• DOI:10.1007/s00285-021-01698-9
• Corpus ID: 220968991

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

@article{Boenkost2021HaldanesFI,
  title={Haldane’s formula in Cannings models: the case of moderately strong selection},
  author={Florin Boenkost and Adri{\'a}n Gonz{\'a}lez Casanova and Cornelia Pokalyuk and A. Wakolbinger},
  journal={Journal of Mathematical Biology},
  year={2021},
  volume={83}
}

• Florin Boenkost, A. González Casanova, +1 author A. Wakolbinger
• Published 5 August 2020
• Materials Science
• Journal of Mathematical Biology

For a class of Cannings models we prove Haldane’s formula, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi (s_N) \sim \frac{2s_N}{\rho ^2}$$\end{document}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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s_N \sim N^{-b}$$\end{document}sN∼N-b and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0< b<1/2$$\end{document}0<b<1/2. Here, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s_N$$\end{document}sN is the selective advantage of an individual carrying the beneficial type, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho ^2$$\end{document}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.