Statistical analysis
For each study, meta-analysis requires the mean, standard deviations (SD) and replicate number (n ) for the N fertilized (X F) and control (X C) treatments. All these data were extracted from the text, tables, figures, or supplemental materials of these publications. If data were presented by figures, Engauge Digitizer (v 10.4) was used to obtain numeric data (https://github.com/markummitchell/engauge-digitizer/releases). If standard errors (SE) were reported, these were transformed to standard deviation (SD) with to the equation:\(\text{SD}=SE\times\sqrt{n}\). Unidentified error bars were assumed to represent SE.
Natural log response ratio (lnRR ) was calculated to access the responses of soil microbial biomass to N fertilization (Hedges et al. 1999). lnRR was calculated as:
\(\ln RR=ln(X_{F}/X_{C})\) (1)
The variance (vi ) of lnRR was approximated as:
\(v_{i}=\frac{({\text{SD}_{F})}^{2}}{n_{F}({X_{F})}^{2}}+\frac{({\text{SD}_{C})}^{2}}{n_{C}({X_{C})}^{2}}\)(2)
where SDF and SDC are the SD for the fertilized and control treatments, respectively;nF and nC are the sample sizes in fertilized and control treatments, respectively
In the analysis, we used the number of replications for weighting:
\(Wr=(N_{F}\times N_{C})/(N_{F}+N_{C})\) (3)
where Wr is the weight associated with each lnRRobservation, NF and NC are the numbers of replications in the fertilized and control.
Publication bias was assessed using funnel plots, by applying a regression test for funnel plot asymmetry (Veroniki et al. 2016). Normal quantile–quantile (Q-Q) plots were inspected to assess normality of the residuals. Only the results where corresponding Q-Q and funnel plots were satisfactory are presented here. For each mean effect size, 95 % confidence interval (CI) were calculated. If the 95 % CI of lnRR did not overlap with 0, the effect of N fertilization on the variable differs significantly at α = 0.05 between the N fertilized and control treated. The percentage changes were presented in the figures as back transformed from the log response ratio (\([e^{\ln\text{RR}}-1]\times 100\%\)). Analysis of variance (ANOVA) was used to compare the effects of different N on soil microbial biomass.
In order to estimate whether the responses of soil microbial biomass (lnRR ) was significantly affected by ecological factors (such as MAT, MAP, background N deposition level, N application rate and application duration) under different N types, regression analyses were used (Humbert et al. 2016; Zhang et al. 2018). The restricted maximum likelihood (REML) method was used to produce final models, which were checked to ensure they conformed to modelling assumptions. The analyses were conducted using the lme4 package in R version. The model were established as follows:
η = A 0 + A 1 ×F 1 + A 2 ×F 2 + A 3 ×F 3 ··· A i ×F i (4)
In this model, η is the response ratio (lnRR ) of various microbial characteristics, such as fungal biomass;F 1, F 2 ···F i are variates that may affect lnRR , such as N addition rate, N fertilized duration, MAT and MAP;A 0, A 1,A 2 ··· A i are coefficients of each variates. In some models, some variates were transformed.Supplementary Online Material 4 listed all the 13 assumed models. Akaike information criterion (AIC) values were used to compare the fit of each model to the data. The model with lower AIC value was the best-fit model.
All the statistical analyses were performed using R 3.5.3 (R Core Team, 2018). The codes were shown inSupplementary Online Material 5 .