Annals of Applied Probability

Asymptotic results on the length of coalescent trees

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

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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.

Article information

Source
Ann. Appl. Probab., Volume 18, Number 3 (2008), 997-1025.

Dates
First available in Project Euclid: 26 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1211819792

Digital Object Identifier
doi:10.1214/07-AAP476

Mathematical Reviews number (MathSciNet)
MR2418236

Zentralblatt MATH identifier
1141.60007

Subjects
Primary: 60F05: Central limit and other weak theorems 60G52: Stable processes 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 05C05: Trees

Keywords
Coalescent process Beta-coalescent stable process Watterson estimator

Citation

Delmas, Jean-François; Dhersin, Jean-Stéphane; Siri-Jegousse, Arno. Asymptotic results on the length of coalescent trees. Ann. Appl. Probab. 18 (2008), no. 3, 997--1025. doi:10.1214/07-AAP476. https://projecteuclid.org/euclid.aoap/1211819792


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