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

For a class of Cannings models we prove Haldane’s formula, π ( s N ) ∼ 2 s N ρ 2 , 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 s N ∼ N - b and 0 < b < 1 / 2 . Here, s N is the sele...

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Bibliographic Details
Published in:Journal of mathematical biology 2021-12, Vol.83 (6-7), p.70-70, Article 70
Main Authors: Boenkost, Florin, González Casanova, Adrián, Pokalyuk, Cornelia, Wakolbinger, Anton
Format: Article
Language:English
Subjects:
Applications of Mathematics
Approximation
Fixation
Gene frequency
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Offspring
Population
Population Density
Population number
Probability
Random variables
Reproduction
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Summary:For a class of Cannings models we prove Haldane’s formula, π ( s N ) ∼ 2 s N ρ 2 , 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 s N ∼ N - b and 0 < b < 1 / 2 . Here, s N is the selective advantage of an individual carrying the beneficial type, and ρ 2 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.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-021-01698-9