Mathematical population genetics and the seed bank coalescent (Noemi Kurt, TU Berlin, Germany)

29.05.2017 15:15 – 17:15

Mathematical population genetics aims at understanding the patterns of genetic variability. Classical models such as the Wrigth-Fisher model provide simple but yet useful tools to understand the impact of random genetic drift, mutation, selection and other evolutionary forces on the long-term behaviour of populations. Such models have been investigated since the early twentieth century, a particularly fruitful viewpoint was provided in the eighties by studying the related backward in time coalescent processes. `Dormancy', for example in the guise of so-called seed banks, may be considered a particular evolutionary force in this context. Seed banks occur in populations where individuals may enter a reversible stage of inactivity that may be of some duration. In the biological literature it is generally believed that the presence of seed banks leads to an increased genetic variablity, and that seed banks may act as a buer against other evolutionary forces. In the rst part of this talk, we will present the classical models of population genetics, in particular the Writght-Fisher model and the Kingman coalescent, and discuss some of their most important properties. In the second part, we will introduce a new mathematical model for a population where individuals may take `dormant forms', and identify a new natural coalescent structure, the seed-bank coalescent, which describes the gene genealogy of such populations. The qualitatively new feature of the seed-bank coalescent is that ancestral lineages are independently blocked at a certain rate from taking part in coalescence events, thus strongly altering the predictions of classical coalescent models. We discuss the long-time behaviour of the population model and the corresponding coalescent, and show that even thought xation of one genetic type happens almost surely, the time to xation is much longer than in classical population models. In the retrospective picture, we show that, the seed-bank coalescent `does not come down from innity', and the time to the most recent common ancestor is highly elevated compared to Kingman's coalescent. This provides a genealogical explanation for the predicted increase in genetic variability. (joint work with J. Blath, A. Gonzalez Casanova, M. Wilke Berenguer (all TU Berlin)).

Lieu

Room 17 15:15-16:00 & Room 17 16:30-17:15, Séminaire "Mathématique Physique"

Organisé par

Section de mathématiques

Intervenant-e-s

Noemi Kurt, TU Berlin, Germany

entrée libre

Classement

Catégorie: Séminaire