### 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 |
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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