A Graph-Neural-Network Approach for Reconstructing Temporal Networks

Reconstructing a minimum reticulation network from phylogenetic trees is used in evolutionary studies. In this thesis, we focus on finding temporal networks using cherry-picking sequences for binary trees with all taxa. Finding such a minimum reticulation temporal network is NP-hard.<br/><br/>We introduce an algorithm to find a minimum...

Classes of Semi-binary Phylogenetic Networks encoded by μ-representations

This thesis is on the subject of phylogenetic networks. These are schematic<br/>visualisations used mainly to investigate the evolutionary history of species,<br/>but which can be used for any set of distinguishable elements which have diverged from a common ancestor through some evolutionary process. The research specifically focuses on a way...

Computing the Scanwidth of Directed Acyclic Graphs

Phylogenetic networks are a specific type of directed acyclic graph (DAG), used to depict evolutionary relationships among, for example, species or other groups of organisms. To solve computationally hard problems, treewidth has been used to parametrize algorithms in phylogenetics. In the hope of simplifying the algorithmic design process, Berry...

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...

Encoding level-k phylogenetic networks

Phylogenetic networks are used to describe evolutionary histories and are a generalisation of evolutionary trees. They can contain so called reticulations, representing reticulate evolution, such as hybridization, lateral gene transfer and recombination. Methods are being developed to construct certain rooted phylogenetic networks from their...

Constructing level-2 phylogenetic networks from trinets

Phylogenetic networks are a generalization of evolutionary trees that can be used to represent reticulate events. Level-k phylogenetic networks are such networks, but with a at most k reticulations per biconnected component of the network. For level-1 networks there exists an algorithm, called TriLoNet (Trinet Level-one Network algorithm), that...

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...