2.3 Soil quality evaluation
The soil quality index (SQI) was evaluated by principal component
analysis (PCA) with soil physico-chemical properties, enzyme activities
and microelements as indicators. The determination procedure includes
three steps: (1) selecting minimum data set (MDS) of indicators; (2)
scoring the MDS indicators using a standard scoring function; (3)
calculating soil quality index (SQI) of five forest types. First, a
variety of soil properties including texture, bulk density, nutrients,
enzyme activities and microelements were added to the indicator dataset,
and correlation analysis was conducted. Secondly, all indicators were
analyzed by PCA, with a varimax rotation to enhance interpretability of
the uncorrelated components (Bernhard Flury & Riedwyl, 1988). Only the
principal components (PC) with eigenvalues>1 and absolute loading
values ≥0.5 can identify representative MDS for further analysis
(Bastida, Luis Moreno, Hernández, & García, 2006). Third, to avoid
information loss and data redundancy, the norm value of each indicator
was calculated. For each PC, the selected indicators obtained the norm
value within 10% of the maximum weighted load for the MDS1. When more
than one indicator was retained in a PC, correlation analysis was
conducted to determine whether these indicators were redundant (Andrews,
Karlen, & Mitchell, 2002). If high variables were highly correlated
(r ≥0.6) with the maximum value, only the highest factor loading
was retained, and the rest would be eliminated from the dataset. Fourth,
a standard scoring function was employed for each indicator in MDS2
(ranging from 0 to 1) (Andrews et al., 2002). The weight of an indicator
was equal to the ratio of its communality with the sum of communalities
of all indicators.
Type S:
\begin{equation}
f(x_{i})=\left\{\begin{matrix}1.0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ,x_{i}\geq x_{2}\\
0.1+\frac{0.9\left(x_{i}-x_{1}\right)}{x_{2}-x_{1}}\ \ ,x_{1}<x_{i}x_{2}\\
0.1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ,x_{i}\leq x_{1}\\
\end{matrix}\right.\ \nonumber \\
\end{equation}(2) Type reverse S:
\begin{equation}
f(x_{i})=\left\{\begin{matrix}0.1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ,x_{i}\geq x_{2}\\
0.1+\frac{0.9\left(x_{2}-x_{i}\right)}{x_{2}-x_{1}}\ \ ,x_{1}<x_{i}x_{2}\\
1.0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ,x_{i}\leq x_{1}\\
\end{matrix}\right.\ \nonumber \\
\end{equation}where f (x) is the score of the indicator ranging from 0.1 to 1, X
is the value of soil indicator, X1 and
X2 are the minimum and maximum values of indicator,
respectively.
Finally, following scoring and weighting for all indicators in the MDS2,
SQI was calculated as follows:
SQI=\(\sum_{i=1}^{n}W_{i}\times S_{i}\)\(\sum_{i=1}^{n}W_{i}\times F_{i}\)
where SQI is the soil quality index ranging from 0 to 1.0,
Wi is the weight of each indicator, Fiis the indicator score, and n is the number of indicators in the final
MDS.