We investigate the dynamics of the Fisher equation for the spreading of micro-organisms in one dimenison subject to both turbulent convection and diffusion. We show that for strong enough turbulence, bacteria , for example, track in a quasilocalized fashion (with remakably long persistance times) sinks in the turbulent field. An important consequence is a large reduction in the carrying capacit...

The Fisher-Kolmogorov-Petrovskii-Piskunov equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimit...