  Logistic growth on a static heterogenous substrate is studied both above and
below the drift-induced delocalization transition. Using stochastic,
agent-based simulations the delocalization of the highest eigenfunction is
connected with the large $N$ limit of the stochastic theory, as the
localization length of the deterministic theory controls the divergence of the
spatial correlation length at the transition. Any finite colony made of
discrete agents is washed away from a heterogeneity with compact support in the
presence of strong wind, thus the transition belongs to the directed
percolation universality class. Some of the difficulties in the analysis of the
extinction transition in the presence of a localized active state are
discussed.
