# A New Pabs Model for Quantitatively Diagnosing Phosphorus Nutritional Status in Corn Plants
## 4 Results  
### Establishment of Pc  
The APSIM model demonstrated strong performance in simulating two key agronomic indicators: plant phosphorus concentration (Figure 3a) and aboveground biomass (Figure 3b). For plant phosphorus concentration, the model achieved a high coefficient of determination (R\({}^{2}\) = 0.967) and a low root mean square error (RMSE = 0.027), indicating a strong agreement between observed and simulated values, with minimal deviations. Similarly, for aboveground biomass, the model exhibited robust predictive accuracy, with an R\({}^{2}\) of 0.956 and an RMSE of 0.219. These results highlight the model's ability to accurately reflect the dynamics of phosphorus uptake and biomass accumulation in maize. Figure 3a illustrates the linear relationship between observed and simulated plant phosphorus concentrations, where the regression Equation y = 0.986x + 0.039 closely aligns the two datasets. In Figure 3b, the relationship between observed and simulated aboveground biomass is represented by this Equation: y = 0.905x + 1.091, further demonstrating the model's strong predictive capability. Both diagrams show data points closely distributed along the 1:1 line, emphasizing the consistency of the model's simulations across a wide range of values. These findings suggest that, with localized parameter adjustments, the APSIM model effectively simulates both plant phosphorus concentration and aboveground biomass within acceptable ranges.  
Figure 3: Comparison between measured and simulated values: (**a**) phosphorus concentration and (**b**) aboveground biomass.  
Variance analysis was conducted on simulated data for plant aboveground biomass and phosphorus concentration across six growth stages: jointing, trumpet, tasseling, silking, grain formation, and milk maturity. This analysis identified phosphorus-sufficient and phosphorus-deficient points, with phosphorus-deficient points defined as those where biomass significantly increased with phosphorus application, and phosphorus-sufficient points showing no such increase. For phosphorus-deficient points, biomass within the same growth stage was plotted as the \(x\)-axis and the corresponding phosphorus concentration as the \(y\)-axis. Linear fitting was applied to derive a regression line. The average biomass of phosphorus-sufficient points was considered the maximum biomass, and a vertical line was drawn from this value on the regression line. The intersection of the vertical line with the regression line determined the minimum phosphorus concentration required for maximum growth, defined as the critical phosphorus concentration. The Pc values for the jointing, trumpet, tasseling, silking, grain formation, and milk maturity stages were calculated as 2.44, 2.05, 1.82, 1.66, 1.45, and 1.27 g/kg, respectively, with corresponding biomass values of 2.14, 4.52, 6.75, 9.32, 13.58, and 18.24 t/ha. These Pc values were then fitted against the maximum aboveground biomass to establish the Pc model (Figure 4). The coefficient of determination (R\({}^{2}\)) for the model was 0.98, indicating an extremely high level of significance (\(p\) < 0.001).