Diffusive processes are often used to represent the formation of spatial patterns in biological systems(1). Here I show how patchiness may be generated in planktonic ecosystems through non-diffusive advection. Plankton distributions in oceanic surface waters can be characterized by the spectra of concentrations obtained along ship transects. Such spectra are inevitably found to have a power-law form over horizontal scales ranging from 1 to 100 km (ref. 2). Phytoplankton have distributions similar to those of physical quantities such as sea surface temperature, with much less variability at shorter length scales. In contrast, zooplankton density may be almost as variable at short scales as long ones(3). Distributions of this form are generated in a model of the turbulent stirring of coupled phytoplankton and zooplankton populations, The characteristic spatial patterns of the phytoplankton and zooplankton are a consequence of the timescales of their response to changes in their environment caused by turbulent advection.