A Mathematical Model of the Brown Tide

Abstract

A differential equation model is proposed for “brown tide” algae blooms in the coastal waters of Long Island which provides a plausible mechanisms for the underlying dynamics. Growth rates depend on annual variations in temperature and salinity. The maximum population density is effectively limited by the availability of a favorable concentration of nutrients, together with zooplankton grazing. Salinity depends on rainfall while nutrient concentration is influenced by tidal flushing. The first of these factors is aperiodic, the second periodic, in time. The resulting nonlinear model distinguishes between ‘fast’ algae growth and ‘slow’ long-term changes in nutrients and salinity. Because of this one can show that explosive increases of algae densities will occur infrenquently at sporadic intervals. Computer trials with the model appear to replicate many, if not all, the essential features of the observed bloom.