  Consider a random permutation of $\{1, \ldots, \lfloor n^{t_2}\rfloor\}$
drawn according to the Ewens measure with parameter $t_1$ and let $K(n, t)$
denote the number of its cycles, where $t\equiv (t_1, t_2)\in\mathbb [0, 1]^2$.
  Next, consider a sample drawn from a large, neutral population of haploid
individuals subject to mutation under the infinitely many sites model of Kimura
whose genealogy is governed by Kingman's coalescent. Let $S(n, t)$ count the
number of segregating sites in a sample of size $\lfloor n^{t_2}\rfloor$ when
mutations arrive at rate $t_1/2$.
  We show that $K(n, (t_1/\log n, t_2))-1$ and $S(n, (t_1/\log n, t_2))$ induce
unique random measures $\Pi_n^K$ and $\Pi_n^S,$ respectively, on the positive
quadrant $[0, \infty)^2.$ Our main result is to show that in the coupling of
$S(n, t)$ and $K(n, t)$ introduced in~\cite{Pitters2019} we have weak
convergence as $n\to\infty$
  \begin{align*}
  (\Pi_n^K, \Pi_n^S)\to_d (\Pi, \Pi),
  \end{align*} where $\Pi$ is a Poisson point process on $[0, \infty)^2$ of
unit intensity. This complements the work in~\cite{Pitters2019} where it was
shown that the process $\{(K(n, t), S(n, t)), t\in [0, 1]^2\},$ appropriately
rescaled, converges weakly to the product of the same one-dimensional Brownian
sheet.
