Asymptotic results on the length of coalescent trees

Jean François Delmas; Jean Stéphane Dhersin; Arno Siri-Jegousse

doi:10.1214/07-AAP476

Asymptotic results on the length of coalescent trees

Jean François Delmas
, Jean Stéphane Dhersin
, Arno Siri-Jegousse

Research output: Contribution to journal › Article › peer-review

Abstract

We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first step to study the asymptotic distribution of a natural estimator of DNA mutation rate for species with large families.

Original language	English
Pages (from-to)	997-1025
Number of pages	29
Journal	Annals of Applied Probability
Volume	18
Issue number	3
DOIs	https://doi.org/10.1214/07-AAP476
Publication status	Published - 1 Jan 2008

Keywords

Beta-coalescent
Coalescent process
Stable process
Watterson estimator

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10.1214/07-AAP476

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title = "Asymptotic results on the length of coalescent trees",

abstract = "We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first step to study the asymptotic distribution of a natural estimator of DNA mutation rate for species with large families.",

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AU - Dhersin, Jean Stéphane

AU - Siri-Jegousse, Arno

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N2 - We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first step to study the asymptotic distribution of a natural estimator of DNA mutation rate for species with large families.

AB - We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first step to study the asymptotic distribution of a natural estimator of DNA mutation rate for species with large families.

KW - Beta-coalescent

KW - Coalescent process

KW - Stable process

KW - Watterson estimator

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DO - 10.1214/07-AAP476

M3 - Article

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SP - 997

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JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 3

ER -

Asymptotic results on the length of coalescent trees

Abstract

Keywords

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