Universität zu Köln

Disanto, Filippo and Wiehe, Thomas ORCID: 0000-0002-8932-2772 (2020). Measuring the external branches of a Kingman tree: A discrete approach. Theor. Popul. Biol., 134. S. 92 - 106. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1096-0325

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Abstract

The Kingman coalescent process is a classical model of gene genealogies in population genetics. It generates Yule-distributed, binary ranked tree topologies - also called histories - with a finite number of n leaves, together with n - 1 exponentially distributed time lengths: one for each layer of the history. Using a discrete approach, we study the lengths of the external branches of Yule distributed histories, where the length of an external branch is defined as the rank of its parent node. We study the multiplicity of external branches of given length in a random history of n leaves. A correspondence between the external branches of the ordered histories of size n and the non-peak entries of the permutations of size n - 1 provides easy access to the length distributions of the first and second longest external branches in a random Yule history and coalescent tree of size n. The length of the longest external branch is also studied in dependence of root balance of a random tree. As a practical application, we compare the observed and expected number of mutations on the longest external branches in samples from natural populations. (C) 2020 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Disanto, Filippo UNSPECIFIED UNSPECIFIED UNSPECIFIED Wiehe, Thomas UNSPECIFIED orcid.org/0000-0002-8932-2772 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-325187
DOI:	10.1016/j.tpb.2020.05.002
Journal or Publication Title:	Theor. Popul. Biol.
Volume:	134
Page Range:	S. 92 - 106
Date:	2020
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1096-0325
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Biology > Institute for Genetics
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language STATISTICAL PROPERTIES; GENETIC DIVERSITY; LENGTH Multiple languages Ecology; Evolutionary Biology; Genetics & Heredity; Mathematical & Computational Biology Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/32518