## The Annals of Applied Probability

### The nested Kingman coalescent: Speed of coming down from infinity

#### Abstract

The nested Kingman coalescent describes the ancestral tree of a population undergoing neutral evolution at the level of individuals and at the level of species, simultaneously. We study the speed at which the number of lineages descends from infinity in this hierarchical coalescent process and prove the existence of an early-time phase during which the number of lineages at time $t$ decays as $2\gamma/ct^{2}$, where $c$ is the ratio of the coalescence rates at the individual and species levels, and the constant $\gamma\approx3.45$ is derived from a recursive distributional equation for the number of lineages contained within a species at a typical time.

#### Article information

Source
Ann. Appl. Probab., Volume 29, Number 3 (2019), 1808-1836.

Dates
First available in Project Euclid: 19 February 2019

https://projecteuclid.org/euclid.aoap/1550566843

Digital Object Identifier
doi:10.1214/18-AAP1440

Mathematical Reviews number (MathSciNet)
MR3914557

Zentralblatt MATH identifier
07057467

#### Citation

Blancas, Airam; Rogers, Tim; Schweinsberg, Jason; Siri-Jégousse, Arno. The nested Kingman coalescent: Speed of coming down from infinity. Ann. Appl. Probab. 29 (2019), no. 3, 1808--1836. doi:10.1214/18-AAP1440. https://projecteuclid.org/euclid.aoap/1550566843

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