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

Hongwei Bi (ENPC & Université Paris-Est & University of International Business and Economics)
Jean-Francois Delmas (ENPC & Université Paris-Est)

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.

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Pages: 1-23

Publication Date: July 20, 2014

DOI: 10.1214/EJP.v19-2939

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