  We introduce a Cannings model with directional selection via a paintbox
construction and establish a strong duality with the line counting process of a
new \emph{Cannings ancestral selection graph} in discrete time. This duality
also yields a formula for the fixation probability of the beneficial type.
Haldane's formula states that for a single selectively advantageous individual
in a population of haploid individuals of size $N$ the prob\-ability of
fixation is asymptotically (as $N\to \infty$) equal to the selective advantage
of haploids $s_N$ divided by half of the offspring variance. For a class of
offspring distributions within Kingman attraction we prove this asymptotics for
sequences $s_N$ obeying $N^{-1} \ll s_N \ll N^{-1/2} $, which is a regime of
"moderately weak selection". It turns out that for $ s_N \ll N^{-2/3} $ the
Cannings ancestral selection graph is so close to the ancestral selection graph
of a Moran model that a suitable coupling argument allows to play the problem
back asymptotically to the fixation probability in the Moran model, which can
be computed explicitly.

Probability