Reconstructing phylogenetic level-1 networks from nondense binet and trinet sets

Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set T of binary binets or trinets over a taxon set X, and constructing such a network whenever it exists. We show that this is NP-hard for trinets but polynomial-time solvable for binets. Moreover, we show that the problem is still polynomial-time solvable for inputs consisting of binets and trinets as long as the cycles in the trinets have size three. Finally, we present an O(3^{|X|} poly(|X|)) time algorithm for general sets of binets and trinets. The latter two algorithms generalise to instances containing level-1 networks with arbitrarily many leaves, and thus provide some of the first supernetwork algorithms for computing networks from a set of rooted 1 phylogenetic networks

Computing galled networks from real data

Motivation: Developing methods for computing phylogenetic networks from biological data is an important problem posed by molecular evolution and much work is currently being undertaken in this area. Although promising approaches exist, there are no tools available that biologists could easily and routinely use to compute rooted phylogenetic networks on real datasets containing tens or hundreds of taxa. Biologists are interested in clades, i.e. groups of monophyletic taxa, and these are usually represented by clusters in a rooted phylogenetic tree. The problem of computing an optimal rooted phylogenetic network from a set of clusters, is hard, in general. Indeed, even the problem of just determining whether a given network contains a given cluster is hard. Hence, some researchers have focused on topologically restricted classes of networks, such as galled trees and level-k networks, that are more tractable, but have the practical draw-back that a given set of clusters will usually not possess such a representation

A Survey of Combinatorial Methods for Phylogenetic Networks

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

Comparative genomics: multiple genome rearrangement and efficient algorithm development

Multiple genome rearrangement by signed reversal is discussed: For a collection of genomes represented by signed permutations, reconstruct their evolutionary history by using signed reversals, i.e. find a bifurcating tree where sampled genomes are assigned to leaf nodes and ancestral genomes (i.e. signed permutations) are hypothesized at internal nodes such that the total reversal distance summed over all edges of the tree is minimized. It is equivalent to finding an optimal Steiner tree that connects the given genomes by signed reversal paths. The key for the problem is to reconstruct all optimal Steiner nodes/ancestral genomes.;The problem is NP-hard and can only be solved by efficient approximation algorithms. Various algorithms/programs have been designed to solve the problem, such as BPAnalysis, GRAPPA, grid search algorithm, MGR greedy split algorithm (Chapter 1). However, they may have expensive computational costs or low inference accuracy. In this thesis, several new algorithms are developed, including nearest path search algorithm (Chapter 2), neighbor-perturbing algorithm (Chapter 3), branch-and-bound algorithm (Chapter 3), perturbing-improving algorithm (Chapter 4), partitioning algorithm (Chapter 5), etc. With theoretical proofs, computer simulations, and biological applications, these algorithms are shown to be 2-approximation algorithms and more efficient than the existing algorithms

Analysis of recombination in molecular sequence data

We present the new and fast method Recco for analyzing a multiple alignment regarding recombination. Recco is based on a dynamic program that explains one sequence in the alignment with the other sequences using mutation and recombination. The dynamic program allows for an intuitive visualization of the optimal solution and also introduces a parameter α controlling the number of recombinations in the solution. Recco performs a parametric analysis regarding α and orders all pareto-optimal solutions by increasing number of recombinations. α is also directly related to the Savings value, a quantitative and intuitive measure for the preference of recombination in the solution. The Savings value and the solutions have a simple interpretation regarding the ancestry of the sequences in the alignment and it is usually easy to understand the output of the method. The distribution of the Savings value for non-recombining alignments is estimated by processing column permutations of the alignment and p-values are provided for recombination in the alignment, in a sequence and at a breakpoint position. Recco also uses the p-values to suggest a single solution, or recombinant structure, for the explained sequence. Recco is validated on a large set of simulated alignments and has a recombination detection performance superior to all current methods. The analysis of real alignments confirmed that Recco is among the best methods for recombination analysis and further supported that Recco is very intuitive compared to other methods.Wir präsentieren Recco, eine neue und schnelle Methode zur Analyse von Rekombinationen in multiplen Alignments. Recco basiert auf einem dynamischen Programm, welches eine Sequenz im Alignment durch die anderen Sequenzen im Alignment rekonstruiert, wobei die Operatoren Mutation und Rekombination erlaubt sind. Das dynamische Programm ermöglicht eine intuitive Visualisierung der optimalen Lösung und besitzt einen Parameter α, welcher die Anzahl der Rekombinationsereignisse in der optimalen Lösung steuert. Recco führt eine parametrische Analyse bezüglich des Parameters α durch, so dass alle pareto-optimalen Lösungen nach der Anzahl ihrer Rekombinationsereignisse sortiert werden können. α steht auch direkt in Beziehung mit dem sogenannten Savings-Wert, der die Neigung zum Einfügen von Rekombinationsereignissen in die optimale Lösung quantitativ und intuitiv bemisst. Der Savings-Wert und die optimalen Lösungen haben eine einfache Interpretation bezüglich der Historie der Sequenzen im Alignment, so dass es in der Regel leicht fällt, die Ausgabe von Recco zu verstehen. Recco schätzt die Verteilung des Savings-Werts für Alignments ohne Rekombinationen durch einen Permutationstest, der auf Spaltenpermutationen basiert. Dieses Verfahren resultiert in p-Werten für Rekombination im Alignment, in einer Sequenz und an jeder Position im Alignment. Basierend auf diesen p-Werten schlägt Recco eine optimale Lösung vor, als Schätzer für die rekombinante Struktur der erklärten Sequenz. Recco wurde auf einem großen Datensatz simulierter Alignments getestet und erzielte auf diesem Datensatz eine bessere Vorhersagegüte in Bezug auf das Erkennen von Alignments mit Rekombination als alle anderen aktuellen Verfahren. Die Analyse von realen Datensätzen bestätigte, dass Recco zu den besten Methoden für die Rekombinationsanalyse gehört und im Vergleich zu anderen Methoden oft leichter verständliche Resultate liefert