The Moran model with selection: Fixation probabilities, ancestral lines, and an alternative particle representation
Sandra Kluth, Ellen Baake
(Submitted on 12 Jun 2013)
We reconsider the Moran model in continuous time with population size $N$, two types, and selection. We introduce a new particle representation, which we call labelled Moran model, and which has the same empirical type distribution 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 do not only recover fixation probabilities, but obtain detailed insight into the number and nature of the selective events that play a role in the fixation process forward in time.