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  • Phylogenetic confidence intervals for the optimal trait value

  • Part of
  • Krzysztof Bartoszek, Serik Sagitov
  • Journal:
    Journal of Applied Probability / Volume 52 / Issue 4 / December 2015
    Published online by Cambridge University Press:
    30 March 2016, pp. 1115-1132
    Print publication:
    December 2015
    • Article
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  • 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.