Leaf-reconstructibility of phylogenetic networks

An important problem in evolutionary biology is to reconstruct the evolutionary history of a set $X$ of species. This history is often represented as a phylogenetic network, that is, a connected graph with leaves labelled by elements in $X$ (for example, an evolutionary tree), which is usually also binary, i.e. all vertices have degree 1 or 3. A common approach used in phylogenetics to build a phylogenetic network on $X$ involves constructing it from networks on subsets of $X$. Here we consider the question of which (unrooted) phylogenetic networks are leaf-reconstructible, i.e. which networks can be uniquely reconstructed from the set of networks obtained from it by deleting a single leaf (its $X$-deck). This problem is closely related to the (in)famous reconstruction conjecture in graph theory but, as we shall show, presents distinct challenges. We show that some large classes of phylogenetic networks are reconstructible from their $X$-deck. This includes phylogenetic trees, binary networks containing at least one non-trivial cut-edge, and binary level-4 networks (the level of a network measures how far it is from being a tree). We also show that for fixed $k$, almost all binary level-$k$ phylogenetic networks are leaf-reconstructible. As an application of our results, we show that a level-3 network $N$ can be reconstructed from its quarnets, that is, 4-leaved networks that are induced by $N$ in a certain recursive fashion. Our results lead to several interesting open problems which we discuss, including the conjecture that all phylogenetic networks with at least five leaves are leaf-reconstructible

A Perl Package and an Alignment Tool for Phylogenetic Networks

Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of evolutionary events acting at the population level, like recombination between genes, hybridization between lineages, and lateral gene transfer. While most phylogenetics tools implement a wide range of algorithms on phylogenetic trees, there exist only a few applications to work with phylogenetic networks, and there are no open-source libraries either. In order to improve this situation, we have developed a Perl package that relies on the BioPerl bundle and implements many algorithms on phylogenetic networks. We have also developed a Java applet that makes use of the aforementioned Perl package and allows the user to make simple experiments with phylogenetic networks without having to develop a program or Perl script by herself. The Perl package has been accepted as part of the BioPerl bundle. It can be downloaded from http://dmi.uib.es/~gcardona/BioInfo/Bio-PhyloNetwork.tgz. The web-based application is available at http://dmi.uib.es/~gcardona/BioInfo/. The Perl package includes full documentation of all its features.Comment: 5 page

Phylogenetic networks: modeling, reconstructibility, and accuracy

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