  We consider a branching particle system where particles reproduce according
to the pure birth Yule process with the birth rate L, 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 s2. 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 Rn2 of the evolutionary rate r2=s2/L. The estimator Rn2 is
proportional to the sample variance Sn2 computed from n trait values. We find
an approximate formula for the standard error of Rn2 based on a neat asymptotic
relation for the variance of Sn2.
