  In a (two-type) Wright-Fisher diffusion with directional selection and
two-way mutation, let $x$ denote today's frequency of the beneficial type, and
given $x$, let $h(x)$ be the probability that, among all individuals of today's
population, the individual whose progeny will eventually take over in the
population is of the beneficial type. Fearnhead [Fearnhead, P., 2002. The
common ancestor at a nonneutral locus. J. Appl. Probab. 39, 38-54] and Taylor
[Taylor, J. E., 2007. The common ancestor process for a Wright-Fisher
diffusion. Electron. J. Probab. 12, 808-847] obtained a series representation
for $h(x)$. We develop a construction that contains elements of both the
ancestral selection graph and the lookdown construction and includes pruning of
certain lines upon mutation. Besides being interesting in its own right, this
construction allows a transparent derivation of the series coefficients of
$h(x)$ and gives them a probabilistic meaning.
