AbstractPlanktonic herbivores forage on phytoplankton cells which were produced at some earlier time and at a distant place. A steady state, one dimension model of the birth, death and eddy diffusion of phytoplankton illustrates phytoplankton smooth both temporal and spatial variations as they are transported. When the eddy diffusivity iskand the phytoplankton doubling time isb, the average distance traveled by a phytoplankton cell is (kb)1/2and the average time spent doing so isb. Only those spatial variations with wavelengths greater than 2π(kb)1/2and temporal variations with periods greater than 2πbwill be observed in the phytoplankton distributions at more than half their original amplitude. Bothkandbcontrol the length scale of phytoplankton distributions in a cartesian coordinate system. Planktonic herbivores view the phytoplankton from a diffusing coordinate system in which the spatial scales of the phytoplankton distribution are transformed into time scale