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113
Fast Folding and Comparison of RNA Secondary Structures (The Vienna RNA Package)
"... Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and bas ..."
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Cited by 614 (112 self)
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Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and base pairing probabilities. An efficient heuristic for the inverse folding problem of RNA is introduced. In addition we present compact and efficient programs for the comparison of RNA secondary structures based on tree editing and alignment. All computer codes are written in ANSI C. They include implementations of modified algorithms on parallel computers with distributed memory. Performance analysis carried out on an Intel Hypercube shows that parallel computing becomes gradually more and more efficient the longer the sequences are.
Application of Phylogenetic Networks in Evolutionary Studies
 SUBMITTED TO MBE 2005
, 2005
"... The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evoluti ..."
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Cited by 441 (10 self)
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The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a treelike manner, analysis of the data may not be best served by using methods that enforce a tree structure, but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic networks should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication andloss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This paper reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined and how they can be interpreted. Additionally, the paper outlines the beginnings of a comprehensive statistical framework for applying split network methods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this paper describes a new program SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances and trees.
NeighborNet: An agglomerative method for the construction of planar phylogenetic networks
"... We introduce NeighborNet, a network construction and data representation method that combines aspects of the neighbor joining (NJ) and SplitsTree. Like NJ, NeighborNet uses agglomeration: taxa are combined into progressively larger and larger overlapping clusters. Like SplitsTree, NeighborNet constr ..."
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Cited by 195 (8 self)
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We introduce NeighborNet, a network construction and data representation method that combines aspects of the neighbor joining (NJ) and SplitsTree. Like NJ, NeighborNet uses agglomeration: taxa are combined into progressively larger and larger overlapping clusters. Like SplitsTree, NeighborNet constructs networks rather than trees, and so can be used to represent multiple phylogenetic hypotheses simultaneously, or to detect complex evolutionary processes like recombination, lateral transfer and hybridization. NeighborNet tends to produce networks that are substantially more resolved than those made with SplitsTree. The method is e#cient (O(n ) time) and is well suited for the preliminary analyses of complex phylogenetic data. We report results of three case studies: one based on mitochondrial gene order data from early branching eukaryotes, another based on nuclear sequence data from New Zealand alpine buttercups (Ranunculi), and a third on poorly corrected synthetic data.
SplitsTree: A Program for Analyzing and Visualizing Evolutionary Data
, 1997
"... Motivation. Real evolutionary data often contains a number of different and sometimes conflicting phylogenetic signals and thus does not always clearly support a unique tree. To address this problem, H.J. Bandelt and A.W.M. Dress developed the method of split decomposition. For ideal data, this met ..."
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Cited by 84 (13 self)
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Motivation. Real evolutionary data often contains a number of different and sometimes conflicting phylogenetic signals and thus does not always clearly support a unique tree. To address this problem, H.J. Bandelt and A.W.M. Dress developed the method of split decomposition. For ideal data, this method gives rise to a tree, whereas less ideal data is represented by a treelike network that may indicate evidence for different and conflicting phylogenies. Results. SplitsTree is an interactive program for analyzing and visualizing evolutionary data, that implements this approach. It also supports a number of distances transformations, the computation of parsimony splits, spectral analysis and bootstrapping. Availability. There are two versions of SplitsTree, an interactive Macintosh version (shareware) and a commandline unix version (public domain). Both are available from: ftp://ftp.unibielefeld.de/pub/math/splits/splitstree2. There is a WWW version running at: http://www.bibiserv...
Inferring Evolutionary Trees with Strong Combinatorial Evidence
 THEORETICAL COMPUTER SCIENCE
, 1997
"... We consider the problem of inferring the evolutionary tree of a set of n species. We propose a quartet reconstruction method which specifically produces trees whose edges have strong combinatorial evidence. Let Q be a set of resolved quartets defined on the studied species, the method computes th ..."
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Cited by 77 (13 self)
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We consider the problem of inferring the evolutionary tree of a set of n species. We propose a quartet reconstruction method which specifically produces trees whose edges have strong combinatorial evidence. Let Q be a set of resolved quartets defined on the studied species, the method computes the unique maximum subset Q of Q which is equivalent to a tree and outputs the corresponding tree as an estimate of the species' phylogeny. We use a characterization of the subset Q due to [6] to provide an O(n 4 ) incremental algorithm for this variant of the NPhard quartet consistency problem. Moreover, when chosing the resolution of the quartets by the FourPoint Method (FPM) and considering the CavenderFarris model of evolution, we show that the convergence rate of the Q method is at worst polynomial when the maximum evolutive distance between two species is bounded. We complete these theoretical results by an experimental study on real and simulated data sets. The results ...
Recovering a tree from the leaf colourations it generates under a Markov model
, 1994
"... We describe a simple transformation that allows for the fast recovery of a tree from the probabilities such a tree induces on the colourations of its leaves under a simple Markov process (with unknown parameters). This generalizes earlier results by not requiring the transition matrices associat ..."
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Cited by 61 (8 self)
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We describe a simple transformation that allows for the fast recovery of a tree from the probabilities such a tree induces on the colourations of its leaves under a simple Markov process (with unknown parameters). This generalizes earlier results by not requiring the transition matrices associated with the edges of the tree to be of a particular form, or to be related by some fixed rate matrix, and by not insisting on a particular distribution of colours at the root of the tree. Applications to taxonomy are outlined briefly in three corollaries.
TTheory  An Overview
 EUROP. J. COMBINATORICS
, 1995
"... TTheory is the name that we adopt for the theory of trees, injective envelopes of metric spaces, and all of the areas that are connected with these topics, which has been developed over the last 1015 years in Bielefeld. Its motivation was originally  and still is to a large extent  the dev ..."
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Cited by 35 (7 self)
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TTheory is the name that we adopt for the theory of trees, injective envelopes of metric spaces, and all of the areas that are connected with these topics, which has been developed over the last 1015 years in Bielefeld. Its motivation was originally  and still is to a large extent  the development of mathematical tools for reconstructing phylogenetic trees. Ttheory expanded considerably when its relationships with the theory of affine buildings, valuated matroids, and decompositions of metrics were discovered. In this paper, we give a brief introduction to this theory, which we hope will serve as a useful reference to some of the main results, and also as a guide for further investigations into what Ttheory has to offer.
Reconstruction of reticulate networks from gene trees
 In Proceedings of the Ninth International Conference on Research in Computational Molecular Biology (RECOMB
, 2005
"... Abstract. One of the simplest evolutionary models has molecular sequences evolving from a common ancestor down a bifurcating phylogenetic tree, experiencing pointmutations along the way. However, empirical analyses of different genes indicate that the evolution of genomes is often more complex than ..."
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Cited by 35 (15 self)
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Abstract. One of the simplest evolutionary models has molecular sequences evolving from a common ancestor down a bifurcating phylogenetic tree, experiencing pointmutations along the way. However, empirical analyses of different genes indicate that the evolution of genomes is often more complex than can be represented by such a model. Thus, the following problem is of significant interest in molecular evolution: Given a set of molecular sequences, compute a reticulate network that explains the data using a minimal number of reticulations. This paper makes four contributions toward solving this problem. First, it shows that there exists a onetoone correspondence between the tangles in a reticulate network, the connected components of the associated incompatibility graph and the netted components of the associated splits graph. Second, it provides an algorithm that computes a most parsimonious reticulate network in polynomial time, if the reticulations contained in any tangle have a certain overlapping property, and if the number of reticulations contained in any given tangle is bounded by a constant. Third, an algorithm for drawing reticulate networks is described and a robust and flexible implementation of the algorithms is provided. Fourth, the paper presents a statistical test for distinguishing between reticulations due to hybridization, and ones due to other events such as lineage sorting or treeestimation error. 1
Phylogenetic supernetworks from partial trees
 IEEE/ACM Transactions in Computational Biology and Bioinformatics
, 2004
"... Abstract—In practice, one is often faced with incomplete phylogenetic data, such as a collection of partial trees or partial splits. This paper poses the problem of inferring a phylogenetic supernetwork from such data and provides an efficient algorithm for doing so, called the Zclosure method. Ad ..."
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Cited by 34 (16 self)
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Abstract—In practice, one is often faced with incomplete phylogenetic data, such as a collection of partial trees or partial splits. This paper poses the problem of inferring a phylogenetic supernetwork from such data and provides an efficient algorithm for doing so, called the Zclosure method. Additionally, the questions of assigning lengths to the edges of the network and how to restrict the “dimensionality ” of the network are addressed. Applications to a set of five published partial gene trees relating different fungal species and to six published partial gene trees relating different grasses illustrate the usefulness of the method and an experimental study confirms its potential. The method is implemented as a plugin for the program SplitsTree4. Index Terms—Molecular evolution, phylogeny, partial trees, networks, closure operations. 1
Metric graph theory and geometry: a survey
 CONTEMPORARY MATHEMATICS
"... The article surveys structural characterizations of several graph classes defined by distance properties, which have in part a general algebraic flavor and can be interpreted as subdirect decomposition. The graphs we feature in the first place are the median graphs and their various kinds of general ..."
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Cited by 32 (8 self)
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The article surveys structural characterizations of several graph classes defined by distance properties, which have in part a general algebraic flavor and can be interpreted as subdirect decomposition. The graphs we feature in the first place are the median graphs and their various kinds of generalizations, e.g., weakly modular graphs, or fibercomplemented graphs, or l1graphs. Several kinds of l1graphs admit natural geometric realizations as polyhedral complexes. Particular instances of these graphs also occur in other geometric contexts, for example, as dual polar graphs, basis graphs of (even ∆)matroids, tope graphs, lopsided sets, or plane graphs with vertex degrees and face sizes bounded from below. Several other classes of graphs, e.g., Helly graphs (as injective objects), or bridged graphs (generalizing chordal graphs), or treelike graphs such as distancehereditary graphs occur in the investigation of graphs satisfying some basic properties of the distance function, such as the Helly property for balls, or the convexity of balls or of the neighborhoods of convex sets, etc. Operators between graphs or complexes relate some of the