# 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}
}
• 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…
3 Citations
Haldane’s formula in Cannings models: the case of moderately weak selection
• Mathematics
Electronic Journal of Probability
• 2021
We introduce a Cannings model with directional selection via a paintbox construction and establish a strong duality with the line counting process of a new Cannings ancestral selection graph in
Asymptotic genealogies for a class of generalized Wright–Fisher models
• Mathematics
Modern Stochastics: Theory and Applications
• 2021
We study a class of Cannings models with population size N having a mixed multinomial offspring distribution with random success probabilities W1, . . . ,WN induced by independent and identically

## References

SHOWING 1-10 OF 42 REFERENCES
Haldane’s formula in Cannings models: the case of moderately weak selection
• Mathematics
Electronic Journal of Probability
• 2021
We introduce a Cannings model with directional selection via a paintbox construction and establish a strong duality with the line counting process of a new Cannings ancestral selection graph in
The probability of fixation of a single mutant in an exchangeable selection model
• Mathematics
Journal of mathematical biology
• 2007
The Cannings exchangeable model for a finite population in discrete time is extended to incorporate selection and applications to evolutionary game theory in finite populations are presented.
Rates of decay for the survival probability of a mutant gene
• K. Athreya
• Mathematics
Journal of mathematical biology
• 1992
Ifqk is the extinction probability of a slightly supercritical branching process with offspring distributionPkr :r = 0, 1, 2,..., then it is shown that if sup ∑rr3pkr, < ∞, inf σ2k > 0, andmk→ 1,
Modelling and simulating Lenski's long-term evolution experiment.
• Mathematics
Theoretical population biology
• 2019
Duality and fixation in $\Xi$-Wright–Fisher processes with frequency-dependent selection
• Mathematics
• 2016
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is
TOTAL VARIATION DISTANCES AND RATES OF CONVERGENCE FOR ANCESTRAL COALESCENT PROCESSES IN EXCHANGEABLE POPULATION MODELS
Haploid population models with non-overlapping generations and fixed population size N are considered. It is assumed that the family sizes 1, - - - , N within a generation are exchangeable random
The fixation probability of beneficial mutations
• Biology
Journal of The Royal Society Interface
• 2008
The aim is to highlight the concrete, testable predictions that have arisen from the theoretical literature, with the intention of further motivating the invaluable interplay between theory and experiment.
Sur un nouveau théorème-limite de la théorie des probabilités
• Mathematics
• 1994
This is a translation of Harald Cram\'er's article, 'On a new limit theorem in probability theory', published in French in 1938 and deriving what is considered by mathematicians to be the first large