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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

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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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