  The Ewens sampling formula was firstly introduced in the context of
population genetics by Warren John Ewens in 1972, and has appeared in a lot of
other scientific fields. There are abundant approximation results associated
with the Ewens sampling formula especially when one of the parameters, the
sample size $n$ or the mutation parameter $\theta$ which denotes the scaled
mutation rate, tends to infinity while the other is fixed. By contrast, the
case that $\theta$ grows with $n$ has been considered in a relatively small
number of works, although this asymptotic setup is also natural. In this paper,
when $\theta$ grows with $n$, we advance the study concerning the asymptotic
properties of the total number of alleles and of the counts of components in
the allelic partition assuming the Ewens sampling formula from the viewpoint of
Poisson approximations.
