes to Find the Perfect Pair with RTIST

MOTIVATION

Consensus methods can be used for reconstructing a species tree from several gene trees which exhibit incompatible topologies due to incomplete lineage sorting. Motivated by the fact that there are no anomalous rooted gene trees with three taxa and no anomalous unrooted gene trees with four taxa in the multispecies coalescent model, several contemporary methods form the gene tree consensus by finding the median tree with respect to the triplet or quartet distance-i.e., estimate the species tree as the tree which minimizes the sum of triplet or quartet distances to the input gene trees. These methods reformulate the solution to the consensus problem as the solution to a recursively-solved dynamic programming problem. We present an iterative, easily-parallelizable approach to finding the exact median triplet tree, and implement it as an open source software package which can also find suboptimal consensus trees within a specified triplet distance to the gene trees. The most time-consuming step for methods of this type is the creation of a weights array for all possible subtree bipartitions. By grouping the relevant calculations and array update operations of different bipartitions of the same subtree together, this implementation finds the exact median tree of many gene trees faster than comparable methods, has better scaling properties with respect to the number of gene trees, and has a smaller memory footprint.

RESULTS

RTIST (Rooted Triple Inference of Species Trees) finds the exact median triplet tree of a set of gene trees. Its runtime and memory footprints scale better than existing algorithms. RTIST can resolve all the non-unique median trees, as well as sub-optimal consensus trees within a user-specified triplet distance to the median. Although it is limited in the number of taxa (≤ 20), its runtime changes little when the number of gene trees is changed by several orders of magnitude.

AVAILABILITY

RTIST is written in C and Python. It is freely available at https://github.com/glebzhelezov/rtist.

Theoretical and practical considerations when using retroelement insertions to estimate species trees in the anomaly zone

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 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 1 000 parsimony-informative RIs as input, ASTRAL_BP successfully reconstructed major clades (i.e clades separated by branches > 0.3 CUs) 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.

wQFM: Highly Accurate Genome-scale Species Tree Estimation from Weighted Quartets

MOTIVATION

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.

RESULTS

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.

AVAILABILITY

wQFM is available in open source form at https://github.com/Mahim1997/wQFM-2020.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Information content of trees: three-taxon statements, inference rules and dependency

The three-taxon statement is the fundamental unit of rooted trees in cladistics, stating that for three terminal taxa, two are more related to each other than to a third. Because of their fundamental role in phylogenetics, three-taxon statements are present in methodological research of various disciplines in evolutionary biology; for example consensus methods, supertree methods, species-tree methods, distance metrics and even phylogenetic reconstruction. However, three-taxon statement methods are subject to important flaws related to information redundancy. Here we aim to study the behaviour of three-taxon statements and the interactions among them in order to enhance their performance in evolutionary studies. We show how specific interactions between three-taxon statements are responsible for the emergence of redundancy and dependency within trees, and how they can be used for the improvement of weighting procedures. Our proposal is subsequently tested empirically in the supertree framework using simulations. We show that three-taxon statements using fractional weights perform much better than classical methods such as MRP (matrix representation with parsimony) or methods using unweighted statements. Our study shows that appropriate fractional weighting of three-taxon statements is of critical importance for removing redundancy in any method using them, such as in consensus, supertrees, distance metrics, and phylogenetic or biogeographical analyses.

Species tree estimation from gene trees by minimizing deep coalescence and maximizing quartet consistency: a comparative study and the presence of pseudo species tree terraces

Species tree estimation from multi-locus datasets 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 multi-locus 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 datasets 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 datasets to have equally optimal trees in the context of phylogenomic inference using summary methods.

Machine learning based imputation techniques for estimating phylogenetic trees from incomplete distance matrices

BACKGROUND

With the rapid growth rate of newly sequenced genomes, species tree inference from genes sampled throughout the whole genome has become a basic task in comparative and evolutionary biology. However, substantial challenges remain in leveraging these large scale molecular data. One of the foremost challenges is to develop efficient methods that can handle missing data. Popular distance-based methods, such as NJ (neighbor joining) and UPGMA (unweighted pair group method with arithmetic mean) require complete distance matrices without any missing data.

RESULTS

We introduce two highly accurate machine learning based distance imputation techniques. These methods are based on matrix factorization and autoencoder based deep learning architectures. We evaluated these two methods on a collection of simulated and biological datasets. Experimental results suggest that our proposed methods match or improve upon the best alternate distance imputation techniques. Moreover, these methods are scalable to large datasets with hundreds of taxa, and can handle a substantial amount of missing data.

CONCLUSIONS

This study shows, for the first time, the power and feasibility of applying deep learning techniques for imputing distance matrices. Thus, this study advances the state-of-the-art in phylogenetic tree construction in the presence of missing data. The proposed methods are available in open source form at https://github.com/Ananya-Bhattacharjee/ImputeDistances .