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This Article is being retracted by the authors as the result of a coding error, correction of which undermines the main conclusions of the study. This was an inadvertent error related to the use of the ‘use=pairwise.complete.obs’ option in the function ‘cor.test’. This function was used to estimate the correlation matrix between all tree-ring series. We had assumed the option pairwise.complete.obs would fully exclude tree-ring series with incomplete records for each time window. Unfortunately, ‘not available’ (NA) values were excluded only on a pairwise base between tree-ring series within each time window. This resulted in shorter time series being retained and inconsistent time windows in recent years and, consequently, a greater chance of higher correlation coefficients. When we excluded all incomplete tree-ring series for each time window in subsequent analyses, as was our original intention, the recent increase in synchrony originally reported in this Article (Figs. 2,3) is, unfortunately, mostly an artefact of this coding error. Because our sensitivity analyses all used the same correlation functions and option, we did not detect this error until S. Klesse, R. Brienen and R. Peters brought it to our attention. In fact, the consistent response in all sensitivity analyses reinforced our original interpretation. The sub-sampling sensitivity analysis (Supplementary Fig. 5b) remains unaffected by this coding error, since samples were selected to maintain a constant sample size and exclude all NAs. However, the increasing synchrony trend in this analysis is of much smaller magnitude and spatial scale than the originally reported trend, and thus would require examination on its own. Because the main conclusion of this paper is now unsupported, all authors agree to this retraction. We thank S. Klesse, R. Brienen and R. Peters for quickly detecting and informing us of this error. More

The above developed intuition is converted into an agent-based evolutionary model in the context of public goods provision. In the proposed evolutionary agent-based model42, all the agents play a linear public goods game by using conditional cooperative strategies, enforcing altruistic punishments based on relative differences in their cooperation tendencies, and imitating successful role models’ social behavior with certain errors. The process is iterated several thousands of generations.Population typeIn the proposed model, the individuals or agents in the population behave like conditional cooperators and the population is heterogeneous in its conditional nature. The agents who are more willing to cooperate are also more willing punish to potential free riders. Each individual is born with an arbitrary conditional cooperative criterion (CCC) and a propensity, β. Both are positive values. The agents with higher CCC donate less frequently than the agents with a higher CCC for the given same amount of past cooperation levels. The same agents can cooperate or enforce altruistic punishments or free ride given the past cooperation levels in the population. β indicates the propensity to implement a conditional cooperative decision and imitate the successful role model’s social behavior. Each agent’s CCC value is drawn from a uniform distribution (0, N), where N is the population size, and β is drawn from a uniform distribution (0, 3). With β = 0 the actions of the individuals are random and with β = 3 the individuals behave like ideal conditional cooperators. With intermediate values the individuals behave like non-ideal conditional cooperators. The consideration is equal to the natural selection designing the conditional cooperative strategies. The combinations of CCC and β create heterogeneous populations with varieties of propensities. The consideration is close to the conditional nature of the population observed in experimental settings12,36.Conditional cooperative decisionThe conditional cooperative decision of the agent is operationalized in the following way43,44. For instance, in the rth round, an agent i (with CCC = CCCi value) donates to the public good with probability, qd,$${q}_{d}= frac{1}{1+mathrm{exp}(-left({n}_{C}-{CCC}_{i}right){upbeta}_{i})}$$
(1)
nC indicates the number of donations in the (r − 1)th round. The parameter βi controls the steepness of the probability function. For the higher βi, the agent is highly sensitive to the (nC-CCCi). For instance, as βi → ∞, the qd is sensitive to the sign of the (nC -CCCi), i.e., if (nC -CCCi)  > 0 then qd = 1 and if (nC -CCCi)  1 and βi  > 2 or with (CCCj-CCCi)  > 2 and βi  > 1, the agent i punishes the agent j with high probability. With (CCCj-CCCi) × βi  2 punishes a higher CCC agent more accurately than a slightly lower CCC agent. A lower CCC agent with β  2 agent i punishes the agent j with a high probability close to one and βi  More

Sampling strategyAll sampling sites were located in the Eifel National park, situated in the south-western part of Germany close to the Belgian border (Supplementary Fig. 1, Supplementary Table 1).In this study the sampling site comprised a forest conversion gradient from a Norway Spruce (Picea abies) monoculture to a European Beech forest (Fagus sylvatica). To reflect the different stages of conversion from spruce to beech, four forest types were defined: pure beech (PB), old beech (OB), young beech (YB) and pure spruce (PS) (Supplementary Table 1, Supplementary Fig. 2).The forest types differed in tree species composition and tree age. The pure beech and pure spruce forest types were monoculture stands. The pure beech stands were approximately 180 years old and partly under special protection through North-Rhine Westphalia (Naturwaldzelle) (Sampling site 01). The spruce monocultures were substantially younger with ca. 60 years old. Spruces of the same age dominated the young beech sampling sites that had only recently been underplanted with beeches. At the old beech sampling sites, beeches had already reached a height of more than 3 m and actions to remove spruces from the forest were conducted.A total of 12 Townsend Malaise traps (three per forest type) were set up in the Eifel National Park, North-Rhine Westphalia, Germany, during July 2016. To ensure that the orientation of the Malaise traps was consistent and to minimize potential biases caused by wind direction and position of sun, the highest point of each trap was set facing south. The traps were left in the field for the full duration of the experiment until April 2017, ensuring that insects were collected from exactly the same locations. In October 2016, two additional traps (Malaise Trap 13, pure spruce and Malaise Trap 14, old beech) were installed at two further sampling sites (Sample Site 13 and Sample Site 14). All traps were equipped with a bottle filled with approximately one litre of absolute ethanol (99,96%) over a 2-week period in July 2016 (13.07–27.07), October 2016 (13.10–27.10), January 2017 (11.01–25.01) and April 2017 (12.04–26.04) (Supplementary Table 2). The ethanol was replaced every week to ensure that the concentration of the preservative ethanol was stable and to avoid loss of insects a mesh filter was used (MICROFIL V Filter White Gridded 0.45 µm-diameter 47 mm & 100 ml Funnel Sterilized). Due to heavy snow during the winter period, new traps were set at the start of the new sampling season in January 2017.Three soil samples were collected around each Malaise trap, from the organic horizon of the top 10 cm layer (excluding the litter layer). Soil sample sites were located 4 m and 5 m away from the trap, forming a triangle in the centre of which the Malaise trap was located (Supplementary Fig. 3). One corner of the sampling triangle was pointing south, while both remaining corners were pointing north west and north east, respectively.Each sampling site was sampled four times in the course of a 1-year period. Soil sampling and Malaise trapping were synchronized and soil sampling was done on day 14 of each Malaise trapping period, when the last bottles were collected (Supplementary Table 3). Each soil sample consisted of approximately twenty 44 mm × 100 mm cores, taken 5 cm apart. A total of 162 soil samples were collected and stored at − 20 °C until further processing.DNA extractionBulk samples from Malaise trapsNon-destructive DNA extraction was performed by overnight incubation in lysis buffer, using a modified protocol of Aljanabi and Martinez (1997). The arthropods were sieved from the collecting ethanol using a mesh filter (MICROFIL V Filter White Gridded 0.45 µm-diameter 47 mm and 100 ml Funnel Sterilized), which was processed with the specimens. The insects were dried for 10 min at room temperature. Depending on biomass, between 15 and 25 ml of extraction buffer (0.4 M NaCl, 10 mM Tris-HCl pH 8.0, 2 mM EDTA pH 8.0) and 2% Sodium dodecyl sulphate (SDS) were added to each bulk sample. Finally, 400 µg Proteinase K was added per ml of lysis buffer and samples were lysed overnight at 52 °C on an orbital shaker at 30 rpm. The next day, the lysate was poured out of the bottles using the MICROFIL V Filter (White Gridded 0.45 µm-Dia 47 mm and 100 ml Funnel Sterilized) and a 6 M NaCl solution was added to the lysate to a concentration of 4 mmol. The samples were vortexed for 30 s, centrifuged at 4700 rpm for 30 s and the supernatant was transferred to a falcon tube and an equal volume of isopropanol was added. After careful mixing by inversion, the tubes were left at − 20 °C for 1 h and subsequently centrifuged at 4700 rpm for 60 min. The supernatant was discarded and the resulting pellet was washed with 20 ml of ice cold 70% ethanol, by centrifuging at 4700 rpm for 15 min. The remaining ethanol was discarded and the pellet was left to dry at 20 °C overnight. The pellet was then resuspended in 1 ml of sterile H2O and stored at − 20 °C until further processing.Soil samplesDNA extraction from the soil samples was conducted using two different extraction methods: a commercial (lysis-based) DNA extraction kit (Macherey-Nagel NucleoSpin Soil) and a (no lysis) phosphate buffer protocol from Taberlet et al. 201240. Each of the triplicated samples were processed individually. After defrosting the soil overnight at 4 °C, the samples were thoroughly mixed, DNA was extracted from 0.5 g of soil per sample using the Macherey-Nagel NucleoSpin Soil Kit following the manufacturer’s protocol.The second DNA extraction method allowed extracellular DNA to be extracted from larger amounts of starting material using a phosphate buffer and did not include a lysis step. Each of the three samples taken per sample site and season were treated individually. Soil samples were removed from the − 20 °C chamber approximately 12 h before DNA extraction and stored at   4 °C overnight. The next morning, each sample was thoroughly mixed and an equal weight of saturated phosphate buffer solution (Na2HPO4; 0.12 M; pH 8)40 was added. Samples were placed in an orbital shaker at 120 rpm for 15 min. Thereafter, duplicates were processed, where two 2 ml Eppendorf tubes were filled with 1.7 ml of the resulting mixture and centrifuged for 10 min at 10,000 g. Four hundred microliters of the resulting supernatant were transferred to a new 2 ml collection tube and 200 μl of SB binding buffer from the Macherey-Nagel NucleoSpin Soil Kit was added. Duplicate lysates were merged by loading onto a single NucleoSpin Soil Column and centrifuged at 10,000 g for 1 min. From this step onwards, the standard manufacturer’s protocol for the Macherey-Nagel NucleoSpin Kit was followed from step 8. DNA was eluted with 50 μl of SE Buffer (Macherey-Nagel). Ten microliters of the resulting DNA eluate was diluted in 90 μl of pure H2O (Sigma), followed by DNA purification using the PowerClean Pro DNA Clean-Up Kit (MO Bio Laboratories, Inc.) following the manufacturer’s protocol. For the purposes of this study, results from the two types of soil extraction were merged.Choice of primers and amplicon library preparationFor amplicon library preparation a primer pair targeting the 313 bp ‘mini barcode’ region of the mitochondrial Cytochrome c Oxidase subunit I gene (COI) was used41. The ‘mini barcode’ primer pair consisted of the forward primer mlCOIintF 5′-ACACTCTTTCCCTACACGACGCTCTTCCGATCTGGWACWGGWTGAACWGTWTAYCCYCC -3′41 and the reverse primer dgHCO2198 5′- GTGACTGGAGTTCAGACGTGTGCTCTTCCGATCTTAAACTTCAGGGTGACCAAARAAYCA-3′41 (Illumina overhang in regular font and primer in bold). Library preparation was carried out using a two-step PCR approach42,43 , whereby PCR1 amplifies the gene region of interest and PCR2 adds the sample index together with the Illumina overhang (indexed primers). For each sample, a unique combination of indexes was chosen.DNA extracts were quantified using the Quantus Fluorometer (Promega). Ten nanograms of template DNA was used for PCR1. PCR1 consisted of 7.5 µl Q5 Hot Start High-Fidelity 2 × Master Mix (New England BioLabs), 1 μl Sigma H2O, 0.5 µl forward Primer (10 µM), 0.5 µl reverse primer (10 µM), 0.5 μl Bovine Serum Albumin (Thermo Scientific) and 1 µl template DNA, making up a total of 15 µl. PCR1 cycling conditions were as follows: 2 min at 98 °C (1 ×); 40 s at 98 °C, 40 s at 45 °C, 30 s at 72 °C (20 ×); 3 min at 72 °C (1 ×). PCR products were purified with 4 µl of HT ExoSAP-IT (Applied Biosystems) to each sample, following the manufacturers’ protocol. For PCR2 (index PCR) the purified PCR products were split into two PCR tubes.For PCR2, each tube contained 12.5 µl Q5 Hot Start High-Fidelity 2X Master Mix (New England BioLabs), 3 µl Sigma H2O, 1.2 µl of index forward primer (10 µM) (AATGATACGGCGACCACCGAGATCTACAC NNNNNNNN ACACTCTTTCCCTACACGACGC TC), 1.2 µl of index reverse primer (10 µM) CAAGCAGAAGACGGCATACGAGAT NNNNNNNN GTGACTGGAGTTCAGACGTGTGCTC) and 8 µl of purified PCR1 product. PCR2 cycling conditions were as follows: 2 min at 98 °C (1 ×); 40 s at 98 °C, 30 s at 55 °C, 30 s at 72 °C (20 ×); 3 min at 72 °C (1 ×). All tagged PCR products were visualised by gel electrophoresis and PCR bands with the expected size were excised and purified using the QIAquick Gel Extraction Kit (Qiagen). Purified PCR products were quantified using the Quantus Fluorometer (Promega) and pooled in equal concentrations. The resulting purified amplicon library pool (3 ng/µl) was sequenced on an Illumina MiSeq (MiSeq Reagent Kit v3, 2 × 300 bp) sequencing platform at Liverpool University’s Centre for Genomic Research (Liverpool, UK). Raw sequence data were deposited in the GenBank short read archive (SRA) under accession numberPRJNA681091 and PRJNA706915.Bioinformatics and data analysisThe raw fastq files were trimmed for the presence of Illumina adapter sequences using Cutadapt version 1.2.1. at the Centre for Genomic Research (Liverpool, UK). Sequences were trimmed using Sickle version 1.200 with a minimum window quality score of 20 and reads shorter than 20 bp were removed after trimming.The fastq sequences were then checked for the presence of the COI primers with Cutadapt version 1.1844 using the following settings: maximum error rate (-e): 0.1, minimum overlap (-O): 20, minimum sequence length (-m): 50. Sequences lacking either the forward or reverse primer were removed and primer pairs were trimmed off from the remaining sequences. Subsequently, paired-end reads were merged with vsearch version 2.7.045. Merged sequences with a length of 293–333 bp were retained for further analysis and filtered with a maxEE threshold of 1.0 using vsearch (version 2.7.0)45 before demultiplexing the fastq sequences using the script split_libraries_fastq.py implemented in QIIME146 using a phred quality threshold of 19. Dereplication, size sorting, denovo chimera detection as well as Operational Taxonomic Unit (OTU) clustering with a 97% cutoff was conducted with vsearch 2.7.045. Finally, an OTU table was built by using the –usearch_global function in vsearch 2.7.045 followed by the python script “uc2otutab.py” (https://drive5.com/python/uc2otutab_py.html). For taxonomy assignment, representative sequences were blasted against the GBOL database (https://www.bolgermany.de/gbol1/identifications downloaded on 2nd of July 2019) using blastn 2.9.0+47.The resulting OTU table was curated with LULU48. Curation started with an initial blasting of OTU representative sequences against each other using blastn (version 2.9.0). The following parameter settings were chosen: ‘query coverage high-scoring sequence pair percent’ (-qcov_hsp_perc) was set to 80, meaning that a sequence was reported as a match when 80% of the query formed an alignment with an entry of the reference file. Secondly, minimum percent identity (-perc_identity) was set to 84, requiring the reference and query sequence to match by at least 84% to be reported as a match. The format of the output file was customized using the –outfmt settings ‘6 qseqid sseqid pident’. The output file included the name of the query sequence and the name of the reference sequence next to the percentage match. The resulting OTU match list was uploaded into R (version 3.5)49 and the R-package ‘lulu’ (version 0.1.0)48 was used to perform post clustering curation using standard settings. The LULU algorithm filters the dataset for artificial OTUs and these were either classified as “daughter OTU” and merged with the corresponding “parent OTU” or were discarded from the dataset.The resulting curated OTU table was loaded into Excel where data was formatted to upload into R (R studio running R version 3.5). Only OTUs with an assignment at species level (blastID ≥ 99%) were used for subsequent analysis. Furthermore, results from the two types of soil extraction were merged.UpsetR plots were prepared using the R package UpSetR (version 1.4.0)50 for visualization of shared arthropod OTUs between sample types in each season. Differences in number of OTU proportions are shown in a Marioko plot prepared with the R package ggplot251. To analyze dissimilarities between communities depending on season and sample type, Permutational Multivariate Analysis of Variance (PERMANOVA) using Jaccard distance matrices for incidence data of detected arthropod species (blastID ≥ 99%) were performed using dplyr (version 0.8.3)52, betapart (version 1.5.1)53 and vegan (version 2.5–6)54. In order to analyse dissimilarity differences in arthropod community composition between the different forests and seasons the Jaccard similarity index (J) was used on a presence-absence matrix based on arthropod species. Calculated Jaccard indices were visualized on a heatmap using the R package ggplot251. Sample completeness curves and sample-size-based R/E curve with extrapolations of Hill numbers for incidence data based on the combined dataset for all forests and seasons were prepared using the R-package iNEXT55 at default settings (40 knots, 95% confidence intervals generated by the bootstrap procedure (50 bootstraps)).To correlate community structure and diversity levels with the different seasons and forest types a Permutational Multivariate Analysis of Variance (PERMANOVA) based on the Jaccard similarity index for a presence-absence matrix of detected arthropod species (blastID ≥ 99%) was performed with the adonis function in R. Differences in arthropod community composition between the different forests and seasons was assessed using the Jaccard similarity index (J), where the higher the index, the more similar the communities. More

Host and siteB. ermanii Chamiss, a deciduous broad-leaved tree species, occurs naturally in open spaces within subalpine and boreal forests in Northeast China, Japan and the Russian Far East.40,41,42 B. ermanii is also a typical tree species of the timberline, because it can resist to severe frost, strong wind and low temperature by ecophysiological and ecomorphological flexiblity.43,44,45 In addition, a rich mycobiome of B. ermanii has been reported,16,46,47 which may facilitate the survival and spread of the host plant.On the northern slope of Changbai Mountain, Northeast China, B. ermanii grows over a broad elevation range from ca. 1700 to 2100 m a.s.l., and forms pure stands along >300 m vertical belt below the timberline.42,48 The establishment of Changbai Nature Reserve (CNR) in 1960 gave strict protection to the Erman’s birch (B. ermanii) forests.49 All our sampling was located within the core region of the CNR. The region has a typical continental temperate monsoon climate, with higher elevations experiencing lower temperature and greater precipitation.50 Soils of the Erman’s birch forests are Permi-Gelic Cambosols, whereas the soils beyond the upper and lower limits of B. ermanii zone are Permafrost cold Cambosols and Umbri-Gelic Cambosols, respectively. Climate change, particularly rising temperature, threatens the populations of B. ermanii and the whole Erman’s birch forest ecosystem in Changbai Mountain.50,51Field sample collectionWe sampled fine roots and neighboring soils for B. ermanii individuals at six elevation-related habitats of B. ermanii on 2–8 September, 2018 (Fig. 1a). These six elevation habitats include the upper limit (2069–2116 m), tree islands (1997–2042 m), treeline (1949–1992 m), pure stands (including two sub-sites isolated by over 2 km; 1900–1926 m), ecotone of dark coniferous forests and Erman’s birch forests (1742–1765 m) and lower limit (sparse individuals in coniferous forests; 1688–1706 m), respectively. In each habitat, 14 trees were randomly selected, and all trees were located more than 20 m apart from other sampled trees to ensure independence of each sample. Neighboring soils and fine roots were collected according to the protocols of Yang et al.28 and Lankau and Keymer,52 respectively. Briefly, with the trunk as center and the DBH as distance from the stem, we collected four soil cores (diameter = 3.5 cm, depth = 10 cm) after removal of litter and mixed them as a single composite soil sample (Fig. 1b). We excavated surface soils near the base of trees and traced roots from the base to terminal fine roots in three directions. The fine roots of three directions were combined as a composite fine root sample, and each raw sub-fine-root section was nearly 6 cm wide and 8 cm long (Fig. 1c, d). All the samples were brought back to the laboratory with ice bags within 8 h. Soil was sieved through a 2-mm mesh and divided into two subsamples: one was stored at 4 °C to determine the soil properties, whereas the other was stored at −40 °C for subsequent DNA extraction. Fine roots were rinsed with sterile water and cut into 1.5-cm segments: one subsample (ca. 80%) was stored at 4 °C to determine root biochemical traits, and the other subsample (ca. 20%) was stored at −40 °C for subsequent DNA extraction. In the field, tree height, canopy diameter, DBH, elevation, slope, latitude, and longitude of each sampled tree were recorded. In total, 84 fine roots and 84 neighboring soils were collected.Fig. 1: Sampling map and procedures in this study.a Sampling map in the core region of CNR: the icons with different colors represent the tree individuals of B. ermanii. Contours were fitted in a map of Google Earth. b The sampling procedure of neighboring soils: each red point represent one soil core with depth 0–10 cm and diameter 3.5 cm. c The sampling procedure of fine roots: each red square (nearly 6 × 8 cm) represent a sub-fine-root system (namely, d).Full size imageMeasurement of soil properties and root traitsWe measured 28 soil properties, including soil pH, moisture, conductivity, dissolved organic carbon, dissolved organic nitrogen (DON), ammonium nitrogen, nitrate nitrogen, total carbon, total nitrogen, total phosphate, total potassium, total calcium, total magnesium, total manganese, total iron, total aluminum, available phosphate, available potassium, available calcium, available magnesium, available manganese, available iron, available aluminum, C/N ratio, C/P ratio and the proportions of clay, silt and sand. The measurement methods of soil pH, moisture, ammonium nitrogen, nitrate nitrogen, total carbon, total nitrogen and total content of other elements followed our recent study.28 In addition, soil conductivity was determined with a soil to water ratio of 1:5 by conductivity meter (Mettler Toledo FE30, Shanghai, China). Mehlich 353 and three-acid-system (nitric acid, perchloric acid, and hydrofluoric acid) were used to extract the available and total content of elements, respectively. Total and available content of phosphate, potassium, calcium, magnesium, manganese, iron, and aluminum were measured using an ICP Optima 8000 (Perkin-Elmer, Waltham, MA, USA). The proportions of clay, silt, and sand were measured by Laser Particle Sizer LS13320 (Beckman, Brea, CA, USA).Eighteen root traits, including root total carbon (RTC), root total nitrogen (RTN), root phosphate, root potassium, root calcium, root magnesium, root manganese, root iron, root aluminum, root C/N ratio, root N/P ratio, lignin, cellulose, hemicellulose, soluble sugar, soluble protein, free amino acid (FAA) and free fatty acids (FFA), were also measured. Specifically, RTC and RTN were determined with a carbon–hydrogen–nitrogen (CHN) elemental analyzer (2400 II CHN elemental analyzer; PerkinElmer, Boston, MA, USA). Root phosphate, root potassium, root calcium, root magnesium, root manganese, root iron, and root aluminum were measured in ICP Optima 8000 (Perkin-Elmer, Waltham, MA, USA). Soluble protein was measured by a dye-binding assay.54 FAA was analyzed by the amino acid analyzer L-8800 (Hitachi, Tokyo, Japan) with leucine as the standard sample. FFA was determined by NEFA FS kits (Diasys, Holzheim, Garman) and the automatic biochemical analyzer AU680 (Olympus, Tokyo, Japan). The measurement methods of lignin, cellulose, hemicellulose, and soluble sugar followed that of our previous study.16Calculation of distance to forest edgeThe location of each tree individual was determined by latitude and longitude. A high-resolution map (treecover2000) on global forest cover at a spatial resolution of 30 m was used as a base map.55 In the map, the areas where forest cover was more than 30% were defined as the “mainland” in the IBT framework and shown as the green grids in ArcGIS (Fig. S1). This standard referred to the proposal of Convention on Climate Change Kyoto.56 Then, we calculated the minimum distance of each tree to the neighboring forest edge (i.e., green grids) by using the function Near of the Proximity tool box in ArcGIS 10.0 (ESRI, Redlands, CA, USA).Sequencing and bioinformaticsSoil total DNA was extracted from 0.5 g of soil by using FastDNA® Spin kit for Soil (MP Biomedicals, Solon, Ohio, USA). Total DNA of fine roots was extracted from 0.3 g of plant tissue by using Qiagen Plant DNeasy kits (Qiagen, Hilden, Germany). PCR procedures, including primers (ITS1-F: CTTGGTCATTTAGAGGAAGTAA, ITS2: GCTGCGTTCTTCATCGATGC) and conditions were described in our previous studies.16,28 The PCR products of all samples were normalized to equimolar amounts and sequenced on the Illumina MiSeq PE300 platform of the Majorbio Company, Shanghai, China.We first merged the paired-end reads using FLASH.57 QIIME 1.9.058 and Cutadapt 1.9.159 were applied for quality filtering, trimming, and chimera removal. Altogether 8,238,146 sequences passed quality filtering (parameters: minlength = 240; maxambigs = 0; phred quality threshold = 30). ITSx 1.0.11 was used to remove the flanking small ribosomal subunit (SSU) and 5.8 S genes,60 leaving the ITS1 region for further analyses. The putative chimeric sequences were removed using a combination of de novo and reference-based chimera checking, with the parameter –non_chimeras_rentention = union in QIMME.61 The remaining sequences were then clustered into operational taxonomic units (OTUs) at 97% similarity threshold by using USEARCH.62 Singletons were also removed during the USERCH clustering process. Fungal taxonomy was assigned to each OTU by using the Ribosomal Database Project Classifier with minimum confidence of 0.8.63 The UNITE v.8.0 (http://unite.ut.ee) release for QIIME served as a reference database for fungal taxonomy.64 The OTU table was then curated with LULU, a post-clustering OTU table curation method, to improve diversity estimates.65After removing non-fungal sequences, the final data set included 7,849,126 fungal sequences covering 6663 OTUs in 168 samples (minimum 4662; maximum 70,779; mean 46,721 sequences per sample). The rarefaction curves of the average observed OTU number are shown in Fig. S2. FUNGuild was used to assign each OTU to a putative functional guild, and the assignments with confidence ranking “possible” were assigned as “unknown” as recommended by the authors.66 We further modified the assignment of EcM fungi (the subject in the present study) and their lineages according to.31 For some OTUs that were simultaneously assigned to endophytic, saprotrophic, or pathogenic fungi, we considered these as endophytes in roots and saprotrophs in soil samples.StatisticsAll statistical analyses were conducted in R 3.5.267 and AMOS 21.0 (AMOS IBM, New York, USA). In order to analyze the alpha diversities of soil fungi and the three most dominant guilds (viz., EcM, endophytic and saprotrophic fungi) at the same sequencing depth, the data set was subsampled to 4662 reads with 30 iterations. The mean number of observed OTUs was used to represent the diversities of total fungi, EcM fungi, endophytic fungi, and saprotrophic fungi, as previously implemented in.15,68 Numbers of EcM fungal lineages and saprotrophic genera, families, orders, and classes of each sample were also calculated based on the same subsampling.First, linear and quadratic regression models were used to determine the effect of elevation on diversities of total fungi, EcM fungi, endophytic fungi, and saprotrophic fungi. The model with lowest Akaike’s information criterion (AIC) value was selected. In order to account for spatial effects, linear mixed-effects models (LMMs) were fitted using the lme4 package69 to analyze the variation in diversities of total fungi, EcM fungi, endophytic fungi, and saprotrophic fungi along the elevation gradient with latitude and longitude as random factors. Corrected Akaike Information Criterion (AICc) for small data sets was used to identify the best mixed-effects model from linear and quadratic polynomial models. The significance of each LMM was tested by the function Anova in the car package.70 Marginal (m) and conditional (c) R2 were calculated by the function r.squaredGLMM in the MuMIn package.71 Marginal R2 (R2m) represents the variance explained by fixed effects, whereas conditional R2 (R2c) represents the variance explained by both fixed and random effects.Second, to test the application of IBT on EcM fungal diversity, DBH and RTC of B. ermanii were chosen as proxies of island area and energy, respectively, whereas DFE was chosen as the proxy of island isolation (i.e., island distance to mainland). Linear regression models were used to assess the species-area, species-energy, and species-isolation relationships. In order to account for spatial effects, LMMs were also used for these independent relationships with latitude and longitude as random factors as described above. Classical power-law function models were used to identify the species-area relationship for EcM fungal diversities in roots and soils using z-values in the formula S = CAz 72 to compare EcM fungi with macroorganisms in previous studies. Furthermore, ordinary least squares (OLS) multiple regression models were performed to identify the relative contributions of DBH, RTC, and DFE on pattern of EcM fungal diversity when considering other predictive variables. Here, five spatial vectors (PCNM1-5) with significant positive spatial autocorrelation (Fig. S3) were obtained by the principal coordinates of neighbor matrices (PCNM) method,73 and added into OLS multiple regression models to consider the possible geographic effect. EcM fungal diversities in roots and soils, 28 soil properties, 18 root traits, elevation, slopes, DBH, tree height, canopy diameter, and DFE were standardized (average = 0 and SD = 1) before the OLS multiple regression analysis. AIC was used to identify the best OLS multiple regression model, as implemented in the MASS package.74 Variance inflation factor (VIF) was calculated for each model by the function vif in the car package. We used the criterion VIF  More

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