Robinson-Foulds Supertrees

<p>Abstract</p> <p>Background</p> <p>Supertree methods synthesize collections of small phylogenetic trees with incomplete taxon overlap into comprehensive trees, or supertrees, that include all taxa found in the input trees. Supertree methods based on the well established Robinson-Foulds (RF) distance have the potential to build supertrees that retain much information from the input trees. Specifically, the RF supertree problem seeks a binary supertree that minimizes the sum of the RF distances from the supertree to the input trees. Thus, an RF supertree is a supertree that is consistent with the largest number of clusters (or clades) from the input trees.</p> <p>Results</p> <p>We introduce efficient, local search based, hill-climbing heuristics for the intrinsically hard RF supertree problem on rooted trees. These heuristics use novel non-trivial algorithms for the SPR and TBR local search problems which improve on the time complexity of the best known (naïve) solutions by a factor of Θ(<it>n</it>) and Θ(<it>n</it>²) respectively (where <it>n </it>is the number of taxa, or leaves, in the supertree). We use an implementation of our new algorithms to examine the performance of the RF supertree method and compare it to matrix representation with parsimony (MRP) and the triplet supertree method using four supertree data sets. Not only did our RF heuristic provide fast estimates of RF supertrees in all data sets, but the RF supertrees also retained more of the information from the input trees (based on the RF distance) than the other supertree methods.</p> <p>Conclusions</p> <p>Our heuristics for the RF supertree problem, based on our new local search algorithms, make it possible for the first time to estimate large supertrees by directly optimizing the RF distance from rooted input trees to the supertrees. This provides a new and fast method to build accurate supertrees. RF supertrees may also be useful for estimating majority-rule(-) supertrees, which are a generalization of majority-rule consensus trees.</p

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

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

Axiomatic opportunities and obstacles for inferring a species tree from gene trees

The reconstruction of a central tendency `species tree' from a large number of conflicting gene trees is a central problem in systematic biology. Moreover, it becomes particularly problematic when taxon coverage is patchy, so that not all taxa are present in every gene tree. Here, we list four apparently desirable properties that a method for estimating a species tree from gene trees could have (the strongest property states that building a species tree from input gene trees and then pruning leaves gives a tree that is the same as, or more resolved than, the tree obtained by first removing the taxa from the input trees and then building the species tree). We show that while it is technically possible to simultaneously satisfy these properties when taxon coverage is complete, they cannot all be satisfied in the more general supertree setting. In part two, we discuss a concordance-based consensus method based on Baum's `plurality clusters', and an extension to concordance supertrees.Comment: 19 pages, 2 figure

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

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, present 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 datasets where a molecular clock may be assumed. Contrary to other phylogenetic methods on partial datasets, 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 datasets of all sizes, including large datasets 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 datasets, 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 datasets

An Arrow-type result for inferring a species tree from gene trees

The reconstruction of a central tendency `species tree' from a large number of conflicting gene trees is a central problem in systematic biology. Moreover, it becomes particularly problematic when taxon coverage is patchy, so that not all taxa are present in every gene tree. Here, we list four desirable properties that a method for estimating a species tree from gene trees should have. We show that while these can be achieved when taxon coverage is complete (by the Adams consensus method), they cannot all be satisfied in the more general setting of partial taxon coverage.Comment: 5 pages, 0 figure

Nested Archimedean copulas: a new class of nonparametric tree structure estimators

Any nested Archimedean copula is defined starting from a rooted phylogenetic tree, for which a new class of nonparametric estimators is presented. An estimator from this new class relies on a two-step procedure where first a binary tree is built and second is collapsed if necessary to give an estimate of the target tree structure. Several examples of estimators from this class are given and the performance of each of these estimators, as well as of the only known comparable estimator, is assessed by means of a simulation study involving target structures in various dimensions, showing that the new estimators, besides being faster, usually offer better performance as well. Further, among the given examples of estimators from the new class, one of the best performing one is applied on three datasets: 482 students and their results to various examens, 26 European countries in 1979 and the percentage of workers employed in different economic activities, and 104 countries in 2002 for which various health-related variables are available. The resulting estimated trees offer valuable insights on the analyzed data. The future of nested Archimedean copulas in general is also discussed