Quartets and unrooted phylogenetic networks

Genome Biology and Evolution, 2011

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.

International Journal for Parasitology, 2005

Phylogenetic analysis has changed greatly in the past decade, including the more widespread appreciation of the idea that evolutionary histories are not always tree-like, and may, thus, be best represented as reticulated networks rather than as strictly dichotomous trees. Reconstructing such histories in the absence of a bifurcating speciation process is even more difficult than the usual procedure, and a range of alternative strategies have been developed. There seem to be two basic uses for a network model of evolution: the display of real but unobservable evolutionary events (i.e. a hypothesis of the true phylogenetic history), and the display of character conflict within the data itself (i.e. a summary of the data). These two general approaches are briefly reviewed here, and the strengths and weaknesses of the different implementations are compared and contrasted. Each network methodology seems to have limitations in terms of how it responds to increasing complexity (e.g. conflict) in the data, and therefore each is likely to be more appropriate for one of the two uses than for the other. Several examples using parasitological data sets illustrate the uses of networks within the context of population biology.

Zoologica Scripta, 2004

Most traditional methods of phylogenetic analysis assume that species evolution can be represented by means of a bifurcating tree model. In many phylogenetic situations, however, some of the evolutionary links between species are due to reticulate evolution. For instance, reticulate models can adequately describe such complicated mechanisms as lateral gene transfer in bacteria or species hybridization. The theoretical concepts of reticulate evolution developed in the 1980s and 1990s need to be supported by appropriate analytical tools and software. In this paper, we present the main features of a new distance-based method for modelling phylogenetic relationships among species by means of reticulated networks (RNs). The method uses the least-squares model to build a RN by gradually improving upon the solution provided by a phylogenetic tree. A computer program facilitating the reconstruction and visualization of reticulate phylogenies is made available to researchers. In the application section, we illustrate the usefulness of the method by studying the evolution of honeybees (genus Apis). The method for reconstructing RNs has been included in the T-Rex (Tree and Reticulogram Reconstruction) package recently developed by the first-named author.

IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2008

Split networks are increasingly being used in phylogenetic analysis. Usually, a simple equal-angle algorithm is used to draw such networks, producing layouts that leave much room for improvement. Addressing the problem of producing better layouts of split networks, this paper presents an algorithm for maximizing the area covered by the network, describes an extension of the equaldaylight algorithm to networks, looks into using a spring embedder, and discusses how to construct rooted split networks.

In biodiversity conservation, one is interested in selecting a subset of taxa for preservation priority. Phylogenetic diversity (PD) provides a quantitative measure for taxon selection on phylogenetic trees. In particular, PD is the total length of the minimal subtree induced by the selected taxa. Recently, it has been shown that on trees the maximal PD score and the corresponding subset of taxa can be computed by a greedy algorithm. However, if evolution is not treelike and networks are a more appropriate illustration of phylogenetic relationships, then the greedy strategy no longer works.

arXiv (Cornell University), 2013

We describe a method that will reconstruct an unrooted binary phylogenetic level-1 network on n taxa from the set of all quartets containing a certain fixed taxon, in O(n 3) time. We also present a more general method which can handle more diverse quartet data, but which takes O(n 6) time. Both methods proceed by solving a certain system of linear equations over GF(2). For a general dense quartet set (containing at least one quartet on every four taxa) our O(n 6) algorithm constructs a phylogenetic level-1 network consistent with the quartet set if such a network exists and returns an (O(n 2) sized) certificate of inconsistency otherwise. This answers a question raised by Gambette, Berry and Paul regarding the complexity of reconstructing a level-1 network from a dense quartet set.

IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2000

Jansson and Sung showed in that, given a dense set of input triplets T (representing hypotheses about the local evolutionary relationships of triplets of species), it is possible to determine in polynomial time whether there exists a level-1 network consistent with T , and if so to construct such a network. They also showed that, unlike in the case of trees (i.e. level-0 networks), the problem becomes NP-hard when the input is non-dense.

Bulletin of Mathematical Biology

Phylogenetic networks are mathematical representations of evolutionary history that are able to capture both tree-like evolutionary processes (speciations) and non-tree-like ‘reticulate’ processes such as hybridization or horizontal gene transfer. The additional complexity that comes with this capacity, however, makes networks harder to infer from data, and more complicated to work with as mathematical objects. In this paper, we define a new, large class of phylogenetic networks, that we call labellable, and show that they are in bijection with the set of ‘expanding covers’ of finite sets. This correspondence is a generalisation of the encoding of phylogenetic forests by partitions of finite sets. Labellable networks can be characterised by a simple combinatorial condition, and we describe the relationship between this large class and other commonly studied classes. Furthermore, we show that all phylogenetic networks have a quotient network that is labellable.

Arxiv preprint arXiv:1005.2108, 2010

Since Darwin, species trees have been used as a simplified description of the relationships which summarize the complicated network N of reality. Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate. Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N. A connected surjective digraph map (CSD) is a map f from one network N to another network M such that every arc is either collapsed to a single vertex or is taken to an arc, such that f is surjective, and such that the inverse image of a vertex is always connected. CSD maps are shown to behave well under composition. It is proved that if there is a CSD map from N to M , then there is a way to lift an undirected version of M into N , often with added resolution. A CSD map from N to M puts strong constraints on N. In general, it may be useful to study classes of networks such that, for any N , there exists a CSD map from N to some standard member of that class.

Bioinformatics, 2013

Motivation: The evolutionary history of species is traditionally represented with a rooted phylogenetic tree. Each tree comprises a set of clusters, i.e. subsets of the species that are descended from a common ancestor. When rooted phylogenetic trees are built from several different datasets (e.g. from different genes), the clusters are often conflicting. These conflicting clusters cannot be expressed as a simple phylogenetic tree; however, they can be expressed in a phylogenetic network. Phylogenetic networks are a generalization of phylogenetic trees that can account for processes such as hybridization, horizontal gene transfer and recombination, which are difficult to represent in standard tree-like models of evolutionary histories. There is currently a large body of research aimed at developing appropriate methods for constructing phylogenetic networks from cluster sets. The CASS algorithm can construct a much simpler network than other available methods, but is extremely slow for large datasets or for datasets that need lots of reticulate nodes. The networks constructed by CASS are also greatly dependent on the order of input data, i.e. it generally derives different phylogenetic networks for the same dataset when different input orders are used. Results: In this study, we introduce an improved CASS algorithm, LNETWORK, which can construct a phylogenetic network for a given set of clusters. We show that LNETWORK is significantly faster than CASS and effectively weakens the influence of input data order. Moreover, we show that LNETWORK can construct a much simpler network than most of the other available methods. Availability: LNETWORK has been built as a Java software package and