  Bertoin and Le Gall (2003) introduced a certain probability measure valued
Markov process that describes the evolution of a population, such that a sample
from this population would exhibit a genealogy given by the so-called
$\Lambda$-coalescent, or coalescent with multiple collisions, introduced
independently by Pitman (1999) and Sagitov (1999). We show how this process can
be extended to the case where lineages can experience mutations. Regenerative
compositions enter naturally into this model, which is somewhat surprising,
considering a negative result by M{\"o}hle (2007).
