A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models

Discrete ancestral problems arising in population genetics are investigated.In the neutral case, the duality concept has been proved ofparticular interest in the understanding of backward in time ancestral processfrom the forward in time branching population dynamics. We show thatduality formulae still are of great use when considering discrete nonneutralWright-Fisher models. This concerns a large class of nonneutral models withcompletely monotone (CM) bias probabilities. We show that most classicalbias probabilities used in the genetics literature fall within this CM class orare amenable to it through some “reciprocal mechanism” which we define.Next, using elementary algebra on CM functions, some suggested novel evolutionarymechanisms of potential interest are introduced and discussed