Site Frequency Spectrum of the Bolthausen-Sznitman Coalescent

Kersting, Götz; Siri‐Jégousse, Arno; Wences, Alejandro H.

doi:10.30757/alea.v18-53

Cited by 6 publications

(1 citation statement)

References 26 publications

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“…From the SNP matrix we can compute the SFS, which is the vector such that its i -th component contains the number of observed mutations shared by exactly i individuals in the sample. This is a statistic widely used in population genetics, both for model selection [Eldon et al, 2015, Freund and Siri-Jégousse, 2021] and for parameter inference [Fu, 1995, Kersting et al, 2021]. In this paper, we use an extension of the SFS, the so-called weighted SFS , which can also be read from the SNP matrix by subsampling the individuals (lines), as explained at the end of the Results section.…”

Section: Introductionmentioning

confidence: 99%

Estimating the Lambda measure in multiple-merger coalescents

Pina

Joly

Siri‐Jégousse

2023

Preprint

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Multiple-merger coalescents, also known as Lambda-colescents, have been used to describe the genealogy of populations that have a skewed offspring distribution or that undergo strong selection. Inferring the characteristic measure Lambda, which describes the rates of the multiple-merger events, is key to understand these processes. So far, most inference methods only work for some particular families of Lambda-coalescents that are described by only one parameter, but not for more general models. This article is devoted to the construction of a non-parametric estimator of Lambda that is based on the observation at a single time of the so-called Site Frequency Spectrum (SFS), which describes the allelic frequencies in a present population sample. First, we produce estimates of the multiple-merger rates by solving a linear system, whose coefficients are obtained by appropriately subsampling the SFS. Then, we use a technique that aggregates the information extracted from the previous step through a kernel type of re-construction to give a non-parametric estimation of the measure Lambda. We give a consistency result of this estimator under mild conditions on the behavior of Lambda around 0. We also show some numerical examples of how our method performs.

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