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.

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.

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 NP-hard quartet consistency problem. Moreover, when chosing the resolution of the quartets by the Four-Point Method (FPM) and considering the Cavender-Farris 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 ...

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 tree-like 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 command-line unix version (public domain). Both are available from: ftp://ftp.uni-bielefeld.de/pub/math/splits/splitstree2. There is a WWW version running at: http://www.bibiserv...

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.

The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a 'fitness' landscape. The dynamics of evolution is hence tightly linked to the structure of the underlying landscape. Global features of landscapes can be described by statistical measures like number of optima, lengths of walks, and correlation functions. The evolution of a quasispecies on such landscapes exhibits three dynamical regimes depending on the replication fidelity: Above the "localization threshold" the population is centered around a (local) optimum. Between localization and "dispersion threshold" the population is still centered around a consensus sequence, which, however, changes in time. For very large mutation rates the population spreads in sequence space like a gas. The critical mutation rates separating the three domains depend strongly on characteristics properties of the fitness landscapes. Statistical characteristics of RNA landscapes are acces...

T-Theory 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 10-15 years in Bielefeld. Its motivation was originally -- and still is to a large extent -- the development of mathematical tools for reconstructing phylogenetic trees. T-theory 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 T-theory has to offer.

Background: Protein space is explored by means of an inverse folding procedure that makes use of knowledge-based potentials of mean force. Results: Computer simulations indicate that amino acid sequences folding into a common shape are distributed homogeneously forming extended percolating networks that span the entire sequence space. Conclusions: The existence of very long neutral paths on all examined protein structures, indicates the existence of neutral networks percolating protein space. The same qualitative results were obtained for some, but not all, restricted amino acid alphabets. In this respect, the sequence-structure map of proteins seems to be very similar to the nucleic acid case.

Abstract. One of the simplest evolutionary models has molecular sequences evolving from a common ancestor down a bifurcating phylogenetic tree, experiencing point-mutations 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 one-to-one 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 tree-estimation error. 1

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 super-network from such data and provides an efficient algorithm for doing so, called the Z-closure 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 plug-in for the program SplitsTree4. Index Terms—Molecular evolution, phylogeny, partial trees, networks, closure operations. 1