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

Optimizing Phylogenetic Supertrees Using Answer Set Programming

The supertree construction problem is about combining several phylogenetic trees with possibly conflicting information into a single tree that has all the leaves of the source trees as its leaves and the relationships between the leaves are as consistent with the source trees as possible. This leads to an optimization problem that is computationally challenging and typically heuristic methods, such as matrix representation with parsimony (MRP), are used. In this paper we consider the use of answer set programming to solve the supertree construction problem in terms of two alternative encodings. The first is based on an existing encoding of trees using substructures known as quartets, while the other novel encoding captures the relationships present in trees through direct projections. We use these encodings to compute a genus-level supertree for the family of cats (Felidae). Furthermore, we compare our results to recent supertrees obtained by the MRP method.Comment: To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 201

MRL and SuperFine+MRL: new supertree methods

<p>Abstract</p> <p>Background</p> <p>Supertree methods combine trees on subsets of the full taxon set together to produce a tree on the entire set of taxa. Of the many supertree methods, the most popular is MRP (Matrix Representation with Parsimony), a method that operates by first encoding the input set of source trees by a large matrix (the "MRP matrix") over {0,1, ?}, and then running maximum parsimony heuristics on the MRP matrix. Experimental studies evaluating MRP in comparison to other supertree methods have established that for large datasets, MRP generally produces trees of equal or greater accuracy than other methods, and can run on larger datasets. A recent development in supertree methods is SuperFine+MRP, a method that combines MRP with a divide-and-conquer approach, and produces more accurate trees in less time than MRP. In this paper we consider a new approach for supertree estimation, called MRL (Matrix Representation with Likelihood). MRL begins with the same MRP matrix, but then analyzes the MRP matrix using heuristics (such as RAxML) for 2-state Maximum Likelihood.</p> <p>Results</p> <p>We compared MRP and SuperFine+MRP with MRL and SuperFine+MRL on simulated and biological datasets. We examined the MRP and MRL scores of each method on a wide range of datasets, as well as the resulting topological accuracy of the trees. Our experimental results show that MRL, coupled with a very good ML heuristic such as RAxML, produced more accurate trees than MRP, and MRL scores were more strongly correlated with topological accuracy than MRP scores.</p> <p>Conclusions</p> <p>SuperFine+MRP, when based upon a good MP heuristic, such as TNT, produces among the best scores for both MRP and MRL, and is generally faster and more topologically accurate than other supertree methods we tested.</p

Algorithms for constructing more accurate and inclusive phylogenetic trees

Despite the unprecedented outpouring of molecular sequence data in phylogenetics, the current understanding of the tree of life is still incomplete. The widespread applications of phylogenies, ranging from drug design to biodiversity conservation, repeatedly remind us of the need for more accurate and inclusive phylogenies. My thesis addresses some of the underlying challenges, by presenting theoretical and empirical results, as well as algorithms for a range of phylogenetic optimization problems. In the first part of this thesis, I develop a heuristic method for the NP-hard unrooted Robinson-Foulds (RF) supertree problem, and show that it yields more accurate supertrees than those obtained from Matrix Representation with Parsimony (MRP) and rooted RF heuristic. In the second, I present an RF distance measure based approach (MulRF) for inferring a species tree from the input multi-copy gene trees, through a generalization of RF distance to multi-labeled trees. Through simulation, I show that this approach, which is independent of gene tree discordance mechanisms, produces more accurate species trees than existing methods when incongruence is caused by gene tree error, duplications and losses, and/or lateral gene transfer. Next, I perform a simulation study to evaluate the performance of Gene Tree Parsimony (GTP) under duplication and duplication and loss cost models and compare it to MulRF method. The objective is to study the effects of various types of sampling (e.g., gene tree and sequence sampling), gene tree error, and duplication and loss rates on the accuracy of the phylogenetic estimates by GTP and MulRF. Next, I present efficient error correction algorithms for gene tree reconciliation based on duplication, duplication and loss, and deep coalescence. In the end, I present NP-completeness proofs for two problems whose complexity was previously unknown

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