Electronic Journal of Probability

A population model with non-neutral mutations using branching processes with immigration

Hongwei Bi and Jean-Francois Delmas

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We consider a stationary continuous model of random size population with non-neutral mutations using a continuous state branching process with non-homogeneous immigration. We assume the type (or mutation) of the immigrants is random given by a constant mutation rate measure. We determine some genealogical properties of this process such as: distribution of the time to the most recent common ancestor (MRCA), bottleneck effect at the time to the MRCA (which might be drastic for some mutation rate measures), favorable type for the MRCA, asymptotics of the number of ancestors.

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 62, 23 pp.

Accepted: 20 July 2014
First available in Project Euclid: 4 June 2016

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 92D10: Genetics {For genetic algebras, see 17D92}
Secondary: 60G10: Stationary processes 60G55: Point processes 60J68: Superprocesses 92D25: Population dynamics (general)

non-neutral mutation branching process immigration bottleneck population model genealogical tree MRCA

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Bi, Hongwei; Delmas, Jean-Francois. A population model with non-neutral mutations using branching processes with immigration. Electron. J. Probab. 19 (2014), paper no. 62, 23 pp. doi:10.1214/EJP.v19-2939. https://projecteuclid.org/euclid.ejp/1465065704

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