Population dynamics in a random environment

We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. A one-loop RG analysis close to the critical dimension d_c=2 predicts a second order phase transition between a subdiffusive regime and a superdiffusive regime, at variance with our numerical results in d=1 which suggest that a new stable mixed fixed point appears. We introduce the idea of proliferation assisted barrier crossing and give a Flory like argument to understand qualitatively the observed diffusive behaviour at this mixed fixed point.