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Exact and approximate limit behaviour of the Yule trees cophenetic index
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.ORCID iD: 0000-0002-5816-4345
2018 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 303, p. 26-45Article in journal (Refereed) Published
Abstract [en]

In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure-birth tree conditioned on n contemporary tips. We show that this normalized phylogenetic balance index is a sub-martingale that converges almost surely and in L-2. 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 propose a way based on the 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. We conduct a power study to investigate how well the cophenetic indices detect deviations from the Yule tree and apply the methodology to empirical phylogenies.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE INC , 2018. Vol. 303, p. 26-45
Keywords [en]
Contraction-type distribution; Cophenetic index; Martingales; Phylogenetics; Significance testing
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-151191DOI: 10.1016/j.mbs.2018.05.005ISI: 000442710200003PubMedID: 29746815OAI: oai:DiVA.org:liu-151191DiVA, id: diva2:1248618
Note

Funding Agencies|Knut and Alice Wallenberg Foundation; Swedish Research Council (Vetenskapsradet) [2017-04951]; Barcelona Graduate School of Mathematics (BGSMath); G S Magnuson Foundation of the Royal Swedish Academy of Sciences [MG2015-0055, MG2017-0066]; Foundation for Scientific Research and Education in Mathematics (SVeFUM)

Available from: 2018-09-17 Created: 2018-09-17 Last updated: 2019-09-04

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