PT  - JOURNAL ARTICLE
AU  - Krzysztof Bartoszek
AU  - Serik Sagitov
TI  - Phylogenetic confidence intervals for the optimal trait value
AID  - 10.1101/005314
DP  - 2014 Jan 01
TA  - bioRxiv
PG  - 005314
4099  - http://biorxiv.org/content/early/2014/05/19/005314.short
4100  - http://biorxiv.org/content/early/2014/05/19/005314.full
AB  - 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.