  We consider branching particle processes on discrete structures like the
hypercube in a random fitness landscape (i.e., random branching/killing rates).
The main question is about the location where the main part of the population
sits at a late time, if the state space is large. For answering this, we take
the expectation with respect to the migration (mutation) and the
branching/killing (selection) mechanisms, for fixed rates. This is intimately
connected with the parabolic Anderson model, the heat equation with random
potential, a model that is of interest in mathematical physics because of the
observed prominent effect of intermittency (local concentration of the mass of
the solution in small islands). We present several advances in the
investigation of this effect, also related to questions inspired from biology.
