Effects of long-term fertilisation on aggregates and dynamics of soil organic carbon in a semi-arid agro-ecosystem in China

Sampling

The soil was sampled annually in October from 1998 to 2012 to a depth of 20 cm. Three replicate soil samples were randomly excavated in each plot using a soil drill (diameter, 4 cm) and then mixed to produce a composite sample. The samples for 1998–2012 were used for the analysis of changes over time. The samples for 1998–2011 (126 samples) had been stored in the station’s soil library and were collected from one of the three replicate treatment plots. The samples for 2012 (27 samples) were used to examine the effects of fertilisation on aggregate distribution, D_v, and SOC content. Visible plant residues were removed, and the samples were manually broken into fragments <10 mm and air-dried at room temperature. Each sample was passed through a 1-mm sieve for determining the distribution of the aggregates, and a subsample was then ground to pass through a 0.25-mm sieve for the determination of total SOC content.

Determination of aggregate distribution

The soil samples were soaked in distilled water for 24 h and mechanically dispersed by ultrasonication for 5 min (Xiao et al., 2014). The samples were analysed with a Longbench Mastersizer 2000 (Malvern Instruments, Malvern, England).

Determination of SOC content

SOC content was determined by Walkley and Black dichromate oxidation (Nelson & Sommers, 1982).

D_v of aggregates

D_v was calculated as:

(1)${\displaystyle \frac{V\left(r<R_i\right)}{V_T}={\left(\frac{R_i}{R_{\max }}\right)}^{3-D_v}}$ where r is the particle diameter, R_i is the diameter of size class i, V (r<R_i) is the total volume of particles with diameters <R_i, V_T is the total volume of particles, R_max is the maximal particle diameter, and D_v is the volume fractal dimension. Logarithms were derived for both sides of the equation, and D_v was obtained from the slopes of the double-logarithmic curves that fit the data.

Path analysis

Path analysis is a supplement and extension of regression analysis that partitions simple correlation coefficients into direct and indirect effects through definite path coefficients among the variables and distinguishes between correlation and causation (Bai et al., 2014; Wright, 1934; Zhang et al., 2005).

The aggregates were categorised into nine size classes: <0.002, 0.002–0.005, 0.005–0.01, 0.01–0.05, 0.05–0.1, 0.1–0.2, 0.2–0.25, 0.25–0.5, and 0.5–1 mm. These nine size classes were categorised into three fractions: macroaggregates (0.25–1 mm), microaggregates (0.05–0.25 mm), and a silt + clay fraction (<0.05 mm). Backward-stepwise regression was used to identify the size class that explained most of the variation in D_v, with criteria for the stepwise regression of probability-of-F-to-enter ≤0.05 and probability-of-F-to remove ≥0.10. The size classes that did not significantly contribute to D_v at P = 0.10 were therefore not included in the regression model.

Path diagrams were used to evaluate the relationships between eight selected size classes and D_v (Fig. 2). The direct effects of the aggregates on D_v are represented by single-headed arrows, and the coefficients of the correlations between the size classes are represented by double-headed arrows. The direct effects are termed path coefficients and are standardised partial regression coefficients in the multiple linear regression of aggregates on D_v (Basta, Pantone & Tabatabai, 1993). The indirect effects are determined from the product of the simple correlation coefficient between aggregate size classes and the path coefficient. The results of the path analysis were determined from the equations (Williams, Demment & Jones, 1990):

(2)${\displaystyle r_{19}=P_{19}+r_{12}{P}_{29}+r_{13}{P}_{39}+r_{14}{P}_{49}+r_{15}{P}_{59}+r_{16}{P}_{69}+r_{17}{P}_{79}+r_{18}{P}_{89}}$ (3)${\displaystyle r_{29}=r_{12}{P}_{19}+P_{29}+r_{23}{P}_{39}+r_{24}{P}_{49}+r_{25}{P}_{59}+r_{26}{P}_{69}+r_{27}{P}_{79}+r_{28}{P}_{89}}$ (4)${\displaystyle r_{39}=r_{13}{P}_{19}+r_{23}{P}_{29}+P_{39}+r_{34}{P}_{49}+r_{35}{P}_{59}+r_{36}{P}_{69}+r_{37}{P}_{79}+r_{38}{P}_{89}}$ (5)${\displaystyle r_{49}=r_{14}{P}_{19}+r_{24}{P}_{29}+r_{34}{P}_{39}+P_{49}+r_{45}{P}_{59}+r_{46}{P}_{69}+r_{47}{P}_{79}+r_{48}{P}_{89}}$ (6)${\displaystyle r_{59}=r_{15}{P}_{19}+r_{25}{P}_{29}+r_{35}{P}_{39}+r_{45}{P}_{59}+P_{59}+r_{56}{P}_{69}+r_{57}{P}_{79}+r_{58}{P}_{89}}$ (7)${\displaystyle r_{69}=r_{16}{P}_{19}+r_{26}{P}_{29}+r_{36}{P}_{39}+r_{46}{P}_{49}+r_{56}{P}_{59}+P_{69}+r_{67}{P}_{79}+r_{68}{P}_{89}}$ (8)${\displaystyle r_{79}=r_{17}{P}_{19}+r_{27}{P}_{29}+r_{37}{P}_{39}+r_{47}{P}_{49}+r_{57}{P}_{59}+r_{67}{P}_{69}+P_{79}+r_{78}{P}_{89}}$ (9)${\displaystyle r_{89}=r_{18}{P}_{89}+r_{28}{P}_{29}+r_{38}{P}_{39}+r_{48}{P}_{49}+r_{58}{P}_{59}+r_{68}{P}_{69}+r_{78}{P}_{79}+P_{89}}$ where r_ij is the simple correlation coefficient between aggregate size class and D_v, P_ij is the path coefficient between aggregate size class and D_v (direct effects), and r_ijP_ij is the indirect effect of aggregate size class on D_v. Subscript designations 1–9 represent the <0.002, 0.002–0.005, 0.005–0.01, 0.05–0.1, 0.1–0.2, 0.2–0.25, 0.25–0.5, 0.5–1 mm aggregates and D_v, respectively.

The residual, U, is an unmeasured variable in the path model that represents the unexplained part of an observed variable and is calculated as (Ige, Akinremi & Flaten, 2007):

(10)${\displaystyle U=\sqrt{1-R^2}}$ where R² is the coefficient of determination of the multiple regression model between aggregate size classes and D_v.

The coefficient of determination for each factor denotes the degree of relative determination between cause and effect, which can be determined by (Bai et al., 2014; Chen et al., 2014):

(11)${\displaystyle D_{yxixj}={\left(P_{yi}\right)}^2,\left(i=j\right);D_{yxixj}=2P_{yi}\times P_{yj}\times r_{ij},\left(i,j=1,2,\dots ,n,i<j\right)}$ where D_yxixj is the coefficient of determination, and y is D_v.