RT Journal Article
SR Electronic
T1 Exact and approximate limit behaviour of the Yule tree’s cophenetic index
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 120931
DO 10.1101/120931
A1 Krzysztof Bartoszek
YR 2017
UL http://biorxiv.org/content/early/2017/03/27/120931.abstract
AB In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure birth tree on n contemporary tips. We show that this normalized phylogenetic balance index is a submartingale that converges almost surely and in L2. We link our work with studies on trees without branch lengths and show that in this case the limit distribution is a contraction type distribution, similar to the Quicksort limit distribution. In the continuous branch case we suggest approximations to the limit distribution. We propose heuristic methods of simulating from these distributions and it may be observed that these algorithms result in reasonable tails. Therefore, we postulate using quantiles of the derived distributions for hypothesis testing, whether an observed phylogenetic tree is consistent with the pure birth process. Simulating a sample by the proposed heuristics is rapid while exact simulation (simulating the tree and then calculating the index) is a time-consuming procedure.