## 3 Results
### Multi-Dimensional Correlation Analysis  
It shows the correlations between maize yield and soil inorganic nitrogen contents, Gs, endogenous hormone concentrations, nitrogen metabolism-related enzyme activities, and photosynthetic enzyme activity (Figure 6A). There were significant correlations between maize yield and soil NH\({}_{4}\)+-N and NO\({}_{3}\)-N contents. The combined application of urea and FA in the U+FA treatment provided sufficient nitrogen to meet the demand of maize during its critical growth stages, resulting in significantly higher yield. Plant endogenous hormones greatly influence plant growth and development, and they are linked to carbohydrate accumulation and yield. At the V12 stage, the IAA concentrations of maize root and leaves were significantly larger in the U+FA treatment than in the U treatment, stimulating the growth of root and the elongation of stems. Furthermore, maize yield was significantly related to Gs, GOGAT, IAA, NR, and GS in leaves and NR in root. The higher concentrations of nitrogen metabolism-related enzymes (e.g., GOGAT, NR, and GS) in the U+FA treatment indicate more active nitrogen assimilation and metabolism.  
As demonstrated by the correlation analysis, the results of the PCA confirmed the Mantel test (Figure 6B). The PCA indicated that the 23 variables were divided into PC1 (81.6%) and PC2 (5.7%). The contribution of FA to responding to these parameters was clear when compared to treatments of U. Meanwhile, the concentration and activities of C and N metabolism-related enzymes were significantly affected by U combined with FA solution. In addition, NO\({}_{3}\)-N content and Gs were dispersed in the second quadrant and had a negative relationship with the other parameters, which were mostly distributed in the first and fourth quadrants. There was a strong correlation between maize yield and PEPC. The PEPC concentration in leaves was significantly greater in the U+FA treatment.  
Figure 6: The correlations between maize yield, concentrations of nitrogen metabolism-related enzymes, concentrations of photosynthetic key enzymes, concentrations of endogenous hormones, and soil available nutrients. (**A**) Mantel test. The thickness of a line indicates the strength of the correlation. The area of a rectangle represents the magnitude of the correlation. Red denotes a positive correlation and blue represents a negative correlation. “**”, “**” and “**” indicate significant correlation at \(p<0.05\), \(p<0.01\) and \(p<0.001\), respective. (**B**) Principal component analysis showing the relationship among yield, NUE, soil nutrients, concentrations of nitrogen metabolism-related enzymes, concentrations of photosynthetic key enzymes of different treatment. (J): jointing stage; V: 12-leaf stage; L: leaves of maize; R: root of maize; Gs: stomatal conductance; IAA: auxin; ZR: zeatin nucleoside; NR: nitrate reductase; NiR: nitrite reductase; GS: glutamine synthetase; GSR: glutathione reductase; GOGAT: glutamate synthase; GLDH: glutamate dehydrogenase; Pn: net photosynthetic rate; Gs: stomatal conductance; Tr: transpiration rate; GA: gibberellin; ABA: abscisic acid; PEPC: phosphoenolpyruvate carboxylase).  
It's possible that U+FA treatment increased the activities of N metabolism-related enzymes, which increased the uptake of maize root nutrients and then affected the concentration of key enzymes in shoot photosynthesis, promoting the TCA cycle, increasing dry matter accumulation, and eventually increasing yield.