Use statistical machine learning to detect nutrient thresholds in Microcystis blooms and microcystin management

•A strategy of the Bayesian framework was developed to guide Microcystis blooms and microcystin risk.•Total phosphorus influences the biomass of Microcystis, whereas total nitrogen determines the risk of microcystin.•The nutrient criteria are crucial for reducing the risk of microcystin.•Critical nutrient thresholds are lake-dependant and counteracted by temperature warming. The frequency of toxin-producing cyanobacterial blooms has increased in recent decades due to nutrient enrichment and climate change. Because Microcystis blooms are related to different environmental conditions, identifying potential nutrient control targets can facilitate water quality managers to reduce the likelihood of microcystins (MCs) risk. However, complex biotic interactions and field data limitations have constrained our understanding of the nutrient-microcystin relationship. This study develops a Bayesian modelling framework with intracellular and extracellular MCs that characterize the relationships between different environmental and biological factors. This model was fit to the across-lake dataset including three bloom-plagued lakes in China and estimated the putative thresholds of total nitrogen (TN) and total phosphorus (TP). The lake-specific nutrient thresholds were estimated using Bayesian updating process. Our results suggested dual N and P reduction in controlling cyanotoxin risks. The total Microcystis biomass can be substantially suppressed by achieving the putative thresholds of TP (0.10 mg/L) in Lakes Taihu and Chaohu, but a stricter TP target (0.05 mg/L) in Dianchi Lake. To maintain MCs concentrations below 1.0 μg/L, the estimated TN threshold in three lakes was 1.8 mg/L, but the effect can be counteracted by the increase of temperature. Overall, the present approach provides an efficient way to integrate empirical knowledge into the data-driven model and is helpful for the management of water resources.