TY - JOUR
T1 - Estimating the Lambda measure in multiple-merger coalescents
JF - bioRxiv
DO - 10.1101/2023.03.10.532088
SP - 2023.03.10.532088
AU - Miró Pina, Verónica
AU - Joly, Émilien
AU - Siri-Jégousse, Arno
Y1 - 2023/01/01
UR - http://biorxiv.org/content/early/2023/05/18/2023.03.10.532088.abstract
N2 - 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.Competing Interest StatementThe authors have declared no competing interest.
ER -