# The Nested Kingman Coalescent: Speed of Coming Down from Infinity

Airam Blancas Benítez, Tim Rogers, Jason Schweinsberg, Arno Siri-Jégousse

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 $\gamma\approx 3.45$ is derived from a recursive distributional equation for the number of lineages contained within a species at a typical time.
Language English 1808–1836 29 Annals of Applied Probability 29 3 19 Feb 2019 10.1214/18-AAP1440 Published - 30 Jun 2019

• math.PR
• 60J25

### Cite this

The Nested Kingman Coalescent : Speed of Coming Down from Infinity. / Benítez, Airam Blancas; Rogers, Tim; Schweinsberg, Jason; Siri-Jégousse, Arno.

In: Annals of Applied Probability, Vol. 29, No. 3, 30.06.2019, p. 1808–1836.

Research output: Contribution to journalArticle

Benítez, AB, Rogers, T, Schweinsberg, J & Siri-Jégousse, A 2019, 'The Nested Kingman Coalescent: Speed of Coming Down from Infinity', Annals of Applied Probability, vol. 29, no. 3, pp. 1808–1836. https://doi.org/10.1214/18-AAP1440
Benítez, Airam Blancas ; Rogers, Tim ; Schweinsberg, Jason ; Siri-Jégousse, Arno. / The Nested Kingman Coalescent : Speed of Coming Down from Infinity. In: Annals of Applied Probability. 2019 ; Vol. 29, No. 3. pp. 1808–1836.
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