Phylogenetic confidence intervals for the optimal trait value

TL;DR

This paper develops new statistical methods to estimate the optimal trait value in evolutionary biology, accounting for unknown phylogenies and trait evolution modeled by Ornstein-Uhlenbeck processes, with proven asymptotic properties.

Contribution

It introduces limit theorems and confidence interval formulas for the optimal trait value under a stochastic evolutionary model with unknown phylogeny.

Findings

Normal approximation for the sample mean in fast adaptation regimes

New confidence interval formulas for trait estimation

Asymptotic results for different adaptation rate domains

Abstract

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.