Supertree Methods Research Articles

Genomes of Endotrypanum monterogeii from Panama and Zelonia costaricensis from Brazil: Expansion of Multigene Families in Leishmaniinae Parasites That Are Close Relatives of Leishmania spp.

The Leishmaniinae subfamily of the Trypanosomatidae contains both genus Zelonia (monoxenous) and Endotrypanum (dixenous). They are amongst the nearest known relatives of Leishmania, which comprises many human pathogens widespread in the developing world. These closely related lineages are models for the genomic biology of monoxenous and dixenous parasites. Herein, we used comparative genomics to identify the orthologous groups (OGs) shared among 26 Leishmaniinae species to investigate gene family expansion/contraction and applied two phylogenomic approaches to confirm relationships within the subfamily. The Endotrypanum monterogeii and Zelonia costaricensis genomes were assembled, with sizes of 29.9 Mb and 38.0 Mb and 9.711 and 12.201 predicted protein-coding genes, respectively. The genome of E. monterogeii displayed a higher number of multicopy cell surface protein families, including glycoprotein 63 and glycoprotein 46, compared to Leishmania spp. The genome of Z. costaricensis presents expansions of BT1 and amino acid transporters and proteins containing leucine-rich repeat domains, as well as a loss of ABC-type transporters. In total, 415 and 85 lineage-specific OGs were identified in Z. costaricensis and E. monterogeii. The evolutionary relationships within the subfamily were confirmed using the supermatrix (3384 protein-coding genes) and supertree methods. Overall, this study showed new expansions of multigene families in monoxenous and dixenous parasites of the subfamily Leishmaniinae.

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

Abstract 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.

Convergence of maximum likelihood supertree reconstruction

<abstract><p>Supertree methods are tree reconstruction techniques that combine several smaller gene trees (possibly on different sets of species) to build a larger species tree. The question of interest is whether the reconstructed supertree converges to the true species tree as the number of gene trees increases (that is, the consistency of supertree methods). In this paper, we are particularly interested in the convergence rate of the maximum likelihood supertree. Previous studies on the maximum likelihood supertree approach often formulate the question of interest as a discrete problem and focus on reconstructing the correct topology of the species tree. Aiming to reconstruct both the topology and the branch lengths of the species tree, we propose an analytic approach for analyzing the convergence of the maximum likelihood supertree method. Specifically, we consider each tree as one point of a metric space and prove that the distance between the maximum likelihood supertree and the species tree converges to zero at a polynomial rate under some mild conditions. We further verify these conditions for the popular exponential error model of gene trees.</p></abstract>

Phylogenetic supertree reveals detailed evolution of SARS-CoV-2

Corona Virus Disease 2019 (COVID-19) caused by the emerged coronavirus SARS-CoV-2 is spreading globally. The origin of SARS-Cov-2 and its evolutionary relationship is still ambiguous. Several reports attempted to figure out this critical issue by genome-based phylogenetic analysis, yet limited progress was obtained, principally owing to the disability of these methods to reasonably integrate phylogenetic information from all genes of SARS-CoV-2. Supertree method based on multiple trees can produce the overall reasonable phylogenetic tree. However, the supertree method has been barely used for phylogenetic analysis of viruses. Here we applied the matrix representation with parsimony (MRP) pseudo-sequence supertree analysis to study the origin and evolution of SARS-CoV-2. Compared with other phylogenetic analysis methods, the supertree method showed more resolution power for phylogenetic analysis of coronaviruses. In particular, the MRP pseudo-sequence supertree analysis firmly disputes bat coronavirus RaTG13 be the last common ancestor of SARS-CoV-2, which was implied by other phylogenetic tree analysis based on viral genome sequences. Furthermore, the discovery of evolution and mutation in SARS-CoV-2 was achieved by MRP pseudo-sequence supertree analysis. Taken together, the MRP pseudo-sequence supertree provided more information on the SARS-CoV-2 evolution inference relative to the normal phylogenetic tree based on full-length genomic sequences.

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

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.

Statistically consistent divide-and-conquer pipelines for phylogeny estimation using NJMerge

BackgroundDivide-and-conquer methods, which divide the species set into overlapping subsets, construct a tree on each subset, and then combine the subset trees using a supertree method, provide a key algorithmic framework for boosting the scalability of phylogeny estimation methods to large datasets. Yet the use of supertree methods, which typically attempt to solve NP-hard optimization problems, limits the scalability of such approaches.ResultsIn this paper, we introduce a divide-and-conquer approach that does not require supertree estimation: we divide the species set into pairwise disjoint subsets, construct a tree on each subset using a base method, and then combine the subset trees using a distance matrix. For this merger step, we present a new method, called NJMerge, which is a polynomial-time extension of Neighbor Joining (NJ); thus, NJMerge can be viewed either as a method for improving traditional NJ or as a method for scaling the base method to larger datasets. We prove that NJMerge can be used to create divide-and-conquer pipelines that are statistically consistent under some models of evolution. We also report the results of an extensive simulation study evaluating NJMerge on multi-locus datasets with up to 1000 species. We found that NJMerge sometimes improved the accuracy of traditional NJ and substantially reduced the running time of three popular species tree methods (ASTRAL-III, SVDquartets, and “concatenation” using RAxML) without sacrificing accuracy. Finally, although NJMerge can fail to return a tree, in our experiments, NJMerge failed on only 11 out of 2560 test cases.ConclusionsTheoretical and empirical results suggest that NJMerge is a valuable technique for large-scale phylogeny estimation, especially when computational resources are limited. NJMerge is freely available on Github (http://github.com/ekmolloy/njmerge).

A Phylogenomic Supertree of Birds

It has long been appreciated that analyses of genomic data (e.g., whole genome sequencing or sequence capture) have the potential to reveal the tree of life, but it remains challenging to move from sequence data to a clear understanding of evolutionary history, in part due to the computational challenges of phylogenetic estimation using genome-scale data. Supertree methods solve that challenge because they facilitate a divide-and-conquer approach for large-scale phylogeny inference by integrating smaller subtrees in a computationally efficient manner. Here, we combined information from sequence capture and whole-genome phylogenies using supertree methods. However, the available phylogenomic trees had limited overlap so we used taxon-rich (but not phylogenomic) megaphylogenies to weave them together. This allowed us to construct a phylogenomic supertree, with support values, that included 707 bird species (~7% of avian species diversity). We estimated branch lengths using mitochondrial sequence data and we used these branch lengths to estimate divergence times. Our time-calibrated supertree supports radiation of all three major avian clades (Palaeognathae, Galloanseres, and Neoaves) near the Cretaceous-Paleogene (K-Pg) boundary. The approach we used will permit the continued addition of taxa to this supertree as new phylogenomic data are published, and it could be applied to other taxa as well.

Constrained incremental tree building: new absolute fast converging phylogeny estimation methods with improved scalability and accuracy

BackgroundAbsolute fast converging (AFC) phylogeny estimation methods are ones that have been proven to recover the true tree with high probability given sequences whose lengths are polynomial in the number of number of leaves in the tree (once the shortest and longest branch weights are fixed). While there has been a large literature on AFC methods, the best in terms of empirical performance was DCM_{NJ}, published in SODA 2001. The main empirical advantage of {DCM}_{NJ} over other AFC methods is its use of neighbor joining (NJ) to construct trees on smaller taxon subsets, which are then combined into a tree on the full set of species using a supertree method; in contrast, the other AFC methods in essence depend on quartet trees that are computed independently of each other, which reduces accuracy compared to neighbor joining. However, {DCM}_{NJ} is unlikely to scale to large datasets due to its reliance on supertree methods, as no current supertree methods are able to scale to large datasets with high accuracy.ResultsIn this study we present a new approach to large-scale phylogeny estimation that shares some of the features of {DCM}_{NJ} but bypasses the use of supertree methods. We prove that this new approach is AFC and uses polynomial time and space. Furthermore, we describe variations on this basic approach that can be used with leaf-disjoint constraint trees (computed using methods such as maximum likelihood) to produce other methods that are likely to provide even better accuracy. Thus, we present a new generalizable technique for large-scale tree estimation that is designed to improve scalability for phylogeny estimation methods to ultra-large datasets, and that can be used in a variety of settings (including tree estimation from unaligned sequences, and species tree estimation from gene trees).

BCD Beam Search: considering suboptimal partial solutions in Bad Clade Deletion supertrees.

Supertree methods enable the reconstruction of large phylogenies. The supertree problem can be formalized in different ways in order to cope with contradictory information in the input. Some supertree methods are based on encoding the input trees in a matrix; other methods try to find minimum cuts in some graph. Recently, we introduced Bad Clade Deletion (BCD) supertrees which combines the graph-based computation of minimum cuts with optimizing a global objective function on the matrix representation of the input trees. The BCD supertree method has guaranteed polynomial running time and is very swift in practice. The quality of reconstructed supertrees was superior to matrix representation with parsimony (MRP) and usually on par with SuperFine for simulated data; but particularly for biological data, quality of BCD supertrees could not keep up with SuperFine supertrees. Here, we present a beam search extension for the BCD algorithm that keeps alive a constant number of partial solutions in each top-down iteration phase. The guaranteed worst-case running time of the new algorithm is still polynomial in the size of the input. We present an exact and a randomized subroutine to generate suboptimal partial solutions. Both beam search approaches consistently improve supertree quality on all evaluated datasets when keeping 25 suboptimal solutions alive. Supertree quality of the BCD Beam Search algorithm is on par with MRP and SuperFine even for biological data. This is the best performance of a polynomial-time supertree algorithm reported so far.

Quarnet Inference Rules for Level-1 Networks

An important problem in phylogenetics is the construction of phylogenetic trees. One way to approach this problem, known as the supertree method, involves inferring a phylogenetic tree with leaves consisting of a set X of species from a collection of trees, each having leaf-set some subset of X. In the 1980s, Colonius and Schulze gave certain inference rules for deciding when a collection of 4-leaved trees, one for each 4-element subset of X, can be simultaneously displayed by a single supertree with leaf-set X. Recently, it has become of interest to extend this and related results to phylogenetic networks. These are a generalization of phylogenetic trees which can be used to represent reticulate evolution (where species can come together to form a new species). It has recently been shown that a certain type of phylogenetic network, called a (unrooted) level-1 network, can essentially be constructed from 4-leaved trees. However, the problem of providing appropriate inference rules for such networks remains unresolved. Here, we show that by considering 4-leaved networks, called quarnets, as opposed to 4-leaved trees, it is possible to provide such rules. In particular, we show that these rules can be used to characterize when a collection of quarnets, one for each 4-element subset of X, can all be simultaneously displayed by a level-1 network with leaf-set X. The rules are an intriguing mixture of tree inference rules, and an inference rule for building up a cyclic ordering of X from orderings on subsets of X of size 4. This opens up several new directions of research for inferring phylogenetic networks from smaller ones, which could yield new algorithms for solving the supernetwork problem in phylogenetics.

Phylogenetic Flexibility via Hall-Type Inequalities and Submodularity

Given a collection tau of subsets of a finite set X, we say that tau is phylogenetically flexible if, for any collection R of rooted phylogenetic trees whose leaf sets comprise the collection tau , R is compatible (i.e. there is a rooted phylogenetic X-tree that displays each tree in R). We show that tau is phylogenetically flexible if and only if it satisfies a Hall-type inequality condition of being ‘slim’. Using submodularity arguments, we show that there is a polynomial-time algorithm for determining whether or not tau is slim. This ‘slim’ condition reduces to a simpler inequality in the case where all of the sets in tau have size 3, a property we call ‘thin’. Thin sets were recently shown to be equivalent to the existence of an (unrooted) tree for which the median function provides an injective mapping to its vertex set; we show here that the unrooted tree in this representation can always be chosen to be a caterpillar tree. We also characterise when a collection tau of subsets of size 2 is thin (in terms of the flexibility of total orders rather than phylogenies) and show that this holds if and only if an associated bipartite graph is a forest. The significance of our results for phylogenetics is in providing precise and efficiently verifiable conditions under which supertree methods that require consistent inputs of trees can be applied to any input trees on given subsets of species.

Patterns and effects of GC3 heterogeneity and parsimony informative sites on the phylogenetic tree of genes

The explosive growth in genomic data has provided novel insights into the conflicting signals hidden in phylogenetic trees. Although some studies have explored the effects of the GC content and parsimony informative sites (PIS) on the phylogenetic tree, the effect of the heterogeneity of the GC content at the first/second/third codon position on parsimony informative sites (GC1/2/3PIS) among different species and the effect of PIS on phylogenetic tree construction remain largely unexplored. Here, we used two different mammal genomic datasets to explore the patterns of GC1/2/3PIS heterogeneity and the effect of PIS on the phylogenetic tree of genes: (i) all GC1/2/3PIS have obvious heterogeneity between different mammals, and the levels of heterogeneity are GC3PIS > GC2PIS > GC1PIS; (ii) the number of PIS is positively correlated with the metrics of “good” gene tree topologies, and excluding the third codon position (C3) decreases the quality of gene trees by removing too many PIS. These results provide novel insights into the heterogeneity pattern of GC1/2/3PIS in mammals and the relationship between GC3/PIS and gene trees. Additionally, it is necessary to carefully consider whether to exclude C3 to improve the quality of gene trees, especially in the super-tree method.

The Performance of Two Supertree Schemes Compared Using Synthetic and Real Data Quartet Input

Despite impressive advancements in technological and theoretical tools, construction of phylogenetic (evolutionary) trees is still a challenging task. The availability of enormous quantities of molecular data has made large-scale phylogenetic reconstruction involving thousands of species, a more viable goal. For this goal, separate trees over different, overlapping subsets of species, representing histories of various markers of these species, are collected. These trees, typically with conflicting signals, are subsequently combined into a single tree over the full set, an operation denoted as supertree construction. The amalgamation of such trees into a single tree lies at the heart of many tasks in phylogenetics, yet remains a daunting endeavor, especially in light of conflicting signals. In this work, we study the performance of matrix representation with parsimony (MRP), the most widely used supertree method to date, when confronted with quartet trees. Quartet trees are the most basic informational unit when amalgamation of unrooted trees is attempted, and they remain relevant in more general settings even though standard supertree methods are not necessarily confined to quartets. This study involves both real and simulated data, and the effects of several parameters on the results are evaluated, revealing a number of anomalies associated with MRP. We show that these anomalies are surmountable when using a recently introduced supertree method, weighted quartet MaxCut (wQMC).

Bad Clade Deletion Supertrees: A Fast and Accurate Supertree Algorithm.

Supertree methods merge a set of overlapping phylogenetic trees into a supertree containing all taxa of the input trees. The challenge in supertree reconstruction is the way of dealing with conflicting information in the input trees. Many different algorithms for different objective functions have been suggested to resolve these conflicts. In particular, there exist methods based on encoding the source trees in a matrix, where the supertree is constructed applying a local search heuristic to optimize the respective objective function. We present a novel heuristic supertree algorithm called Bad Clade Deletion (BCD) supertrees. It uses minimum cuts to delete a locally minimal number of columns from such a matrix representation so that it is compatible. This is the complement problem to Matrix Representation with Compatibility (Maximum Split Fit). Our algorithm has guaranteed polynomial worst-case running time and performs swiftly in practice. Different from local search heuristics, it guarantees to return the directed perfect phylogeny for the input matrix, corresponding to the parent tree of the input trees, if one exists. Comparing supertrees to model trees for simulated data, BCD shows a better accuracy (F1 score) than the state-of-the-art algorithms SuperFine (up to 3%) and Matrix Representation with Parsimony (up to 7%); at the same time, BCD is up to 7 times faster than SuperFine, and up to 600 times faster than Matrix Representation with Parsimony. Finally, using the BCD supertree as a starting tree for a combined Maximum Likelihood analysis using RAxML, we reach significantly improved accuracy (1% higher F1 score) and running time (1.7-fold speedup).

Integrative modeling of gene and genome evolution roots the archaeal tree of life

A root for the archaeal tree is essential for reconstructing the metabolism and ecology of early cells and for testing hypotheses that propose that the eukaryotic nuclear lineage originated from within the Archaea; however, published studies based on outgroup rooting disagree regarding the position of the archaeal root. Here we constructed a consensus unrooted archaeal topology using protein concatenation and a multigene supertree method based on 3,242 single gene trees, and then rooted this tree using a recently developed model of genome evolution. This model uses evidence from gene duplications, horizontal transfers, and gene losses contained in 31,236 archaeal gene families to identify the most likely root for the tree. Our analyses support the monophyly of DPANN (Diapherotrites, Parvarchaeota, Aenigmarchaeota, Nanoarchaeota, Nanohaloarchaea), a recently discovered cosmopolitan and genetically diverse lineage, and, in contrast to previous work, place the tree root between DPANN and all other Archaea. The sister group to DPANN comprises the Euryarchaeota and the TACK Archaea, including Lokiarchaeum, which our analyses suggest are monophyletic sister lineages. Metabolic reconstructions on the rooted tree suggest that early Archaea were anaerobes that may have had the ability to reduce CO2 to acetate via the Wood-Ljungdahl pathway. In contrast to proposals suggesting that genome reduction has been the predominant mode of archaeal evolution, our analyses infer a relatively small-genomed archaeal ancestor that subsequently increased in complexity via gene duplication and horizontal gene transfer.

Phylogenomic Reconstruction of the Oomycete Phylogeny Derived from 37 Genomes.

The oomycetes are a class of microscopic, filamentous eukaryotes within the Stramenopiles-Alveolata-Rhizaria (SAR) supergroup which includes ecologically significant animal and plant pathogens, most infamously the causative agent of potato blight Phytophthora infestans. Single-gene and concatenated phylogenetic studies both of individual oomycete genera and of members of the larger class have resulted in conflicting conclusions concerning species phylogenies within the oomycetes, particularly for the large Phytophthora genus. Genome-scale phylogenetic studies have successfully resolved many eukaryotic relationships by using supertree methods, which combine large numbers of potentially disparate trees to determine evolutionary relationships that cannot be inferred from individual phylogenies alone. With a sufficient amount of genomic data now available, we have undertaken the first whole-genome phylogenetic analysis of the oomycetes using data from 37 oomycete species and 6 SAR species. In our analysis, we used established supertree methods to generate phylogenies from 8,355 homologous oomycete and SAR gene families and have complemented those analyses with both phylogenomic network and concatenated supermatrix analyses. Our results show that a genome-scale approach to oomycete phylogeny resolves oomycete classes and individual clades within the problematic Phytophthora genus. Support for the resolution of the inferred relationships between individual Phytophthora clades varies depending on the methodology used. Our analysis represents an important first step in large-scale phylogenomic analysis of the oomycetes. IMPORTANCE The oomycetes are a class of eukaryotes and include ecologically significant animal and plant pathogens. Single-gene and multigene phylogenetic studies of individual oomycete genera and of members of the larger classes have resulted in conflicting conclusions concerning interspecies relationships among these species, particularly for the Phytophthora genus. The onset of next-generation sequencing techniques now means that a wealth of oomycete genomic data is available. For the first time, we have used genome-scale phylogenetic methods to resolve oomycete phylogenetic relationships. We used supertree methods to generate single-gene and multigene species phylogenies. Overall, our supertree analyses utilized phylogenetic data from 8,355 oomycete gene families. We have also complemented our analyses with superalignment phylogenies derived from 131 single-copy ubiquitous gene families. Our results show that a genome-scale approach to oomycete phylogeny resolves oomycete classes and clades. Our analysis represents an important first step in large-scale phylogenomic analysis of the oomycetes.

A supertree pipeline for summarizing phylogenetic and taxonomic information for millions of species.

We present a new supertree method that enables rapid estimation of a summary tree on the scale of millions of leaves. This supertree method summarizes a collection of input phylogenies and an input taxonomy. We introduce formal goals and criteria for such a supertree to satisfy in order to transparently and justifiably represent the input trees. In addition to producing a supertree, our method computes annotations that describe which grouping in the input trees support and conflict with each group in the supertree. We compare our supertree construction method to a previously published supertree construction method by assessing their performance on input trees used to construct the Open Tree of Life version 4, and find that our method increases the number of displayed input splits from 35,518 to 39,639 and decreases the number of conflicting input splits from 2,760 to 1,357. The new supertree method also improves on the previous supertree construction method in that it produces no unsupported branches and avoids unnecessary polytomies. This pipeline is currently used by the Open Tree of Life project to produce all of the versions of project’s “synthetic tree” starting at version 5. This software pipeline is called “propinquity”. It relies heavily on “otcetera”—a set of C++ tools to perform most of the steps of the pipeline. All of the components are free software and are available on GitHub.

Multiple Approaches to Phylogenomic Reconstruction of the Fungal Kingdom.

Fungi are possibly the most diverse eukaryotic kingdom, with over a million member species and an evolutionary history dating back a billion years. Fungi have been at the forefront of eukaryotic genomics, and owing to initiatives like the 1000 Fungal Genomes Project the amount of fungal genomic data has increased considerably over the last 5 years, enabling large-scale comparative genomics of species across the kingdom. In this chapter, we first review fungal evolution and the history of fungal genomics. We then review in detail seven phylogenomic methods and reconstruct the phylogeny of 84 fungal species from 8 phyla using each method. Six methods have seen extensive use in previous fungal studies, while a Bayesian supertree method is novel to fungal phylogenomics. We find that both established and novel phylogenomic methods can accurately reconstruct the fungal kingdom. Finally, we discuss the accuracy and suitability of each phylogenomic method utilized.

FastRFS: fast and accurate Robinson-Foulds Supertrees using constrained exact optimization.

MotivationThe estimation of phylogenetic trees is a major part of many biological dataset analyses, but maximum likelihood approaches are NP-hard and Bayesian MCMC methods do not scale well to even moderate-sized datasets. Supertree methods, which are used to construct trees from trees computed on subsets, are critically important tools for enabling the statistical estimation of phylogenies for large and potentially heterogeneous datasets. Supertree estimation is itself NP-hard, and no current supertree method has sufficient accuracy and scalability to provide good accuracy on the large datasets that supertree methods were designed for, containing thousands of species and many subset trees.ResultsWe present FastRFS, a new method based on a dynamic programming method we have developed to find an exact solution to the Robinson-Foulds Supertree problem within a constrained search space. FastRFS has excellent accuracy in terms of criterion scores and topological accuracy of the resultant trees, substantially improving on competing methods on a large collection of biological and simulated data. In addition, FastRFS is extremely fast, finishing in minutes on even very large datasets, and in under an hour on a biological dataset with 2228 species.Availability and ImplementationFastRFS is available on github at https://github.com/pranjalv123/FastRFSSupplementary information Supplementary data are available at Bioinformatics online.

Triplet MaxCut: a new toolkit for rooted supertree

Summary The rapid increase of molecular, as well as other types, of available classification data has created the need to combine this data into a unified hypothesis. Supertree methods are essential when amalgamating phylogenetic information from various, possibly conflicting, sources into a single tree. The goal of a supertree algorithm is to satisfy maximally each such source of information in the output tree. Triplets, rooted trees over three leaves, are the minimal piece of such information when dealing with rooted trees. Due to its fundamental role in phylogenetics, extensive effort has been dedicated to several aspects regarding triplets’ research. We have devised a new tool, Triplet MaxCut (TMC), performing various operations in rooted supertree, principally amalgamating rooted trees based on amalgamating rooted triplets. The utility and efficiency of the algorithm is demonstrated by both simulation study and four real data supertree inputs.