2.2 SOC and TN storage estimation and statistical analysis
SOC and TN storage were calculated using the FD and ESM methods respectively. The lightest soil mass was referred as the equivalent soil mass (Lee et al., 2009):
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ FDstock}_{\text{SOC\ or\ TN}}=\text{Con}_{\text{SOC\ or\ TN}}*\text{Soil}_{\text{BD}}*h*10^{-1}\)(1)
\(\text{\ \ \ \ \ \ \ \ \ ESMstock}_{\text{SOC\ or\ TN}}=\text{FDstock}_{\text{SOC\ or\ TN}}-M_{\text{ex}}*\frac{C_{\text{sn}}}{1000}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\)(2)\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ M}_{\text{ex}}=\sum_{1}^{n}\text{Soil}_{\text{BD}}*100-M_{\text{ref}}\)(3)
where \(\text{FDstock}_{\text{SOC\ or\ TN}}\) and\(\text{ESMstock}_{\text{SOC\ or\ TN}}\) represent the SOC or TN storage estimated based on the FD and ESM methods, respectively;\(\text{Con}_{\text{SOC\ or\ TN}}\) indicates the concentration of SOC or TN; \(\text{Soil}_{\text{BD}}\) and \(h\) represent soil bulk density and sample depths, respectively; \(M_{\text{ref}}\ \)is the reference soil mass (the lightest soil mass), and \(M_{\text{ex}}\ \)is the excess soil mass. All the constants in Eqs. (1)-(3) are unit conversion factors.
Due to unavailable soil BD data in some studies, the following non-linear equations were used to estimate the BD (Song et al., 2005):
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{Soil}_{\text{BD}}=1.3770*Exp\left(-0.0048*\text{Con}_{\text{SOC}}\right)\text{\ \ \ }\)(4)
where BD is soil bulk density (Mg m-3) with a given concentration of SOC (g kg-1). In addition, 1.3770 and -0.0048 are empirical coefficients.
Different soil depths were sampled within this study (0-20, 20-30, 30-40, 40-60, 60-100 cm). In order to make comparable estimates of SOC or TN changes to the same depth and to include more experimental results from particular regions (southwest China), the storage changes with irregular sample depths (h, cm) were adjusted to those of the top 20 cm of the soil sample using following equations (Yang et al., 2011):
\(Y=1-\beta^{h}\)(5)\(\backslash n\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ C}_{20}=\frac{1-\beta^{20}}{1-\beta^{h}}*C_{h}\)(6)
where \(Y\) is the cumulative proportion of the SOC or TN storage from the surface to a specific depth h (cm); \(\beta\) is the relative rate of decrease in the SOC or TN storage at specific depth (0.9786 for SOC and 0.9831 for TN, respectively) (Jobbágy and Jackson, 2000; 2001).\(\text{\ \ C}_{20}\) is the expected SOC or TN storage adjusted to the top 20 cm soil layer at a specific site; h is the sample depths available in each study (cm); \(C_{h}\) is measured SOC or TN storage at sample depth \(h\) (cm) at a specific site.
We used the mean (Mean), standard deviation (SD), sample size (\(n\)), standard error (SE) and 95% confidence interval (95%CI) to characterize the variations of selected datasets. The SE and 95%CI were calculated as follows:
\(SE=SD/\sqrt{n}\) (7)
If the SD data was missing, we would convert the coefficient of variation of the entire database (Geisseler and Scow, 2014).
The natural logarithm of the response ratio (RR) was employed to quantify the effect (Hedges et al., 1999):
\(\ \ \ \ \ \ \ \ \ \ lnRR=\ln{(\text{RR}_{d}}/\text{RR}_{c})=ln\text{RR}_{d}-lnRR_{C}\)(8)
where \(\text{RR}_{d}\) and \(\text{RR}_{c}\) are the values of the control and experimental groups.
The statistical distribution of the lnRR calculated in this way was found to be nearly normal, and only minor biases were detected (Hedges et al., 1999). The variances (V) were calculated by:
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ V=\frac{\text{SD}_{d}^{2}}{n_{d}M_{d}^{2}}+\frac{\text{SD}_{c}^{2}}{n_{c}M_{c}^{2}}\)(9)
where \(\text{SD}_{d}\) and \(\text{SD}_{c}\) represent the standard deviation of the control group and the experimental group, respectively. In general, the land use pattern (native forest) with the least degree of damage is the control group in deforestation, and the cropland with the greatest intensity of activity disturbance is the land restoration control group; nd and nc are the numbers of control and experimental groups; \(M_{d}\) is the average of SOC or TN storage in the control group, and \(M_{\text{c\ }}\)is the average of the SOC or TN storage corresponding to the experimental group.
The reciprocal of the variance was used as the weight (W) for each lnRR:
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ W=1/V\)(10)
The overall mean response ratio (lnRR++) and the SE of lnRR++ were then calculated as:
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ lnRR}_{++}=\frac{\sum_{i=1}^{m}{\sum_{j=1}^{k}W_{\text{ij}R_{\text{ij}}}}}{\sum_{i=1}^{m}{\sum_{j=1}^{k}W_{\text{ij}}}}\)(11)\(\backslash n\ \ \ \ \ \ \ \ \ \ \ \ SE\left(\text{lnRR}_{++}\right)=1/\sqrt{\sum_{i=1}^{m}{\sum_{j=1}^{k}W_{\text{ij}}}}\)(12)
The lnRR++ and 95%CI can be converted by [EXP (lnRR++) - 1] × 100%. We defined that if the 95%CI is larger than zero, the effect of the treatment is considered as significant.
Statistical analyses were performed with IBM SPSS 20.0 (SPSS Inc., Chicago, USA). The normality of the data was tested by using the Shapiro-Wilk test (Stephens,1975). Because some datasets failed to meet the assumptions underlying parametric statistical tests, nonparametric procedures were applied to conduct further analysis. Correlation analysis was applied to examine relationships of response change of SOC and TN storage (only for cumulative SOC/TN storage on ESM basis) with other impact factors: climate factors, and geographical factors, the duration of LUCCs, and soil physicochemical properties. All differences discussed are significant at the P < 0.05 probability level unless otherwise stated.