  We reconsider the Moran model in continuous time with population size $N$,
two allelic types, and selection. We introduce a new particle representation,
which we call the labelled Moran model, and which has the same distribution of
type frequencies as the original Moran model, provided the initial values are
chosen appropriately. In the new model, individuals are labelled $1,2, \dots,
N$; neutral resampling events may take place between arbitrary labels, whereas
selective events only occur in the direction of increasing labels. With the
help of elementary methods only, we not only recover fixation probabilities,
but also obtain detailed insight into the number and nature of the selective
events that play a role in the fixation process forward in time.
