2006/11/01 by Michael G. B. Blum, Olivier François, Svante Janson · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Earth and Planetary Sciences · Mathematics · #Bayesian Methods and Mixture Models #Evolution and Paleontology Studies #Genomics and Phylogenetic Studies #math.PR #msc:05C05 #msc:60C05 #msc:60F05 #msc:92D15
paper · pdf · doi:10.1214/105051606000000547
published as Annals of Applied Probability 2006, Vol. 16, No. 4, 2195-2214 · Published at http://dx.doi.org/10.1214/105051606000000547 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2006/11/01 · arxiv created 2007/02/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
For two decades, the Colless index has been the most frequently used statistic for assessing the balance of phylogenetic 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.