A simulation study comparing supertree and combined analysis methods using SMIDGen

<p>Abstract</p> <p>Background</p> <p>Supertree methods comprise one approach to reconstructing large molecular phylogenies given multi-marker datasets: trees are estimated on each marker and then combined into a tree (the "supertree") on the entire set of taxa. Supertrees can be constructed using various algorithmic techniques, with the most common being matrix representation with parsimony (MRP). When the data allow, the competing approach is a combined analysis (also known as a "supermatrix" or "total evidence" approach) whereby the different sequence data matrices for each of the different subsets of taxa are concatenated into a single supermatrix, and a tree is estimated on that supermatrix.</p> <p>Results</p> <p>In this paper, we describe an extensive simulation study we performed comparing two supertree methods, MRP and weighted MRP, to combined analysis methods on large model trees. A key contribution of this study is our novel simulation methodology (Super-Method Input Data Generator, or <it>SMIDGen</it>) that better reflects biological processes and the practices of systematists than earlier simulations. We show that combined analysis based upon maximum likelihood outperforms MRP and weighted MRP, giving especially big improvements when the largest subtree does not contain most of the taxa.</p> <p>Conclusions</p> <p>This study demonstrates that MRP and weighted MRP produce distinctly less accurate trees than combined analyses for a given base method (maximum parsimony or maximum likelihood). Since there are situations in which combined analyses are not feasible, there is a clear need for better supertree methods. The source tree and combined datasets used in this study can be used to test other supertree and combined analysis methods.</p

Polynomial supertree methods in phylogenomics: algorithms, simulations and software

One of the objectives in modern biology, especially phylogenetics, is to build larger clades of the Tree of Life. Large-scale phylogenetic analysis involves several serious challenges. The aim of this thesis is to contribute to some of the open problems in this context. In computational phylogenetics, supertree methods provide a way to reconstruct larger clades of the Tree of Life. We present a novel polynomial time approach for the computation of supertrees called FlipCut supertree. Our method combines the computation of minimum cuts from graph-based methods with a matrix representation method, namely Minimum Flip Supertrees. Here, the input trees are encoded in a 0/1/?-matrix. We present a heuristic to search for a minimum set of 0/1-flips such that the resulting matrix admits a directed perfect phylogeny. In contrast to other polynomial time approaches, our results can be interpreted in the sense that we try to minimize a global objective function, namely the number of flips in the input matrix. We extend our approach by using edge weights to weight the columns of the 0/1/?-matrix. In order to compare our new FlipCut supertree method with other recent polynomial supertree methods and matrix representation methods, we present a large scale simulation study using two different data sets. Our findings illustrate the trade-off between accuracy and running time in supertree construction, as well as the pros and cons of different supertree approaches. Furthermore, we present EPoS, a modular software framework for phylogenetic analysis and visualization. It fills the gap between command line-based algorithmic packages and visual tools without sufficient support for computational methods. By combining a powerful graphical user interface with a plugin system that allows simple integration of new algorithms, visualizations and data structures, we created a framework that is easy to use, to extend and that covers all important steps of a phylogenetic analysis

Fast and accurate supertrees: towards large scale phylogenies

Phylogenetics is the study of evolutionary relationships between biological entities; phylogenetic trees (phylogenies) are a visualization of these evolutionary relationships. Accurate approaches to reconstruct hylogenies from sequence data usually result in NPhard optimization problems, hence local search heuristics have to be applied in practice. These methods are highly accurate and fast enough as long as the input data is not too large. Divide-and-conquer techniques are a promising approach to boost scalability and accuracy of those local search heuristics on very large datasets. A divide-and-conquer method breaks down a large phylogenetic problem into smaller sub-problems that are computationally easier to solve. The sub-problems (overlapping trees) are then combined using a supertree method. 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 are methods that encode the source trees in a matrix and the supertree is constructed applying a local search heuristic to optimize the respective objective function. The most widely used supertree methods use such local search heuristics. However, to really improve the scalability of accurate tree reconstruction by divide-and-conquer approaches, accurate polynomial time methods are needed for the supertree reconstruction step. In this work, we present approaches for accurate polynomial time supertree reconstruction in particular Bad Clade Deletion (BCD), a novel heuristic supertree algorithm with polynomial running time. BCD uses minimum cuts to greedily delete a locally minimal number of columns from a matrix representation to make it compatible. 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. BCD can take support values of the source trees into account without an increase in complexity. We show how reliable clades can be used to restrict the search space for BCD and how those clades can be collected from the input data using the Greedy Strict Consensus Merger. Finally, we introduce 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 BCD with beam search extension is still polynomial. We present an exact and a randomized subroutine to generate suboptimal partial solutions. In our thorough evaluation on several simulated and biological datasets against a representative set of supertree methods we found that BCD is more accurate than the most accurate supertree methods when using support values and search space restriction on simulated data. Simultaneously BCD is faster than any other evaluated method. The beam search approach improved the accuracy of BCD on all evaluated datasets at the cost of speed. We found that BCD supertrees can boost maximum likelihood tree reconstruction when used as starting tree. Further, BCD could handle large scale datasets where local search heuristics did not converge in reasonable time. Due to its combination of speed, accuracy, and the ability to reconstruct the parent tree if one exists, BCD is a promising approach to enable outstanding scalability of divide-and-conquer approaches.Die Phylogenetik studiert die evolutionären Beziehungen zwischen biologischen Entitäten. Phylogenetische Bäume sind eine Visualisierung dieser Beziehungen. Akkurate Ansätze zur Rekonstruktion von Phylogenien aus Sequenzdaten führen in der Regel zu NP-schweren Optimierungsproblemen, sodass in der Praxis lokale Suchheuristiken angewendet werden müssen. Diese Methoden liefern akkurate Bäume und sind schnell genug, solange die Eingabedaten nicht zu groß werden. Teile-und-herrsche-Verfahren sind ein vielversprechender Ansatz, um Skalierbarkeit und Genauigkeit dieser lokalen Suchheuristiken auf sehr großen Datensätzen zu verbessern. Beim Teile-und-herrsche-Ansatz zerlegt man ein großes phylogenetisches Problem in kleinere Teilprobleme, die einfacher und schneller zu lösen sind. Die Teilprobleme, in diesem Fall überlappende Teilbäume, müssen dann zu einem gesamtheitlichen Baum kombiniert werden. Superbaummethoden verschmelzen solche überlappenden phylogenetischen Bäume zu einem Superbaum, der alle Taxa der Eingangsbäume enthält. Die Herausforderung bei der Superbaumrekonstruktion besteht darin, mit widersprüchlichen Eingabebäumen umzugehen. Es wurden viele verschiedene Algorithmen mit unterschiedlichen Zielfunktionen entwickelt, um solche Widersprüche möglichst sinnvoll aufzulösen. Verfahren, die auf der Kodierung der Eingabebäume als Matrixrepräsentation basieren, sind am weitesten verbreitet. Die zum Auflösen der Konflikte verwendeten Zielfunktionen führen in der Regel zu NP-schweren Optimierungsproblemen, sodass in der Praxis auch hier lokale Suchheuristiken zum Einsatz kommen. Da diese Ansätze nicht wesentlich besser mit der Größe der Eingabedaten skalieren als die direkte Rekonstruktion aus Sequenzdaten, werden für die Superbaumrekonstruktion in Teile-undherrsche-Ansätzen akkurate Polynomialzeitmethoden benötigt. Diese Arbeit beschäftigt sich mit der akkuraten Rekonstruktion von Superbäumen in Polynomialzeit. Wir präsentieren Bad Clade Deletion (BCD), eine neue Polynomialzeitheuristik zur Superbaumrekonstruktion. BCD verwendet minimale Schnitte in Graphen, um eine minimale Anzahl von Spalten aus der Matrixrepräsentation zu löschen, sodass diese konfliktfrei wird. Im Gegensatz zu lokalen Suchheuristiken garantiert BCD die Rekonstruktion einer perfekten Phylogenie, sofern eine solche für die Eingabematrix existiert. BCD ermöglicht es, Gütekriterien der Eingabebäume zu berücksichtigen, ohne dass sich dadurch die Komplexität erhöht. Weiterhin zeigen wir, wie zuverlässige Kladen verwendet werden können, um den Suchraum für BCD einzuschränken und wie man diese mit Hilfe des Greedy Strict Consensus Mergers aus den Eingabedaten gewinnen kann. Schließlich stellen wir eine Strahlensuche für BCD vor. Diese erlaubt es eine bestimmte Anzahl suboptimaler Teillösungen (anstatt nur der optimalen) zu berücksichtigen, um so das Gesamtergebnis zu verbessern. Die Worst-Case-Laufzeit der Strahlensuche ist immer noch polynomiell. Zur Berechnung suboptimaler Teillösungen stellen wir einen exakten und einen randomisierten Algorithmus vor. In einer ausführlichen Evaluation auf mehreren simulierten und biologischen Datensätzen vergleichen wir BCD mit einer repräsentativen Auswahl an Superbaummethoden. Wir haben herausgefunden, dass BCD bei Verwendung von Gütekriterien und Suchraumbeschränkung auf simulierten Daten genauer ist als die akkuratesten evaluierten Superbaummethoden. Gleichzeitig ist BCD deutlich schneller als alle evaluierten Methoden. Die Strahlensuche verbessert die Qualität der BCD-Bäume auf allen Datensätzen, allerdings auf Kosten der Laufzeit. Weiterhin fanden wir heraus, dass ein BCD-Superbaum, der als Startbaum verwendet wird, die Qualität einer Maximum-Likelihood-Baumrekonstruktion verbessern kann. Außerdem kann BCD Datensätze verarbeiten, die so groß sind, dass lokale Suchheuristiken auf diesen nicht mehr in angemessener Zeit konvergieren. Aufgrund der Kombination aus Geschwindigkeit, Genauigkeit und der Fähigkeit, den Elternbaum zu rekonstruieren, sofern ein solcher existiert, ist BCD ein vielversprechender Ansatz um die Skalierbarkeit von Teile-und-herrsche-Methoden entscheidend zu verbessern

Inferring Species Trees from Incongruent Multi-Copy Gene Trees Using the Robinson-Foulds Distance

We present a new method for inferring species trees from multi-copy gene trees. Our method is based on a generalization of the Robinson-Foulds (RF) distance to multi-labeled trees (mul-trees), i.e., gene trees in which multiple leaves can have the same label. Unlike most previous phylogenetic methods using gene trees, this method does not assume that gene tree incongruence is caused by a single, specific biological process, such as gene duplication and loss, deep coalescence, or lateral gene transfer. We prove that it is NP-hard to compute the RF distance between two mul-trees, but it is easy to calculate the generalized RF distance between a mul-tree and a singly-labeled tree. Motivated by this observation, we formulate the RF supertree problem for mul-trees (MulRF), which takes a collection of mul-trees and constructs a species tree that minimizes the total RF distance from the input mul-trees. We present a fast heuristic algorithm for the MulRF supertree problem. Simulation experiments demonstrate that the MulRF method produces more accurate species trees than gene tree parsimony methods when incongruence is caused by gene tree error, duplications and losses, and/or lateral gene transfer. Furthermore, the MulRF heuristic runs quickly on data sets containing hundreds of trees with up to a hundred taxa.Comment: 16 pages, 11 figure

Parallelizing superFine

The estimation of the Tree of Life, a rooted binary tree representing how all extant species evolved from a common ancestor, is one of the grand challenges of modern biology. Research groups around the world are attempting to estimate evolutionary trees on particular sets of species (typically clades, or rooted subtrees), in the hope that a final "supertree" can be produced from these smaller estimated trees through the addition of a "scaffold" tree of randomly sampled taxa from the tree of life. However, supertree estimation is itself a computationally challenging problem, because the most accurate trees are produced by running heuristics for NP-hard problems. In this paper we report on a study in which we parallelize SuperFine, the currently most accurate and efficient supertree estimation method. We explore performance of these parallel implementations on simulated data-sets with 1000 taxa and biological data-sets with up to 2,228 taxa. Our study reveals aspects of SuperFine that limit the speed-ups that are possible through the type of outer-loop parallelism we exploit.(undefined

An experimental study of Quartets MaxCut and other supertree methods

<p>Abstract</p> <p>Background</p> <p>Supertree methods represent one of the major ways by which the Tree of Life can be estimated, but despite many recent algorithmic innovations, matrix representation with parsimony (MRP) remains the main algorithmic supertree method.</p> <p>Results</p> <p>We evaluated the performance of several supertree methods based upon the Quartets MaxCut (QMC) method of Snir and Rao and showed that two of these methods usually outperform MRP and five other supertree methods that we studied, under many realistic model conditions. However, the QMC-based methods have scalability issues that may limit their utility on large datasets. We also observed that taxon sampling impacted supertree accuracy, with poor results obtained when all of the source trees were only sparsely sampled. Finally, we showed that the popular optimality criterion of minimizing the total topological distance of the supertree to the source trees is only weakly correlated with supertree topological accuracy. Therefore evaluating supertree methods on biological datasets is problematic.</p> <p>Conclusions</p> <p>Our results show that supertree methods that improve upon MRP are possible, and that an effort should be made to produce scalable and robust implementations of the most accurate supertree methods. Also, because topological accuracy depends upon taxon sampling strategies, attempts to construct very large phylogenetic trees using supertree methods should consider the selection of source tree datasets, as well as supertree methods. Finally, since supertree topological error is only weakly correlated with the supertree's topological distance to its source trees, development and testing of supertree methods presents methodological challenges.</p

Advancing Divide-And-Conquer Phylogeny Estimation Using Robinson-Foulds Supertrees

One of the Grand Challenges in Science is the construction of the Tree of Life, an evolutionary tree containing several million species, spanning all life on earth. However, the construction of the Tree of Life is enormously computationally challenging, as all the current most accurate methods are either heuristics for NP-hard optimization problems or Bayesian MCMC methods that sample from tree space. One of the most promising approaches for improving scalability and accuracy for phylogeny estimation uses divide-and-conquer: a set of species is divided into overlapping subsets, trees are constructed on the subsets, and then merged together using a "supertree method". Here, we present Exact-RFS-2, the first polynomial-time algorithm to find an optimal supertree of two trees, using the Robinson-Foulds Supertree (RFS) criterion (a major approach in supertree estimation that is related to maximum likelihood supertrees), and we prove that finding the RFS of three input trees is NP-hard. We also present GreedyRFS (a greedy heuristic that operates by repeatedly using Exact-RFS-2 on pairs of trees, until all the trees are merged into a single supertree). We evaluate Exact-RFS-2 and GreedyRFS, and show that they have better accuracy than the current leading heuristic for RFS

Accuracy of phylogeny reconstruction methods combining overlapping gene data sets

Background The availability of many gene alignments with overlapping taxon sets raises the question of which strategy is the best to infer species phylogenies from multiple gene information. Methods and programs abound that use the gene alignment in different ways to reconstruct the species tree. In particular, different methods combine the original data at different points along the way from the underlying sequences to the final tree. Accordingly, they are classified into superalignment, supertree and medium-level approaches. Here, we present a simulation study to compare different methods from each of these three approaches. Results We observe that superalignment methods usually outperform the other approaches over a wide range of parameters including sparse data and gene-specific evolutionary parameters. In the presence of high incongruency among gene trees, however, other combination methods show better performance than the superalignment approach. Surprisingly, some supertree and medium-level methods exhibit, on average, worse results than a single gene phylogeny with complete taxon information. Conclusions For some methods, using the reconstructed gene tree as an estimation of the species tree is superior to the combination of incomplete information. Superalignment usually performs best since it is less susceptible to stochastic error. Supertree methods can outperform superalignment in the presence of gene-tree conflict