2013/07/25 by Hongwei Bi, Bi, Hongwei, Jean‐François Delmas +2
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1307.6749
22 pages
arxiv created 2013/07/25 · openalex publication_date 2013/07/25 · arxiv updated 2013/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.