Persistence of harmful algal blooms under conditions of internal phosphorus loading

Phosphorus release from sediments in lakes can trigger harmful algal blooms, significantly impacting lake ecosystems and necessitating effective management strategies. This study presents a mathematical analysis of a dynamic model incorporating such internal phosphorus loadings and their impact on algal growth. The model accounts for both light and phosphorus limitations on cell growth, as well as the seasonal variability of temperature and light, leading to a periodically forced non-linear system of ordinary differential equations. Using the theory of periodic semiflows and Floquet multipliers, we establish both necessary and sufficient conditions for long-term survival of algae (uniform persistence). This approach provides a threshold result for algae survival and the existence of a non-trivial periodic solution. Through numerical simulations, we illustrate our results and provide insights into the role of internal phosphorus loadings. In particular, our simulations illustrate that an integrated strategy reducing both watershed inflows and sediment phosphorus outperforms measures that focus on just one source of phosphorus.