Phylogenetic confidence intervals for the optimal trait value
Journal article, 2015

We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree is modelled 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 sample mean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean is approximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.



Ornstein-Uhlenbeck process

Central limit theorem


conditionedYule process


K. Bartoszek

Uppsala University

Serik Sagitov

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Journal of Applied Probability

0021-9002 (ISSN)

Vol. 52 4 1115-1132

Stochastic models of gene and species trees

Swedish Research Council (VR) (2010-5623), 2011-01-01 -- 2013-12-31.

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Areas of Advance

Life Science Engineering (2010-2018)



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