On Computing the Maximum Parsimony Score of a Phylogenetic Network

Phylogenetic networks are used to display the relationship of different species whose evolution is not treelike, which is the case, for instance, in the presence of hybridization events or horizontal gene transfers. Tree inference methods such as Maximum Parsimony need to be modified in order to be applicable to networks. In this paper, we discuss two different definitions of Maximum Parsimony on networks, "hardwired" and "softwired", and examine the complexity of computing them given a network topology and a character. By exploiting a link with the problem Multicut, we show that computing the hardwired parsimony score for 2-state characters is polynomial-time solvable, while for characters with more states this problem becomes NP-hard but is still approximable and fixed parameter tractable in the parsimony score. On the other hand we show that, for the softwired definition, obtaining even weak approximation guarantees is already difficult for binary characters and restricted network topologies, and fixed-parameter tractable algorithms in the parsimony score are unlikely. On the positive side we show that computing the softwired parsimony score is fixed-parameter tractable in the level of the network, a natural parameter describing how tangled reticulate activity is in the network. Finally, we show that both the hardwired and softwired parsimony score can be computed efficiently using Integer Linear Programming. The software has been made freely available

Phylogenetic Networks Do not Need to Be Complex: Using Fewer Reticulations to Represent Conflicting Clusters

Phylogenetic trees are widely used to display estimates of how groups of species evolved. Each phylogenetic tree can be seen as a collection of clusters, subgroups of the species that evolved from a common ancestor. When phylogenetic trees are obtained for several data sets (e.g. for different genes), then their clusters are often contradicting. Consequently, the set of all clusters of such a data set cannot be combined into a single phylogenetic tree. Phylogenetic networks are a generalization of phylogenetic trees that can be used to display more complex evolutionary histories, including reticulate events such as hybridizations, recombinations and horizontal gene transfers. Here we present the new CASS algorithm that can combine any set of clusters into a phylogenetic network. We show that the networks constructed by CASS are usually simpler than networks constructed by other available methods. Moreover, we show that CASS is guaranteed to produce a network with at most two reticulations per biconnected component, whenever such a network exists. We have implemented CASS and integrated it in the freely available Dendroscope software

A Practical Algorithm for Reconstructing Level-1 Phylogenetic Networks

Recently much attention has been devoted to the construction of phylogenetic networks which generalize phylogenetic trees in order to accommodate complex evolutionary processes. Here we present an efficient, practical algorithm for reconstructing level-1 phylogenetic networks - a type of network slightly more general than a phylogenetic tree - from triplets. Our algorithm has been made publicly available as the program LEV1ATHAN. It combines ideas from several known theoretical algorithms for phylogenetic tree and network reconstruction with two novel subroutines. Namely, an exponential-time exact and a greedy algorithm both of which are of independent theoretical interest. Most importantly, LEV1ATHAN runs in polynomial time and always constructs a level-1 network. If the data is consistent with a phylogenetic tree, then the algorithm constructs such a tree. Moreover, if the input triplet set is dense and, in addition, is fully consistent with some level-1 network, it will find such a network. The potential of LEV1ATHAN is explored by means of an extensive simulation study and a biological data set. One of our conclusions is that LEV1ATHAN is able to construct networks consistent with a high percentage of input triplets, even when these input triplets are affected by a low to moderate level of noise

Drawing explicit phylogenetic networks and their integration into SplitsTree

<p>Abstract</p> <p>Background</p> <p>SplitsTree provides a framework for the calculation of phylogenetic trees and networks. It contains a wide variety of methods for the import/export, calculation and visualization of phylogenetic information. The software is developed in Java and implements a command line tool as well as a graphical user interface.</p> <p>Results</p> <p>In this article, we present solutions to two important problems in the field of phylogenetic networks. The first problem is the visualization of explicit phylogenetic networks. To solve this, we present a modified version of the equal angle algorithm that naturally integrates reticulations into the layout process and thus leads to an appealing visualization of these networks. The second problem is the availability of explicit phylogenetic network methods for the general user. To advance the usage of explicit phylogenetic networks by biologists further, we present an extension to the SplitsTree framework that integrates these networks. By addressing these two problems, SplitsTree is among the first programs that incorporates <it>implicit </it>and <it>explicit </it>network methods together with standard phylogenetic tree methods in a graphical user interface environment.</p> <p>Conclusion</p> <p>In this article, we presented an extension of SplitsTree 4 that incorporates explicit phylogenetic networks. The extension provides a set of core classes to handle explicit phylogenetic networks and a visualization of these networks.</p

TriLoNet: Piecing together small networks to reconstruct reticulate evolutionary histories

Phylogenetic networks are a generalisation of evolutionary trees that can be used to represent reticulate processes such as hybridisation and recombination. Here we introduce a new approach called TriLoNet to construct such networks directly from sequence alignments which works by piecing together smaller phylogenetic networks. More specifically, using a bottom up approach similar to Neighbor-Joining, TriLoNet constructs level-1 networks (networks that are somewhat more general than trees) from smaller level-1 networks on three taxa. In simulations we show that TriLoNet compares well with Lev1athan, a method for reconstructing level-1 networks from three-leaved trees. In particular, in simulations we find that Lev1athan tends to generate networks that overestimate the number of reticulate events as compared with those generated by TriLoNet. We also illustrate TriLoNet’s applicability using simulated and real sequence data involving recombination, demonstrating that it has the potential to reconstruct informative reticulate evolutionary histories. TriLoNet has been implemented in JAVA and is freely available at https://www.uea.ac.uk/computing/TriLoNet