A MODEL OF PHYTOPLANKTON GROWTH ON MULTIPLE NUTRIENTS BASED ON THE MICHAELIS-MENTEN-MONOD UPTAKE, DROOPS GROWTH AND LIEBIGS-LAW

A model of phytoplankton population growing on more than one potential ly limiting nutrient is formulated and investigated. The model is base d on the Michaelis-Menten-Monod uptake function for each nutrient, the Droop's function for growth of phytoplankton and Liebig's law for gro wth on different nutrients. The model is analyzed in a simple set up o f phytoplankton culture reactor. Conditions are specified for which st eady phytoplankton existence state is stable. Since growth depends on internal nutrient content, the limiting nutrient may be recognized as the one having the smallest content in phytoplankton relative to the s ubsistence quota. According to the model, in steady state during equal limitation by several nutrients, the Redfield ratio is equal to the r atio of subsistence quotas and to the ratio of uptake rates. Contrary to wide spread use, the ratio of nutrients in water is not the Redfiel d ratio but a function of the growth rate. In oligotrophic waters, how ever, nutrients are in another ratio that may be used as an analog to the Redfield ratio in phytoplankton. The model may be used as a submod el of larger ecosystem models. (C) 1997 Elsevier Science B.V.