Asymptotic and Transient Dynamics of a Stoichiometric Algal Growth Model with Two-Stage Phosphate Uptake

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1668-1696, August 2024.
Abstract. Exploring the mechanism of phosphate ([math]) uptake by algae is essential to accurate prediction and a comprehensive understanding of harmful algal blooms (HABs). Previous experimental studies have revealed the existence of two distinct [math] pools, namely the surface-adsorbed [math] pool and the intracellular [math] pool, in certain species of algae. Motivated by these observations, a novel stoichiometric model, which incorporates a two-stage [math] uptake process, is proposed and analyzed to investigate the impact of these [math] pools on algal growth. Model validation results show that with proper parameterizations, this model can accurately capture algal growth dynamics in the laboratory and in the field. The asymptotic dynamics are explored through a complete mathematical analysis and the transient dynamics are explored through multiscale analysis, revealing the driving mechanism of different growth phases of algae. Furthermore, we derive an approximate formula for estimating the switching time from high to low growth rate in algae, which can serve as a valuable tool for predicting the duration of HABs. These findings contribute to the strengthening of prediction and improving understanding of HABs.