Genealogical distance under selection

We study the genealogical distance of two randomly chosen individuals in a population that evolves according to a two type Moran model with mutation and selection. We prove that this distance is stochastically smaller than the corresponding distance in the neutral model, when the population size is large. Moreover, we prove convergence of the genealogical distance under selection to the distance in the neutral case, when the system is in equilibrium and the selection parameter tends to infinity.