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

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−α,α)-coalescent for α∈(1,2). We prove in a setting of moderate selection that the fixation probability πN of the advantageous allele is asymptotically equal to α1∕(α−1)sN1∕(α−1), where sN is the selection strength of the advantageous allele. Our proof uses duality with a suitable Λ-ancestral selection graph.