Extracting Conflict-free Information from Multi-labeled Trees

A multi-labeled tree, or MUL-tree, is a phylogenetic tree where two or more leaves share a label, e.g., a species name. A MUL-tree can imply multiple conflicting phylogenetic relationships for the same set of taxa, but can also contain conflict-free information that is of interest and yet is not obvious. We define the information content of a MUL-tree T as the set of all conflict-free quartet topologies implied by T, and define the maximal reduced form of T as the smallest tree that can be obtained from T by pruning leaves and contracting edges while retaining the same information content. We show that any two MUL-trees with the same information content exhibit the same reduced form. This introduces an equivalence relation in MUL-trees with potential applications to comparing MUL-trees. We present an efficient algorithm to reduce a MUL-tree to its maximally reduced form and evaluate its performance on empirical datasets in terms of both quality of the reduced tree and the degree of data reduction achieved.Comment: Submitted in Workshop on Algorithms in Bioinformatics 2012 (http://algo12.fri.uni-lj.si/?file=wabi

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

Cophylogeny Reconstruction Allowing for Multiple Associations Through Approximate Bayesian Computation

Phylogenetic tree reconciliation is extensively employed for the examination of coevolution between host and symbiont species. An important concern is the requirement for dependable cost values when selecting event-based parsimonious reconciliation. Although certain approaches deduce event probabilities unique to each pair of host and symbiont trees, which can subsequently be converted into cost values, a significant limitation lies in their inability to model the invasion of diverse host species by the same symbiont species (termed as a spread event), which is believed to occur in symbiotic relationships. Invasions lead to the observation of multiple associations between symbionts and their hosts (indicating that a symbiont is no longer exclusive to a single host), which are incompatible with the existing methods of coevolution. Here, we present a method called AmoCoala (an enhanced version of the tool Coala) that provides a more realistic estimation of cophylogeny event probabilities for a given pair of host and symbiont trees, even in the presence of spread events. We expand the classical 4-event coevolutionary model to include 2 additional outcomes, vertical and horizontal spreads, that lead to multiple associations. In the initial step, we estimate the probabilities of spread events using heuristic frequencies. Subsequently, in the second step, we employ an approximate Bayesian computation (ABC) approach to infer the probabilities of the remaining 4 classical events (cospeciation, duplication, host switch, and loss) based on these values. By incorporating spread events, our reconciliation model enables a more accurate consideration of multiple associations. This improvement enhances the precision of estimated cost sets, paving the way to a more reliable reconciliation of host and symbiont trees. To validate our method, we conducted experiments on synthetic datasets and demonstrated its efficacy using real-world examples. Our results showcase that AmoCoala produces biologically plausible reconciliation scenarios, further emphasizing its effectiveness

MUL-Tree Pruning for Consistency and Compatibility

A multi-labelled tree (or MUL-tree) is a rooted tree leaf-labelled by a set of labels, where each label may appear more than once in the tree. We consider the MUL-tree Set Pruning for Consistency problem (MULSETPC), which takes as input a set of MUL-trees and asks whether there exists a perfect pruning of each MUL-tree that results in a consistent set of single-labelled trees. MULSETPC was proven to be NP-complete by Gascon et al. when the MUL-trees are binary, each leaf label is used at most three times, and the number of MUL-trees is unbounded. To determine the computational complexity of the problem when the number of MUL-trees is constant was left as an open problem. Here, we resolve this question by proving a much stronger result, namely that MULSETPC is NP-complete even when there are only two MUL-trees, every leaf label is used at most twice, and every MUL-tree is either binary or has constant height. Furthermore, we introduce an extension of MULSETPC that we call MULSETPComp, which replaces the notion of consistency with compatibility, and prove that MULSETPComp is NP-complete even when there are only two MUL-trees, every leaf label is used at most thrice, and every MUL-tree has constant height. Finally, we present a polynomial-time algorithm for instances of MULSETPC with a constant number of binary MUL-trees, in the special case where every leaf label occurs exactly once in at least one MUL-tree

Cophylogeny reconstruction via an approximate bayesian computation

Despite an increasingly vast literature on cophylogenetic reconstructions for studying host-parasite associations, understanding the common evolutionary history of such systems remains a problem that is far from being solved. Most algorithms for host-parasite reconciliation use an event-based model, where the events include in general (a subset of) cospeciation, duplication, loss, and host switch. All known parsimonious event-based methods then assign a cost to each type of event in order to find a reconstruction of minimum cost. The main problem with this approach is that the cost of the events strongly influences the reconciliation obtained. Some earlier approaches attempt to avoid this problem by finding a Pareto set of solutions and hence by considering event costs under some minimization constraints. To deal with this problem, we developed an algorithm, called Coala, for estimating the frequency of the events based on an approximate Bayesian computation approach. The benefits of this method are 2-fold: (i) it provides more confidence in the set of costs to be used in a reconciliation, and (ii) it allows estimation of the frequency of the events in cases where the data set consists of trees with a large number of taxa. We evaluate our method on simulated and on biological data sets. We show that in both cases, for the same pair of host and parasite trees, different sets of frequencies for the events lead to equally probable solutions. Moreover, often these solutions differ greatly in terms of the number of inferred events. It appears crucial to take this into account before attempting any further biological interpretation of such reconciliations. More generally, we also show that the set of frequencies can vary widely depending on the input host and parasite trees. Indiscriminately applying a standard vector of costs may thus not be a good strategy

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

Phylogenetic networks that are their own fold-ups

Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted directed acyclic graphs whose leaves are labelled by, for example, species. A number of mathematically interesting classes of phylogenetic networks are known. These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain "fold-up" and "un-fold" operations that link them with concepts arising within the theory of, for example, graph fibrations. Despite this exciting link, the structural complexity of stable phylogenetic networks is still relatively poorly understood. Employing the popular tree-based, reticulation-visible, and tree-child properties which allow one to gauge this complexity in one way or another, we provide novel characterizations for when a stable phylogenetic network satisfies either one of these three properties

Managing and analyzing phylogenetic databases

The ever growing availability of phylogenomic data makes it increasingly possible to study and analyze phylogenetic relationships across a wide range of species. Indeed, current phylogenetic analyses are now producing enormous collections of trees that vary greatly in size. Our proposed research addresses the challenges posed by storing, querying, and analyzing such phylogenetic databases. Our first contribution is the further development of STBase, a phylogenetic tree database consisting of a billion trees whose leaf sets range from four to 20000. STBase applies techniques from different areas of computer science for efficient tree storage and retrieval. It also introduces new ideas that are specific to tree databases. STBase provides a unique opportunity to explore innovative ways to analyze the results from queries on large sets of phylogenetic trees. We propose new ways of extracting consensus information from a collection of phylogenetic trees. Specifically, this involves extending the maximum agreement subtree problem. We greatly improve upon an existing approach based on frequent subtrees and, propose two new approaches based on agreement subtrees and frequent subtrees respectively. The final part of our proposed work deals with the problem of simplifying multi-labeled trees and handling rogue taxa. We propose a novel technique to extract conflict-free information from multi-labeled trees as a much smaller single labeled tree. We show that the inherent problem in identifying rogue taxa is NP-hard and give fixed-parameter tractable and integer linear programming solutions

Supertree-like methods for genome-scale species tree estimation

A critical step in many biological studies is the estimation of evolutionary trees (phylogenies) from genomic data. Of particular interest is the species tree, which illustrates how a set of species evolved from a common ancestor. While species trees were previously estimated from a few regions of the genome (genes), it is now widely recognized that biological processes can cause the evolutionary histories of individual genes to differ from each other and from the species tree. This heterogeneity across the genome is phylogenetic signal that can be leveraged to estimate species evolution with greater accuracy. Hence, species tree estimation is expected to be greatly aided by current large-scale sequencing efforts, including the 5000 Insect Genomes Project, the 10000 Plant Genomes Project, the (~60000) Vertebrate Genomes Project, and the Earth BioGenome Project, which aims to assemble genomes (or at least genome-scale data) for 1.5 million eukaryotic species in the next ten years. To analyze these forthcoming datasets, species tree estimation methods must scale to thousands of species and tens of thousands of genes; however, many of the current leading methods, which are heuristics for NP-hard optimization problems, can be prohibitively expensive on datasets of this size. In this dissertation, we argue that new methods are needed to enable scalable and statistically rigorous species tree estimation pipelines; we then seek to address this challenge through the introduction of three supertree-like methods: NJMerge, TreeMerge, and FastMulRFS. For these methods, we present theoretical results (worst-case running time analyses and proofs of statistical consistency) as well as empirical results on simulated datasets (and a fungal dataset for FastMulRFS). Overall, these methods enable statistically consistent species tree estimation pipelines that achieve comparable accuracy to the dominant optimization-based approaches while dramatically reducing running time