(3)
where, X i and Yi denote the measured and fitted δ values of the soil, respectively, andN is the number of available data.
The structural equation model is a multivariate statistical technique that has emerged as a synthesis of path analysis, factor analysis, and maximum likelihood analysis. It can partition direct and indirect effects and estimate the strengths of these multiple effects found in natural ecosystems. The structural equation model was constructed based on the significances of the linear regressions between the formation efficiency of mineral-protected SOM and all the available mineralogical properties and the compositional properties of litter and microbial- residues in SOM as well as microbial communities, and the significances of selected parameters in stepwise regression. The fit of the final structural equation model was evaluated usingχ 2 and P tests (P > 0.05 of chi-squared test indicated overall fit of the data with the model). The structural equation model analysis was conducted using AMOS 21.0 software (Amos Development Corporation, Chicago, IL, USA).
Principal component analysis of functional C groups expressed as relative abundance of the whole C spectrum or functional microbial groups expressed as the relative abundance of whole phospholipid fatty acid profiles was conducted to determine the effects of the litter and clay mineral types. The principal component analysis was performed using SPSS 21.0 software.