Universität zu Köln

Wirtz, Johannes M. (2019). Coalescent Theory and Yule Trees in time and space. PhD thesis, Universität zu Köln.

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Abstract

Mathematically, Coalescent Theory describes genealogies within a population in the form of (binary) trees. The original Coalescent Model is based on population models that are evolving neutrally. With respect to graph isomorphy, the tree-structures it provides can be equivalently described in a discrete setting by the Yule Process. As a population evolves (in time), the genealogy of the population is subject to change, and so is the tree structure associated with it. A similar statement holds true if the population is assumed to be recombining; then, in space, i.e. along the genome, the genealogy of a sample may be subject to change in a similar way. The two main focuses of this thesis are the description of the processes that shape the genealogy in time and in space, making use of the relation between Coalescent and Yule Process. As for the process in time, the presented approach differs from existing ones mainly in that the population considered is strictly finite. The results we obtain are of mainly theoretical nature. In case of the process along the genome, we focus on mathematical properties of Linkage Disequilibrium, a quantity that is relevant in the analysis of population-genetical data. Similarities and differences between the two are discussed, and a possibility of performing similar analyses when the assumption of neutrality is abandoned is pointed out.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Wirtz, Johannes M. wirtzj0@uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-93311
Date:	2019
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Biology > Institute for Genetics
Subjects:	Natural sciences and mathematics
Uncontrolled Keywords:	Keywords Language Coalescent Theory, Yule Process, Time Reversal of Markov Chains English
Date of oral exam:	9 January 2019
Referee:	Name Academic Title Wiehe, Thomas Prof. Dr. Krug, Joachim Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/9331