Universität zu Köln

Disanto, Filippo, Schlizio, Anna and Wiehe, Thomas (2013). Yule-generated trees constrained by node imbalance. Math. Biosci., 246 (1). S. 139 - 148. NEW YORK: ELSEVIER SCIENCE INC. ISSN 1879-3134

Full text not available from this repository.

Abstract

The Yule process generates a class of binary trees which is fundamental to population genetic models and other applications in evolutionary biology. In this paper, we introduce a family of sub-classes of ranked trees, called Omega-trees, which are characterized by imbalance of internal nodes. The degree of imbalance is defined by an integer 0 <= omega. For caterpillars, the extreme case of unbalanced trees, omega = 0. Under models of neutral evolution, for instance the Yule model, trees with small to are unlikely to occur by chance. Indeed, imbalance can be a signature of permanent selection pressure, such as observable in the genealogies of certain pathogens. From a mathematical point of view it is interesting to observe that the space of Omega-trees maintains several statistical invariants although it is drastically reduced in size compared to the space of unconstrained Yule trees. Using generating functions, we study here some basic combinatorial properties of Omega-trees. We focus on the distribution of the number of subtrees with two leaves. We show that expectation and variance of this distribution match those for unconstrained trees already for very small values of omega. (C) 2013 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Disanto, Filippo UNSPECIFIED UNSPECIFIED UNSPECIFIED Schlizio, Anna UNSPECIFIED UNSPECIFIED UNSPECIFIED Wiehe, Thomas UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-472585
DOI:	10.1016/j.mbs.2013.08.008
Journal or Publication Title:	Math. Biosci.
Volume:	246
Number:	1
Page Range:	S. 139 - 148
Date:	2013
Publisher:	ELSEVIER SCIENCE INC
Place of Publication:	NEW YORK
ISSN:	1879-3134
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PHYLOGENETIC TREES; CHERRIES; MODELS Multiple languages Biology; Mathematical & Computational Biology Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/47258