Nonlinear interactions, diffusion, transport and locomotion of species
are described by a system of reaction-diffusion-advection equations.
Its transient and stationary nonequilibrium solutions in space and tim
e are considered as patchy patterns in natural chemical or biological
communities. Recent results on the general mechanism of spatial patter
n formation after flux-induced instabilities of a spatially uniform sp
ecies distribution as well as on the effect of hydrodynamic forcing on
spatial patterns in a minimal plankton model are summarized.