  We study numerically and analytically the dynamics of a sedimenting
suspension of active, reproducing particles, such as growing bacteria in a
gravitational field. In steady state we find a non-equilibrium phase transition
between a `sedimentation' regime, analogous to the sedimentation equilibrium of
passive colloids, and a `uniform' regime, in which the particle density is
constant in all but the top and bottom of the sample. We discuss the importance
of fluctuations in particle density in locating the phase transition point, and
report the kinetics of sedimentation at early times.
