Accounting for nutrient processing time in mathematical models of phytoplankton growth

Abstract

In mathematical models, the decoupling of the kinetics of nutrient assimilation and growth under transient conditions is traditionally handled by using either time lags (which are dynamically unsatisfactory) or multiple intracellular nutrient compartments (which are difficult to paramaterize). We use the estimated time required for nutrient processing to calculate the quantity of processed nutrient held within the cells. We then determine growth rate by the mean cell content of processed nutrient. The resulting model successfully simulates the transient growth of nitrogen-limited cultures of Chlamydomonas reinhardii and Isochrysis galbana. The model can be fully parameterized from relatively simple data sets and generates overshoots and time delays without exhibiting the dynamical instability characteristic of previously published time-lag formulations.