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arXiv · 2310.09045

On the fixation probability of an advantageous allele in a population with skewed offspring distribution

Matthias Birkner·Florin Boenkost·Iulia Dahmer·Cornelia Pokalyuk
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Abstract

Consider an advantageous allele that arises in a haploid population of size $N$ evolving in continuous time according to a skewed reproduction mechanism, which generates under neutrality genealogies lying in the domain of attraction of a Beta$(2-\alpha, \alpha)$-coalescent for $\alpha \in (1,2)$. We prove in a setting of moderate selection that the fixation probability $\pi_N$ of the advantageous allele is asymptotically equal to $\alpha^{1/(\alpha-1)} s_N^{1/(\alpha-1)} $ , where $s_N$ is the selection strength of the advantageous allele. Our proof uses duality with a suitable $\Lambda$-ancestral selection graph.

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Matthias Birkner, Florin Boenkost, Iulia Dahmer, Cornelia Pokalyuk. 2023-10-13. On the fixation probability of an advantageous allele in a population with skewed offspring distribution. https://arxiv.org/abs/2310.09045

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