Multispecies Coalescent: Theory and Applications in Phylogenetics

Species tree estimation is a basic part of many biological research projects, ranging from answering basic evolutionary questions (e.g., how did a group of species adapt to their environments?) to addressing questions in functional biology. Yet, species tree estimation is very challenging, due to processes such as incomplete lineage sorting, gene duplication and loss, horizontal gene transfer, and hybridization, which can make gene trees differ from each other and from the overall evolutionary history of the species. Over the last 10–20 years, there has been tremendous growth in methods and mathematical theory for estimating species trees and phylogenetic networks, and some of these methods are now in wide use. In this survey, we provide an overview of the current state of the art, identify the limitations of existing methods and theory, and propose additional research problems and directions. Expected final online publication date for the Annual Review of Ecology, Evolution, and Systematics, Volume 52 is November 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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FastMulRFS: fast and accurate species tree estimation under generic gene duplication and loss models

Bioinformatics ◽

10.1093/bioinformatics/btaa444 ◽

2020 ◽

Vol 36 (Supplement_1) ◽

pp. i57-i65 ◽

Cited By ~ 3

Author(s):

Erin K Molloy ◽

Tandy Warnow

Keyword(s):

Gene Duplication ◽

Species Tree ◽

Supplementary Information ◽

Biological Research ◽

Generic Model ◽

Species Trees ◽

Basic Part ◽

Gene Duplication And Loss ◽

Tree Estimation ◽

Scalable Methods

Abstract Motivation Species tree estimation is a basic part of biological research but can be challenging because of gene duplication and loss (GDL), which results in genes that can appear more than once in a given genome. All common approaches in phylogenomic studies either reduce available data or are error-prone, and thus, scalable methods that do not discard data and have high accuracy on large heterogeneous datasets are needed. Results We present FastMulRFS, a polynomial-time method for estimating species trees without knowledge of orthology. We prove that FastMulRFS is statistically consistent under a generic model of GDL when adversarial GDL does not occur. Our extensive simulation study shows that FastMulRFS matches the accuracy of MulRF (which tries to solve the same optimization problem) and has better accuracy than prior methods, including ASTRAL-multi (the only method to date that has been proven statistically consistent under GDL), while being much faster than both methods. Availability and impementation FastMulRFS is available on Github (https://github.com/ekmolloy/fastmulrfs). Supplementary information Supplementary data are available at Bioinformatics online.

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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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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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FastMulRFS: Fast and accurate species tree estimation under generic gene duplication and loss models

10.1101/835553 ◽

2019 ◽

Cited By ~ 2

Author(s):

Erin K. Molloy ◽

Tandy Warnow

Keyword(s):

Gene Duplication ◽

Species Tree ◽

Biological Research ◽

Generic Model ◽

Species Trees ◽

Basic Part ◽

Heterogeneous Datasets ◽

Gene Duplication And Loss ◽

Tree Estimation ◽

Scalable Methods

AbstractMotivationSpecies tree estimation is a basic part of biological research but can be challenging because of gene duplication and loss (GDL), which results in genes that can appear more than once in a given genome. All common approaches in phylogenomic studies either reduce available data or are error-prone, and thus, scalable methods that do not discard data and have high accuracy on large heterogeneous datasets are needed.ResultsWe present FastMulRFS, a polynomial-time method for estimating species trees without knowledge of orthology. We prove that FastMulRFS is statistically consistent under a generic model of GDL when adversarial GDL does not occur. Our extensive simulation study shows that FastMulRFS matches the accuracy of MulRF (which tries to solve the same optimization problem) and has better accuracy than prior methods, including ASTRAL-multi (the only method to date that has been proven statistically consistent under GDL), while being much faster than both methods.AvailabilityFastMulRFS is available on Github (https://github.com/ekmolloy/fastmulrfs).

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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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Comparing Methods for Species Tree Estimation With Gene Duplication and Loss

10.1101/2021.02.05.429947 ◽

2021 ◽

Author(s):

James Willson ◽

Mrinmoy Saha Roddur ◽

Tandy Warnow

Keyword(s):

Gene Duplication ◽

Data Bank ◽

Species Tree ◽

Biological Research ◽

Gene Trees ◽

Species Trees ◽

Tree Inference ◽

Multiple Copies ◽

Gene Duplication And Loss ◽

Tree Estimation

AbstractSpecies tree inference from gene trees is an important part of biological research. One confounding factor in estimating species trees is gene duplication and loss which can lead to gene trees with multiple copies of the same gene. In recent years there have been several new methods developed to address this problem that have substantially improved on earlier methods; however, the best performing methods (ASTRAL-Pro, ASTRID-multi, and FastMulRFS) have not yet been directly compared. In this study, we compare ASTRAL-Pro, ASTRID-multi, and FastMulRFS under a wide variety of conditions. Our study shows that while all three have very good accuracy, nearly the same under many conditions, ASTRAL-Pro and ASTRID-multi are more reliably accurate than FastMuLRFS, and that ASTRID-multi is often faster than ASTRAL-Pro. The datasets generated for this study are freely available in the Illinois Data Bank at https://databank.illinois.edu/datasets/IDB-2418574

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

10.1101/594911 ◽

2019 ◽

Author(s):

Mazharul Islam ◽

Kowshika Sarker ◽

Trisha Das ◽

Rezwana Reaz ◽

Md. Shamsuzzoha Bayzid

Keyword(s):

Incomplete Lineage Sorting ◽

Gene Tree ◽

Estimation Method ◽

Species Tree ◽

Mcmc Methods ◽

Consistent Estimate ◽

Gene Trees ◽

Species Trees ◽

Lineage Sorting ◽

Tree Estimation

AbstractBackgroundSpecies 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.

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Disjoint Tree Mergers for Large-Scale Maximum Likelihood Tree Estimation

Algorithms ◽

10.3390/a14050148 ◽

2021 ◽

Vol 14 (5) ◽

pp. 148

Author(s):

Minhyuk Park ◽

Paul Zaharias ◽

Tandy Warnow

Keyword(s):

Maximum Likelihood ◽

Gene Tree ◽

Input Sequence ◽

Species Tree ◽

Estimation Methods ◽

Biological Research ◽

Species Trees ◽

Basic Part ◽

Large Trees ◽

Tree Estimation

The estimation of phylogenetic trees for individual genes or multi-locus datasets is a basic part of considerable biological research. In order to enable large trees to be computed, Disjoint Tree Mergers (DTMs) have been developed; these methods operate by dividing the input sequence dataset into disjoint sets, constructing trees on each subset, and then combining the subset trees (using auxiliary information) into a tree on the full dataset. DTMs have been used to advantage for multi-locus species tree estimation, enabling highly accurate species trees at reduced computational effort, compared to leading species tree estimation methods. Here, we evaluate the feasibility of using DTMs to improve the scalability of maximum likelihood (ML) gene tree estimation to large numbers of input sequences. Our study shows distinct differences between the three selected ML codes—RAxML-NG, IQ-TREE 2, and FastTree 2—and shows that good DTM pipeline design can provide advantages over these ML codes on large datasets.

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Impact of Ghost Introgression on Coalescent-based Species Tree Inference and Estimation of Divergence Time

10.1101/2022.01.11.475787 ◽

2022 ◽

Author(s):

XiaoXu Pang ◽

Da-Yong Zhang

Keyword(s):

Incomplete Lineage Sorting ◽

Divergence Time ◽

Species Tree ◽

Gene Trees ◽

Species Trees ◽

Lineage Sorting ◽

Multispecies Coalescent ◽

Tree Inference ◽

Tree Methods ◽

The Impact

The species studied in any evolutionary investigation generally constitute a very small proportion of all the species currently existing or that have gone extinct. It is therefore likely that introgression, which is widespread across the tree of life, involves "ghosts," i.e., unsampled, unknown, or extinct lineages. However, the impact of ghost introgression on estimations of species trees has been rarely studied and is thus poorly understood. In this study, we use mathematical analysis and simulations to examine the robustness of species tree methods based on a multispecies coalescent model under gene flow sourcing from an extant or ghost lineage. We found that very low levels of extant or ghost introgression can result in anomalous gene trees (AGTs) on three-taxon rooted trees if accompanied by strong incomplete lineage sorting (ILS). In contrast, even massive introgression, with more than half of the recipient genome descending from the donor lineage, may not necessarily lead to AGTs. In cases involving an ingroup lineage (defined as one that diverged no earlier than the most basal species under investigation) acting as the donor of introgression, the time of root divergence among the investigated species was either underestimated or remained unaffected, but for the cases of outgroup ghost lineages acting as donors, the divergence time was generally overestimated. Under many conditions of ingroup introgression, the stronger the ILS was, the higher was the accuracy of estimating the time of root divergence, although the topology of the species tree is more prone to be biased by the effect of introgression.

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How to Tackle Phylogenetic Discordance in Recent and Rapidly Radiating Groups? Developing a Workflow Using Loricaria (Asteraceae) as an Example

Frontiers in Plant Science ◽

10.3389/fpls.2021.765719 ◽

2022 ◽

Vol 12 ◽

Author(s):

Martha Kandziora ◽

Petr Sklenář ◽

Filip Kolář ◽

Roswitha Schmickl

Keyword(s):

Incomplete Lineage Sorting ◽

Gene Tree ◽

Species Tree ◽

Secondary Contact ◽

Gene Trees ◽

Species Trees ◽

Lineage Sorting ◽

Phylogenetic Discordance ◽

Gene Tree Discordance ◽

High Degree

A major challenge in phylogenetics and -genomics is to resolve young rapidly radiating groups. The fast succession of species increases the probability of incomplete lineage sorting (ILS), and different topologies of the gene trees are expected, leading to gene tree discordance, i.e., not all gene trees represent the species tree. Phylogenetic discordance is common in phylogenomic datasets, and apart from ILS, additional sources include hybridization, whole-genome duplication, and methodological artifacts. Despite a high degree of gene tree discordance, species trees are often well supported and the sources of discordance are not further addressed in phylogenomic studies, which can eventually lead to incorrect phylogenetic hypotheses, especially in rapidly radiating groups. We chose the high-Andean Asteraceae genus Loricaria to shed light on the potential sources of phylogenetic discordance and generated a phylogenetic hypothesis. By accounting for paralogy during gene tree inference, we generated a species tree based on hundreds of nuclear loci, using Hyb-Seq, and a plastome phylogeny obtained from off-target reads during target enrichment. We observed a high degree of gene tree discordance, which we found implausible at first sight, because the genus did not show evidence of hybridization in previous studies. We used various phylogenomic analyses (trees and networks) as well as the D-statistics to test for ILS and hybridization, which we developed into a workflow on how to tackle phylogenetic discordance in recent radiations. We found strong evidence for ILS and hybridization within the genus Loricaria. Low genetic differentiation was evident between species located in different Andean cordilleras, which could be indicative of substantial introgression between populations, promoted during Pleistocene glaciations, when alpine habitats shifted creating opportunities for secondary contact and hybridization.

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