Prediction of nano, fine, and medium colloidal phosphorus in agricultural soils with machine learning

Soil colloids have been shown to play a critical role in soil phosphorus (P) mobility and transport. However, identifying the potential mechanisms behind colloidal P (P_coll) release and the key influencing factors remains a blind spot. Herein, a machine learning approach (random forest (RF) coupled with partial dependence plot analyses) was applied to determine the effects of different soil physicochemical parameters on P_coll content in three colloidal subfractions (i.e., nano- (NC): 1-20 nm, fine- (FC): 20-220 nm and medium-sized colloids (MC): 220-450 nm) based on a regional dataset of 12 farmlands in Zhejiang Province, China. RF successfully predicted P_coll content (R² = 0.98). Results showed that colloidal- organic carbon (OC_coll) and minerals were the major determinants of total P_coll content (1-450 nm); their critical values for increasing P_coll release were 87.0 mg L^-1 for OC_coll, 11.0 mg L^-1 for iron (Fe_coll) or aluminium (Al_coll), 2.6 mg L^-1 for calcium (Ca_coll), 9.0 mg L^-1 for magnesium (Mg_coll), 2.5 mg L^-1 for silicon (Si_coll), and 1.4 mg L^-1 for manganese (Mn_coll). Among three colloidal subfractions, the major factors determining P_coll were soil Olsen-P (P_Olsen; 125.0 mg kg^-1), Ca_coll (2.5 mg L^-1), and colloidal P saturation (21.0%) in NC; Mn_coll (1.5 mg L^-1), Mg_coll (6.8 mg L^-1), and P_Olsen (135.0 mg kg^-1) in FC; while Mn_coll (1.5 mg L^-1), Al_coll (2.5 mg L^-1), and Fe_coll (3.8 mg L^-1) in MC, respectively. OC_coll had a considerable effect in the three fractions, with critical values of 80.0 mg L^-1 in NC or FC, and 50.0 mg L^-1 in MC. Our study concluded that the information gleaned using the RF model can be used as crucial evidence to identify the key determinants of different size fractionated P_coll contents. However, we still need to discover one or more easy-to-measure parameters that can help us better predict P_coll.