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The datasetWe curated and explored 695 published 16S rRNA gene samples from cryospheric ecosystems (Methods section and Supplementary Table 7), including polar ice sheets, mountain glaciers and their proglacial lakes, permafrost soils and the coastal ocean under the influence of glacier runoff, and compared these to 3552 published 16S rRNA gene samples from non-cryospheric ecosystems, including temperate and tropical lakes and soils (Supplementary Table 7). This approach allowed us to identify and explore features specific to the cryospheric microbiome and compare it to other environmental microbiomes. However, we note a geographical bias towards polar regions in current publicly available repositories, and the paucity of alpine samples specifically highlights the need to further characterise these habitats given that they are among the most endangered cryospheric ecosystems globally. This bias is further compounded by the inconsistent methodologies applied across studies (e.g. primer pairs and sequencers used). To account for potential primer biases, we analysed two 16S rRNA primer pairs (Primer Pair 1, PP1: 341f-785r; Primer Pair 2, PP2: 515f-806r)12,13 commonly used in amplicon high-throughput sequencing. In total, this dataset contains 241,502,708 paired sequence reads, resulting in 530,254 and 410,931 amplicon sequence variants (ASVs) for PP1 and PP2, respectively. Moreover, all taxonomic analyses were performed at the genus level, to account for the limitations of 16s rRNA amplicon data. To gain deeper insights into the functional space of the cryospheric microbiome, we compared 34 published metagenomes from cryospheric ecosystems with 56 metagenomes from similar but non-cryospheric ecosystems (Fig. 1A). Given the difficulty of obtaining high-quality metagenomes from cryospheric ecosystems, we restricted our analyses to glacier surfaces, ice-covered lakes, and Antarctic soils. Although our analyses were limited to samples where raw sequence data are available (Methods section), the breadth of habitats covered are representative of the most abundant cryospheric ecosystems, e.g., glacier ice, cryoconites, subglacial lakes and sea ice. On the other hand, several niches such as glacier snow, glacier-fed rivers/streams, and the full-breadth of permafrost may not entirely be represented due to data unavailability. We reanalysed all metagenomes using the same bioinformatic pipeline (IMP3; see Methods section) to avoid analytical biases. Overall, the metagenomic analyses from 2,427,818,072 paired reads yielded 41,068,842 gene sequences. Thus, we here present a catalogue representing a snapshot of the functional diversity in the cryospheric microbiome, integrating across diverse habitats. This represents what we believe to be the first global overview of the functional repertoire of the Earth’s cryosphere compared to other ecosystems.Fig. 1: A unique cryospheric microbiome.A Geographic distribution of the 16 S rRNA gene samples for the two primer pairs (PP) and metagenomes for both cryospheric and non-cryospheric ecosystems, where GPS coordinates were available on NCBI. Symbol size denotes the number of samples per site (see Supplementary Table 7). B Phylogenetic tree based on abundant ASVs ( >0.5% relative abundance in at least one sample) in the PP1 dataset. The heatmap (inner rings) shows the presence (at a  > 0.5% relative abundance threshold) of ASVs in the four ecosystem types of the cryosphere (ice and snow, terrestrial, coastal ocean and freshwater). The barplot (outer ring) represents the coefficient for the SVM classifier analysis, highlighting discriminating ASVs. C Sorensen’s phylogenetic index of β-diversity (n1 = n2 = 84,461 for PP1, and n1 = n2 = 99,000 for PP2) and D β-MNTD calculated across pairs of samples in the cryospheric samples (Cryo-Cryo), pairs of cryospheric and non-cryospheric samples (Cryo-Others) and pairs of non-cryospheric (Others-Others) samples (sample sizes are listed in Supplementary Table 2). The top panel (shades of blue) is for PP1, the bottom one (shades of red) for PP2; two-sided Wilcoxon tests were performed to assess significance in panels C and D; the Holm method was used to correct for multiple testing (****: 0–0.0001). Boxplots depict the median and the 25th and 75th quartiles, whiskers extend to values within 1.5 times the interquartile range, and the remaining points are outliers. Effect sizes and exact p-values are available in Supplementary Table 2. Source data are provided as a Source Data file.Full size imageA cryospheric microbiomeGiven the communal constraints imposed by the harsh environment of cryospheric ecosystems (e.g., low temperature, oligotrophy), we expected them to harbour a specific microbiome. Accordingly, machine-learning classification (logistic regression models, Methods) based on community composition was able to differentiate between cryospheric and non-cryospheric microbiomes with high accuracy (balanced accuracy >0.96, Supplementary Table 1). Both primer pairs consistently yielded a high classification accuracy and especially a high precision. Interestingly, many of the discriminating cryospheric ASVs were spread widely across the bacterial tree of life (Fig. 1A and Supplementary Fig. 1).The notion that a part of the microbiome is specific to the cryosphere is also strongly supported by phylogenetic analyses of the 16 S rRNA gene amplicon dataset. First, we found higher pairwise phylogenetic overlap among cryospheric samples than among cryospheric/non-cryospheric or non-cryospheric samples (Sorensen’s index, Fig. 1C; Wilcoxon test, Holm adj. p  More

Experimental dataThe dataset used in this study is the global long-term air quality indicator data of 5577 regions from 2010 to 2014 extracted by Betancourt et al.14 based on the TOAR database (https://gitlab.jsc.fz-juelich.de/esde/machine-learning/aq-bench/-/blob/master/resources/AQbench_dataset.csv)29. As shown in Fig. 3, the monitoring sites include 15 regions, including EUR (Europe), NAM (North America), and EAS (East Asia), and are mainly distributed in NAM (North America), EUR (Europe) and EAS (East Asia). The dataset mainly includes the geographical location information of the monitoring site, such as longitude and latitude, the area to which it belongs, altitude, etc., and the site environment information, such as population density, night light intensity, and vegetation coverage. Since it is difficult to directly quantify factors such as the degree of industrial activity and the degree of human activity, environmental information such as the average light intensity at night and population density are used as proxy variables for the above factors. The ozone indicator records the hourly ozone concentration from air quality observation points in various regions and aggregates the collected ozone time series in units of one year into one indicator. Using a longer aggregation period can be used to average short-term weather fluctuations. The experimental data have a total of 35 input variables, including 4 categorical attributes and 31 continuous attributes. The predictor variable is the average ozone concentration in each region from 2010 to 2014. The specific variable names and descriptions14 are shown in the supplementary materials. A total of 4/5 of the total samples were used as the training set, and 1/5 were used as the test set.Figure 3Global distribution of monitoring sites.Full size imageResults of BO-XGBoost-RFEAccording to the XGBoost-RFE algorithm for feature selection, XGBoost-RFE combined with the cross-validation method is used to calculate the selected feature set in each RFE stage for fivefold cross-validation, and the mean absolute error (MAE) is used as the evaluation criterion to finally determine the number of features with the lowest mean absolute error (MAE). At the same time, the Bayesian optimization algorithm is used to adjust the hyper-parameters of XGBoost-RFE, and then the feature subset with the lowest cross-validation mean absolute error (MAE) is obtained. The main parameters of the XGBoost model in this article include the learning_rate, n_estimators, max_depth, gamma, reg_alpha, reg_lambda, colsample_bytree, and subsample. All parameters used in the model are shown in the supplementary material. Within the given parameter range, the Bayesian optimization algorithm is used, the mean absolute error (MAE) of the XGBoost-RFE fivefold cross-validation is used as the objective function, and the number of iterations is controlled to be 100. We obtained the hyperparameter combination corresponding to the lowest MAE and the corresponding optimal feature subset. The iterative process of Bayesian optimization is shown in Fig. 4.Figure 4Iterative process of Bayesian optimization.Full size imageThe parameter range and optimized value of XGBoost-RFE are shown in Table 1. The XGBoost-RFE feature selection results under the above optimized hyperparameters are shown in Fig. 5. The number of features in the feature subset with the lowest mean absolute error is 22, and the MAE is 2.410.Table 1 Main hyper-parameter range and optimized value.Full size tableFigure 5XGBoost-RFE feature selection results: Cross-validation MAE under optimal hyperparameter combination.Full size imageAdditionally, the XGBoost-RFE feature selection model without Bayesian optimization is compared with the algorithm in this study. The default parameters of the underlying model XGBoost are set to learning_rate as 0.3, max_depth as 6, gamma as 0, colsample_bytree as 1, subsample as 1, reg_alpha as 1, and reg_lambda as 0. The comparison results are shown in Table 2. The results show that the XGBoost-RFE cross-validation MAE without parameter tuning is larger than that of the algorithm in this study, and the dimension of the feature subset obtained is also higher than that of the algorithm in this study.Table 2 Comparison of MAE and feature num before and after BO.Full size tablePrediction resultsTo test the prediction accuracy of the prediction model with the optimal subset obtained by BO-XGBoost-RFE, three indexes, MAE, RMSE and R2, are used to evaluate the prediction results, and the expressions are as follows:$$begin{array}{*{20}c} {MAE = frac{1}{n}mathop sum limits_{i = 1}^{n} left| {left( {y_{i} – widehat{{y_{i} }}} right)} right|} \ end{array}$$
(8)
$$begin{array}{*{20}c} {RMSE = sqrt {frac{1}{n}mathop sum limits_{i = 1}^{n} left( {y_{i} – widehat{{y_{i} }}} right)^{2} } } \ end{array}$$
(9)
$$begin{array}{*{20}c} {R^{2} = 1 – frac{{mathop sum nolimits_{i = 1}^{n} left( {widehat{{y_{i} }} – y_{i} } right)^{2} }}{{mathop sum nolimits_{i = 1}^{n} left( {y_{i} – overline{{y_{i} }} } right)^{2} }}} \ end{array}$$
(10)
n indicates the number of samples, yi is the true value, (widehat{{y_{i} }}) is the predicted value and (overline{{y_{i} }}) indicates the mean value of the predicted value.The XGBoost-RFE feature selection algorithm based on Bayesian optimization in this study is compared with feature selection using full features and features selected by the Pearson correlation coefficient, which measures the correlation between two variables. In this study, the correlation with predictor variables was selected to be less than 0.1, and the variables with correlations greater than 0.9 were deleted to avoid multicollinearity.XGBoost, random forest, support vector regression machine, and KNN algorithms were used to predict ozone concentration with full features, features selected by Pearson’s correlation coefficient, and features based on BO-XGBoost-RFE. According to the evaluation indicators described above, the comparison of the prediction performance results of the three algorithms before and after dimensionality reduction can be obtained. The MAE, RMSE and R2 results of each prediction model are shown in Table 3.Table 3 MAE, RMSE and R2 of each prediction model.Full size tableAmong the four prediction models, random forest has the lowest MAE and RMSE and the highest R2 based on three different dimensions of data and therefore has the best prediction performance. The prediction accuracy of all four prediction models based on Pearson correlation is lower than that based on BO-XGBoost-RFE, indicating that only selecting features by correlation cannot accurately extract important variables. Although the RMSE of the support vector regression model based on BO-XGBoost-RFE is slightly lower than the RMSE based on full features, the prediction accuracy of XGBoost, RF, KNN after feature selection of BO-XGBoost-RFE is higher than that based on full features and Pearson correlation. Among the four prediction models, random forest has obtained the highest prediction accuracy. The MAE based on BO-XGBoost-RFE is 5.0% and 1.4% lower than that based on the Pearson correlation coefficient and the full-feature-based model, and the RMSE is reduced by 5.1%, 1.8%, R2 improved by 4.3%, 1.4%. Additionally, the XGBoost model achieved the greatest improvement in accuracy. The MAE was reduced by 5.9% and 1.7%, the RMSE was reduced by 5.2% and 1.7%, and the R2 was improved by 4.9% and 1.4% compared with the Pearson correlation coefficient-based and full-feature-based models, respectively. This indicates that feature selection based on BO-XGBoost-RFE effectively extracts important features, improves prediction accuracy based on multiple prediction models, and has better dimensionality reduction performance.Figure 6 shows the importance of each feature obtained by using the random forest prediction model, reflecting the degree of influence of each variable on the prediction results of the global multi-year average near-ground ozone concentration. The most important variables that affect the prediction results according to the ranking of feature importance are altitude, relative altitude, and latitude, followed by night light intensity within a radius of 5 km, population density and nitrogen dioxide concentration, while the proxy variables for vegetation cover have a relatively weak effect on the prediction of ozone concentration.Figure 6Feature importance in random forest.Full size image More

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DesignPlant richness. Sixteen locally frequent native plant species in the barren mountain areas (around Taizhou University, Zhejiang, China) invaded by the exotic plant Symphyotrichum subulatum60 were selected as the native species pool. These species were chosen because they spanned the dicotyledon plant taxonomy (including 7 Orders, 10 Families, and 14 Genus, in the Class Magnoliopsida), differed widely in their functional traits (related to height, life form, dominance in local communities, and leaf habit) (Supplementary Table 3), and were occasionally found to be associated with the invasive species Symphyotrichum subulatum60 in the local secondary-succession communities. With this species pool, we were able to imitate the locally natural, spatially stochastic, compositionally ruderal, and functionally varied plant community61, which is a typical attribute of the secondary-succession communities in the local barren mountains invaded by the exotic plant Symphyotrichum subulatum. Based on this native species pool, monocultures of each species (16 total), and random mixtures of 2, 4 or 8 species (with 10, 10, or 9 distinct assemblages, respectively) were designed, creating a complete set (Fig. 1d) of 45 different plant assemblages (pots) in total. Each plant assemblage was replicated 6 times, for a total of 270 pots. To eliminate the non-random effects during the 1-year development of the 270 pots, their distributions were randomized, such that not all replicates of an assemblage were next to each other (Fig. 1d–f).DroughtAfter 1-year development of the native plant assemblages, three drought treatments (non-, moderate-, and intensive-drought) were manipulated by adjusting irrigation using automatic drip irrigation systems, with 100%, 50%, and 25% of the equivalent to the amount received in the areas where native species were collected, respectively. Two random complete sets were selected for each drought treatment, each complete set being composed of 45 different plant assemblages (Fig. 1d–f).Exotic plant invasionNine months after drought treatment, the two complete sets (Fig. 1d) of each drought treatment were randomly exposed (invasion) or not exposed to (non-invasion) the invasive species Symphyotrichum subulatum (Michx.) G. L. Nesom (Fig. 1e, f). S. subulatum, an annual herbaceous plant native to North America, is a common invasive species in the subtropical and tropical regions of China18,60, and tends to interact with the native species via, for example, competing for space and resources62,63, enriching for pathogens or herbivores, and changing soil faunal, bacterial or fungal microbiomes18,64,65.ExperimentThe experiment based on the design mentioned above was conducted at Taizhou University, Zhejiang province, China (28.66°N, 121.39°E). The seeds of the 16 native plant species (Supplementary Table 3) and the soil were collected from nearby mountain areas (Wugui, 28.65°N, 121.38°E; Baiyun, 28.67°N, 121.42°E; Beigu, 28.86°N, 121.11°E). The seed-mixtures were obtained by mixing seeds of the 16 species pro rata, in proportion to germination rates. The soil (fine-loamy, mixed, semiative, mosic, Humic Hapludults) was sieved to pass a 2-mm mesh, and thoroughly mixed. 270 plastic pots (72 cm length × 64 cm width × 42 cm depth) were prepared, and each was filled with a 27-cm soil layer, followed by a 10-cm mixture of soil and vermiculite-compost to provide water-, air- and fertility-support for germination, seedling establishment, and plant growth (Supplementary Table 4).Native plant assemblagesAll the 270 pots were placed inside a plastic shelter, which allowed for both air ventilation and protection from rain. Each pot was sown with a seed-mixture of ca. 800 seeds. One month after germination, for each pot, the undesired seedlings were removed manually according to the plant richness design (Fig. 1d–f), and thus 32 vigorous seedlings (with the same number of seedlings per species, e.g., 4 seedlings for each species of the 8-species mixtures) were spatial-evenly retained. In this manner, the plant richness was manipulated for each plant assemblage. During the development of the 270 plant assemblages, the soil volumetric water content was controlled at ca. 20%, which was similar to that of the nearby mountainous soil, using the automatic drip irrigation systems. Weeds and undesired species were removed monthly (Fig. 1f).Drought treatmentAfter 1-year development of native plant assemblages, the drought treatments (non-, moderate-, and intensive-drought) were manipulated according to the experimental design mentioned above (Fig. 1d, e). Two complete sets (Fig. 1d) of different plant assemblages (2 × 45 pots) were selected for each drought treatment. Every other week, 40 pots each drought treatment were randomly selected for measuring soil water content and soil temperature at the depth of 0–20 cm, using the ProCheck analyzer (Decagon, Pullman, Washington, USA), and irrigation was adjusted accordingly using automatic drip irrigation systems. The irrigation for non-, moderate-, or intensive-drought was adjusted to accomplish an irrigation level amounts to 100%, 50%, or 25% that of the mountain areas where seeds were collected. Because of the distinct seasonal temperature and evaporation conditions, the irrigation frequencies were approximately daily in May-September, every other day in March–April and October–December, and weekly in January–February. With this manipulation, the volumetric soil water contents of non-, moderate-, and intensive-drought were controlled within ranges of 13.8–23.4%, 6.8–13.7%, and 1.4–7.4%, respectively, throughout the manipulation of drought treatment (Fig. 1e, f). Eight months after drought introduction, fresh litter was collected form the two replicate pots of each drought treatment, and then oven-dried at 40 °C, cut into ca. 2-cm pieces, and filled into litterbags (2-g litter in each litterbag).Invasion treatmentNine months after drought introduction, one complete set (45 pots) of the plant assemblages (Fig. 1d) from each drought treatment, was chosen and exposed to invasion disturbance by sowing 50 seeds of S. subulatum in each pot, and the other was specified as the non-invasion treatment (Fig. 1e, f). The prepared litterbags were embedded under the litter-layer of each pot (5 litterbags in each pot), correspondingly.SamplingSix months after invasion introduction, one litterbag was collected for litter-fauna extraction. Nine months after invasion, five soil cores (20-cm depth) were collected with augers (6.4 cm in diameter) and mixed for extraction of soil-fauna, and measurement of soil property and enzyme activity (Fig. 1f). The aboveground biomass of both native and invasive plants in each pot was harvested, sorted to species, oven-dried to a constant mass at 80 °C, and weighed. The belowground plant biomass was also sampled, sorted to native and invasive groups, oven-dried, and weighed (Fig. 1f).Plant, litter-, and soil-faunal communitiesPlant communitySince exotic plant invasion was treated as a disturbance factor, the biomass of the invasive species S. subulatum was not included for analyses concerning plant community and ecosystem (multi)functionality. The aboveground biomasses of native plant species in each of the 270 pots were collected for plant community analysis.Litter- and soil-faunal communitiesOne litterbag or fifty grams of mixed-soil samples were used for litter- or soil-fauna extraction using a Tullgren funnel apparatus (dry funnel method)66. The obtained microarthropods were stored in 70% alcohol, identified with double-tube anatomical lens, and classified to Family level. For both litter and soil samples, the numbers (abundances) of all faunal taxa were counted for litter/soil-faunal community analysis.Phylogenetic information of plant, litter-, and soil-faunal communitiesSimilar procedures were used to construct the plant and faunal phylogenetic trees. First, protein sequences of 12 faunal mitochondrial coding genes and 16 plant plastid coding genes (Supplementary Data 1) were obtained by searching plant or faunal taxonomies from NCBI protein database (https://www.ncbi.nlm.nih.gov/protein/) with Edirect software (https://www.ncbi.nlm.nih.gov/books/NBK179288/). All available sequences at plant species level or faunal Family level were fetched. If unavailable, the missing sequences were sampled from plant genus or faunal Order level. Sequoiadendron giganteum and Echinococcus were specified as out-group references for plant and faunal trees, respectively. Then, the sequences of each plant or faunal taxon were clustered at 97% or 90% identity independently, and the centroids were used as representative markers. The markers were aligned with MUSCLE67, followed by concatenation. Finally, using MEGA X68, the maximum likelihood trees were constructed based on BioNJ initial trees69 and 500 bootstrap checking nodal support. The parameters for plant tree construction were specified as follow: 70% partial deletion (with 4824 positions retained) and the best-fit substitution model JTT + G + I + F70,71; parameters for faunal tree: 90% partial deletion (2778 positions) and LG + G + I + F model71,72. The Linux codes for processing the protein sequences were submitted to GitHub (https://github.com/YuanGe-Lab/JZW_2022/tree/main/linux)The plant and faunal taxonomies, representative markers, and marker accessions are provided as Supplementary Data 1.Ecosystem function-related variablesA total of 14 individual function-related variables were collected. These variables belonged to three functional groups: (1) biomass production, including aboveground and belowground biomass of native plants, light interception efficiency, litter-fauna abundance, and soil-fauna abundance; (2) soil properties, including contents of soil organic carbon, soil nitrogen, soil phosphorus, and GRSP (relating to soil physical properties and stocks of carbon and nutrient73); and (3) processes, including rate of litter decomposition, and activities of β-glucosidase, protease, nitrate reductase and dehydrogenase.Light interception efficiency, the fraction of incident photosynthetically active radiation (PAR) intercepted by each plant community canopy, was determined between 12:00 and 14:00 on clear days using LI-191R line PAR sensors (LI-COR Inc., NE, USA), and the mean of 4 measurements (monthly from May to August the third year; Fig. 1f) was used. Total soil organic carbon and nitrogen were measured with an elemental analyzer (vario Max; Elementar, Germany). Total soil phosphorus was determined using the molybdenum blue method with a UV–visible spectrophotometer (Shimadzu, Kyoto, Japan). GRSP was determined using the method described by Shen et al.18. Litter decomposition rate was assessed by embedding litterbags and fitting litter mass loss against decomposition time (Fig. 1f). Enzyme activities were analyzed by the spectrophotometric method using the substrates, p-Nitrophenyl-β-d-glucopyranoside (pNPG; for β-glucosidase), caseinate (protease), nitrate (nitrate reductase) and triphenyltetrazolium chloride (TTC; dehydrogenase)18.Quantifying community stability and multifunctional stabilityCommunity data was comprised of native plant biomasses or faunal abundances, and the associated phylogenetic information. Multifunctionality data was comprised of 14 function-related variables, each variable (V) being transformed (V’) using the formula ({V}^{{prime} }=frac{V-{{{{{rm{min }}}}}}left(Vright)}{{{{{{rm{sd}}}}}}left(Vright)}) to guarantee even contribution to global variance. We calculated community similarity (1 minus Weighted-UniFrac distance) and multifunctional similarity (1 minus Bray–Curtis distance), based on the community data and the multifunctionality data, respectively. The specific subsets of each symmetric similarity matrix were used to assess three different aspects of stability: (1) Invariability (against stochastic fluctuations), reflected as the pairwise similarities (1476 pairs) within treatment groups, at same plant richness*drought*invasion condition; (2) Drought resistance, the similarities (2148 pairs) between drought (moderate- and intensive-drought) and non-drought treatments, at same plant richness*invasion condition; and (3) Invasion resistance, the similarities (n = 1611 pairs) between invasion and non-invasion treatments, at same plant richness*drought condition (Supplementary Fig. 1).We also assessed the three aspects of stability of each individual function in a similar way, but by calculating the similarity using the formula ({{{{{{{mathrm{SIM}}}}}}}}_{{ij}}=1-frac{|{V}_{i}-{V}_{j}|}{{V}_{i}+{V}_{j}}) (Vi and Vj are ith and jth elements in a function vector; SIMij is the similarity between Vi and Vj).Statistics and reproducibilityPERMANOVA (10,000 randomizations) was conducted to test the influences of the manipulated factors on ecosystem multifunctionality or communities of plant, litter- and soil-fauna, using “vegan::adonis” in R74. Mantel test (10,000 randomizations; Spearman’s R) was conducted to test the community-community or the community-multifunctionality relationships, using “vegan::mantel” in R74.As each similarity-pair of each aspect of community or multifunctional stability mentioned above was in strict correspondence to single level of each manipulated factor (plant richness, drought, and invasion) (Supplementary Fig.  1), the direct/indirect effects of treatments on the community or multifunctional stability can be assessed using SEM. To test direct and indirect effects (by modulating community stability) of the manipulated factors on multifunctional stability, we built three SEMs (Fig. 1a–c) based on three different aspects of stability (i.e., invariability, drought resistance, and invasion resistance) under the conditions of corresponding parings of manipulated factors (Supplementary Fig. 1), with the LAVAAN package75. The standardized paths (direct effects) in SEMs can be conceived as the partial correlations after teasing all side effects away. Bootstrapping with 10,000 randomizations was conducted to generate the unbiased mean effect. The significance of effect was tested using a Mantel-like permutation (10,000 randomizations) test76, where the null hypotheses (H0) were that the independent factors plant richness, drought, and invasion, had no direct/indirect effects (effect = 0) on multifunctional stability. Based on H0, permutation procedure was conducted by permuting the index of dependent factors (both columns and rows of a symmetric matrix; Supplementary Fig. 1) simultaneously to gain null models and null effects. p-values (probability of H0 acceptance) were calculated as the percentage of observed positive (or negative) effect that was greater (or less) than the null effects. We also assessed the direct and indirect effects of factors on the stability of each individual function based on the same SEMs, to consolidate our findings on multifunctional stability. The R codes and examples solving the permutation test for the significance of effects derived from SEMs that based on multidimensional similarity (or distance) were submitted to GitHub (https://github.com/YuanGe-Lab/JZW_2022/tree/main/R). All the analyses were conducted using R (https://www.r-project.org).Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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