Some combinatorial problems on binary rooted trees occurring in population genetics

Details Some combinatorial problems on binary rooted trees occurring in population genetics Some combinatorial problems on binary rooted trees occurring in population genetics

2011-12-06

arxiv.org/abs/1112.1295v2

Mathematics

Combinatorics

Scientific paper

Models in evolutionary biology are intimately linked to the tree paradigm. Given a direction by time, ancestry relationship between species, individuals, alleles or cells can be depicted as a rooted tree. Of particular interest are binary rooted unordered trees. These can be further classified into shape trees, phylogenetic trees, ranked trees and labelled ranked trees. In this work we want to focus on several combinatorial aspects concerning these classes of trees. We consider enumerations and probabilistic properties of these trees when generated under the random coalescent process. We derive several summary statistics which serve to characterize 'typical' trees.

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