We  consider an  initial Eve-population  and a  population  of neutral
  mutants, such that  the total population dies out  in finite time.  We
  describe the evolution of  the Eve-population and the total population
  with continuous  state branching  processes, and the  neutral mutation
  procedure  can  be  seen  as  an immigration  process  with  intensity
  proportional  to the  size of  the  population. First  we establish  a
  Williams' decomposition of the genealogy of the total population given
  by a continuous random tree, according to the ancestral lineage of the
  last individual  alive. This allows us  give a closed  formula for the
  probability of  simultaneous extinction of the  Eve-population and the
  total population.