Deciphering nonlinear effects of climate and eutrophication synergies on Microcystis blooms using a causal inference framework.

Harmful cyanobacterial blooms (CyanoHABs) pose a significant threat to global water quality. Although eutrophication and climate change are recognized as key drivers of CyanoHABs proliferation, their synergistic effects remain elusive, hindering effective mitigation strategies. Here, we present a causal inference framework that leverages state-space reconstruction and empirical dynamic modeling to unravel the complex, nonlinear interactions governing CyanoHABs dynamics. Focusing on Microcystis blooms dynamics in Dianchi Lake (China), our approach uniquely integrates causal inference with time-series embedding, reconstructing the ecosystem's hidden dynamics in a higher-dimensional geometric space. This foundation enables us to rigorously quantify causal drivers-such as nutrient loading and temperature-while overcoming the limitations of traditional correlation-based analyses. Our causal network analysis reveals distinct nonlinear responses of chlorophyll-a (Chl-a) concentration and Microcystis density to different nutrient drivers. Specifically, we found that in-lake total phosphorus (TP) exerts a stronger causal influence on overall algal dynamics than total nitrogen (TN). In contrast, external nutrient loading shows greater influence over Microcystis density compared to in-lake nutrients. Through scenario simulations, we further demonstrate that rising air temperatures amplify Chl-a concentration and Microcystis biomass through increased water temperatures, whereas precipitation-induced nutrient changes preferentially stimulate Chl-a production over Microcystis growth. Notably, we identified contrasting seasonal response patterns, with Chl-a exhibiting greater sensitivity to dry-season conditions while Microcystis density responded more strongly to wet-season drivers. By bridging mechanistic understanding and predictive modeling, our work offers a transformative tool for forecasting and managing CyanoHABs in changing climates.