Age statistics in the Moran population model

We analyze the age structure in the Moran model for population genetics. Limit distributions for the age of an individual and the order statistics are computed. The limiting distribution for the life of an individual is shown to be a (shifted) geometric distribution. By an argument that draws on recent conclusions from a model for solitons the limiting order statistics are shown to be convolutions of geometric random variables. Finally, the number of individuals at a certain age is shown to be associated with limiting Bernoulli random variables, via a class of difference-differential functional equations.