Orienting undirected phylogenetic networks

This paper studies the relationship between undirected (unrooted) and directed (rooted) phylogenetic networks. We describe a polynomial-time algorithm for deciding whether an undirected nonbinary phylogenetic network, given the locations of the root and reticulation vertices, can be oriented as a directed nonbinary phylogenetic network....

Creating phylogenetic networks from clusters

In biology, phylogenetics is the study of the evolutionary history of and relations between e.g. species. Such data are often represented in trees. Remarkably, trees lack the representation of reticulation events, such as hybridization, while such events are believed to be important. One of the reasons why trees are widely used, is the enormous...

Treewidth based algorithms for Tree Containment in phylogenetics

TreeContainment is a well-known problem within phylogenetics, which asks whether a binary phylogenetic tree is embedded in a binary phylogenetic network. For this problem, Jones, Weller and van Iersel (2022) have created an algorithm that uses dynamic programming on tree-decompositions to achieve a running time that is exponential in the tree...

Encoding undirected and semi-directed binary phylogenetic networks by quarnets

Phylogenetic networks generalize evolutionary trees and are commonly used to represent evolutionary relationships between species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer. In this thesis all quarnets, networks on four species, of a network are assumed to be known. We prove that...

An algorithm for reconstructing level-2 phylogenetic networks from trinets

Evolutionary histories for species that cross with one another or exchange genetic material can be represented by leaf-labelled, directed graphs called phylogenetic networks. A major challenge in the burgeoning area of phylogenetic networks is to develop algorithms for building such networks by amalgamating small networks into a single large...

Comparing the topology of phylogenetic network generators

Phylogenetic networks represent evolutionary history of species and can record natural reticulate evolutionary processes such as horizontal gene transfer and gene recombination. This makes phylogenetic networks a more comprehensive representation of evolutionary history compared to phylogenetic trees. Stochastic processes for generating...

Applicability of several rooted phylogenetic network algorithms for representing the evolutionary history of SARS-CoV-2

Background: Rooted phylogenetic networks are used to display complex evolutionary history involving so-called reticulation events, such as genetic recombination. Various methods have been developed to construct such networks, using for example a multiple sequence alignment or multiple phylogenetic trees as input data. Coronaviruses are known...

Rooted binary level-3 phylogenetic networks are encoded by quarnets

Phylogenetic networks generalize evolutionary trees and are commonly used to represent evolutionary relationships between species that undergo reticulate processes such as hybridization, recombination and lateral gene transfer. Recently, there has been great interest in knowing which networks are determined or encoded by their trinets, that are...

Recognizing and realizing cactus metrics

The problem of realizing finite metric spaces in terms of weighted graphs has many applications. For example, the mathematical and computational properties of metrics that can be realized by trees have been well-studied and such research has laid the foundation of the reconstruction of phylogenetic trees from evolutionary distances. However,...

New FPT algorithms for finding the temporal hybridization number for sets of phylogenetic trees

We study the problem of finding a temporal hybridization network for a set of phylogenetic trees that minimizes the number of reticulations. First, we introduce an FPT algorithm for this problem on an arbitrary set of t binary trees with n leaves each with a running time of O(5^k*n*m) where k is the minimum temporal hybridization number. We also...

Rearrangement operations on unrooted phylogenetic networks

Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree prune and regraft), and TBR (tree bisection and reconnection). Recently, these operations have been...

Orienting phylogenetic networks

This thesis provides you with basic information on graph theory as well as phylogenetic networks, it studies the relationship between undirected (unrooted) and directed (rooted) phylogenetic networks, based on the manuscript 'Rooting for phylogenetic networks' . Undirected phylogenetic networks can be oriented to become a directed network. In...

Reconstructing Tree-Child Networks from Reticulate-Edge-Deleted Subnetworks

Network reconstruction lies at the heart of phylogenetic research. Two well-studied classes of phylogenetic networks include tree-child networks and level-k networks. In a tree-child network, every non-leaf node has a child that is a tree node or a leaf. In a level-k network, the maximum number of reticulations contained in a biconnected...

Computing Measures for Tree-Basedness of Phylogenetic Networks

Phylogenetic networks are a type of directed acyclic graph used to represent evolutionary relationships that contain events such as hybridization or horizontal gene transfer. When a network<br/>lacks such events it is a phylogenetic tree. Some phylogenetic networks that are not trees can<br/>however be represented as a tree with additional...

Measuring how far a nonbinary phylogenetic network is from being tree-based

In computational biology, phylogenetic trees are used to describe evolutionary history. This can be done more generally using phylogenetic networks, which can also describe nontreelike events such as hybridization. Some phylogenetic networks can be obtained from a base tree, a rooted spanning tree with the same leaf set, by adding linking edges....

Exploring the Tiers of Rooted Phylogenetic Network Space Using Tail Moves

Popular methods for exploring the space of rooted phylogenetic trees use rearrangement moves such as rooted Nearest Neighbour Interchange (rNNI) and rooted Subtree Prune and Regraft (rSPR). Recently, these moves were generalized to rooted phylogenetic networks, which are a more suitable representation of reticulate evolutionary histories, and...

Finding a most parsimonious or likely tree in a network with respect to an alignment

Phylogenetic networks are often constructed by merging multiple conflicting phylogenetic signals into a directed acyclic graph. It is interesting to explore whether a network constructed in this way induces biologically-relevant phylogenetic signals that were not present in the input. Here we show that, given a multiple alignment A for a set...

Binets: Fundamental Building Blocks for Phylogenetic Networks

Phylogenetic networks are a generalization of evolutionary trees that are used by biologists to represent the evolution of organisms which have undergone reticulate evolution. Essentially, a phylogenetic network is a directed acyclic graph having a unique root in which the leaves are labelled by a given set of species. Recently, some...