Nonlinear forcing of carbon, nitrogen and phosphorus distribution revealed by a hybrid machine learning-constraint line approach in the Pearl River Basin, China

The coupled cycles of carbon, nitrogen and phosphorus in multi-media are essential for elements geochemical cycles and ecosystem functions. However, it makes more challenges in identifying the driving mechanism for spatial elements distribution, as climate change and human activities are complex. In this study, a machine learning-coupled constraining theory (ML-CLT) model for identifying environmental drivers had been proposed. The impact mechanisms of spatial element distribution had been deeply explored from key driving factors. Coupling-decoupling processes across multiple media had been analyzed through a partial least squares structural equation model (PLS-SEM). We have moved beyond the traditional approaches for judging the environment drivers based on a single importance. Meanwhile, the variable potential of environment drivers is introduced to quantify the overall contribution on different elements heterogeneous distribution. The post-optimized constrained line theory compensates for the loss of factor importance by random forest. The results show that carbon, nitrogen, and phosphorus had exhibited a coexistence of randomness and clustering in spatial distribution. Precipitation (R² = 0.94) and temperature (R² = 0.87) had been identified by the ML-CLT model as factors with the strongest constraining effects. Despite low importance in Random Forest (RF) model, LULC had displayed the greatest regulatory potential for most elements (e.g., phosphorus in water and soil). Coupling analysis had revealed that carbon − nitrogen and carbon − phosphorus coupling relationships had become highly unstable under high-intensity human activities.