Asymptotic and Transient Dynamics of a Stoichiometric Algal Growth Model with Two-Stage Phosphate Uptake
Shufei Gao, Sanling Yuan, Anglu Shen, Hao Wang
Source abstract
Abstract. Exploring the mechanism of phosphate ([Formula: see text]) 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 [Formula: see text] pools, namely the surface-adsorbed [Formula: see text] pool and the intracellular [Formula: see text] pool, in certain species of algae. Motivated by these observations, a novel stoichiometric model, which incorporates a two-stage [Formula: see text] uptake process, is proposed and analyzed to investigate the impact of these [Formula: see text] 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.
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