Modeling the growth and sporulation dynamics of the macroalga Ulva in mixed-age populations in cultivation and the formation of green tides

Ulva is a widespread green algal genus with important ecological roles and promising potential as a seagriculture crop. One of the major challenges when cultivating Ulva is sudden biomass disappearance, likely caused by uncontrolled and unpredicted massive sporulation. However, the dynamics of this process are still poorly understood. In this study, we propose a mathematical model describing the biomass accumulation and degradation of Ulva, considering the potential impact of sporulation inhibitors. We developed a differential equation model describing the time evolution of Ulva biomass. Our model simulates biomass in compartments of different Ulva "age"classes, with varying growth and sporulation rates. Coupled with these classes is a differential equation describing the presence of a sporulation inhibitor, produced and secreted by the algae. Our model mimics observed Ulva dynamics. We present Ulva's biomass accumulation under different initial algae population, age distributions and sporulation rates. Furthermore, we simulate water replacement, effectively depleting the sporulation inhibitor, and examine its effects on Ulva's biomass accumulation. The model developed in this work is the first step towards understanding the dynamics of Ulva growth and degradation. Future work refining and expanding our results should prove beneficial to the ecological research and industrial growth of Ulva.