Which Critically Branching Populations Persist?

The question how quick the individuals must spread out in order to overcome the clumping caused by a critical branching has been studied in [GRW] and [GW2] for a class of multitype branching populations on Rd. Here, an extension of the results to the genuine multitype branching case is presented, which relies on a more detailed analysis of the individual ancestral process [LWa]. Also, several advances and open problems around the question whether a recurrent migration together with a spatially homogeneous critical branching excludes persistence of the population are discussed.