Jointly with Stochastik Kolloquium GU Frankfurt
Université de Grenoble
Abstract: We will introduce and study a variant of a well-known model in population genetics, namley Muller's ratchet, which is seen as one explanation of the ubiquity of sexual selection in Nature. Consider a population of N individuals, each of them carrying a type in N_0. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type k has the same selective advantage over all individuals with type k′>k, and type k mutates to type k+1 at a constant rate (in the classical Muller's ratchet, the selective advantage is proportional to k′−k). For a regime of selection strength and mutation rates which is between the regimes of weak and strong selection/mutation, we obtain the asymptotic rate of the click times of the ratchet (i.e. the times at which the hitherto minimal (`best') type in the population is lost), and reveal the quasi-stationary type frequency profile between clicks. The large population limit of this profile is characterized as the normalized attractor of a ``dual'' hierarchical multitype logistic system. An important role in the proofs is played by a graphical representation of the model, both forward and backward in time, and a central tool is the ancestral selection graph decorated by mutations.
Charline Smadi "Quasi-equilibria and click times for a variant of Muller's ratchet"
