STEM: species tree estimation using maximum likelihood for gene trees under coalescence

Laura S. Kubatko; Bryan C. Carstens; L. Lacey Knowles

doi:10.1093/bioinformatics/btp079

PRANC: ML species tree estimation from the ranked gene trees under coalescence

Bioinformatics ◽

10.1093/bioinformatics/btaa605 ◽

2020 ◽

Vol 36 (18) ◽

pp. 4819-4821

Author(s):

Anastasiia Kim ◽

James H Degnan

Keyword(s):

Maximum Likelihood ◽

Gene Tree ◽

Species Tree ◽

Supplementary Information ◽

Supplementary Data ◽

Gene Trees ◽

Multispecies Coalescent ◽

Branch Lengths ◽

Tree Topologies ◽

Tree Estimation

Abstract Summary PRANC computes the Probabilities of RANked gene tree topologies under the multispecies coalescent. A ranked gene tree is a gene tree accounting for the temporal ordering of internal nodes. PRANC can also estimate the maximum likelihood (ML) species tree from a sample of ranked or unranked gene tree topologies. It estimates the ML tree with estimated branch lengths in coalescent units. Availability and implementation PRANC is written in C++ and freely available at github.com/anastasiiakim/PRANC. Supplementary information Supplementary data are available at Bioinformatics online.

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SpeciesRax: A tool for maximum likelihood species tree inference from gene family trees under duplication, transfer, and loss.

10.1101/2021.03.29.437460 ◽

2021 ◽

Author(s):

Benoit Morel ◽

Paul Schade ◽

Sarah Lutteropp ◽

Tom A. Williams ◽

Gergely J. Szöllösi ◽

...

Keyword(s):

Maximum Likelihood ◽

Gene Family ◽

Gene Families ◽

Species Tree ◽

Likelihood Method ◽

Gene Trees ◽

Informative Signal ◽

Tree Inference ◽

Species Tree Inference ◽

Family Trees

Species tree inference from gene family trees is becoming increasingly popular because it can account for discordance between the species tree and the corresponding gene family trees. In particular, methods that can account for multiple-copy gene families exhibit potential to leverage paralogy as informative signal. At present, there does not exist any widely adopted inference method for this purpose. Here, we present SpeciesRax, the first maximum likelihood method that can infer a rooted species tree from a set of gene family trees and can account for gene duplication, loss, and transfer events. By explicitly modelling events by which gene trees can depart from the species tree, SpeciesRax leverages the phylogenetic rooting signal in gene trees. SpeciesRax infers species tree branch lengths in units of expected substitutions per site and branch support values via paralogy-aware quartets extracted from the gene family trees. Using both empirical and simulated datasets we show that SpeciesRax is at least as accurate as the best competing methods while being one order of magnitude faster on large datasets at the same time. We used SpeciesRax to infer a biologically plausible rooted phylogeny of the vertebrates comprising $188$ species from $31612$ gene families in one hour using $40$ cores. SpeciesRax is available under GNU GPL at https://github.com/BenoitMorel/GeneRax and on BioConda.

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Phylogenomic terraces: presence and implication in species tree estimation from gene trees

10.1101/2020.04.19.048843 ◽

2020 ◽

Author(s):

Ishrat Tanzila Farah ◽

Md Muktadirul Islam ◽

Kazi Tasnim Zinat ◽

Atif Hasan Rahman ◽

Md Shamsuzzoha Bayzid

Keyword(s):

Incomplete Lineage Sorting ◽

Gene Tree ◽

Species Tree ◽

Gene Trees ◽

Species Trees ◽

Lineage Sorting ◽

Deep Coalescence ◽

Tree Estimation ◽

Tree Space ◽

Multiple Species

AbstractSpecies tree estimation from multi-locus dataset 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 formalized the concept of “phylogenomic terraces” in the species tree space, where multiple species trees with distinct topologies may have exactly the same optimization score (quartet score, extra lineage score, etc.) with respect to a collection of gene trees. We investigated the presence and implication of terraces in species tree estimation from multi-locus data 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. Our experiments, on a collection of dataset simulated under ILS, indicate that MDC-based methods may achieve competitive or identical quartet consistency score as MQC but could be significantly worse than MQC in terms of tree accuracy – demonstrating the presence and affect of phylogenomic terraces. This is the first known study that formalizes the concept of phylogenomic terraces in the context of species tree estimation from multi-locus data, and reports the presence and implications of terraces in species tree estimation under ILS.

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Overtraining often results in topologically incorrect species trees with maximum likelihood methods

10.1101/140780 ◽

2017 ◽

Author(s):

Damien M. de Vienne ◽

Fran Supek ◽

Toni Gabaldon

Keyword(s):

Maximum Likelihood ◽

Species Tree ◽

Small Sample ◽

Optimization Process ◽

Evolutionary Relationships ◽

Gene Trees ◽

Species Trees ◽

Tree Reconstruction ◽

Reference Tree ◽

Gold Standard Reference

AbstractBackgroundOvertraining occurs when an optimization process is applied for too many steps, leading to a model describing noise in addition to the signal present in the data. This effect may affect typical approaches for species tree reconstruction that use maximum likelihood optimization procedures on a small sample of concatenated genes. In this context, overtraining may result in trees better describing the specific evolutionary history of the sampled genes rather than the sought evolutionary relationships among the species.ResultsUsing a cross-validation-like approach on real and simulated datasets we showed that overtraining occurs in a significant fraction of cases, leading to species trees that are more distant from a gold-standard reference tree than a previously considered (and rejected) solution in the optimization process. However, we show that the shape of the likelihood curve is informative of the optimal stopping point. As expected, overtraining is aggravated in smaller gene samples and in datasets with increased levels of topological variation among gene trees, but occurs also in controlled, simulated scenarios where a common underlying topology is enforced.ConclusionsOvertraining is frequent in species tree reconstruction and leads to a final tree that is worse in describing the evolutionary relationships of the species under study than an earlier (and rejected) solution encountered during the likelihood optimization process. This result should help develop specific methods for species tree reconstruction in the future, and may improve our understanding of the complexity of tree likelihood landscapes.

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Complexity of the simplest species tree problem

Molecular Biology and Evolution ◽

10.1093/molbev/msab009 ◽

2021 ◽

Author(s):

Tianqi Zhu ◽

Ziheng Yang

Keyword(s):

Maximum Likelihood ◽

Estimation Error ◽

Gene Tree ◽

Species Tree ◽

Ancestral Population ◽

Statistical Efficiency ◽

Multispecies Coalescent ◽

Full Likelihood ◽

Tree Methods ◽

Tree Estimation

Abstract The multispecies coalescent (MSC) model provides a natural framework for species tree estimation accounting for gene-tree conflicts. While a number of species tree methods under the MSC have been suggested and evaluated using simulation, their statistical properties remain poorly understood. Here we use mathematical analysis aided by computer simulation to examine the identifiability, consistency, and efficiency of different species tree methods in the case of three species and three sequences under the molecular clock. We consider four major species-tree methods including concatenation, two-step, independent-sites maximum likelihood (ISML) and maximum likelihood (ML). We develop approximations that predict that the probit transform of the species tree estimation error decreases linearly with the square root of the number of loci. Even in this simplest case major differences exist among the methods. Fulllikelihood methods are considerably more efficient than summary methods such as concatenation and two-step. They also provide estimates of important parameters such as species divergence times and ancestral population sizes while these parameters are not identifiable by summary methods. Our results highlight the need to improve the statistical efficiency of summary methods and the computational efficiency of full likelihood methods of species tree estimation.

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Consistency of SVDQuartets and Maximum Likelihood for Coalescent-based Species Tree Estimation

10.1101/523050 ◽

2019 ◽

Cited By ~ 2

Author(s):

Matthew Wascher ◽

Laura Kubatko

Keyword(s):

Maximum Likelihood ◽

Species Tree ◽

Gene Trees ◽

Data Types ◽

Coalescent Model ◽

Multispecies Coalescent ◽

Consistency Results ◽

True Tree ◽

Tree Inference ◽

Statistical Consistency

AbtractNumerous methods for inferring species-level phylogenies under the coalescent model have been proposed within the last 20 years, and debates continue about the relative strengths and weaknesses of these methods. One desirable property of a phylogenetic estimator is that of statistical consistency, which means intuitively that as more data are collected, the probability that the estimated tree has the same topology as the true tree goes to 1. To date, consistency results for species tree inference under the multispecies coalescent have been derived only for summary statistics methods, such as ASTRAL and MP-EST. These methods have been found to be consistent given true gene trees, but may be inconsistent when gene trees are estimated from data for loci of finite length (Roch et al., 2019). Here we consider the question of statistical consistency for four taxa for SVDQuartets for general data types, as well as for the maximum likelihood (ML) method in the case in which the data are a collection of sites generated under the multispecies coalescent model such that the sites are conditionally independent given the species tree (we call these data Coalescent Independent Sites (CIS) data). We show that SVDQuartets is statistically consistent for all data types (i.e., for both CIS data and for multilocus data), and we derive its rate of convergence. We additionally show that ML is consistent for CIS data under the JC69 model, and discuss why a proof for the more general multilocus case is difficult. Finally, we compare the performance of maximum likelihood and SDVQuartets using simulation for both data types.

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wQFM: Statistically Consistent Genome-scale Species Tree Estimation from Weighted Quartets

10.1101/2020.11.30.403352 ◽

2020 ◽

Author(s):

Mahim Mahbub ◽

Zahin Wahab ◽

Rezwana Reaz ◽

M. Saifur Rahman ◽

Md. Shamsuzzoha Bayzid

Keyword(s):

Incomplete Lineage Sorting ◽

Gene Tree ◽

Accurate Method ◽

Species Tree ◽

Estimation Methods ◽

Gene Trees ◽

Species Trees ◽

Lineage Sorting ◽

Tree Estimation ◽

Source Form

AbstractMotivationSpecies 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 allows for a statistically consistent way of estimating species trees. However, handling weighted quartets is challenging.ResultsWe 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.AvailabilitywQFM is available in open source form at https://github.com/Mahim1997/wQFM-2020.

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Consistency of SVDQuartets and Maximum Likelihood for Coalescent-Based Species Tree Estimation

Systematic Biology ◽

10.1093/sysbio/syaa039 ◽

2020 ◽

Vol 70 (1) ◽

pp. 33-48 ◽

Cited By ~ 1

Author(s):

Matthew Wascher ◽

Laura Kubatko

Keyword(s):

Maximum Likelihood ◽

Gene Tree ◽

Species Tree ◽

Gene Trees ◽

Data Types ◽

Multispecies Coalescent ◽

Consistency Results ◽

True Tree ◽

Tree Inference ◽

Statistical Consistency

Abstract Numerous methods for inferring species-level phylogenies under the coalescent model have been proposed within the last 20 years, and debates continue about the relative strengths and weaknesses of these methods. One desirable property of a phylogenetic estimator is that of statistical consistency, which means intuitively that as more data are collected, the probability that the estimated tree has the same topology as the true tree goes to 1. To date, consistency results for species tree inference under the multispecies coalescent (MSC) have been derived only for summary statistics methods, such as ASTRAL and MP-EST. These methods have been found to be consistent given true gene trees but may be inconsistent when gene trees are estimated from data for loci of finite length. Here, we consider the question of statistical consistency for four taxa for SVDQuartets for general data types, as well as for the maximum likelihood (ML) method in the case in which the data are a collection of sites generated under the MSC model such that the sites are conditionally independent given the species tree (we call these data coalescent independent sites [CIS] data). We show that SVDQuartets is statistically consistent for all data types (i.e., for both CIS data and for multilocus data), and we derive its rate of convergence. We additionally show that ML is consistent for CIS data under the JC69 model and discuss why a proof for the more general multilocus case is difficult. Finally, we compare the performance of ML and SDVQuartets using simulation for both data types. [Consistency; gene tree; maximum likelihood; multilocus data; hylogenetic inference; species tree; SVDQuartets.]

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SODA: Multi-locus species delimitation using quartet frequencies

10.1101/869396 ◽

2019 ◽

Cited By ~ 2

Author(s):

Maryam Rabiee ◽

Siavash Mirarab

Keyword(s):

Species Delimitation ◽

Branch Length ◽

Large Datasets ◽

Species Tree ◽

Gene Trees ◽

Species Trees ◽

Very Large Datasets ◽

Tree Inference ◽

Group A ◽

Tree Estimation

AbstractMotivationSpecies delimitation, the process of deciding how to group a set of organisms into units called species, is one of the most challenging problems in evolutionary computational biology. While many methods exist for species delimitation, most based on the coalescent theory, few are scalable to very large datasets and methods that scale tend to be not accurate. Species delimitation is closely related to species tree inference from discordant gene trees, a problem that has enjoyed rapid advances in recent years.ResultsIn this paper, we build on the accuracy and scalability of recent quartet-based methods for species tree estimation and propose a new method called SODA for species delimitation. SODA relies heavily on a recently developed method for testing zero branch length in species trees. In extensive simulations, we show that SODA can easily scale to very large datasets while maintaining high accuracy.AvailabilityThe code and data presented here are available on https://github.com/maryamrabiee/[email protected]

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ASTRID: Accurate Species TRees from Internode Distances

10.1101/023036 ◽

2015 ◽

Cited By ~ 1

Author(s):

Pranjal Vachaspati ◽

Tandy Warnow

Keyword(s):

Good Accuracy ◽

Incomplete Lineage Sorting ◽

Current Method ◽

Species Tree ◽

Estimation Methods ◽

Gene Trees ◽

Species Trees ◽

Lineage Sorting ◽

Tree Estimation ◽

Source Form

Background: Incomplete 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. Results: We 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. Conclusions: ASTRID 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.

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