Séminaire Orléans

Rare selection and coordination

by Maite Wilke Berenguer (Bochum/Berlin)

Salle de Séminaires (Orléans)

Salle de Séminaires


We analyse a family of two-types Wright-Fisher models with selection in a random environment. We introduce rare in addition to weak selection to the model and provide a criterion to quantify the impact of different shapes of selection on the fate of the weakest allele.

As is common for these models we obtain a dual pair of a branching-coalescing process describing the genealogy and a diffusion describing the evolution of the frequency of a selectively weaker allele, with jumps resulting from rare selection. The jumps in the "diffusion" result from coordination in the dual particle system. The generator of the jump component has a representation in terms of the generator of the dual of the non-coordinated (weak) selection, which we refer to as Griffiths' representation.

This representation observed and used by Griffiths in the case of $\Lambda$-coalescents the Wright-Fisher diffusion is a key ingredient in the proof of the criterion for extinction, because it allows for a Lyapunov-function-type argument.

This is joint work with A. González Casanova (UNAM) and D. Spanó (Warwick)

Lien : https://greenlight.lal.cloud.math.cnrs.fr/b/nil-wp9-ydg