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 powe

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

Edge Ratchet and Simulated Annealing to Improve RF Score of the Supertree of Life

Constructing the Supertree of Life can provide crucially valuable knowledge to address many critical contemporary challenges such as fighting diseases, improving global agriculture, and protecting ecosystems to name a few. However, building such a tree is among the most complicated and challenging scientific problems. In the case of biological data, the true species tree is not available. Hence, the accuracy of the supertree is usually evaluated based on its similarity to the given source input trees. In this work, we aim at improving the accuracy of the supertree in terms of its cumulative Robinson Foulds (RF) distance to the source trees. This problem is NP-hard. Therefore, we have to resort to heuristic algorithms. We have two main contributions in this work. First, we propose a new technique, Edge Ratchet, which is used in a hill-climbing based algorithm to deal with local optimum problem. Second, we develop a Simulated Annealing algorithm to minimize total RF distance of the supertree to the source trees. Our results demonstrate that these two algorithms are able to improve the accuracy of the best existing supertree algorithms with regard to RF distance

Reweaving the tapestry: a supertree of birds

Supertrees are a useful method of constructing large-scale phylogenies by assembling numerous smaller phylogenies that have some, but not necessarily all, taxa in common. Birds are an obvious candidate for supertree construction as they are the most abundant land vertebrates on the planet and no comprehensive phylogeny of both extinct and extant species currently exists. In order to construct supertrees, primary analysis of characters is required. One such study, presented here, describes two new partial specimens belonging to the Primobucconidae from the Green River Formation of Wyoming (USA), which were assigned to the species Primobucco mcgrewi. Although incomplete, these specimens had preserved anatomical features not seen in other material. An attempt to further constrain their phylogenetic position was inconclusive, showing only that the Primobucconidae belong in a clade containing the extant Coraciiformes and related taxa. Over 700 such studies were used to construct a species-level supertree of Aves containing over 5000 taxa. The resulting tree shows the relationships between the main avian groups, with only a few novel clades, some of which can be explained by a lack of information regarding those taxa. The tree was constructed using a strict protocol which ensures robust, accurate and efficient data collection and processing; extending previous work by other authors. Before creating the species-level supertree the protocol was tested on the order Galliformes in order to determine the most efficient method of removing non-independent data. It was found that combining non-independent source trees via a “mini-supertree” analysis produced results more consistent with the input source data and, in addition, significantly reduced computational load. Another method for constructing large-scale trees is via a supermatrix, which is constructed from primary data collated into a single, large matrix. A molecular-only tree was constructed using both supertree and supermatrix methods, from the same data, again of the order Galliformes. Both methods performed equally as well in producing trees that fit the source data. The two methods could be considered complementary rather than conflicting as the supertree took a long time to construct but was very quick to calculate, but the supermatrix took longer to calculate, but was quicker to construct. Dependent upon the data at hand and the other factors involved, the choice of which method to use appears, from this small study, to be of little consequence. Finally an updated species-level supertree of the Dinosauria was also constructed and used to look at diversification rates in order to elucidate the “Cretaceous explosion of terrestrial life”. Results from this study show that this apparent burst in diversity at the end of the Cretaceous is a sampling artefact and in fact, dinosaurs show most of their major diversification shifts in the first third of their history

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

Mega-phylogeny approach for comparative biology: an alternative to supertree and supermatrix approaches

Abstract Background Biology has increasingly recognized the necessity to build and utilize larger phylogenies to address broad evolutionary questions. Large phylogenies have facilitated the discovery of differential rates of molecular evolution between trees and herbs. They have helped us understand the diversification patterns of mammals as well as the patterns of seed evolution. In addition to these broad evolutionary questions there is increasing awareness of the importance of large phylogenies for addressing conservation issues such as biodiversity hotspots and response to global change. Two major classes of methods have been employed to accomplish the large tree-building task: supertrees and supermatrices. Although these methods are continually being developed, they have yet to be made fully accessible to comparative biologists making extremely large trees rare. Results Here we describe and demonstrate a modified supermatrix method termed mega-phylogeny that uses databased sequences as well as taxonomic hierarchies to make extremely large trees with denser matrices than supermatrices. The two major challenges facing large-scale supermatrix phylogenetics are assembling large data matrices from databases and reconstructing trees from those datasets. The mega-phylogeny approach addresses the former as the latter is accomplished by employing recently developed methods that have greatly reduced the run time of large phylogeny construction. We present an algorithm that requires relatively little human intervention. The implemented algorithm is demonstrated with a dataset and phylogeny for Asterales (within Campanulidae) containing 4954 species and 12,033 sites and an rbcL matrix for green plants (Viridiplantae) with 13,533 species and 1,401 sites. Conclusion By examining much larger phylogenies, patterns emerge that were otherwise unseen. The phylogeny of Viridiplantae successfully reconstructs major relationships of vascular plants that previously required many more genes. These demonstrations underscore the importance of using large phylogenies to uncover important evolutionary patterns and we present a fast and simple method for constructing these phylogenies.</p

Postprocessing phylogenies

Es werden immer mehr phylogenetische Bäume berechnet. Die berechneten Verwandtschaften zwischen den Arten können sich allerdings widersprechen. In diesem Fall sind Werkzeuge notwendig, welche die Höhe des Unterschiedes berechnen, die Gemeinsamkeiten zweier Bäume extrahieren und mehrere Bäume zusammenfassen indem sie die Unterschiede minimieren. Diese Werkzeuge werden unter dem Begriff ``Phylogenetic Postprocessing'' zusammengefasst. In dieser Arbeit werden zwei Aspekte des Phylogenetischen Postprocessings im Detail untersucht. Zuerst werden Baumdistanzen untersucht. Diese evaluieren den Unterschied zweier Bäume. Die meisten Maße berücksichtigen dabei nur die topologische Information. Allerdings tragen auch die Kantenlängen der Bäume Informationen, da sie z.B. eine Schätzung der Menge an Unterschied zwischen zwei Sequenzen sind. Ein Maß, welches sowohl die Topologie als auch die Kantenlängen berücksichtigt, ist die Länge des kürzesten Weges durch den Raum aller Bäume mit Kantenlängen. Dies ist die geodätische Distanz. Hier präsentieren wir einen exakten Algorithmus um die geodätische Distanz zu berechnen, der in exponentieller Zeit läuft. Vergleiche mit ihren Approximationen zeigen, dass es einen bestimmten Weg gibt, der die geodätische Distanz gut annähert und in linearer Zeit berechnet werden kann. Phylogenetische Bäume können auch daraufhin untersucht werden, ob sie statistisch ähnlich oder unterschiedlich sind. Dabei kann ein topologisches Distanzmaß als Teststatistik verwendet und die assoziierten p-Werte werden unter einer Nullverteilung der Bäume berechnet werden. Bei diskreten Testverfahren, muss allerdings die Testgröße konservativ gewählt werden, d.h. sie darf das Signifikanzniveau nicht überschreiten. Wir zeigen ein Beispiel auf, bei dem ein Test abgeändert werden muss um dies zu gewährleisten. Der zweite Aspekt ist die Kombination von Bäumen oder allgemein phylogenetischen Datensätzen. Genbäume mit sich überschneidenden Artenmengen können zu einem sogenannten Supertree zusammengefügt werden. Eine andere Möglichkeit ist bereits die Genalignments zu kombinieren. Dabei werden die Genalignments aneinandergehangen, d.h. zu einem sogenannten Superalignment kombiniert. Anschließend wird eine Phylogenie aus diesem langen Alignment berechnet. Es gibt auch die dritte Möglichkeit, die Daten auf einer Stufe zwischen Superalignment und Supertree zu kombinieren. Mit Hilfe von Simulationen von Genalignments entlang Modellbäumen können Methoden von diesen drei Stufen verglichen werden. Wir untersuchen verschiedene Parameter, z.B. vollständige oder sich überschneidende Artenmengen, gleiche oder unterschiedliche Substitutionsparameter oder unterschiedliche Gentopologien. Die Simulationen zeigen gute Ergebnisse der Matrix-Representation-Methoden im Vergleich zu anderen Supertreemethoden. Weiterhin ist Superalignment gut geeignet bei unterschiedlichen Parametern zwischen den Genen, aber problematisch wenn es viele Unterschiede zwischen den wahren Genbäumen gibt. Zusätzlich zu diesem praktischen Vergleich von Supertreemethoden sind auch theoretische und praktische Aspekte von Interesse. Daher untersuchen wir die Nullmodelle, die der Supertreerekonstruktion zugrunde liegen. Ein solches Nullmodell ist die Gleichverteilung der Splits, also jeder möglichen Unterteilung der Arten in zwei Mengen. Es stellt sich heraus, dass nur diese Verteilung angemessene Eigenschaften hat, wenn wenig Information vorhanden ist. Ein zweites Nullmodell ist die Gleichverteilung der Bäume. Diese fügt allerdings eine Verzerrung zugunsten bestimmter Baumstrukturen in splitbasierte Supertreemethoden ein. Diese Verzerrung kann auf die ungleiche Verteilung der Splits in diesem Nullmodell zurückgeführt werden. Schließlich kann ein Supertree auch als Median-Tree definiert werden, also als Baum, der die totale Distanz zu allen Bäumen in der Menge minimiert. Der Majority-Rule Consensus wurde als Median-Tree-Methode für Bäume mit gleichen Artenmengen beschrieben. Für Bäume mit sich überschneidenden Artenmengen gibt als allerdings unterschiedliche Ausprägungen, und zwar MR(-)supertrees und MR(+)supertrees. Wir präsentieren Algorithmen um die entsprechenden Distanzen im Matrix-Representation-Framework zu berechnen. Durch die Anwendung ihrer Implementierungen auf simulierte Datensätze sehen wir deutlich bessere Ergebnisse für MR(-) im Vergleich zu MR(+). Es ist naheliegend diesen Unterschied auf eine Verzerrung zugunsten bestimmter Baumstrukturen in MR(+) zurückzuführen. Zusammenfassend sehen wir, dass die zwei Aspekte des Phylogenetischen Postprocessings, also Baumdistanzen und Baumkombinationsmethoden, nicht unabhängig sind, sondern durch die Definition des Median-Trees verbunden. Daher wird unser Verständnis von Baumdistanzen auch die Kombination von Bäumen beeinflussen und umgekehrt.More and more phylogenetic trees are generated, and it frequently occurs that the inferred relationships contradict each other. In this case, tools are necessary which evaluate the amount of difference between two trees, extract the congruencies of two trees, and combine multiple trees by minimizing the incongruencies. These tools are summarized by the term ``phylogenetic postprocessing''. In this thesis, two aspects of phylogenetic postprocessing are investigated in detail. First, tree distance computations evaluate the amount of difference between two trees. Most measures only take the topological information into account. There are a few measures that additionally focus on the branch lengths of the trees. One of these is the length of the shortest path in the space of weighted trees, also known as the geodesic distance. Here, an exact, but exponential-time, algorithm to compute the geodesic distance is presented. Comparisons with its approximations show that there is a particular path that approximates the geodesic distance well and that can be computed in linear time. Phylogenetic trees can also be tested for being statistically similar or different. Then a topological distance measure can be used as a test statistic where the associated p-value is computed under a null distribution of trees. Discrete tests must ensure that the size of the test is conservative, i.e. the size must not exceed the significance level. We present one example where a test has to be modified to ensure this property. Second, gene trees on overlapping taxon sets can be combined into a so-called supertree. Another possibility is to combine the gene alignments directly, namely, to concatenate the gene alignments into a superalignment and to reconstruct a phylogeny from this long alignment. There is also the possibility to combine the data at a level between superalignment and supertree methods. Simulations of gene alignments along model gene trees allow for the comparison of methods from all three levels. We investigate different settings, e.g. complete or overlapping taxon sets, equal or different substitution parameters or different gene topologies. The results show a good performance of matrix representation methods compared to other supertree and medium-level methods. Furthermore, superalignment is well applicable in the case of differing parameters between genes but is problematic when a high level of incongruence is present among the true gene trees. Additionally to the practical evaluation of supertree methods, theoretical and algorithmic aspects are of interest. Therefore we study different null models underlying supertree reconstruction. We find only the distribution of equally likely splits to behave in an appropriate way if little information is present. In contrast, the distribution of equally likely trees inserts a tree shape bias in split-based supertree methods. This bias can be traced back to the unequal split distribution in the null model. Finally, a supertree can also be defined by minimizing the total distance to the trees in the set, i.e. as a median tree. The majority-rule consensus is described as a median tree method for trees on the same taxon set. For trees on overlapping taxon sets, however, different specifications can be used, namely MR(-)supertrees and MR(+)supertrees. We present algorithms to compute the respective distances in the matrix representation framework. Applying their implementation to simulated data sets shows a clearly better performance of MR(-) compared to MR(+). This discrepancy is likely to trace back to a tree shape bias in MR(+). To conclude, we see that the two aspect of phylogenetic postprocessing, tree distances and tree combination methods, are not independent. Instead, they are linked by the definition of the median tree. Thus our understanding of tree distances influences data combination methods and vice versa

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