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June 2019 The nested Kingman coalescent: Speed of coming down from infinity
Airam Blancas, Tim Rogers, Jason Schweinsberg, Arno Siri-Jégousse
Ann. Appl. Probab. 29(3): 1808-1836 (June 2019). DOI: 10.1214/18-AAP1440

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.

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Airam Blancas. Tim Rogers. Jason Schweinsberg. Arno Siri-Jégousse. "The nested Kingman coalescent: Speed of coming down from infinity." Ann. Appl. Probab. 29 (3) 1808 - 1836, June 2019. https://doi.org/10.1214/18-AAP1440

Information

Received: 1 March 2018; Published: June 2019
First available in Project Euclid: 19 February 2019

zbMATH: 07057467
MathSciNet: MR3914557
Digital Object Identifier: 10.1214/18-AAP1440

Subjects:
Primary: 60J25
Secondary: 60J80, 92D15, 92D25

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 3 • June 2019
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