Why does nature force the creation of proteobacteria community in the estuarine ecosystem? - A theoretical model

Estuarine ecosystems are among the most dynamic and ecologically significant environments, shaped by intricate interactions among microbial communities, such as proteobacteria and their predator. Proteobacteria, owing to their remarkable tolerance to salinity and unique mixotrophic capabilities, dominate this ecosystem. These traits raise a fundamental ecological question: do proteobacteria act as stabilising agents in estuarine health, and why has evolution favoured their multifunctionality over strict autotrophy or heterotrophy? This study presents a novel theoretical framework, comprising both deterministic and stochastic models, emphasizing key phenomenological traits of mixotrophic proteobacteria in estuarine ecosystems. The autotrophic component is captured using Secchi depth as a proxy for light availability and photosynthetic potential, while heterotrophic behaviour is linked to salinity-driven nutrient uptake. Through analytical exploration and numerical simulations, we find that salinity serves as a crucial control parameter, producing characteristic oscillatory dynamics and a "bubbling effect" that delineates transitions between stability and instability. The photosynthetic capability of mixotrophic proteobacteria emerges as a critical stabilizing mechanism, particularly under fluctuating salinity and turbidity conditions. Our model identifies critical thresholds for Secchi depth, salinity-driven microzooplankton grazing and nutrient inflow-outflow that underpin estuarine stability. The stochastic extension, incorporating Gaussian white noise, demonstrates that under strong environmental noise, microzooplankton are more prone to extinction than proteobacteria. This work lays a theoretical foundation for future ecological modelling and adaptive estuarine management in the context of climate-driven change.