  We consider the classic problem of estimating T, the total number of species
in a population, from repeated counts in a simple random sample. We look first
at the Chao-Lee estimator: we initially show that such estimator can be
obtained by reconciling two estimators of the unobserved probability, and then
develop a sequence of improvements culminating in a Dirichlet prior Bayesian
reinterpretation of the estimation problem. By means of this, we obtain
simultaneous estimates of T, of the normalized interspecies variance $\gamma^2$
and of the parameter $\lambda$ of the prior. Several simulations show that our
estimation method is more flexible than several known methods we used as
comparison; the only limitation, apparently shared by all other methods, seems
to be that it cannot deal with the rare cases in which $\gamma^2 >1$
