Asymptotic sampling formulae for Lambda-coalescents

作者：Berestycki Julien^*; Berestycki Nathanael; Limic Vlada

来源：Annales de l Institut Henri Poincare-Probabilites et Statistiques, 2014, 50(3): 715-731.

DOI：10.1214/13-AIHP546

• Lambda-coalescents
• Speed of coming down from infinity
• Exchangeable coalescents
• Sampling formulae
• Infinite allele model
• Genetic variation

We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy is given by a Lambda-coalescent. This allows us to derive an exact formula for the asymptotic behavior of the site and allele frequency spectrum and the number of segregating sites, as the sample size tends to infinity. Some of our results hold in the case of a general Lambda-coalescent that comes down from infinity, but we obtain more precise information under a regular variation assumption. In this case, we obtain results of independent interest for the time at which a mutation uniformly chosen at random was generated. This exhibits a phase transition at alpha = 3/2, where alpha is an element of(1,2) is the exponent of regular variation.

• 出版日期2014-8