  A simple way to model phenotypic evolution is to assume that after splitting,
the trait values of the sister species diverge as independent Brownian motions.
Relying only on a prior distribution for the underlying species tree
(conditioned on the number, n, of extant species) we study the random vector
(X_1,...,X_n) of the observed trait values. In this paper we derive compact
formulae for the variance of the sample mean and the mean of the sample
variance for the vector (X_1,...,X_n).
  The key ingredient of these formulae is the correlation coefficient between
two trait values randomly chosen from (X_1,...,X_n). This interspecies
correlation coefficient takes into account not only variation due to the random
sampling of two species out of n and the stochastic nature of Brownian motion
but also the uncertainty in the phylogenetic tree. The latter is modeled by a
(supercritical or critical) conditioned branching process. In the critical case
we modify the Aldous-Popovic model by assuming a proper prior for the time of
origin.
