2012/07/31 by Krzysztof Bartoszek, Serik Sagitov · 3 citations
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Mathematics · #Confidence interval #Evolution and Genetic Dynamics #Evolution and Paleontology Studies #Genomics and Phylogenetic Studies #Interval (graph theory) #Limit (mathematics) #Sample (material) #Sample size determination #Trait #Tree (set theory) #Value (mathematics) #msc:60J70 #msc:60J85 #msc:62F25 #msc:62M05 #msc:62P10 #msc:92B99 #q-bio.PE #stat.AP
paper · pdf · doi:10.1239/jap/1450802756
published as Journal of Applied Probability 52(4):1115-1132, 2015
arxiv created 2014/11/07 · openalex publication_date 2015/12/01 · openalex created_date 2016/06/24 · arxiv updated 2020/11/23 · openalex updated_date 2026/08/05
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.