Ecology

Relative species abundance distribution
In order to evaluate sample quality, we analysed both the Relative Species Abundance distribution (RSA) and the rarefaction curves. For each sample, we compared the RSA derived by shotgun and 16S sequencing. RSA histograms in logarithmic scale show that the distributions obtained by shotgun and 16S have similar shape at phylum level (Fig. 1a, b). In Fig. 1b, the 16S sample is characterized by a more patchy distribution, having identified less phyla. At phylum level, both strategies produce positively skewed samples in the log2-transformed distributions, except for 16S outliers, because none of the phyla is significantly rare (Fig. 2a).
Figure 1

RSA histograms in logarithmic scale (Preston plots 21) of bacterial abundances in one sample selected as anexample (caeca25): (a) genera sampled by shotgun sequencing, (b) genera sampled by 16S rRNA sequencing, (c) phyla sampled by shotgun sequencing and (d) phyla sampled by 16S sequencing.

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Figure 2

Box plot of the RSA skewness of bacterial communities at (a) phylum level and (b) genus level. Bacterial communities are sampled with (left) shotgun sequencing and (right) 16S sequencing.

Full size image

On the other hand, at genus level, the two strategies display different shapes (Fig. 1c, d, Supplementary Fig. S1, S2, S3, S4). Indeed, the log2-transformed distributions derived by shotgun sequencing generally have a skewness closer to zero compared to those obtained by 16S, i.e. are more symmetrical (Figure 2b): a paired Student’s t-test on the skewness shows a significant difference between them (P = 8·10–6). This indicates that shotgun samples are characterized by a higher sampling size. According to Preston, left-skewed shapes of the RSA can be explained as artefacts of small sample size21,22, since insufficient sampling of the original space produces a truncation of the left tail of the RSA, increasing its skewness.
In shotgun samples, the RSA skewness at genus level is related to the total number of reads (Supplementary Fig. S5): the shotgun samples with the lowest total number of reads have the largest skewness. Specifically, Supplementary Figure S5 shows that shotgun samples cluster in two groups, one characterized by a low number of reads (# reads  500,000, 50/78 samples) and a less skewed RSA.
Noticeably, the high-skewness group includes all 9 samples from 1st day, all 15 crop samples from 14th day and 4 out of 18 crop samples from 35th day. The samples collected at day 1 were very poor in terms of biomass and the crop samples contained more feed residues than caecal samples, making the DNA extraction less efficient both in terms of DNA quantity and quality. For the comparative analysis we removed samples with less than 500,000 reads being characterized by a low quality. This choice was corroborated by the analysis of the rarefaction curves, showing that shotgun samples with less than 500,000 reads do not reach a plateau in terms of identified genera (Supplementary Fig. S6). All the 50 samples included in the comparative analysis have a total number of reads  > 500,000 and a skewness lower than the median of 16S samples, indicating a good sampling depth. Since included samples were characterized by a high microbial load, we are confident to extend the results of the following analyses only to samples with few contaminant DNA and low cross-contaminations. Nonetheless, we have shown that shotgun samples have a RSA similar to 16S samples when a low number of total reads is available, thus hypothesizing that in differential analyses carried on samples with a low microbial load regime, shotgun sequencing could perform similarly to 16S sequencing or even worse.
For a balanced comparison, also 16S samples corresponding to the discarded shotgun samples were removed.
Differential analysis for the experimental conditions
Since in many situations a metagenomic analysis is used to discriminate between different experimental conditions, we compared the results of differential analysis performed on reads obtained by the two strategies. To this aim, we analysed the fold changes of genera abundances between compartments of the GI tract and between sampling times (Fig. 3 for caeca vs crop, Supplementary Fig. S7 for 14th vs. 35th day) common to both sequencing strategies (288 genera for caeca vs crop, and 246 for 14th vs. 45th day). Comparing the genera abundances between caeca and crop, 16S identified 108 statistically significant differences (adjusted P  More

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Sprouting behaviour of potato tubers
In this study, the stored tubers exhibited clear variety-specific differences in sprouting behaviour, with the Agata variety being the earliest and the Hermes variety the latest to sprout. However, within each variety, there were differences in sprouting time depending on the soil in which the tubers had grown (Suppl. Table 1). These soil-dependent differences in sprouting were greatest in the Fabiola variety (sprouting time ranged from 135 to 169 days after harvest) and least significant in the Hermes variety (158 to 168 days after harvest). By examining the storage stability of tubers broken down by soil type, we found that tubers grown in soil from the field site in Karnabrunn sprouted on average up to 9 days later than the tubers from other soils. The chemical profile of the soil collected in Karnabrunn was similar to that of the other farmland soils, especially those from Kettlasbrunn. The soil collected in Tulln showed reduced K and P contents compared to those of the other farmland soils. As expected, the potting soil differed most significantly from the other soils, i.e., there was no clay, and the exchange capacity was substantially higher than that of the farmland soils (Suppl. Table S2). Statistical analysis revealed that the chemical parameters of the soils did not correlate with the sprouting behaviour of tubers (data not shown).
Sequencing results
The sequencing of 16S rRNA gene amplicons of tubers, sprouts and soil samples yielded 9,158,550 high-quality merged reads, corresponding to an average of 33,920 reads per sample. All sequences were cut to a read length of 360 bp. To ensure sufficient diversity by maintaining an adequate sequencing depth, samples with a low read number were excluded from the analysis. Therefore, the data of four samples were excluded from further analysis (LC_T3_PS; LC_T7_K; H_T6_K: LC_T7_T; H_T6_K; F_T7_K). A detailed explanation for the sample naming can be found in Table 1. Sequencing reads from all 270 samples were clustered into operational taxonomic units (OTUs), which resulted in 11,485 OTUs with an average of 42,537 OTUs per sample.
Table 1 Abbreviation of sample names.
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The bacterial community of potato tubers during storage
To test whether the bacterial community in potato tubers changes during storage, the 16S rRNA gene amplicon data of the potato tubers of the Agata, Lady Claire and Hermes varieties, cultivated in five different soil types (T2), stored until dormancy break (T6) and until sprouting (T7) were analysed as well as samples of the sprouts (T7_Sprouts) (Fig. 1). Cultivation of the cultivar Fabiola in the soil Kettlasbrunn B did not yield sufficient tubers for analysis throughout the whole storage period, i.e., no data were available for T7 and the sprouts. Therefore, community data for the Fabiola variety were not included in the following statistical analysis.
Figure 1

Overview of potato cultivars, sampling time points and corresponding BBCH stages investigated in this study. After harvesting four tuber varieties (Agata, Fabiola, Lady Claire and Hermes) from five different soil types (T2), tubers were stored at 8–10 °C in darkness. After 2 (T3), 5 (T4) and 10 weeks (T5), tubers were sampled. To consider the individual dormancy break (T6) of each variety, tubers were sampled according to the BBCH scale at stage 03. The same procedure was performed for samples that were taken at sprouting at stage 05 (T7). Additionally, at T7, sprout samples were taken. At each sampling time point, tuber/sprout samples were used for 16S rRNA gene amplicon sequencing. The red circles mark sites on the tubers that show visible signs of sprouting.

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For the statistical analysis, we selected only OTUs that showed at least 0.01% relative abundance (1425 OTUs) and that were present in at least two of three replicates (1395 rOTUs). We considered them “reproducibly occurring OTUs” (rOTUs)2.
For calculation of alpha diversity values, read numbers were rarefied to 6785 reads in each sample. The permutation ANOVA of rOTU richness (9999 permutations) revealed significant differences in the bacterial community of tubers and sprouts between cultivars, time points and soil types (observed for cultivar (F value = 3.963, P value = 0.0211*), for time point (F value = 4.762, P value = 0.0021*) and for soil type (F value = 3.779, P value = 0.0057**). The same results were obtained with Simpson’s index for the factors cultivar (F value = 4.594, P value = 0.01*), time point (F value = 6.741, P value = 0.0004***) and soil type (F value = 5.123, P value = 0.0008***) (Suppl. Table S3). Overall, the statistical analysis showed that the soil type had the strongest impact on the microbial community in potato tubers, followed by time point and cultivar.
Similarly, the bacterial community composition (beta diversity) in potato tubers was significantly affected by the storage time, soil type and plant variety. The CAP ordination plot indicated a shift in the bacterial community of tubers from harvest to dormancy break and sprouting, which could be proven by PERMANOVA on the Bray–Curtis dissimilarity distance matrix (R2 = 0.113, P value = 0.0004***) (Fig. 2A). Additionally, the bacterial communities in tubers grown in different soil types (R2 = 0.255, P value = 0.0004***) and of different varieties were significantly different from one other (R2 = 0.027, P value = 0.0021**) (Suppl. Table S4). The results for the factor time point (P value = 0.01**), genotype (P value = 0.01**) and soil type (P value = 0.01**) could be confirmed by the multivariate generalized linear model for multivariate abundance data on the Bray–Curtis dissimilarity distance matrix (999 permutations) (Suppl. Table S4).
Figure 2

Constrained analysis of principal coordinates (CAP) of Bray–Curtis dissimilarities. CAP based on the V5–V7 regions of the 16S rRNA gene investigated for (A) tubers of the varieties (Agata, Lady Claire and Hermes) sampled at T2, T6 and T7 and (B) tubers of the varieties (Agata, Lady Claire and Hermes) sampled at T2-7 as well as sprout samples at T7. An overview of potato cultivars, soil types and sampling time points is shown in Fig. 1.

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The dynamics of bacterial communities in potato tubers during storage
To obtain more in-depth insight into the changes in community composition during storage, we compared the bacterial communities in tubers of the Agata, Lady Claire and Hermes varieties grown in potting soil at six different timepoints: T2 (harvest), T3 (2 weeks after harvesting), T4 (5 weeks after harvesting), T5 (10 weeks after harvesting), T6 (dormancy break), T7 (sprouting) and in the corresponding sprouts (T7_Sprouts) (Fig. 1). We focused here on tubers grown in potting soil, since the cultivation of potatoes in farmland soil did not yield sufficient tubers to be analysed throughout the entire storage period.
Again, we filtered data for OTUs with at least 0.01% relative abundance and “reproducibly occurring OTUs”. After both filtering steps, 1108 rOTUs remained. Before calculating alpha values, read numbers were rarefied to 6761 reads in each sample. The permutation ANOVA of richness and evenness (9999 permutations) did not reveal differences in the alpha diversity of the tuber microbiome between cultivars but between time points (observed species F value = 6.159, P value = 0.0004*** and Simpson’s index F value = 2.216, P value = 0.0263*) (Suppl. Table S3). The bacterial richness of each cultivar declined significantly during the period between harvest (T2) and the dormancy break (T6) (Suppl. Figure S1B). The CAP scaling plot of six different time points during storage and the corresponding sprouts indicated a shift from harvest to sprouting (Fig. 2B). The PERMANOVA on the Bray–Curtis dissimilarity distance (9999 permutations) revealed that the microbiomes of tuber samples differed significantly between the cultivars (R2 = 0.069, P value = 0.0004***) and time points (R2 = 0.221, P value = 0.0001***) (Suppl. Table S4). The test results for cultivar (P value = 0.01**) and time point (P value = 0.01**) were confirmed by the multivariate generalized linear model for multivariate abundance data on the Bray–Curtis dissimilarity distance matrix (999 permutations) (Suppl. Table S4). To identify the bacterial taxa that changed over time during storage, differentially abundant rOTUs were calculated with the random forest function and visualized in Fig. 3 at the genus level. The relative abundance of Staphylococcus sp. increased during the period from harvesting (T2) to dormancy breaking (T6) from approximately 0% to 11% relative abundance. A similar result was visible for Propionibacterium sp. and Acinetobacter sp. The relative abundance of both was approximately 2% in tubers after harvesting (T2) and increased during storage to 8% and 9% in dormancy broken tubers (T6), respectively, whereas the relative abundance of the taxa Iamia sp. and Nocardioides sp. decreased from approximately 10% after harvesting to 4% and 6% in already sprouted tubers (T7), respectively (Suppl. Tables S5 and S6).
Figure 3

Differentially abundant taxa at the genus level. Visualization of differentially abundant taxonomic groups at the genus level of the bacterial community in tubers of three different potato cultivars (Agata, Hermes and Lady Claire) at all sampling time points T2-7 as well as in sprout samples at T7. Differentially abundant taxa were calculated with the function varSelRF48 and visualized in barplot with the function group.abundant.taxa of the R package RAM47.

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Taxa associated with short, medium or long storage stability
To identify the bacterial taxa in the potato tuber microbiome associated with early or late potato tuber sprouting, sample data were grouped into short, medium and long storage abilities based on the individual storage time (in days from harvest until sprouting) of the samples. The data of all samples, including those of cultivar Fabiola, were considered for the following analysis (Fig. 1). After filtering for the OTUs with at least 0.01% relative abundance and presence in at least two of three replicates, 813 rOTUs were obtained. To identify rOTUs associated with short, medium or long storage stability at the beginning and end of the storage period of the potato tubers, two different analysis steps were performed. In the first step, differentially abundant rOTUs depending on storage stability (short, medium or long) and storage time points (T2, T6 and T7) were calculated with the random forest function (Suppl. Table S7). In a second step, a correlation matrix based on Spearman’s rank correlation was calculated based on the previously described factor storage stability and storage time points to identify positive or negative interactions between rOTUs (Suppl. Table S8). The same rOTUs obtained with random forest analysis, as well as with the correlation matrix, based on Spearman analysis, were filtered and named key OTUs (Suppl. Table 9). Even if both analysis steps do not provide the same evidence, they provide a meaningful indication of which OTUs are related to the factors, storage stability and storage time point. In total, we identified 24 key OTUs. The relative abundance of nine key OTUs was associated with long storage stability, meaning that the OTUs were significantly increased in samples where dormancy break (T6) and sprouting (T7) started late. These key OTUs are members of the orders Flavobacteriales, Cytophagales, Sphingobacteriales, Gaiellales, Corynebacteriales, Caulobacterales, Methylophilales and Solirubrobacterales. Additionally, the relative abundance of eight rOTUs was associated with short storage stability. These rOTUs are members of the orders Enterobacteriales, Pseudomonadales, Myxococcales, Rhizobiales, Bacillales and Burkholderiales. The relative abundance of seven key OTUs was associated with medium storage stability.
Testing the effect of selected bacterial taxa on potato tuber sprouting
In the next step, we tested whether the bacterial taxa that correlated with longer storability can directly affect the sprouting of potato tubers. Therefore, we screened a collection of bacteria isolated from seed potatoes18,20 for isolates that are homologous in the 16S rRNA gene to the key OTUs identified in the statistical analysis. We identified two isolates that were homologous to OTU_14 (Flavobacterium sp.), which correlated with late sprouting. The selected isolates were tested in an in vitro sprouting assay adapted from Hartmann et al.21. Tuber discs treated with cultures of Flavobacterium sp. isolates (AIT1165 and AIT1181) resulted in sprout growth inhibition compared to control discs treated with sterile tryptic soy broth (Fig. 4). Furthermore, we observed significant individual differences in the sprouting behaviour of the tested buds. Differences in sprouting behaviour are only partly genotype-dependent, but these differences might also be due to the natural developmental variability between buds. The apical eye on a tuber usually begins to sprout first, marking the start of the apical dominance stage22. For the sprouting assay performed in this study, we took several buds from one tuber independently of their position.
Figure 4

In vitro potato tuber sprouting assay results. Tuber buds of three different varieties (Lady Claire, Ditta and Agata) were treated with two different isolates of Flavobacterium sp. (AIT1165 and AIT1181). For evaluation, bud growth was assessed according to the first principal growth stages of the BBCH scale. Hereby, the first stage 00 is considered innate or enforced dormancy with no sprouting at all, followed by stages 01 and 02, which represent the beginning of sprouting when sprouts are visible with sizes up to  More

Phylogenetic analysis
A 1444 bp fragment of the 16S rRNA gene was amplified from the P. eucalypticola strain NP-1 T, sequenced and the sequence deposited in GenBank under accession number MN 238,862. A similarity search with this sequence was performed using EzBioCloud. Thirty valid species belonging to P. fluorescens intrageneric group (IG) proposed by Mulet et al.15 exhibited at least 97% similarity with NP-1 T, and these include P. vancouverensis ATCC 700688 T (98.8% similarity), P. moorei DSM12647T (98.8% similarity), P. koreensis Ps9-14 T (98.8% similarity), P. parafulva NBRC16636T (98.5% similarity) and P. reinekei Mt-1 T (98.5% similarity). The similarities with the other 25 species are provided in Supplementary Table S1. A phylogenetic tree based on the 16S rRNA sequence was constructed and is shown in Fig. 1. Strain NP-1 T forms a weakly supported cluster with P. kuykendallii NRRL B-59562 T, but both strains are situated on separate branches. Strain NP-1 T grouped in none known group or subgroup within P. fluorescens lineage, and it clusters of the outer edge of a much larger group containing several Pseudomonas groups/subgroups. However, Pseudomonas species cannot be identified based only on 16S rRNA analysis.
Figure 1

Neighbor-joining phylogenetic tree based on the 16S rRNA gene of Pseudomonas eucalypticola NP-1T and phylogenetically close members of Pseudomonas. The evolutionary distances were computed using the Jukes-Cantor method. The optimal tree with a sum of branch length = 0.23535266 is shown. The percentage of replicate trees in which the associated taxa clustered together in the bootstrap test (1000 replicates) is shown next to the branches. Cellvibrio japonicus Ueda107T was used as outgroup.

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The MLSA approach based on the concatenated sequences of the partial 16S rRNA, gyrB, rpoB and rpoD genes, has been demonstrated to greatly facilitate the identification of new Pseudomonas strains16. According to the 16S rRNA alignment, 33 species from P. fluorescens IG and one species from P. pertucinogena IG were selected for MLSA. The concatenated sequences of the type strains of each selected species comprised a total of 3813 bp (Supplementary Table S2) and were used for phylogenetic tree construction. The analysis of concatenated gene sequences indicated that strain NP-1 T belongs to the P. fluorescens lineage, and this finding was supported by a bootstrap value of 91% (Fig. 2).However, NP-1 T still cannot be determined which group belongs to17.
Figure 2

Neighbor-joining phylogenetic tree based on concatenated 16S rRNA, gyrB, rpoB and rpoD gene partial of Pseudomonas eucalypticola NP-1T and the type strains of other Pseudomonas species. The evolutionary distances were computed using the Jukes-Cantor method. The evolutionary distances were computed using the Jukes-Cantor method e optimal tree with the sum of branch length = 1.37677586 is shown. The percentage of replicate trees in which the associated taxa clustered together in the bootstrap test (1000 replicates) is shown next to the branches.

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For further identification of NP-1 T, a phylogenomic tree inferred with GBDP was constructed by using Type (Strain) Genome Server (TYGS)18, and all reference type strains and their genome sources are listed in Supplementary Table S3. The result showed the presence of an independent branch supported by a bootstrap value of 88% that can be differentiated from the other Pseudomonas species type strains (Fig. 3) and revealed that NP-1 T clustered with P. coleopterorum LMG 28558 T and P. rhizosphaerae LMG 21640 T which affiliated with P. fluorescens IG, but does not belong to any group. Strain NP-1 T was not be affiliated with any previously described Pseudomonas species and can thus be considered to represent a novel species. Based on above-described the results, P. coleopterorum, P. rhizosphaerae, P. graminis and P. lutea were selected for further analysis with NP-1 T.
Figure 3

Phylogenomic tree of strain NP-1T and related type strains of the genus Pseudomonas available on the TYGS database. The tree inferred with FastME 2.1.6.1 based on GBDP distances calculated from the genome sequences. The branch lengths are scaled in terms of the GBDP distance formula d5. The numbers above the branches show the GBDP pseudo-bootstrap support values  > 60% from 100 replications, and the average branch support is 94.6%.

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General taxonomic genome feature
The draft genome assembly of strain NP-1 T contains 6,401,699 bp. The genome of NP-1 T, which consists of one chromosome and one plasmid, has been deposited in GenBank under the accession numbers CP056030 and CP056031, respectively. The genome has a G + C content of 63.96 mol%, as determined from the complete genome sequence, and 83.45% of the genome is coding and consists of 5,788 genes. The similarity of the genome of P. eucalypticola NP-1 T to other publicly available genomes of closely related Pseudomonas species was determined using ANI, digital DDH and G + C mol %5,6,7,8,9. Each of these comparisons yielded different ANIm and ANIb values, but the highest ANIb and ANIm values of 78.7 and 86.5 were obtained for NP-1 T and P. rhizosphaerae LMG 21640 T. The similarity between P. coleopterorum LMG 28558 T and NP-1 T was higher than that between P. graminis DSM 11363 T and P. lutea LMG 21974 T (Table 1). All ANIb and ANIm values obtained from the comparisons of NP-1 T with the other tested species were below 95%, which confirmed that strain NP-1 T belongs to an independent species. The TETRA frequencies between NP-1 T and the other tested type strains were lower than 0.99, which is the recommended cutoff value for species (Table 2). The digital DNA-DNA hybridization (dDDH) comparison with the draft genome of the type strain NP-1 T yielded low percentages ( More

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Study area
The study was conducted across the Loess Plateau (33°43′–41°16′N, 100°54′–114°33′E) (Fig. 1a), which represents approximately 6.5% of the total area of China6. The study area is dominated by temperate, arid, and semiarid continental monsoon climates. The annual evaporation is 1400–2000 mm, and the annual temperature ranges from 3.6 °C in the northwest to 14.3 °C in the southeast on the Loess Plateau7, while the annual precipitation ranges from 150 to 800 mm, where 55–78% of the precipitation falls from June to September7. The annual solar radiation ranges from 5.0 × 109 to 6.7 × 109 J m−2. The vegetation zones are forest, forest-steppe, typical-steppe, desert-steppe, and steppe-desert zones8 from southeast to northwest.
Figure 1

Locations of the Loess Plateau region in China (a) and the sampling sites (b); image data processed by ArcGIS 10.5 http://developers.arcgis.com.

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Field sampling
According to the different climate zones and vegetation types, five classic sampling sites were selected (Fig. 1b) on the Loess Plateau, which were Yangling, Changwu, Fuxian, Ansai, and Shenmu from south to north. Drilling equipment (assembled by Xi’an Qinyan Drilling Co. Ltd, China) was used to collect soil samples from soil surface down to bedrock. At each sampling site, disturbed soil samples were collected to determine the SAP and SAK concentrations, pH, soil particle composition, and soil organic matter contents. In addition, disturbed soil samples were collected from the middle of the soil column at 1-m intervals (i.e., 0.5 m, 1.5 m, 2.5 m, 3.5 m, etc.). The drilling and sampling work was carried out from April 28 to June 28, 2016. The total numbers of disturbed soil samples collected from Yangling, Changwu, Fuxian, Ansai, and Shenmu were 103, 205, 181, 161, and 58, respectively, and the corresponding soil drilling depths were 103.5 m, 204.5 m, 187.5 m, 161.6 m, and 56.6 m, respectively.
Laboratory analyses
Undisturbed soil samples were air-dried, separated, and passed through 0.25-mm or 2-mm sieves. SAP and SAK were extracted with ammonium lactate solution and detected by spectrophotometry and flame photometry. Soil total nitrogen (STN) concentrations were determined by the Kjeldahl digestion procedure9. Soil total phosphorus (STP) concentrations were determined by molybdenum antimony blue colorimetry10. The soil organic carbon (SOC) contents were analyzed by dichromate oxidation method11. The soil particle composition was determined by laser diffraction (Mastersizer 2000, Malvern Instruments, Malvern, UK)12. According to the mixture of soil and water mass ratio of 1:1, the pH value was determined with a pH meter equipped with a calibrated combined glass electrode. The soil water content (SWC) was determined by the mass loss after drying to constant mass in an oven at 105 °C13. The calcium carbonate content was determined by the acid-neutralization method14.
Geostatistical analysis
The geostatistical analysis was chosen to determine the spatial structure of the spatially dependent soil properties15, where a semivariogram was employed to quantify the spatial patterns of the variables. The equation for the semivariogram is16:

$$ {text{R}}left( {text{h}} right) , = frac{1}{{2{text{N}}left( {text{h}} right)}}mathop sum limits_{{{text{i}} = 1}}^{{{text{N}}left( {text{h}} right)}} left[ {{text{Z}}left( {{text{x}}_{{text{i}}} } right){-}{text{Z}}left( {{text{x}}_{{{text{i}} + {text{h}}}} } right)} right]^{{2}} , $$
(1)

where for each site i, N(h) is the number of pairs separated by h, and Z(xi) is the value at location xi and Z(xi+h) for xi+h. There are four semivariogram models (spherical, exponential, linear, and Gaussian), which can be employed to describe the semivariogram, and the best fitting model is selected according to the smallest residual sum of squares (RSS) and the largest coefficient of determination (R2). The equation of each semivariogram model is16:
Exponential model:

$$ {text{R}}left( {text{h}} right) = {text{C}}_{0} + {text{C}}left[ {({1}{-}{text{exp}}( – {text{h}}/{text{A}}_{0} )} right] $$
(2)

Linear Model:

$$ {text{R}}left( {text{h}} right) = {text{C}}_{0} + left[ {{text{h}}left( {{text{C}}/{text{A}}_{0} } right)} right] $$
(3)

Spherical Model:

$$ {text{R}}left( {text{h}} right) = {text{C}}0 + {text{C}}left[ {{1}.{5}left( {{text{h}}/{text{A}}_{0} } right) – 0.{5}left( {{text{h}}/{text{A}}_{0} } right)^{{3}} } right] ;;;;;;;;; {text{h}} le {text{A}}0 $$
(4)

$$ {text{R}}left( {text{h}} right) = {text{C}}_{0} + {text{C}};;;;;;;;;;{text{h}} ge {text{A}}0 $$
(5)

Gaussian Model:

$$ {text{R}}left( {text{h}} right) = {text{C}}_{0} + {text{C}}left[ {{1} – {text{exp}}left( { – {text{h}}^{{2}} /{text{A}}_{0}^{{2}} } right)} right] $$
(6)

where C0 indicates the nugget value, which is the short-range structure that occurs at distances smaller than the sampling interval, microheterogeneity, and experimental error; C0 + C is the sill indicating the random and structural variation, and; A0 is the range indicating the spatial correlation at different distances.
Statistical analysis
Descriptive statistical analyses (maximum, minimum, average, and coefficient of variation), Pearson’s correlation analysis, and linear regression analysis was performed with SPSS 16.0 (IBM SPSS, Chicago, IL, USA). Geostatistical analysis was performed with GS + software (version 7.05). More

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