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 .