dc.contributor.author González Casanova, Adrian dc.contributor.author Smadi, Charline dc.contributor.author Wakolbinger, Anton dc.date.accessioned 2022-11-30T13:09:16Z dc.date.available 2022-11-30T13:09:16Z dc.date.issued 2022-11-30 dc.identifier.uri http://publications.mfo.de/handle/mfo/3993 dc.description.abstract Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. 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 en_US $k+1$ at a constant rate. This model is thus a variation of the classical Muller's ratchet: there 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, and also via the distribution of the final minimal displacement in a branching random walk with one-sided steps. 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. dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2022-18 dc.subject Mullers ratchet en_US dc.subject Click rate en_US dc.subject Quasi-equilibrium en_US dc.subject Tournament selection en_US dc.subject Harris graphical representation en_US dc.subject Duality en_US dc.subject Ancestral selection graph en_US dc.subject First passage percolation en_US dc.title Quasi-Equilibria and Click Times for a Variant of Muller's Ratchet en_US dc.type Preprint en_US dc.rights.license Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. de dc.rights.license This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. en dc.identifier.doi 10.14760/OWP-2022-18 local.scientificprogram OWRF 2022 local.series.id OWP-2022-18 en_US local.subject.msc 60 en_US local.subject.msc 92 en_US dc.identifier.urn urn:nbn:de:101:1-2022121211155619126574 dc.identifier.ppn 1826796088
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