A spatial model of phytoplankton patchiness

The one-dimensional theory of critical-length scales of phytoplankton patchiness is developed to include phytoplankton growth and herbivore grazing as functions of time and space. The critical-length scale L c for the pathch is then determined by the initial spatial distribution and concentration of the limiting nutrient and herbivores in addition to the daily averaged values of the growth and loss processes. The response of an initial phytoplankton patch to the stresses of turbulent diffusion, nutrient depletion, light periodicity, and nocturnal or continuous herbivore grazing is investigated numerically for several oceanic conditions. Nocturnal grazing, while less stressful on primary production than continous grazing, results in lower phytoplankton standing stocks. Increase in biomass of vertically migrating zooplankton results in a net loss of nutrient which might otherwise be egested, recycled, and utilized in the euphotic zone under continuous grazing conditions. The Ivlev constant is shown via sensitivity analysis to be a significant parameter ultimately influencing phytoplankton production. It is demonstrated numerically that diffusion of phytoplankton cells from areas of high concentration to low concentration prevents the local extinction of the standing stock, thereby rendering a positive herbivore grazing-threshold unnecessary for ecosystem stability.