2.4 Statistical analysis
Community intra-annual biomass stability was calculated annually as μ/σ
(Ma et al., 2017), where μ is the intra-annual (from May to September)
temporal mean community biomass, and σ is its standard deviation. The
dominant species (Leymus chinensis , Agropyron cristatum ,Achnatherum sibiricum and Stipa grandis ) and functional
group biomass stability were
calculated annually using the same method. A higher value of community
stability means a lower intra-annual variability of community biomass
(Lehman et al., 2000).
Species asynchrony, which refers to the asynchronous response of species
to environmental fluctuations (Loreau et al., 2008), was calculated as:
\(\varphi_{x}=1-\sigma^{2}/\left(\sum_{l=1}^{T}\sigma_{l}\right)\)
where \(\varphi_{x}\) is intra-annual species synchrony,\(\sigma^{2}\ \)and \(\sigma_{l}\) are the variance of intra-annual
community biomass, and\(\ \)the standard deviation of biomass of speciesl in a plot with T species. Intra-annual species
asynchrony ranges between 0 and 1, higher values correspond to higher
asynchronous dynamics between species within the community is, and vice
versa.
Simple linear regression was used to analyze the inter-annual variation
of mean temperature and accumulated precipitation for different
distribution patterns, community biomass, relative biomass of functional
group/dominant species, community species richness, species richness of
functional group, and intra-annual biomass stability of
community/dominant species/functional group, with the slope representing
the rate of change. Stepwise regression and correlation analysis were
used to analyze the relationships between different distribution
patterns of mean temperature and accumulated precipitation with
community biomass intra-annual stability, relative biomass intra-annual
stability of functional groups, and relative biomass/biomass
intra-annual stability of dominant species. Simple regression is used to
analyze relationships between community biomass, functional groups
biomass intra-annual stability, species richness, dominant species
biomass intra-annual stability, species asynchrony and community biomass
intra-annual stability.
To address mechanisms determining community stability in response to
different seasonal change patterns in temperature and precipitation,
structural equation modeling (SEM) was employed to estimate how climatic
factors (mean temperature and accumulated precipitation in each
combination month) and biological factors (community biomass, species
richness, species asynchrony, functional groups intra-annual stability
and dominant species intra-annual stability) contribute to the
intra-annual stability of community biomass. Simple linear regression
was used to check bivariate relationships between all the variables and
filter the variables available to ensure that the linear model was
appropriate (Table S1). By testing for covariance, we found that none of
the climatic and biological factors showed significant covariance, so
all the variables were put into SEM for analysis (Table S2). Based on
regression weight estimation, the initial model was simplified and
non-significant path and state variables were eliminated, and the final
model contained only statistically significant paths that could not be
rejected (Table S3). Accuracy of the model was confirmed using a
Chi-squared test, the Akaike
Information Criterion (AIC) and the root-mean-square errors of
approximation (RMSEA). The model has a good fit when Chi-squared
test \(\chi^{2}\geq 0,\ \)P
> 0.05, and RMSEA ≤ 0.05. Structural equation model
analysis was performed by AMOS 22.0, and the SPSS 19.0 software package
was employed for all other tests.
RESULTS