Supertree Algorithm Research Articles

Integrating Phylogenies with Chronology to Assemble the Tree of Life.

Reconstructing the global Tree of Life necessitates computational approaches to integrate numerous molecular phylogenies with limited species overlap into a comprehensive supertree. Our survey of published literature shows that individual phylogenies are frequently restricted to specific taxonomic groups due to the expertise of investigators and molecular evolutionary considerations, resulting in any given species present in a minuscule fraction of phylogenies. We present a novel approach, called the chronological supertree algorithm (Chrono-STA), that can build a supertree of species from such data by using node ages in published molecular phylogenies scaled to time. Chrono-STA builds a supertree of organisms by integrating chronological data from molecular timetrees. It fundamentally differs from existing approaches that generate consensus phylogenies from gene trees with missing taxa, as Chrono-STA does not impute nodal distances, use a guide tree as a backbone, or reduce phylogenies to quartets. Analyses of simulated and empirical datasets show that Chrono-STA can combine taxonomically restricted timetrees with extremely limited species overlap. For such data, approaches that impute missing distances or assemble phylogenetic quartets did not perform well. We conclude that integrating phylogenies via temporal dimension enhances the accuracy of reconstructed supertrees that are also scaled to time.

Speeding up iterative applications of the BUILD supertree algorithm.

The Open Tree of Life (OToL) project produces a supertree that summarizes phylogenetic knowledge from tree estimates published in the primary literature. The supertree construction algorithm iteratively calls Aho's Build algorithm thousands of times in order to assess the compatability of different phylogenetic groupings. We describe an incrementalized version of the Build algorithm that is able to share work between successive calls to Build. We provide details that allow a programmer to implement the incremental algorithm BuildInc, including pseudo-code and a description of data structures. We assess the effect of BuildInc on our supertree algorithm by analyzing simulated data and by analyzing a supertree problem taken from the OpenTree 13.4 synthesis tree. We find that BuildInc provides up to 550-fold speedup for our supertree algorithm.

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.

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).

Gene Tree Construction and Correction Using SuperTree and Reconciliation.

The supertree problem asking for a tree displaying a set of consistent input trees has been largely considered for the reconstruction of species trees. Here, we rather explore this framework for the sake of reconstructing a gene tree from a set of input gene trees on partial data. In this perspective, the phylogenetic tree for the species containing the genes of interest can be used to choose among the many possible compatible "supergenetrees", the most natural criteria being to minimize a reconciliation cost. We develop a variety of algorithmic solutions for the construction and correction of gene trees using the supertree framework. A dynamic programming supertree algorithm for constructing or correcting gene trees, exponential in the number of input trees, is first developed for the less constrained version of the problem. It is then adapted to gene trees with nodes labeled as duplication or speciation, the additional constraint being to preserve the orthology and paralogy relations between genes. Then, a quadratic time algorithm is developed for efficiently correcting an initial gene tree while preserving a set of "trusted" subtrees, as well as the relative phylogenetic distance between them, in both cases of labeled or unlabeled input trees. By applying these algorithms to the set of Ensembl gene trees, we show that this new correction framework is particularly useful to correct weakly-supported duplication nodes. The C++ source code for the algorithms and simulations described in the paper are available at https://github.com/UdeM-LBIT/SuGeT.

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.

Reconstructing (super)trees from data sets with missing distances: not all is lost.

The wealth of phylogenetic information accumulated over many decades of biological research, coupled with recent technological advances in molecular sequence generation, presents significant opportunities for researchers to investigate relationships across and within the kingdoms of life. However, to make best use of this data wealth, several problems must first be overcome. One key problem is finding effective strategies to deal with missing data. Here, we introduce Lasso, a novel heuristic approach for reconstructing rooted phylogenetic trees from distance matrices with missing values, for data sets where a molecular clock may be assumed. Contrary to other phylogenetic methods on partial data sets, Lasso possesses desirable properties such as its reconstructed trees being both unique and edge-weighted. These properties are achieved by Lasso restricting its leaf set to a large subset of all possible taxa, which in many practical situations is the entire taxa set. Furthermore, the Lasso approach is distance-based, rendering it very fast to run and suitable for data sets of all sizes, including large data sets such as those generated by modern Next Generation Sequencing technologies. To better understand the performance of Lasso, we assessed it by means of artificial and real biological data sets, showing its effectiveness in the presence of missing data. Furthermore, by formulating the supermatrix problem as a particular case of the missing data problem, we assessed Lasso's ability to reconstruct supertrees. We demonstrate that, although not specifically designed for such a purpose, Lasso performs better than or comparably with five leading supertree algorithms on a challenging biological data set. Finally, we make freely available a software implementation of Lasso so that researchers may, for the first time, perform both rooted tree and supertree reconstruction with branch lengths on their own partial data sets.

Invariant based quartet puzzling

BackgroundFirst proposed by Cavender and Felsenstein, and Lake, invariant based algorithms for phylogenetic reconstruction were widely dismissed by practicing biologists because invariants were perceived to have limited accuracy in constructing trees based on DNA sequences of reasonable length. Recent developments by algebraic geometers have led to the construction of lists of invariants which have been demonstrated to be more accurate on small sequences, but were limited in that they could only be used for trees with small numbers of taxa. We have developed and tested an invariant based quartet puzzling algorithm which is accurate and efficient for biologically reasonable data sets.ResultsWe found that our algorithm outperforms Maximum Likelihood based quartet puzzling on data sets simulated with low to medium evolutionary rates. For faster rates of evolution, invariant based quartet puzzling is reasonable but less effective than maximum likelihood based puzzling.ConclusionsThis is a proof of concept algorithm which is not intended to replace existing reconstruction algorithms. Rather, the conclusion is that when seeking solutions to a new wave of phylogenetic problems (super tree algorithms, gene vs. species tree, mixture models), invariant based methods should be considered. This article demonstrates that invariants are a practical, reasonable and flexible source for reconstruction techniques.

Comparative Performance of Supertree Algorithms in Large Data Sets Using the Soapberry Family (Sapindaceae) as a Case Study

For the last 2 decades, supertree reconstruction has been an active field of research and has seen the development of a large number of major algorithms. Because of the growing popularity of the supertree methods, it has become necessary to evaluate the performance of these algorithms to determine which are the best options (especially with regard to the supermatrix approach that is widely used). In this study, seven of the most commonly used supertree methods are investigated by using a large empirical data set (in terms of number of taxa and molecular markers) from the worldwide flowering plant family Sapindaceae. Supertree methods were evaluated using several criteria: similarity of the supertrees with the input trees, similarity between the supertrees and the total evidence tree, level of resolution of the supertree and computational time required by the algorithm. Additional analyses were also conducted on a reduced data set to test if the performance levels were affected by the heuristic searches rather than the algorithms themselves. Based on our results, two main groups of supertree methods were identified: on one hand, the matrix representation with parsimony (MRP), MinFlip, and MinCut methods performed well according to our criteria, whereas the average consensus, split fit, and most similar supertree methods showed a poorer performance or at least did not behave the same way as the total evidence tree. Results for the super distance matrix, that is, the most recent approach tested here, were promising with at least one derived method performing as well as MRP, MinFlip, and MinCut. The output of each method was only slightly improved when applied to the reduced data set, suggesting a correct behavior of the heuristic searches and a relatively low sensitivity of the algorithms to data set sizes and missing data. Results also showed that the MRP analyses could reach a high level of quality even when using a simple heuristic search strategy, with the exception of MRP with Purvis coding scheme and reversible parsimony. The future of supertrees lies in the implementation of a standardized heuristic search for all methods and the increase in computing power to handle large data sets. The latter would prove to be particularly useful for promising approaches such as the maximum quartet fit method that yet requires substantial computing power.

Fast and Consistent Estimation of Species Trees Using Supermatrix Rooted Triples

Concatenated sequence alignments are often used to infer species-level relationships. Previous studies have shown that analysis of concatenated data using maximum likelihood (ML) can produce misleading results when loci have differing gene tree topologies due to incomplete lineage sorting. Here, we develop a polynomial time method that utilizes the modified mincut supertree algorithm to construct an estimated species tree from inferred rooted triples of concatenated alignments. We term this method SuperMatrix Rooted Triple (SMRT) and use the notation SMRT-ML when rooted triples are inferred by ML. We use simulations to investigate the performance of SMRT-ML under Jukes-Cantor and general time-reversible substitution models for four- and five-taxon species trees and also apply the method to an empirical data set of yeast genes. We find that SMRT-ML converges to the correct species tree in many cases in which ML on the full concatenated data set fails to do so. SMRT-ML can be conservative in that its output tree is often partially unresolved for problematic clades. We show analytically that when the species tree is clocklike and mutations occur under the Cavender-Farris-Neyman substitution model, as the number of genes increases, SMRT-ML is increasingly likely to infer the correct species tree even when the most likely gene tree does not match the species tree. SMRT-ML is therefore a computationally efficient and statistically consistent estimator of the species tree when gene trees are distributed according to the multispecies coalescent model.

Fast Computation of Supertrees for Compatible Phylogenies with Nested Taxa

Typically, supertree methods combine a collection of source trees in which just the leaves are labeled by taxa. In such methods the resulting supertree is also leaf labeled. An underlying assumption in these methods is that across all trees in the collection, no two of the taxa are nested; for example, "buttercups" and "plants" are nested taxa. Motivated by Page, the first supertree algorithm for allowing the source trees to collectively have nested taxa is called AncestralBuild. Here, in addition to taxa labeling the leaves, the source trees may have taxa labeling some of their interior nodes. Taxa-labeling interior nodes are at a higher taxonomic level than that of their descendants (for example, genera versus species). Analogous to the supertree method Build for deciding the compatibility of a collection of source trees in which just the leaves are labeled, AncestralBuild is a polynomial-time algorithm for deciding the compatibility of a collection of source trees in which some of the interior nodes are also labeled by taxa. Although a more general method, in this paper we show that the original description of AncestralBuild can be modified so that the running time is as fast as the current fastest running time for Build. Fast computation for deciding compatibility is essential if one is to make use of phylogenetic databases that contain thousands of trees on tens of thousands of taxa. This is particularly so as AncestralBuild is incorporated as a basic tool inside more general supertree methods (that is, methods that always output a tree regardless of the compatibility of the source trees). We apply the method to propose a comprehensive phylogeny of the strepsirrhines, a major group of the primates.

Molecular and morphological supertree of stony corals (Anthozoa: Scleractinia) using matrix representation parsimony

The supertree algorithm matrix representation with parsimony was used to combine existing hypotheses of coral relationships and provide the most comprehensive species-level estimate of scleractinian phylogeny, comprised of 353 species (27% of extant species), 141 genera (63%) and 23 families (92%) from all seven suborders. The resulting supertree offers a guide for future studies in coral systematics by highlighting regions of concordance and conflict in existing source phylogenies. It should also prove useful in formal comparative studies of character evolution. Phylogenetic effort within Scleractinia has been taxonomically uneven, with a third of studies focussing on the Acroporidae or its most diverse genera. Sampling has also been geographically non-uniform, as tropical, reef-forming taxa have been considered twice as often as non-reef species. The supertree indicated that source trees concur on numerous aspects of coral relationships, such as the division between robust versus complex corals and the distant relationship between families in Archaeocoeniina. The supertree also supported the existence of a large, taxonomically diverse and monophyletic group of corals with many Atlantic representatives having exsert corallites. Another large, unanticipated clade consisted entirely of solitary deep-water species from three families. Important areas of ambiguity include the relationship of Astrocoeniidae to Pocilloporidae and the relative positions of several, mostly deep-water genera of Caryophylliidae. Conservative grafting of species at the base of congeneric groups with uncontroversial monophyletic status resulted in a more comprehensive, though less resolved tree of 1016 taxa.