  The approximation of the Feynman-Kac semigroups by systems of interacting
particles is a very active research field, with applications in many different
areas. In this paper, we study the parallelization of such approximations. The
total population of particles is divided into sub-populations, referred to as
\emph{islands}. The particles within each island follow the usual selection /
mutation dynamics. We show that the evolution of each island is also driven by
a Feynman-Kac semigroup, whose transition and potential can be explicitly
related to ones of the original problem. Therefore, the same genetic type
approximation of the Feynman-Kac semi-group may be used at the island level;
each island might undergo selection / mutation algorithm. We investigate the
impact of the population size within each island and the number of islands, and
study different type of interactions. We find conditions under which
introducing interactions between islands is beneficial. The theoretical results
are supported by some Monte Carlo experiments.
