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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 attractionof a Beta$(2-\alpha, \alpha)$-coalescent for $\alpha \in (1,2)$. We prove in asetting of moderate selection that the fixation probability $\pi_N$ of theadvantageous allele is asymptotically equal to $\alpha^{1/(\alpha-1)}s_N^{1/(\alpha-1)}$ , where $s_N$ is the selection strength of the advantageousallele. Our proof uses duality with a suitable $\Lambda$-ancestral selectiongraph.

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