Asymptotic sampling formulae for Λ-coalescents

Journal article

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 Λ-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 ∞. Some of our results hold in the case of a general Λ-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 α = 3/2, where α ∈ (1, 2) is the exponent of regular variation. © Association des Publications de l'Institut Henri Poincaré, 2014.

Authors: Berestycki, J; Berestycki, N; Limic, V

• Publisher: Institute of Mathematical Statistics
• Journal: Annales de l'institut Henri Poincare (B) Probability and Statistics
• Volume: 50
• Issue: 3
• Pages: 715-731
• Publication date: 2014-01-01
• DOI: 10.1214/13-AIHP546
• ISSN: 0246-0203
• Language: English
• Keywords: Genetic variation; Exchangeable coalescents; Λ-coalescents; Speed of coming down from infinity; Infinite allele model; Sampling formulae