## 3 Results
### Correlation and Multiple Regression of Soil Chemical Properties and the Gene Copy Number
\begin{table}
\begin{tabular}{l l l l l l l l l l l l l l} \hline \hline
**Genes** & **pH** & **EC** & **OM** & **TN** & **P** & **K** & **Ca** & **Mg** & **DOC** & _Aamo_ & _Bamo_ & _nirK_ & _nosZI_ & _nosZII_ \\  & **15** & **dS m\({}^{-1}\)** & **\%** & **\%** & **mg kg\({}^{-1}\)** & **cmol” kg\({}^{-1}\)** & **mg kg\({}^{-1}\)** & **Copy Number \({}^{-1}\)** & **DyS** & \\ \hline _Aamo_ & \(-\)0.07 & \(-\)0.03 & 0.283 & 0.254 & 0.133 & 0.367 & 0.200 & \(-\)0.02 & 0.783 & \({}^{*}\) & 1.000 & 0.183 & \(-\)0.35 & 0.633 & 0.250 \\ _Bamo_ & 0.100 & 0.067 & 0.767 & \({}^{*}\) & 0.695 & 0.650 & 0.683 & \({}^{*}\) & 0.350 & 0.400 & 0.283 & 0.183 & 1.000 & 0.050 & 0.533 & 0.717\({}^{*}\) \\ _nirK_ & \(-\)0.63 & \(-\)0.25 & 0.050 & \(-\)0.05 & 0.117 & \(-\)0.30 & \(-\)0.333 & \(-\)0.03 & \(-\)0.35 & \(-\)0.03 & 0.050 & 1.000 & \(-\)0.50 & 0.167 \\ _nosZI_ & 0.217 & 0.500 & 0.750 & \({}^{*}\) & 0.780 & \({}^{*}\) & 0.583 & 0.667 & \({}^{*}\) & 0.717\({}^{*}\) & 0.567 & 0.717\({}^{*}\) & 0.633 & 0.533 & \(-\)0.50 & 1.000 & 0.650 \\ _nosZII_ & 0.000 & 0.250 & 0.750 & \({}^{*}\) & 0.763 & \({}^{*}\) & 0.767 & \({}^{*}\) & 0.717\({}^{*}\) & 0.583 & 0.467 & 0.700 \({}^{*}\) & 0.250 & 0.717 \({}^{*}\) & 0.167 & 0.650 & 1.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlation coefficient showing the relationship of the edaphic factors and the gene copy number. Visualization and Analysis of Soil Variabilities Found in the Different Paddy Fields Established through Decades of Long-Term Compost and NPK + Compost Fertilization  
A summary of the overall effects of the fertilization treatments on the paddy fields' variabilities was achieved through the PCA of their gene abundances and soil edaphic factors (Table 5 and Figure 3). Eigenvalues higher than 1 were observed for PC 1-5 with cumulative loading of 96%. PC1 and PC2 contributed 50% and 17%, respectively, resulting in an overall loading of 67%. The greatest loading effect for PC1 came from the individual loading factors TN, K, NO\({}_{3}\).N, OM, and Ca, followed by _nosZI_, P\({}_{2}\)O\({}_{5}\), and _nosZII_, cumulating in a 50% soil variability. A 17% of the overall soil variability was attributed to PC2 contributed by DOC, NH\({}_{4}\).N, archeal _amoA_, and Na. The ordination plot of the PCA visualized the overall variability in soil the edaphic factors and the abundances of the nitrogen cycling-related genes and their effect on the clustering of soil treatments. The PC1 clearly separates the unfertilized (NF) from the Compost and NPK + compost treatments. The prominent clustering of the NF treatment is partly attributed to the effect of the _nirK_ gene abundance. The PC2 further created a sub-clustering of the Compost and NPK + compost treatments. The distinct separation of the Compost treatment is mainly attributed to DOC, EC, and archeal _amoA_ gene abundance, and the Na loading factor. On the other hand, the clustering of the NPK + compost treatment is partly affected by NH\({}_{4}\).N, pH, P, Ca, Mg, and DION. The cumulative effects of all of the loading factors coming from gene abundances and soil edaphic factors contribute to the overall soil variability and clustering of the characteristic paddy fields established through decades of long-term compost and NPK + compost fertilization. Figure 2: Linear relationship between abundances of nitrogen cycling-related genes and their major soil chemical determinant selected based on multiple regression analysis: the archaeal _amoA_ gene abundance and dissolved organic carbon (DOC) (**A**), the bacterial _amoA_ gene abundance and total nitrogen (**B**), the _nosZI_ gene abundance and total nitrogen (**C**), and the _nosZII_ gene abundance and total nitrogen (**D**).