Data analyses
The meteorological data was obtained fromhttp://cdc.cma.gov.cn/home.do, where the mean value of 30
years (1979-2009) was used for analysis. The piecewise SEM (Lefcheck
2016) were employed to evaluate the direct and indirect effects of
predictor variables (including geographic and climatic factors and leaf
functional traits) on trichome density. A backward stepwise selection
procedure was used to simplifying the model until the AIC value began to
increase and P value was above 0.05. The sampled sites were
considered as a random effect with linear mixed models (LMMs) in our
analyses (Lefcheck 2016, Ali et al 2020). For all endogenous variables,
the conditional R2c (all factors, including the random
effect) and marginal R2m values were estimated their
variations (Lefcheck 2016). In the piecewise SEM, the effect of each
predictor on the endogenous variables was accounted for through their
standardized path coefficients. The piecewise SEM and LMM models were
separately implemented with the piecewise SEM package (Lefcheck 2016)
and the nlme R package. To avoid the model complexity, all geographic
variables (latitude, longitude and altitude) and climatic variables
(MAT, MAP, aridity index (AI), potential evapotranspiration (PET), and
MMSR) were clustered by principal component analysis (PCA). All
variables, used in piecewise SEM, were log-transformed and then
standardized. Moreover, one-way ANOVA was employed to test the
differences in trichome density between the field samples and common
garden population samples. To determine the direction of trait variation
in response to environmental changes, linear regressions were performed
to correlate environmental factors with trichome density. The above
analyses were carried out with R version 3.6.1 (R Development Core Team,
available from www.r-project.org/, accessed 2019) and SigmaPlot 10.0
(Systat Software, Inc., R.ichmod, CA, USA).