  We study the effect of advection and noise on the field theory for directed
percolation (DP). We show that even a very small advective velocity is enough
to change the universality class of the dynamic phase transition. When the
noise is taken to be proportional to the square root of the population density,
we find an additional nonequilibrium 'spinodal' line separating a region where
an exponentially decreasing density is metastable, from another one in which it
is unstable. If the noise is instead linear in the density, the phase diagram
changes dramatically both quantitatively and qualitatively, and the spinodal
line becomes a true phase boundary. We briefly discuss possible applications of
our results to microbial sedimentation and population dynamics in rivers.
