  We use interacting particle systems to investigate survival and extinction of
a species with colonies located on each site of $\mathbb {Z}^d$. In each of the
four models studied, an individual in a local population can reproduce, die or
migrate to neighboring sites. We prove that an increase of the death rate when
the local population density is small (the Allee effect) may be critical for
survival, and that the migration of large flocks of individuals is a possible
solution to avoid extinction when the Allee effect is strong. We use
attractiveness and comparison with oriented percolation, either to prove the
extinction of the species, or to construct nontrivial invariant measures for
each model.
