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