A Structure Theorem for Rooted Binary Phylogenetic Networks and Its Implications for Tree-Based Networks

Motivation: Genetic material is transferred in a non-reproductive manner across species more frequently than commonly thought, particularly in the bacteria kingdom. On one hand, extant genomes are thus more properly considered as a fusion product of both reproductive and non-reproductive genetic transfers. This has motivated researchers to adopt phylogenetic networks to study genome evolution. On the other hand, a gene’s evolution is usually tree-like and has been studied for over half a century. Accordingly, the relationships between phylogenetic trees and networks are the basis for the reconstruction and verification of phylogenetic networks. One important problem in verifying a network model is determining whether or not certain existing phylogenetic trees are displayed in a phylogenetic network. This problem is formally called the tree containment problem. It is NP-complete even for binary phylogenetic networks. Results: We design an exponential time but efficient method for determining whether or not a phylogenetic tree is displayed in an arbitrary phylogenetic network. It is developed on the basis of the so-called reticulation-visible property of phylogenetic networks.

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 mathbb {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 phylogenetic networks.

Phylogenetic networks are powerful models for representing evolutionary history in studies of genome evolution involving reticulation events. The complex structure of phylogenetic networks makes their inference challenging, especially for large numbers of taxa. To better understand the full space of phylogenetic networks, we derive closed-form formulas for counting binary phylogenetic networks with two and three reticulation events. In addition, we also use our approach to give a simple proof of the known asymptotic result for a fixed number of reticulations.

The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation.

The important role of homologous recombination has been extensively demonstrated to be fundamental for genetic variation in bacterial genomes. In contrast to extracellular or facultative intracellular bacteria, obligate intracellular bacteria are considered to be less prone to recombination, especially for their core genomes. In Rickettsia, only antigen-related genes were identified to have experienced homologous recombination. In this study, we employed evolutionary genomic approaches to investigate the impact of recombination on the core genome of Rickettsia. Phylogenetic network and phylogenetic compatibility matrix analyses are clearly consistent with the hypothesis that recombination has occurred frequently during Rickettsia evolution. 28% of Rickettsia core genes (194 out of 690) are found to present the evidence of recombination under four independent statistical methods. Further functional classification shows that these recombination events occur across all functional categories, with a significant overrepresentation in the cell wall/membrane/envelope biogenesis, which may provide a molecular basis for the parasite adaptation to host immunity. This evolutionary genomic analysis provides insight into the substantial role of recombination in the evolution of the intracellular pathogenic bacteria Rickettsia.

The -ORIENTATION problem asks whether it is possible to orient an undirected graph to a directed phylogenetic network of a desired network class . This problem arises, for example, when visualising evolutionary data, as popular methods such as Neighbor-Net are distance-based and inevitably produce undirected graphs. The complexity of -ORIENTATION remains open for many classes , including binary tree-child networks, and practical methods are still lacking. In this paper, we propose (1) an exact FPT algorithm for -ORIENTATION, applicable to any class admitting a tractable membership test, and parameterised by the reticulation number and the maximum size of minimal basic cycles, and (2) a very fast heuristic for TREE-CHILD ORIENTATION. While the state-of-the-art for -ORIENTATION is a simple exponential time algorithm whose computational bottleneck lies in searching for appropriate reticulation vertex placements, our methods significantly reduce this search space. Experiments show that, although our FPT algorithm is still exponential, it significantly outperforms the existing method. The heuristic runs even faster but with increasing false negatives as the reticulation number grows. Given this trade-off, we also discuss theoretical directions for improvement and biological applicability of the heuristic approach.

Phylogenetic networks are used to represent evolutionary relationships between species in biology. Such networks are often categorized into classes by their topological features, which stem from both biological and computational motivations. We study two network classes in this paper: tree-based networks and orchard networks. Tree-based networks are those that can be obtained by inserting edges between the edges of an underlying tree. Orchard networks are a recently introduced generalization of the class of tree-child networks. Structural characterizations have already been discovered for tree-based networks; this is not the case for orchard networks. In this paper, we introduce cherry covers—a unifying characterization of both network classes—in which we decompose the edges of the networks into so-called cherry shapes and reticulated cherry shapes. We show that cherry covers can be used to characterize the class of tree-based networks as well as the class of orchard networks. Moreover, we also generalize these results to non-binary networks.

L-fucokinase (FUK) and GDP-fucose pyrophosphorylase (GFPP) salvage free L-fucose and synthesize the valuable nucleotide-sugar GDP-L-fucose (GDP-Fuc). Some organisms express these enzymes as one bifunctional polypeptide called L-fucokinase/GDP-fucose pyrophosphorylase (FKP), which has attracted attention for use in the chemoenzymatic synthesis of GDP-Fuc. Despite the documented use of the FKP from Bacteroides fragilis (BfFKP), the evolutionary origins of these enzymes and their relationships to monofunctional FUKs and GFPPs are poorly understood. We hypothesized that biochemical characterization of these proteins coupled with an evolutionary analysis would uncover the natural diversity of FKPs, facilitating the discovery of new biocatalysts. Phylogenetic and sequence similarity network (SSN) analyses distinguished FKPs from FUKs and GFPPs, leading to the hypothesis that FKPs originate from one ancestral fusion event between these domains. To evaluate possible functional diversity within the FKP family, we recombinantly expressed and purified a putative FKP from the thermophilic bacterium Thermophagus xiamenensis (TxFKP). This enzyme exhibited in vitro kinase and pyrophosphorylase activities and demonstrated subtle kinetic differences compared to BfFKP. While alanine scanning mutational analysis of the TxFKP FUK and GFPP domains supported the role of conserved residues that TxFKP uses to coordinate substrate binding and catalysis, other mutations in the TxFKP GFPP domain influenced kinase activity differentially for the substrates L-fucose and D-arabinose, showing an unprecedented role for the GFPP domain in FUK substrate specificity. Finally, thermal shift profiles of TxFKP and BfFKP were biphasic and provided new insights into how these enzymes have evolved to respond to different sugar substrates.

Given a rooted, binary phylogenetic network and a rooted, binary phylogenetic tree, can the tree be embedded into the network? This problem, called \textsc{Tree Containment}, arises when validating networks constructed by phylogenetic inference methods.We present the first algorithm for (rooted) \textsc{Tree Containment} using the treewidth $t$ of the input network $N$ as parameter, showing that the problem can be solved in $2^{O(t^2)}\cdot|N|$ time and space.

[This corrects the article DOI: 10.1371/journal.pcbi.1007347.].

In phylogenetics, tree-based networks are used to model and visualize the evolutionary history of species where reticulate events such as horizontal gene transfer have occurred. Formally, a tree-based network N consists of a phylogenetic tree T (a rooted, binary, leaf-labeled tree) and so-called reticulation edges that span between edges of T. The network N is typically visualized by drawing T downward and planar and reticulation edges with one of several different styles. One aesthetic criteria is to minimize the number of crossings between tree edges and reticulation edges. This optimization problem has not yet been researched. We show that, if reticulation edges are drawn x-monotone, the problem is NP-complete, but fixed-parameter tractable in the number of reticulation edges. If, on the other hand, reticulation edges are drawn like “ears”, the crossing minimization problem can be solved in quadratic time.

A large class of phylogenetic networks can be obtained from trees by the addition of horizontal edges between the tree edges. These networks are called tree-based networks. We present a simple necessary and sufficient condition for tree-based networks and prove that a universal tree-based network exists for any number of taxa that contains as its base every phylogenetic tree on the same set of taxa. This answers two problems posted by Francis and Steel recently. A byproduct is a computer program for generating random binary phylogenetic networks under the uniform distribution model.