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.