*4.3. Data Analysis*

The means, standard deviations (SD), and coefficients of variation (CV) of the leaf element concentrations and their ratios, and soil physicochemical properties were calculated. Differences between QT and IM were evaluated by Independent-Samples *t*-test. Pearson correlations analysis was used to evaluate the relationship between *S. chamaejasme* leaf ecological stoichiometry and the soil physicochemical properties across the 29 sampling sites.

The degree of homeostasis (*H*) was calculated by plotting the log-transformed values of leaf elements and soil from 29 sites, where the *H* is the inverse of the slope [2]:

Log (leaf element concentration or stoichiometry) = α + (1/H) log (soil element concentration or stoichiometry).

To determine the degree of stoichiometric homeostasis, the method that was proposed by Persson et al. [12] was used. Standardized major axis regression analyses were conducted for C, N, P, K, and C:N:P:K ratios for leaves (The R package 'smatr 30 ) [72]. Since the slope was expected to be ≥ 0, one-tailed *t*-tests with α = 0.1 were used. If the regression was nonsignificant (*p* > 0.1), 1/H was set to zero, and the organism was considered 'strictly homeostatic'. Species with 1/H = 1 were considered not homeostatic. All the datasets with significant regressions and 0 < H < 1 were categorized as: 0 < 1/H < 0.25: 'homeostatic'; 0.25 < 1/H < 0.5: 'weakly homeostatic'; 0.5 < 1/H < 0.75: 'weakly plastic'; 1/H > 0.75 'plastic'. For 1/H > 1, 1/H close to 1 indicates weak or no stoichiometric homeostasis, and 1/H much larger than 1 indicates 'homeostatic'.

In order to determine the influence of climate factors, we obtained raw daily precipitation and temperature data (2010–2019) from the China Meteorological Administration and calculated the annual precipitation and temperature using the Kriging interpolation method in ArcGIS (ESRI (Environmental Systems Research Institute), Redlands, CA, USA). Therefore, climate data for the mean annual temperature (MAT) and mean annual precipitation (MAP) for the sample sites were obtained. Regression analyses were performed to determine the correlation of the leaf element contents and climate factors (MAT, MAP). Scatter plots were used to visualize the relationships among the leaf element contents and climate factors (MAT, MAP), and liner regression equations were developed.

We determined the relative importance of the soil, MAP, and MAT for leaf C, N, P, and K heterogeneity across all the sites, respectively, using mixed effects models. In these models, soil, MAP, MAT, and their interaction were fitted as fixed factors, and region was fitted as a random factor (The R package 'lme40 , 'lmerTest', 'glmm.hp', 'readxl', 'ade4). The soil data (soil C, N, P, K, AP, AK, AN, NN, WC, pH, Ec) were processed by principal component analysis (PCA; The R package 'Vegan', 'FactoMineR', 'factoextra'), then the number of first axis was used as the soil parameter (Tables S7–S9; Figure S2). Leaf C, N, P, K, and climatic data (MAP and MATA) heterogeneity were log-transformed to linearized the data.

Partial least squares path modeling (PLS-PM) was employed to explore the direct, indirect, and interactive effects between all the environmental variables for leaf element contents (The R package 'plspm'). The model included the following variables: Leaf elements (P, K), climate factors (MAT, MAP), and soil factors (K, AK, NN, and pH for leaf P in IM, P, AN and NN for leaf K in IM, P, AP, NN and pH for leaf P in QT, C, K, AP, WC, and pH for leaf K in QT), after testing for collinearity of soil factors with the multivariate analog of *Levene's* test using the "*betadisper*" function in the vegan package. The indirect effects are defined as multiplied path coefficients between the predictor and response variables, including all the possible paths excluding the direct effect. The final model was chosen among all constructed models based on the Goodness of Fit (GOF) statistic according to the model's overall predictive power.

#### **5. Conclusions**

To our knowledge this is the first study to comprehensively research the chemistry of multiple nutritional elements (C, N, P, K) and their ratios in *S. chamaejasme* leaves and its surrounding soil physiochemical properties and quantify the potential controls and variability at a large scale. We found that there was no obvious difference between the leaf C, N, and P content in *S. chamaejasme* from the QT and IM, but the leaf K concentration was significantly higher in QT than that in IM. Inconsistent with the variation of leaf element contents and ratios, the soil physiochemical properties of *S. chamaejasme*-infested areas varied remarkably, and most of them were greater in QT. Our results clearly showed that there was no significant correlation between *S. chamaejasme* leaf ecological stoichiometry and soil physicochemical properties, which supported the fact that the nutrient concentrations and stoichiometry of wide-ranging species tend to be insensitive to variation in soil nutrient availability.

Besides, the different homeostasis strength of C, N, K, and their ratios in *S. chamaejasme* leaves across all the sites were observed, which indicated that *S. chamaejasme* could be more conservative in their use of nutrients improving their adaptation to diverse conditions. Both the C and N content of *S. chamaejasme* leaves were unaffected by any climatic factors, but the leaf P and K were affected differently in QT and IM. Besides, the MAP or MAT contribution was stronger in the leaf elements than soil by using mixed effects models, which illustrated once more the relatively weak effect of soil physicochemical properties on leaf elements. Finally, we conducted a partial least squares path modeling analysis to examine the different effects of soil and climatic on leaf P and K of *S. chamaejasme*. These results suggest that *S. chamaejasme* adapts to changing environments by adjusting its relationships with climate or soil factors to improve their chances of survival and spread in degraded grasslands.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/plants11151943/s1, Table S1: Leaf element contents of *S. chamaejasme* in different sample sites in this study (Mean ± SD); Table S2: Soil physiochemical properties in different sample sites in this study (Mean ± SD); Table S3: Relationship between *S. chamaejasme* leaf stoichiometry and soil physicochemical properties in Northern China ; Table S4: Summary of linear mixed effects model analyzing the effects of soil, MAT, and MAP on variation of C, N, P, and K concentrations in *S. chamaejasme* leaves, using soil, MAP, MAT, and their interaction as fixed effects. Region was taken as a random factor; Table S5: Summary of the total effects on the leaf P and K of *S. chamaejasme* in Qinghai Tibet Plateau (QT) and Inner Mongolia Plateau (IM); Table S6: The geographical and climatic information associated with the sample sites in this study; Table S7: Eigenvalues of the soil PCA; Table S8: Loadings of the soil PCA; Table S9: Site scores of the soil PCA; Figure S1: Heat map of Pearson correlations among *S. chamaejasme* leaf P content, soil P and AP content, soil water content (SWC), mean annual precipitation (MAP), and altitude (ALT) in IM region; Figure S2: Biplot for the first two axes of soil physicochemical properties.

**Author Contributions:** Conceptualization, L.G. and D.H.; methodology, L.G. and L.L.; software, H.M.; validation, L.L., L.Z. and H.Z.; formal analysis, W.H.; investigation, H.M. and L.Z.; resources, L.L. and H.Z.; writing—original draft preparation, L.G.; writing—review and editing, W.H., V.J.S. and K.W.; visualization, K.W.; supervision, D.H.; funding acquisition, D.H. and W.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** Please add: This research was funded by The Climate-Smart Grassland Ecosystem Management Project (CSMG-C-03), Special Aid Fund for Qinghai Province (2020-QY-210), International Collaboration Fund of Department of Science and Technology of Shaanxi Province (2020KW-030), China Agriculture Research System (CARS-34).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

