Labellable Phylogenetic Networks

2010

Since Darwin, species trees have been used as a simplified description of the relationships which summarize the complicated network N of reality. Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate. Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N. A connected surjective digraph map (CSD) is a map f from one network N to another network M such that every arc is either collapsed to a single vertex or is taken to an arc, such that f is surjective, and such that the inverse image of a vertex is always connected. CSD maps are shown to behave well under composition. It is proved that if there is a CSD map from N to M , then there is a way to lift an undirected version of M into N , often with added resolution. A CSD map from N to M puts strong constraints on N. In general, it may be useful to study classes of networks such that, for any N , there exists a CSD map from N to some standard member of that class.

2008

We prove that Nakhleh's latest 'metric' for phylogenetic networks separates distinguishable phylogenetic networks, and that a slight modification of it provides a true distance on the class of all phylogenetic networks.

Genome Biology and Evolution, 2011

The evolutionary history of a set of species is usually described by a rooted phylogenetic tree. Although it is generally undisputed that bifurcating speciation events and descent with modifications are major forces of evolution, there is a growing belief that reticulate events also have a role to play. Phylogenetic networks provide an alternative to phylogenetic trees and may be more suitable for data sets where evolution involves significant amounts of reticulate events, such as hybridization, horizontal gene transfer, or recombination. In this article, we give an introduction to the topic of phylogenetic networks, very briefly describing the fundamental concepts and summarizing some of the most important combinatorial methods that are available for their computation.

2008

We prove that Nakhleh's latest 'metric' for phylogenetic networks is a metric on the classes of tree-child phylogenetic networks, of semi-binary time consistent tree-sibling phylogenetic networks, and of multi-labeled phylogenetic trees.We also prove that it separates distinguishable phylogenetic networks. In this way, it becomes the strongest dissimilarity measure for phylogenetic networks available so far.

IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2004

Phylogenetic networks model the evolutionary history of sets of organisms when events such as hybrid speciation and horizontal gene transfer occur. In spite of their widely acknowledged importance in evolutionary biology, phylogenetic networks have so far been studied mostly for specific data sets. We present a general definition of phylogenetic networks in terms of directed acyclic graphs (DAGs) and a set of conditions. Further, we distinguish between model networks and reconstructible ones and characterize the effect of extinction and taxon sampling on the reconstructibility of the network. Simulation studies are a standard technique for assessing the performance of phylogenetic methods. A main step in such studies entails quantifying the topological error between the model and inferred phylogenies. While many measures of tree topological accuracy have been proposed, none exist for phylogenetic networks. Previously, we proposed the first such measure, which applied only to a restricted class of networks. In this paper, we extend that measure to apply to all networks, and prove that it is a metric on the space of phylogenetic networks. Our results allow for the systematic study of existing network methods, and for the design of new accurate ones.

Systematic Biology, 2015

A binary phylogenetic network may or may not be obtainable from a tree by the addition of directed edges (arcs) between tree arcs. Here, we establish a precise and easily tested criterion (based on "2-SAT") that efficiently determines whether or not any given network can be realized in this way. Moreover, the proof provides a polynomialtime algorithm for finding one or more trees (when they exist) on which the network can be based. A number of interesting consequences are presented as corollaries; these lead to some further relevant questions and observations, which we outline in the conclusion. [Algorithm, Antichain, Phylogenetic network, phylogenetic tree, reticulate evolution, 2-SAT.]

Discrete Mathematics, 1988

trees are used in biology to illustrate postulated ancestral relationships between species and are often called phylogenetic trees. They can be characterized in graph theoretic terms by certain classes of labelled trees. Disjoint subsets of the labelling set are assigned to tree vertices so that all pendant vertices and any vertices of degree two are labelled. Here we determine exact and asymptotic numbers for two classes of trees in which multiple vertex labels are allowed.

The Scientific World Journal, 2014

Several polynomial time computable metrics on the class of semibinary tree-sibling time consistent phylogenetic networks are available in the literature; in particular, the problem of deciding if two networks of this kind are isomorphic is in P. In this paper, we show that if we remove the semibinarity condition, then the problem becomes much harder. More precisely, we prove that the isomorphism problem for generic tree-sibling time consistent phylogenetic networks is polynomially equivalent to the graph isomorphism problem. Since the latter is believed not to belong to P, the chances are that it is impossible to define a metric on the class of all tree-sibling time consistent phylogenetic networks that can be computed in polynomial time.

IEEE IEEE/ACM …, 2008

Abstract-The assessment of phylogenetic network reconstruction methods requires the ability to compare phylogenetic networks. This is the first in a series of papers devoted to the analysis and comparison of metrics for tree-child time-consistent phylogenetic networks on the same set of taxa. In this paper, we study three metrics that have already been introduced in the literature: the Robinson-Foulds distance, the tripartition distance, and the -distance. They generalize to networks the classical Robinson-Foulds or partition distance for phylogenetic trees. We analyze the behavior of these metrics by studying their least and largest values and when they achieve them. As a by-product of this study, we obtain tight bounds on the size of a tree-child time-consistent phylogenetic network. . His research interests are split between number theory (mainly, arithmetical properties of curves of genus 2) and computational biology (mainly, mathematical models of evolution). . Her research is centered on mathematical models in computational and systems biology.

Journal of Computational Biology, 2007

Phylogenetic networks are models of evolution that go beyond trees, incorporating non-tree-like biological events such as recombination (or more generally reticulation), which occur either in a single species (meiotic recombination) or between species (reticulation due to lateral gene transfer and hybrid speciation). The central algorithmic problems are to reconstruct a plausible history of mutations and non-tree-like events, or to determine the minimum number of such events needed to derive a given set of binary sequences, allowing one mutation per site. Meiotic recombination, reticulation and recurrent mutation can cause conflict or incompatibility between pairs of sites (or characters) of the input. Previously, we used "conflict graphs" and "incompatibility graphs" to compute lower bounds on the minimum number of recombination nodes needed, and to efficiently solve constrained cases of the minimization problem. Those results exposed the structural and algorithmic importance of the non-trivial connected components of those two graphs.