Patchiness in plankton populations

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Abstract
We consider and contrast two mechanisms for the production of spatial pattern in an excitable medium model for plankton populations. The first is Turing or diffusion-driven instability. We find that, since in a turbulent environment the effective diffusivities of phytoplankton and zooplankton are similar, this mechanism is unlikely to produce observable spatial pattern in the ocean. The second mechanism is spatially varying forcing of the system. In order to display the sensitivity to small spatial variation in forcing, we consider the dynamics of an ordinary differential equation system with spatial perturbations to parameters and initial conditions. In the absence of diffusion the excitable nature of the system means that small perturbations can produce very sharp spatial structures, when diffusion is introduced, we find that this patchiness can persist on realistic scales.