Harmful algal blooms are increasingly recognized as a threat to the integrity of freshwater reservoirs, which serve as water supplies, wildlife habitats, and recreational attractions. While algal growth and accumulation is controlled by many environmental factors, the relative importance of these factors is unclear, particularly for turbid eutrophic systems. Here we develop and compare two models that test the relative importance of vertical mixing, light, and nutrients for explaining chlorophyll-a variability in shallow (2–3 m) embayments of a eutrophic reservoir, Jordan Lake, North Carolina. One is a multiple linear regression (statistical) model and the other is a process-based (mechanistic) model. Both models are calibrated using a 15-year data record of chlorophyll-a concentration (2003–2018) for the seasonal period of cyanobacteria dominance (June–October). The mechanistic model includes a novel representation of vertical mixing and is calibrated in a Bayesian framework, which allows for data-driven inference of important process rates. Both models show that chlorophyll-a concentration is much more responsive to nutrient variability than mixing, light, or temperature. While both models explain approximately 60% of the variability in chlorophyll-a, the mechanistic model is more robust in cross-validation and provides a more comprehensive assessment of algal drivers. Overall, these models indicate that nutrient reductions, rather than changes in mixing or background turbidity, are critical to controlling cyanobacteria in a shallow eutrophic freshwater system.