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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065704

Digital Object Identifier
doi:10.1214/EJP.v19-2939

Mathematical Reviews number (MathSciNet)
MR3238782

Zentralblatt MATH identifier
1312.60104

Subjects
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)

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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References

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