Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS-UMR 8089, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France
Copyright © 2009 Thierry E. Huillet. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Discrete ancestral problems arising in population genetics are investigated.
In the neutral case, the duality concept has been 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 nonneutral
Wright-Fisher models. This concerns a large class of nonneutral 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.