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A duality approach to the genealogies of discrete nonneutral Wright-Fisher models. (English) Zbl 1201.92048
Summary: 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 processes 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.

MSC:
92D10 Genetics and epigenetics
92D15 Problems related to evolution
60J99 Markov processes
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