### 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 2γ /ct
^{2} , where c is the ratio of the coalescence rates at the individual and species levels, and the constant γ ≈ 3.45 is derived from a recursive distributional equation for the number of lineages contained within a species at a typical time.

Original language | English |
---|---|

Pages (from-to) | 1808–1836 |

Number of pages | 29 |

Journal | Annals of Applied Probability |

Volume | 29 |

Issue number | 3 |

Early online date | 19 Feb 2019 |

DOIs | |

Publication status | Published - 19 Feb 2019 |

### Keywords

- Coming down from infinity
- Gene tree
- Kingman's coalescent
- Nested coalescent
- Recursive distributional equation
- Species tree

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Annals of Applied Probability*,

*29*(3), 1808–1836. https://doi.org/10.1214/18-AAP1440

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

Research output: Contribution to journal › Article

*Annals of Applied Probability*, vol. 29, no. 3, pp. 1808–1836. https://doi.org/10.1214/18-AAP1440

}

TY - JOUR

T1 - The Nested Kingman Coalescent

T2 - Speed of Coming Down from Infinity

AU - Benítez, Airam Blancas

AU - Rogers, Tim

AU - Schweinsberg, Jason

AU - Siri-Jégousse, Arno

N1 - 24 pages

PY - 2019/2/19

Y1 - 2019/2/19

N2 - 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 2γ /ct 2 , where c is the ratio of the coalescence rates at the individual and species levels, and the constant γ ≈ 3.45 is derived from a recursive distributional equation for the number of lineages contained within a species at a typical time.

AB - 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 2γ /ct 2 , where c is the ratio of the coalescence rates at the individual and species levels, and the constant γ ≈ 3.45 is derived from a recursive distributional equation for the number of lineages contained within a species at a typical time.

KW - Coming down from infinity

KW - Gene tree

KW - Kingman's coalescent

KW - Nested coalescent

KW - Recursive distributional equation

KW - Species tree

UR - http://www.scopus.com/inward/record.url?scp=85063355266&partnerID=8YFLogxK

U2 - 10.1214/18-AAP1440

DO - 10.1214/18-AAP1440

M3 - Article

VL - 29

SP - 1808

EP - 1836

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 3

ER -