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

TL;DR

This paper models a stationary population with non-neutral mutations using a continuous state branching process with immigration, analyzing genealogical properties like MRCA distribution and mutation effects.

Contribution

It introduces a novel continuous population model incorporating non-neutral mutations and derives key genealogical properties within this framework.

Findings

Distribution of time to MRCA determined

Bottleneck effects at MRCA identified

Asymptotics of ancestor count analyzed

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.