A new polynomial for describing Phylogenetic Networks

Bachelor thesis (2022)

Authors

M. van de Klok Electrical Engineering, Mathematics and Computer Science

Contributors

L.J.J. van Iersel Discrete Mathematics and Optimization - EEMCS (supervisor 1)
K. Marynets Mathematical Physics - EEMCS (coach)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2022 Margot van de Klok
Phylogenetic networks Phylogenetic trees Unfolding
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Published Date

13-07-2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

Describing phylogenetic trees or networks with a polynomial is a tool to distinguish between them. In this thesis, a new polynomial for describing rooted binary internally labeled phylogenetic networks and trees is introduced based on the research of P. Liu and J. Pons et al. Two different cases are considered, one where the reticulation nodes have distinct labels λi and one where the reticulation nodes have the same label λ. There are a few conjectures stated about the uniqueness of the polynomial and the relation of the polynomial with the primary subtrees and their monomial. Also the folding and unfolding of a network is described. Furthermore, an algorithm is provided with which a tree can be made out of different monomials. With use of the lemma that states when a tree can be folded to a network, it can be determined if the tree can be folded to a network.