2.5 Data analysis
We used linear mixed-effect models to test for the effects of warming and N addition on plant dominance, flowering phenology and soil characteristics. We treated warming, N treatment, species and year as fixed factors, and the six blocks as random factors. P< 0.05 and P < 0.001 were used to indicate significance and strong significance. First Optimization software (7D-Soft High Technology Inc.) was used to fit the phenological equation. Structural equation modeling (SEM) was used to study the direct and indirect effects of temperature and nitrogen addition on dominance of different species. SEM analysis was performed by AMOS 21.0 (AMOS Development Co.). We employed chi-square (χ2), P value, the root means square error of approximation, normed fit index, incremental fit index and Akaike information criterion to evaluate the goodness of fit of the model. Other statistical analyses were performed in R4.2.2.