The generalized Robinson-Foulds metric

The Robinson-Foulds (RF) metric is arguably the most widely used measure of phylogenetic tree similarity, despite its well-known shortcomings: For example, moving a single taxon in a tree can result in a tree that has maximum distance to the original one; but the two trees are identical if we remove the single taxon. To this end, we propose a natural extension of the RF metric that does not simply count identical clades but instead, also takes similar clades into consideration. In contrast to previous approaches, our model requires the matching between clades to respect the structure of the two trees, a property that the classical RF metric exhibits, too. We show that computing this generalized RF metric is, unfortunately, NP-hard. We then present a simple Integer Linear Program for its computation, and evaluate it by an all-against-all comparison of 100 trees from a benchmark data set. We find that matchings that respect the tree structure differ significantly from those that do not, underlining the importance of this natural condition.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

The generalized Robinson-Foulds distance for phylogenetic trees

The Robinson-Foulds (RF) distance, one of the most widely used metrics for comparing phylogenetic trees, has the advantage of being intuitive, with a natural interpretation in terms of common splits, and it can be computed in linear time, but it has a very low resolution, and it may become trivial for phylogenetic trees with overlapping taxa, that is, phylogenetic trees that share some but not all of their leaf labels. In this article, we study the properties of the Generalized Robinson-Foulds (GRF) distance, a recently proposed metric for comparing any structures that can be described by multisets of multisets of labels, when applied to rooted phylogenetic trees with overlapping taxa, which are described by sets of clusters, that is, by sets of sets of labels. We show that the GRF distance has a very high resolution, it can also be computed in linear time, and it is not (uniformly) equivalent to the RF distance.This research was partially supported by the Spanish Ministry of Science, Innovation and Universitiesand the European Regional Development Fund through project PGC2018-096956-B-C43 (FEDER/MICINN/AEI), and by the Agency for Management of University and Research Grants (AGAUR) throughgrant 2017-SGR-786 (ALBCOM).Peer ReviewedPostprint (published version

On the accuracy of language trees

Historical linguistics aims at inferring the most likely language phylogenetic tree starting from information concerning the evolutionary relatedness of languages. The available information are typically lists of homologous (lexical, phonological, syntactic) features or characters for many different languages. From this perspective the reconstruction of language trees is an example of inverse problems: starting from present, incomplete and often noisy, information, one aims at inferring the most likely past evolutionary history. A fundamental issue in inverse problems is the evaluation of the inference made. A standard way of dealing with this question is to generate data with artificial models in order to have full access to the evolutionary process one is going to infer. This procedure presents an intrinsic limitation: when dealing with real data sets, one typically does not know which model of evolution is the most suitable for them. A possible way out is to compare algorithmic inference with expert classifications. This is the point of view we take here by conducting a thorough survey of the accuracy of reconstruction methods as compared with the Ethnologue expert classifications. We focus in particular on state-of-the-art distance-based methods for phylogeny reconstruction using worldwide linguistic databases. In order to assess the accuracy of the inferred trees we introduce and characterize two generalizations of standard definitions of distances between trees. Based on these scores we quantify the relative performances of the distance-based algorithms considered. Further we quantify how the completeness and the coverage of the available databases affect the accuracy of the reconstruction. Finally we draw some conclusions about where the accuracy of the reconstructions in historical linguistics stands and about the leading directions to improve it.Comment: 36 pages, 14 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

Polyhedral geometry of Phylogenetic Rogue Taxa

It is well known among phylogeneticists that adding an extra taxon (e.g. species) to a data set can alter the structure of the optimal phylogenetic tree in surprising ways. However, little is known about this "rogue taxon" effect. In this paper we characterize the behavior of balanced minimum evolution (BME) phylogenetics on data sets of this type using tools from polyhedral geometry. First we show that for any distance matrix there exist distances to a "rogue taxon" such that the BME-optimal tree for the data set with the new taxon does not contain any nontrivial splits (bipartitions) of the optimal tree for the original data. Second, we prove a theorem which restricts the topology of BME-optimal trees for data sets of this type, thus showing that a rogue taxon cannot have an arbitrary effect on the optimal tree. Third, we construct polyhedral cones computationally which give complete answers for BME rogue taxon behavior when our original data fits a tree on four, five, and six taxa. We use these cones to derive sufficient conditions for rogue taxon behavior for four taxa, and to understand the frequency of the rogue taxon effect via simulation.Comment: In this version, we add quartet distances and fix Table 4

Evolutionary Inference via the Poisson Indel Process

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classical evolutionary process, the TKF91 model, is a continuous-time Markov chain model comprised of insertion, deletion and substitution events. Unfortunately this model gives rise to an intractable computational problem---the computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a new stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The new model is closely related to the TKF91 model, differing only in its treatment of insertions, but the new model has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared to separate inference of phylogenies and alignments.Comment: 33 pages, 6 figure

Edit distance metrics for measuring dissimilarity between labeled gene trees

Les arbres phylogénétiques sont des instruments de biologie évolutive offrant de formidables moyens d'étude pour la génomique comparative. Ils fournissent des moyens de représenter des mécanismes permettant de modéliser les relations de parenté entre les espèces ou les membres de familles de gènes en fonction de la diversité taxonomique, ainsi que des observations et des renseignements sur l'histoire évolutive, la structure et la variation des processus biologiques. Cependant, les méthodes traditionnelles d'inférence phylogénétique ont la réputation d'être sensibles aux erreurs. Il est donc indispensable de comparer les arbres phylogénétiques et de les analyser pour obtenir la meilleure interprétation des données biologiques qu'ils peuvent fournir. Nous commençons par aborder les travaux connexes existants pour déduire, comparer et analyser les arbres phylogénétiques, en évaluant leurs bonnes caractéristiques ainsi que leurs défauts, et discuter des pistes d'améliorations futures. La deuxième partie de cette thèse se concentre sur le développement de mesures efficaces et précises pour analyser et comparer des paires d'arbres génétiques avec des nœuds internes étiquetés. Nous montrons que notre extension de la métrique bien connue de Robinson-Foulds donne lieu à une bonne métrique pour la comparaison d'arbres génétiques étiquetés sous divers modèles évolutifs, et qui peuvent impliquer divers événements évolutifs.Phylogenetic trees are instruments of evolutionary biology offering great insight for comparative genomics. They provide mechanisms to model the kinship relations between species or members of gene families as a function of taxonomic diversity. They also provide evidence and insights into the evolutionary history, structure, and variation of biological processes. However, traditional phylogenetic inference methods have the reputation to be prone to errors. Therefore, comparing and analysing phylogenetic trees is indispensable for obtaining the best interpretation of the biological information they can provide. We start by assessing existing related work to infer, compare, and analyse phylogenetic trees, evaluating their advantageous traits and flaws, and discussing avenues for future improvements. The second part of this thesis focuses on the development of efficient and accurate metrics to analyse and compare pairs of gene trees with labeled internal nodes. We show that our attempt in extending the popular Robinson-Foulds metric is useful for the preliminary analysis and comparison of labeled gene trees under various evolutionary models that may involve various evolutionary events