Phylogenetic confidence intervals for the optimal trait value
Artikel i vetenskaplig tidskrift, 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.

phylogenetics

Central limit theorem

Ornstein-Uhlenbeck process

macroevolution

conditionedYule process

martingales

Författare

K. Bartoszek

Serik Sagitov

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet

Journal of Applied Probability

0021-9002 (ISSN)

Vol. 52 4 1115-1132

Stokastiska modeller av gen- och artträd

Vetenskapsrådet (VR), 2011-01-01 -- 2013-12-31.

Ämneskategorier

Matematik

Styrkeområden

Livsvetenskaper och teknik

DOI

10.1239/jap/1450802756