Encoding undirected and semi-directed binary phylogenetic networks by quarnets
L. Nipius (TU Delft - Electrical Engineering, Mathematics and Computer Science)
L.J.J. van Iersel – Mentor (TU Delft - Discrete Mathematics and Optimization)
Y. Murakami – Graduation committee member (TU Delft - Discrete Mathematics and Optimization)
G.F. Nane – Graduation committee member (TU Delft - Applied Probability)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
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 each recoverable undirected or semi-directed binary level-2 phylogenetic network without redundant biconnected components is encoded by its set of quarnets, meaning that the network is uniquely determined by its quarnets. Furthermore, two decomposition theorems for undirected and semi-directed binary phylogenetic networks are presented. These decomposition theorems are proved for undirected binary phylogenetic networks for all levels and for semi-directed binary phylogenetic networks that are at most level-2.