Estimating the Lambda measure in multiple-merger coalescents

Miró Pina, Verónica, Joly, Émilien and Siri-Jégousse, Arno

Theoretical Population Biology, 2023, vol. 154, issue C, 94-101

Abstract: Multiple-merger coalescents, also known as Λ-coalescents, have been used to describe the genealogy of populations that have a skewed offspring distribution or that undergo strong selection. Inferring the characteristic measure Λ, 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 Λ-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 the density of Λ 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 Λ. We give a consistency result of this estimator under mild conditions on the behavior of Λ around 0. We also show some numerical examples of how our method performs.

Keywords: Coalescent theory; Multiple merger; Site frequency spectrum; Non-parametric estimation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:154:y:2023:i:c:p:94-101

DOI: 10.1016/j.tpb.2023.09.002

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