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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 haploidindividuals subject to mutation under the infinitely many sites model of Kimurawhose genealogy is governed by Kingman's coalescent. Let $S(n, t)$ count thenumber of segregating sites in a sample of size $\lfloor n^{t_2}\rfloor$ whenmutations arrive at rate $t_1/2$.  We show that $K(n, (t_1/\log n, t_2))-1$ and $S(n, (t_1/\log n, t_2))$ induceunique random measures $\Pi_n^K$ and $\Pi_n^S,$ respectively, on the positivequadrant $[0, \infty)^2.$ Our main result is to show that in the coupling of$S(n, t)$ and $K(n, t)$ introduced in~\cite{Pitters2019} we have weakconvergence 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 $[0, \infty)^2$ ofunit intensity. This complements the work in~\cite{Pitters2019} where it wasshown that the process $\{(K(n, t), S(n, t)), t\in [0, 1]^2\},$ appropriatelyrescaled, converges weakly to the product of the same one-dimensional Browniansheet.

Poisson limit for the number of cycles in a random permutation and the number of segregating sites