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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 oftype frequencies as the original Moran model, provided the initial values arechosen appropriately. In the new model, individuals are labelled $1,2, \dots,N$; neutral resampling events may take place between arbitrary labels, whereasselective events only occur in the direction of increasing labels. With thehelp of elementary methods only, we not only recover fixation probabilities,but also obtain detailed insight into the number and nature of the selectiveevents that play a role in the fixation process forward in time.

The Moran model with selection: Fixation probabilities, ancestral lines, and an alternative particle representation