  Discrete ancestral problems arising in population genetics are investigated.
In the neutral case, the duality concept has proved of particular interest in
the understanding of backward in time ancestral process from the forward in
time branching population dynamics. We show that duality formulae still are of
great use when considering discrete non-neutral Wright-Fisher models. This
concerns a large class of non-neutral models with completely monotone (CM) bias
probabilities. We show that most classical bias probabilities used in the
genetics literature fall within this CM class or are amenable to it through
some `reciprocal mechanism' which we define. Next, using elementary algebra on
CM functions, some suggested novel evolutionary mechanisms of potential
interest are introduced and discussed.
