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Phylogenetic confidence intervals for the optimal trait value
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Chalmers University of Technology and the Unversity of Gothenburg.
2015 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 4, 1115-1132 p.Article in journal (Refereed) Published
Abstract [en]

We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree ismodelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein–Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the samplemean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean isapproximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

Place, publisher, year, edition, pages
2015. Vol. 52, no 4, 1115-1132 p.
Keyword [en]
Central limit theorem; conditioned Yule process; macroevolution; martingales; Ornstein–Uhlenbeck process; phylogenetics
National Category
Probability Theory and Statistics Evolutionary Biology
Research subject
Mathematical Statistics; Statistics
Identifiers
URN: urn:nbn:se:uu:diva-241872DOI: 10.1239/jap/1450802756ISI: 000368467600014OAI: oai:DiVA.org:uu-241872DiVA: diva2:781828
Funder
Swedish Research Council, 621-2010-5623The Foundation for Baltic and East European StudiesKnut and Alice Wallenberg FoundationThe Royal Swedish Academy of Sciences
Available from: 2015-01-19 Created: 2015-01-19 Last updated: 2017-12-05Bibliographically approved

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Bartoszek, Krzysztof

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