2.4 Data analyses
All data analysis and plotting were performed in R 3.5.1 (https://www.r-project.org/) using the nlme , vegan,and ggplot2 packages. All original data were tested for normality prior to the statistical analysis using the Shapiro-Wilk normality method, and log-transformed if necessary. All data used in this study are available from the figshare (https://figshare.com/s/4e7061a904f66d1a4504) and from the online supplementary file.
Relative height (RH), relative abundance (RA) and relative cover (RC) were calculated by normalizing the species-specific absolute height, abundance and cover against the total height, abundance and cover for each plot. Simpson’s evenness index (𝐸) (Simpson 1949) was adopted to evaluate the community evenness. Species’ importance value (IV) was used to assess species-specific dominance, which is quantified as the mean of relative height, relative abundance, and relative coverage (Whittaker 1965).
\(RH=\frac{\text{Height\ of\ a\ species}}{\text{Height\ of\ all\ species}}\ \times 100\%\)(1),
\(RA=\frac{\text{Abundance\ of\ a\ species}}{\text{Abundance\ of\ all\ species}}\ \times 100\%\)(2),
\(RC=\frac{\text{Coverage\ of\ a\ species}}{\text{Coverage\ of\ all\ species}}\ \times 100\%\)(3),
\(E=\frac{D^{{}^{\prime}}}{S}\) (4),
\(D^{{}^{\prime}}=1/\sum_{i=1}^{S}\text{RA}_{i}^{2}\) (5),
\(IV=\frac{RH+RA+RC}{3}\) (6),
where \(D^{{}^{\prime}}\) is the Simpson’s reciprocal indices of diversity (Simpson 1949), S is the total number of species studied in this study (eight) and \(\text{RA}_{i}\) is the relative abundance for each species in each plot. Experimental warming-induced changes in each variable were calculated from the paired plots per block:
\(Warming-induced\ changes=\frac{W_{v}-A_{v}}{A_{v}}\times 100\%\)(7),
where \(W_{v}\) and \(A_{v}\) were observed values from warming and ambient treatments, respectively.
We used linear mixed-effects (LME) models (Zuur et al. 2009) to assess the effects of warming on soil temperature, soil moisture, soil inorganic N, species-specific phenology, Simpson’s evenness index and species dominance. All these variables were continuously observed from 2011 to 2013. In these LME models, we set warming, year, and their interactions as fixed effects and plot nested within block as random effects, because. We assessed the impacts of warming on plant phenology phases and species dominance separately for each species. Residuals and residual variances for all variables satisfied the assumptions of normality and homogeneity.
Linear mixed effects models was also used to explore the relation between warming-induced shifts in species-specific plant phenology and the corresponding changes in species dominance. To account for the variations, block, year and species were considered as random effects in those LME models. Redundancy analysis (RDA) with treatment (ambient and warm) and environmental factors (soil temperature, soil moisture, and soil inorganic N) as explanatory variables was utilized to explore the potential factors affecting species phenology and dominance. The importance of each explanatory variable was calculated by forward selection with 999 unrestricted permutations. The RDAs were performed separately for each plant phenological event and for species dominance.