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. Simpsonâs evenness index (đ¸)
(Simpson 1949) was adopted to evaluate
the community evenness. Speciesâ 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 Simpsonâs 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, Simpsonâs 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.