Haldane’s formula in Cannings models: the case of moderately strong selection

  • For a class of Cannings models we prove Haldane’s formula, π(sN)∼2sNρ2, for the fixation probability of a single beneficial mutant in the limit of large population size N and in the regime of moderately strong selection, i.e. for sN∼N−b and 0<b<1/2. Here, sN is the selective advantage of an individual carrying the beneficial type, and ρ2 is the (asymptotic) offspring variance. Our assumptions on the reproduction mechanism allow for a coupling of the beneficial allele’s frequency process with slightly supercritical Galton–Watson processes in the early phase of fixation.
Metadaten
Author:Florin Boenkost, Adrián González Casanova, Cornelia Pokalyuk, Anton WakolbingerGND
URN:urn:nbn:de:hebis:30:3-590279
DOI:https://doi.org/10.1007/s00285-021-01698-9
ISSN:1432-1416
ISSN:0303-6812
Parent Title (German):Journal of Mathematical Biology
Publisher:Springer
Place of publication:Berlin ; Heidelberg ; New York
Document Type:Article
Language:English
Date of Publication (online):2021/12/06
Date of first Publication:2021/12/06
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2022/03/17
Tag:Branching process approximation; Cannings model; Directional selection; Probability of fixation
Volume:83
Issue:70
Page Number:31
HeBIS-PPN:494723807
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - Namensnennung 4.0