  Estimating the number $n$ of unseen species from a $k-$sample displaying only
$p\leq k$ distinct sampled species has received attention for long. It requires
a model of species abundance together with a sampling model. We start with a
discrete model of iid stochastic species abundances, each with Gibbs-Poisson
distribution. A $k-$sample drawn from the $n-$species abundances vector is the
one obtained while conditioning it on summing to $k$% . We discuss the sampling
formulae (species occupancy distributions, frequency of frequencies) in this
context. We then develop some aspects of the estimation of $n$ problem from the
size $k$ of the sample and the observed value of $P_{n,k}$, the number of
distinct sampled species. It is shown that it always makes sense to study these
occupancy problems from a Gibbs-Poisson abundance model in the context of a
population with infinitely many species. From this extension, a parameter
$\gamma $ naturally appears, which is a measure of richness or diversity of
species. We rederive the sampling formulae for a population with infinitely
many species, together with the distribution of the number $P_{k}$ of distinct
sampled species. We investigate the estimation of $\gamma $ problem from the
sample size $k$ and the observed value of $P_{k}$. We then exhibit a large
special class of Gibbs-Poisson distributions having the property that sampling
from a discrete abundance model may equivalently be viewed as a sampling
problem from a random partition of unity, now in the continuum. When $n$ is
finite, this partition may be built upon normalizing $% n$ infinitely divisible
iid positive random variables by its partial sum. It is shown that the sampling
process in the continuum should generically be biased on the total length
appearing in the latter normalization. A construction with size-biased sampling
from the ranked normalized jumps of a subordinator is also supplied, would the
problem under study present infinitely many species. We illustrate our point of
view with many examples, some of which being new ones.
