A Consistent Estimator of the Evolutionary Rate

We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate λ, conditioned on the observed number of particles to be equal n. Particles are assumed to move independently on the real line according to the Brownian motion with the local variance σ 2 . In this paper we treat n particles as a sample of related species. The spatial Brownian motion of a particle describes the development of a trait value of interest (e.g. log-body-size). We propose an unbiased estimator of the evolutionary rate ρ 2 =σ 2 /λ. The estimator is proportional to the sample variance computed from n trait values. We find an approximate formula for the standard error of based on a neat asymptotic relation for the variance of .