  We study a population model of fixed size undergoing strong selection where
individuals accumulate beneficial mutations, namely the Moran model with
selection. In a specific setting with strong selection, Schweinsberg showed
that the genealogy of the population is described by the so-called
Bolthausen-Sznitman's coalescent. In this paper we sophisticate the model by
splitting the population into two adversarial subgroups, that can be
interpreted as two different alleles, one of which has a weak selective
advantage over the other. We show that the proportion of disadvantaged
individuals converges to the solution of a stochastic differential equation
(SDE) as the population's size goes to infinity, named the
$\Lambda$-Wright-Fisher SDE with selection. This stochastic differential
equation already appeared in the $\Lambda$-lookdown model with selection
studied by Bah and Pardoux, in the case where the population's genealogy is
described by Bolthausen-Sznitman's coalescent.
