  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.
