  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 $t_1/2$.
  Our main result comprises two different couplings of the above models for all
parameters $n\geq 2,$ $t\in [0, 1]^2$ such that in both couplings one has weak
convergence of processes as $n\to\infty$ \begin{align*}
  \left\{\frac{(K(n, s), S(n, t))-(s_1s_2, t_1t_2)\log n}{\sqrt{\log n}}, s,
t\in [0, 1]^2\right\}\to\{(\mathscr B(s), \mathscr B(t)), s, t\in [0, 1]^2\},
\end{align*} where $\mathscr B$ is a one-dimensional Brownian sheet. This
generalises and unifies a number of well-known results.
