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bioRxiv · 10.1101/799627

Site Frequency Spectrum of the Bolthausen-Sznitman coalescent

Kersting, G.·Siri-Jegousse, A.·Wences, A. H.
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Abstract

We derive explicit formulas for the two first moments of he site frequency spectrum (SFSn,b)1[≤]b[≤]n-1 of the Bolthausen-Sznitman coalescent along with some precise and efficient approximations, even for small sample sizes n. These results provide new L2-asymptotics for some values of b = o(n). We also study the length of internal branches carrying b > n/2 individuals. In this case we obtain the distribution function and a convergence in law. Our results rely on the random recursive tree construction of the Bolthausen-Sznitman coalescent.

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Kersting, G., Siri-Jegousse, A., Wences, A. H.. 2019-10-10. Site Frequency Spectrum of the Bolthausen-Sznitman coalescent. https://doi.org/10.1101/799627

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