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The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2006 (English)In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 16, no 4, 2195-2214 p.Article in journal (Refereed) Published
Abstract [en]

For two decades, the Colless index has been the most frequently used statistic for assessing the balance of phylogenctic trees. In this article, this statistic is studied under the Yule and uniform model of phylogenetic trees. The main tool of analysis is a coupling argument with another well-known index called the Sackin statistic. Asymptotics for the mean, variance and covariance of these two statistics are obtained, as well as their limiting joint distribution for large phylogenies. Under the Yule model, the limiting distribution arises as a solution of a functional fixed point equation. Under the uniform model, the limiting distribution is the Airy distribution. The cornerstone of this study is the fact that the probabilistic models for phylogenetic trees are strongly related to the random permutation and the Catalan models for binary search trees.

Place, publisher, year, edition, pages
2006. Vol. 16, no 4, 2195-2214 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-22664DOI: 10.1214/105051606000000547ISI: 000243782000017OAI: oai:DiVA.org:uu-22664DiVA: diva2:50437
Available from: 2007-01-19 Created: 2007-01-19 Last updated: 2017-12-07Bibliographically approved

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Janson, Svante

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