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 Ω-trees, which are characterized by imbalance of internal nodes. The degree of imbalance is defined by an integer 0 ≤ ω. For caterpillars, the extreme case of unbalanced trees, ω = 0. Under models of neutral evolution, for instance the Yule model, trees with small ω 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 Ω-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 Ω-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 ω.
journal_name
Math Bioscijournal_title
Mathematical biosciencesauthors
Disanto F,Schlizio A,Wiehe Tdoi
10.1016/j.mbs.2013.08.008subject
Has Abstractpub_date
2013-11-01 00:00:00pages
139-47issue
1eissn
0025-5564issn
1879-3134pii
S0025-5564(13)00210-1journal_volume
246pub_type
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