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PatientsStool samples from a total of 52 patients with varying stages of CKD were collected in this study: CKD3A (n = 12), CKD3B (n = 11), CKD4 (n = 15), CKD5 (n = 4) and ESRD (n = 10) (Table 1). Patients’ characteristics are summarized in Table 1. Among 52 patients, 31 were reported to have Type 2 diabetes mellitus and 7 patients were reported to have human immunodeficiency virus (HIV) infection. As expected, urine protein creatinine ratio, serum creatinine and blood urea nitrogen level increased with progressing stages of CKD (CKD 3A to ESRD). There was no significant difference in fat, protein, carbohydrates, dietary fiber and calorie intake between CKD patients with different stages (Supplementary Table S1).Table 1 Patients’ characteristics.Full size tableAlpha and beta-diversityRichness and Shannon index were not significantly different between different patient groups, meanwhile the CKD5 group showed a significant decrease in Simpson diversity compared with CKD 3A (FDR  More

Phylogenetic analysisFor both the mycobiont and photobiont molecular phylogenies from multi-locus sequence data (nrITS, mtSSU and RPB1 for the mycobiont (140 samples) and nrITS, psbJ-L and COX2 for the photobiont (139 samples) were inferred (Supplementary Figs. S1 and S3 online). Additionally, phylogenies based solely on the marker nrITS were calculated (Supplementary Figs. S2 and S4 online), to include samples where the additional markers were not available. Both analyses include only accessions from the study sites (Fig. 1; Table 1). The phylogenies based on the multi-locus data were congruent to the clades of the phylogenies based on the marker nrITS. Thus, in the following, the focus will be only on the latter.MycobiontThe final data matrix for the phylogeny based on the marker nrITS comprised 306 single sequences with a length of 550 bp. It included sequences of the families Lecanoraceae and Lecideaceae. The phylogenetic tree was midpoint rooted and shows a total of 19 strongly supported clades on species level, assigned to five genera. The backbone is not supported and therefore the topology will not be discussed. All genera are clearly assigned to their family level and are strongly supported. Only Lecanora physciella forms an extra clade as sister to the families Lecideaceae and Lecanoraeae, which is not the case at the multimarker phylogeny. L. physciella has still an uncertain status, because of morphological similarities to both sister families6. The clade of the genus Lecidea revealed seven species (L. andersonii, L. polypycnidophora, L. UCR1, L. sp. 5, L. lapicida, L. cancriformis and L. sp. 6), Lecanora five species (L. physciella, L. sp. 2, L. fuscobrunnea, L. cf. mons-nivis, L. sp. 3), Carbonea three species (C. sp. URm1, C. vorticosa, C. sp. 2), and Lecidella three species (L. greenii, L. siplei, L. sp. nov2). The samples allocated to the genus Rhizoplaca were monospecific (R. macleanii). The taxonomical assignment of the obtained sequences were based on the studies of Ruprecht et al.48 and Wagner et al.10.PhotobiontThe final data matrix for the phylogeny based on the marker nrITS comprised 281 single sequences with a length of 584 bp. The phylogenetic tree was midpoint rooted and shows six strongly supported clades, assigned to seven different OTU levels67, using the concept of Muggia et al.51 and Ruprecht et al.48. All of the OTUs belong to the genus Trebouxia (clades A, I, S), comprising Tr_A02, Tr_A04a, Tr_I01, Tr_I17, Tr_S02, Tr_S15 and Tr_S18. Photobiont sequences taken from Perez-Ortega et al.50, which were labelled only with numbers, were renamed to assign them to the appropriate OTUs48.Analysis of spatial distributionIn general, the most common mycobionts species were Lecidea cancriformis (94 of the 306 samples), Rhizoplaca macleanii (51 samples) and Lecidella greenii (37 samples), followed by Carbonea sp. 2 (13 samples), C. vorticosa (11 samples), Lecidea polypycnidophora (10 samples) and Lecidella siplei (10 samples; see Supplementary Fig. S5 online). Nine mycobiont species were found exclusively in area 5 (MDV, 78°S): Carbonea vorticosa, Lecanora cf. mons-nivis, L. sp. 2, Lecidea lapicida, L. polypycnidophora, L. sp. 5, L. sp. 6, L. UCR1 and Rhizoplaca macleanii. On the other hand, only Lecidea cancriformis was found in all the six areas; Lecanora fuscobrunnea was present in all the areas with the exception of area 2.The most common photobiont OTUs were Tr_A02 (165 of the 281 samples) and Tr_S02 (59 samples), both of them occurring in all the six different areas, followed by Tr_S18 (32 samples), Tr_S15 (10 samples, confined to area 5) and Tr_I01 (10 samples). However, of the 149 photobiont accessions of area 5, 134 (89.93%) were assigned to Tr_A02. This percentage is much higher than in the other areas (area 1: 44.44%, area 2: 69.23%, area 3: 21.74%, area 4a: 7.69%, area 4b: 6.67%), even if those samples with mycobionts occurring exclusively in area 5 (see above) were excluded (76.56% of the 64 remaining samples are assigned to Tr_A02).The alpha, beta and gamma diversity values are given in Table 2. For the mycobionts, the alpha diversity of the communities was the highest in area 5 (8.93, which results in nine species) and the lowest in area 4b (two species, 1.88). In contrast, for the photobionts, the lowest alpha diversity value was found in area 5 (two OTUs, 1.50) and the highest in area 4a (four OTUs, 4.06). Thus, referring to this, area 5 plays a remarkable role: compared to the other areas, it shows the highest diversity of mycobiont species on the one hand and the lowest diversity of photobiont OTUs on the other hand.Table 2 Number of lichen samples, number of identified mycobiont species and photobiont OTUs, as well as alpha, beta and gamma diversity values of mycobiont species/photobiont OTUs for the different areas.Full size tableThe beta diversity values (diversity of local assemblages) for mycobiont species and photobiont OTUs are quite similar (1.69 and 1.64, respectively). This is in contrast to gamma diversity values: the overall diversity for the different areas within the whole region is much higher for the mycobionts (ten species, 9.92) than for the photobionts (three OTUs, 3.35).For mycobionts, the overall sample coverage equals to 0.993. That means that the probability for an individual of the community to belong to a sampled species is 99.3%, or, from another point of view, the probability for an individual of the whole community to belong to a species that has not been sampled is 0.7%. The sample coverage is highest for area 4b (1.000) and lowest for area 2 (0.771). Sample coverage values of the other areas are in between (area 1: 0.895, area 3: 0.931, area 4a: 0.939, area 5: 0.981). The rarefaction/extrapolation curves for the mycobiont species (see Supplementary Fig. S6a) suggest that for any sample size up to the specified level of sample coverage of 0.95, alpha diversity within area 4b is significantly lower than alpha diversity within any other area, and alpha diversity within area 5 is significantly greater than that of area 4a and 4b (based on 95% confidence intervals).For photobionts, the overall sample coverage as well as the sample coverages of area 1, area 2, area 3, area 4b as well as area 5 is equal 1.000. Only the sample coverage of area 4a (0.951) differs. The rarefaction/extrapolation curves for the photobiont OTUs (see Supplementary Fig. S6b) suggest that for any sample size up to the specified level of sample coverage of 0.95, alpha diversity within area 1 is significantly lower than alpha diversity of area 3 and 4a and significantly greater than that of area 5. Alpha diversity of area 5 is significantly lower than that of area 1, area 3 and area 4a.Influence of environmental factors (elevation, precipitation and temperature)First, the proportion of the OTU Tr_A02 samples was significantly correlated to BIO10 means of the areas (R = 0.87, p = 0.022; see Supplementary Fig. S7 online): the higher the temperature mean values of the warmest quarter of an area, the higher the proportion of samples containing photobionts that are assigned to Tr_A02.The alpha diversity values of mycobiont species significantly positively correlated with BIO10 (R = 0.88, p = 0.021; see Supplementary Fig. S8 online): the higher the temperature mean values of the warmest quarter, the higher the mycobiont diversity within this particular area.Furthermore, the differences in mycobiont species community composition were significantly related to BIO10 (constrained principal coordinate analysis: F = 14.7137, p = 0.001, see Supplementary Fig. S9 online), BIO12 (F = 2.7535, p = 0.012), elevation (F = 2.5108, p = 0.025) and the geographic separation of the samples (Mantel statistic r = 0.1288, p = 0.0002).The differences in community composition of photobiont OTUs were related significantly to BIO10 (constrained principal coordinate analysis: F = 48.5952, p = 0.001, see Supplementary Fig. S10 online), BIO12 (F = 4.4848, p = 0.008), elevation (F = 6.8608, p = 0.002), and physical distance (Mantel statistic r = 0.4472, p = 0.0001).Haplotype analysisHaplotype networks were computed for the mycobiont species and photobiont OTUs with h ≥ 2 and at least one haplotype with n ≥ 3 (Carbonea sp. 2, Lecanora fuscobrunnea, Lecidea cancriformis, Lecidella greenii, L. siplei, L. sp. nov2 and Rhizoplaca macleanii, as well as Tr_A02, Tr_I01 and Tr_S02), in both cases based on nrITS sequence data (Figs. 2, 3). The samples of Carbonea vorticosa (11) were all assigned to a single haplotype, which was also true for Lecidea polypycnidophora (10 samples), Tr_S15 (10 samples) and Tr_S18 (32 samples). Figure 3b, c illustrate the subdivision of Tr_I0151 into Tr_I01j35,48 and Tr_I01k (in this study), and the subdivision of Tr_S02 into Tr_S0235, and Tr_S02b and Tr_S02c48.Figure 2Haplotype networks of mycobiont species with h ≥ 2 and at least one haplotype with n ≥ 3, showing the spatial distribution within the different areas, based on nrITS data. (a) Carbonea sp. 2, (b) Lecanora fuscobrunnea, (c) Lecidea cancriformis, (d) Lecidella greenii, (e) Lecidella siplei, (f) Lecidella sp. nov2, (g) Rhizoplaca macleanii. Roman numerals at the center of the pie charts refer to the haplotype IDs; the italic numbers next to the pie charts give the total number of samples per haplotype. The circle sizes reflect relative frequency within the species; the frequencies were clustered in ten (e.g. the circles of all haplotypes making up between 20 and 30% have the same size). Note: only complete sequences were included.Full size imageFigure 3Haplotype networks of photobiont OTUs with h ≥ 2 and at least one haplotype with n ≥ 3, showing the spatial distribution within the different areas, based on nrITS data. (a) Tr_A02, (b) Tr_I01, (c) Tr_S02. Roman numerals at the center of the pie charts refer to the haplotype IDs; the italic numbers next to the pie charts give the total number of samples per haplotype. The circle sizes reflect relative frequency within the species; the frequencies were clustered in ten (e.g. the circles of all haplotypes making up between 20 and 30% have the same size). Note: only complete sequences were included.Full size imageThe haplotype networks include pie charts showing the occurrence of the different haplotypes within the different areas. All haplotypes of Rhizoplaca macleanii are restricted to area 5, as well as Lecidella greenii mainly to area 5 and areas 1 and 4a, and Lecidella sp. 2 to areas 2 and 3. However, all other species do not suggest a spatial pattern with different haplotypes being specific for different areas. Moreover, the distribution turned out to be rather unspecific, with a great part of the haplotypes found in multiple areas. For the sake of completeness, additionally, haplotype networks based on multi-locus sequence data were computed for the most abundant mycobiont species and photobiont OTU with multi-locus data available (Lecidea cancriformis and Tr_S02). Not surprisingly, those networks show a greater number of different haplotypes, but they also do not allow conclusions concerning spatial patterns of area specific haplotypes (see Supplementary Fig. S11 online).Diversity and specificity indices of mycobiont species and photobiont OTUsThe diversity and specificity indices for the different mycobiont species and photobiont OTUs are given in Supplementary Table S8 online.For the sample locations of mycobiont species with n ≥ 10, BIO10 was strongly correlated to the specificity indices NRI (net relatedness index) and significantly correlated to PSR (phylogenetic species richness) and 1 – J′ (Pielou evenness index). BIO12 was significantly correlated to NRI, PSR and 1 – J′. Figure 4 illustrates these correlations: the higher the BIO10 and BIO12 mean values, the higher was the NRI (phylogenetic clustering of the photobiont symbiotic partners), the lower was the PSR (increased phylogenetically relatedness of photobiont symbiotic partners) and the higher was 1 – J′ (less numerically evenness of the photobiont symbiotic partners). Thus, for the mean values of the sample locations of a mycobiont species, a comparatively high temperature of the warmest quarter and high annual precipitation occurs with associated photobionts that are phylogenetically clustered and closer related to each other. The lowest values of NRI and the highest values of PSR were developed by Lecidea cancriformis and Lecanora fuscobrunnea, which also showed the lowest BIO10 and BIO12 mean values at their sample sites. On the contrary, the highest values of NRI and PSR were developed by Rhizoplaca macleanii, which also had the highest BIO10 and BIO12 means.Figure 4Correlation plots. Specificity indices NRI (net relatedness index), PSR (phylogenetic species richness and 1 – J′ (Pielou evenness index) against mean values of BIO10 (mean temperature of warmest quarter) and BIO12 (annual precipitation) for mycobiont species with n ≥ 10.Full size imageFor the sample locations of photobiont OTUs with n ≥ 10, elevation significantly negatively correlated with h (number of haplotypes) and Hd (haplotype diversity): the higher the mean elevation of sample sites, the lower the number of haplotypes and the lower the probability that two randomly chosen haplotypes are different (Fig. 5). The highest values of h and Hd were shown by Tr_A02, Tr_I01 and Tr_S02, which occurred at sample sites with comparatively low elevations. In contrast, Tr_S15 and Tr_S18 occurred at very high elevations and showed very low values of h and Hd.Figure 5Correlation plots. Diversity indices h (number of haplotypes) and Hd (haplotype diversity) against mean elevation of sample sites for photobiont OTUs with n ≥ 10.Full size imageAnalysis of mycobiont–photobiont associationsBipartite networks were calculated for all associations between mycobiont species (lower level) and the respective photobiont OTUs (higher level) for all areas (Fig. 6). The H2′ value (overall level of complementary specialization of all interacting species) was highest in area 2 (0.921), indicating a network with mostly specialized interactions: within this network, with the exception of Lecidea andersonii, the mycobiont species are associated exclusively with one single photobiont OTU. The second highest H2′ value was developed by area 4b (0.710); in contrast, area 4a showed the lowest H2′ value (0.260), with the most abundant mycobiont species Lecidea cancriformis showing associations with five different photobiont OTUs. The H2′ values of area 1, area 3 and area 5 indicate medium specification.Figure 6Bipartite networks showing the associations between mycobiont species and photobiont OTUs for the different areas. Rectangles represent species/OTUs, and the width is proportional to the number of samples. Associated species/OTUs are linked by lines whose width is proportional to the number of associations.Full size imageIn addition, the bipartite networks illustrate the different occurrence of mycobiont species and photobiont OTUs within the different areas: For example, in area 1 (and area 2), five (seven) different mycobiont species are associated with only three different photobiont OTUs. In contrast, in area 4b, only two different mycobiont species are associated with four different photobiont OTUs. In area 5, the number of associated photobiont OTUs is also four, but those four OTUs are associated with 16 different mycobiont species.The network matrix giving all the associations between the mycobiont species and photobiont OTUs is presented in Supplementary Table S9 online. More

Bigg’s killer whale photo-identification datasetThe dataset of this study includes photos of Bigg’s killer whale individuals accumulated over a period of 8 years (2011–2018), from the coastal waters of southeastern Alaska down to central California15. None of these animals were directly approached explicitly for this study. All photo-identification data was collected under federally authorized research licenses or from beyond mandated minimum viewing distances.Supplementary Figure S1 visualizes a series of example images of this dataset. Each image contains one or more individuals. In addition to the identification name of the individual(s), further metadata such as photographer, GPS-coordinates, date, and time are provided. Every identification label is an alphanumeric sequence based on the animals’ ecotype (T—Transient), order of original documentation (e.g. T109), and order of birth (e.g. T109A2—the second offspring of the first offspring of T109)15.A parsing procedure was designed to verify, analyze, and prepare the image data, guaranteeing adequate preparation for subsequent machine (deep) learning methods. Results of the entire data parsing procedure are presented in Fig. 2 and Supplementary Table S1. Figure 2 visualizes the number of identified individuals, together with the total amount of occurrences in descending order, considering (1) all images, and (2) only photos including a single label. General statistics with respect to the entire dataset are reported in the caption of Fig. 2. Supplementary Table S1 illustrates the 10 most commonly occurring individuals across all 8 years of data, considering all images including single and multiple labels, compared to photos only containing a single label.The dataset exhibits a substantial class imbalance, as evidenced by the exponential decline in frequencies per killer whale individual (see Fig. 2). Especially for real-world datasets, such unbalanced data partitioning is a common and well-known phenomenon, also referred to as long-tailed data distribution79. Such long-tailed data distributions are divided into two sections79: (1) the Head region—representing the most commonly identified killer whale individuals, and (2) the Long-Tail region—visualizing a significantly larger number of killer whale individuals, however, with considerably less occurrences. For the purpose of this pilot study, the top-100 most commonly occurring killer whale individuals were selected for supervised classification and as boundary between the head and long-tail area (see Fig. 2). The defined boundary of the top-100 killer whales (head region) represents approximately 1/4 (100 out of 367) of the individuals, however, covering about 2/3 (55,305 out of 86,789) of the entire dataset of single-labeled images.Figure 2Bigg’s killer whale image long-tailed data distribution (2011–2018), summing up a total of 121,095 identification images, with 86,789 containing single labels, as well as 34,306 photos including multiple labels, resulting in 367 identified individuals (average number of images per individual (approx)456, standard deviation (approx)442). The two colored graphs visualize the number of identification images per whale in descending order w.r.t. all images, including single and multiple labels (purple curve) and those only containing a single label (green curve). Furthermore, an exemplary data point is visualized for both curves, presenting the number of identification images in relation to a selected number of whales, here for the top-100, clearly describing the exponential decline. Moreover, the number of animals at which the total amount of identification images is More

Selection-switch experimentThe dataset used for this article is previously published14, but we include a brief summary for completeness: Natural seawater was collected and used to inoculate microcosms in a 2 × 2 factorial crossover design with 3 replicates conducted for 50 days, which were sampled 18 times during the experiment. Half of the microcosms were given high (H) resource supply, whereas the other half were given low (L) resource supply. The factor of resource supply level was constant throughout the experiment. The other factor was the selection regime, which meant that the microcosms were either given continuous supply of nutrients (favouring K-selection, and hence the designation K) or being pulse-fed with nutrients after diluting the contents of the microcosms with growth medium (favouring r-selection, designated R). The active selection regime was switched at the experimental halfway point (between days 28 and 29), yielding two selection groups designated as RK and KR.DNA was extracted from the collected samples, and the V3-V4 region of the bacterial 16S-rRNA gene was amplified with PCR using broad-coverage primers and the index sequences were ligated. The amplicon library was pooled and sequenced with two runs on an Illumina MiSeq machine. The reads are available at the European Nucleotide Archive with accession number ERS7182426-ERS7182513.The USEARCH pipeline47 (v11) was used to remove low-quality reads and cluster the reads into OTUs at 97% similarity level. Finally, the taxonomy of the OTUs was determined by the Sintax classifier using data from the RPD training set (v.16) where the confidence threshold was set to 80%.Quantification of bacterial densityFor each sample, the bacterial density was quantified using flow cytometry (BC Accuri C6)14. In brief, the bacterial communities were diluted in 0.1x TE buffer, mixed with 2x SYBR Green II RNA gel stain (ThermoFisher Scientific) and incubated in the dark at room temperature for 15 minutes. Then, each sample was measured for 2.5 minutes at 35 μL min−1 with an FL1-H (533/30 nm) threshold of 3000. We gated the bacterial population as those events with an FL1-A ( > 10^4) and FSC-A (< 10^5). The raw flow cytometry data files are available at https://doi.org/10.6084/m9.figshare.15104409.Alignment and phylogentic treeThe selection-switch dataset was acquired directly from the authors14. This dataset consists of a total of 206 samples. Two of these samples were taken from the communities from which the reactors were inoculated, whereas the other samples were taken from the microcosms with 17 time points x 4 regimes x 3 replicates. We discarded the inoculum samples for further analysis. The OTU reference sequences were aligned with SINA version 1.6.148 using the SILVA Release 138 NR 99 SSU dataset49. Using this aligment, the phylogentic tree was constructed by neighbour-joining using MEGA X50 with default parameters.Filtering and preprocessingThe mean number of reads per sample was 63,460 with standard deviation 31,411. For our analysis, we wanted to estimate the abundance of each OTU as accurately as possible and therefore skipped any correction for unequal sequencing depth. Read counts for each OTU in each sample were divided by the total number of reads for the sample, generating relative abundances. Thereafter, all OTUs having a maximum abundance (across all samples) below a certain threshold, were removed. Three levels of filtering thresholds (as count proportions) were applied: High level at ( 5cdot 10^{-3} ), medium level at ( 1cdot 10^{-3} ) and low level at ( 5cdot 10^{-4}). The purpose of the filtering was to remove rare OTUs in order to avoid noise and spurious correlations11. For obtaining estimates of absolute abundances, the relative abundances were scaled by the estimate of total bacterial cell density for each sample. The phyloseq package (version 1.36.0)51 and the R programming language (version 4.1.1)52 facilitated this procedure. In addition, we wrote an R-package named micInt (version 0.18.0, available at https://github.com/AlmaasLab/micInt) to facilitate and provide a pipeline for the analysis.Similarity measures and addition of noiseFor this study, we used two similarity measures, the Pearson correlation and the Spearman correlation. A similarity measure, as referred to in this article, can be thought of as a function (f: mathbb {R}^ntimes mathbb {R}^n rightarrow D) where ( D = [-1,1] ). In this regard, (fleft( {mathbf {x}},{mathbf {y}}right) ) is the similarity of two abundance vectors ( {mathbf {x}} ) and ({mathbf {y}}) belonging to different OTUs, where (fleft( {mathbf {x}},{mathbf {y}}right) = 1) indicates perfect correlation, (fleft( {mathbf {x}},{mathbf {y}}right) = 0) indicates no correlation and (fleft( {mathbf {x}},{mathbf {y}}right) = -1) indicates perfect negative correlation. Noise was added to distort patterns of double zeros, which otherwise could result in spurious correlations. Given two vectors ( {mathbf {x}} ) and ( {mathbf {y}} ) of abundances, normally distributed noise was added to each of the abundance vectors, and the similarity measure has invoked thereafter: Given a similarity measure f, the similarity between the abundance vectors after adding noise is given by:$$begin{aligned} f^*left( {mathbf {x}},{mathbf {y}}right) =fleft( {mathbf {x}} +varvec{varepsilon _x},{mathbf {y}}+varvec{varepsilon _y }right) , end{aligned}$$ (1) where (varvec{varepsilon _x}) and ( varvec{varepsilon _y} ) are random vector where all components are independent and normally distributed with mean zero and variance ( gamma ^2 ). The level of noise ( gamma ) was determined by the smallest non-zero relative abundance ( x_{mathrm {min}} ) in the dataset and a fixed constant s called the magnitude factor, such that ( gamma = scdot x_{mathrm {min}}). For no noise, ( s=0 ), for low noise ( s=1 ), for middle noise ( s=10 ) and for high noise ( s=100 ).Network creationSignificance of the pairwise OTU associations were determined by the ReBoot procedure introduced by Faust et al.22 and shares the underlying algorithm used in the CoNet Cytoscape package53. This approach accepts a dataset of microbial abundances and a similarity measure, and evaluates for each pair of OTUs in the dataset the null hypothesis ( H_0 ): “The association between the OTUs is caused by chance”. By bootstrapping over the samples, the similarity score of each pair of OTUs is estimated, forming a bootstrap distribution. By randomly permuting the pairwise abundances of OTUs and finding the pairwise similarity scores, a bootstrap distribution is formed. The bootstrap and permutation distribution are then compared with a two-sided Z-test (based on the normal distribution) to evaluate whether the difference is statistically significant. For this, the z-value, p-value and q-value (calculated by the Benjamini-Hochberg-Yekutieli procedure54) are provided for each pair of OTUs in the dataset. Our ReBoot approach is based on the R-package ccrepe (version 1.28.0)55, but is integrated into the micInt package with the following major changes: The original ReBoot uses renormalization of the permuted abundances to keep the sum-to-constant constraint. Whereas this is reasonable to do with relative abundances, our modified version enables turning this feature off when we analyse data with absolute abundances. Optimizations have been made to memory use and CPU consumption to enable analyses of large datasets. In contrast to the usual ReBoot procedure, networks generated by the different similarity measures are not merged by p-value, but kept as they are. For our analysis the number of bootstrap and permutation iterations was set to 1000. All OTUs being absent in more than ( ncdot 10^{-frac{4}{n}} ) samples, where n is the total number of samples, were excluded through the errthresh argument but still kept for renormalization (if turned on). The associations were made across all samples, even the ones belonging to a different selection group or resource supply.Dynamic PCoA visualizationAll samples in the dataset were used for PCoA ordination, where the Bray-Curtis distance metric between the samples was applied before creating the decomposition. After the ordination was computed, the samples were divided into four facets based on their combination of current selection regime and resource supply. Finally, all samples belonging to the same microcosm were connected by a line in chronological order and the line was given a separate style based on the resource supply and coloured to visually distinguish it from the two other replicate microcosm within the same facet.Permutational multivariate analysis of varianceSequential PERmutational Multivariate Analysis of VAriance (PERMANOVA) of the samples was conducted on the absolute abundances, where only the samples from day 28 and 50 were included. These sample points correspond to time just before the experimental selection-regime crossover and a point at the end of the experiment. These days were selected because they were the most likely to capture the composition of stable communities in contrast to transient ones. The procedure was carried out by the function adonis from the R package vegan (version 2.5-7) with ( 10^6 ) permutations. The dependent data given to the function was the matrix of one minus the Spearman correlation of the samples (in order to resample dissimilarity), while the independent variables were the selection group (first variable) and the current selection regime (second variable).Network visualizationThe networks were plotted by the R package igraph (version 1.2.6)56. Network modules were found by the walktrap25 algorithm implemented in igraph with the setting steps=20, including the positive edges only. Later, the negative edges were added and the networks plotted with the community labelling.The time dynamics of the networks were visualised by taking the former network and adjusting the node colour and size, as well as the edge colour. For this, a certain combination of selection group (i.e RK) and resource supply (i.e H) was chosen. Further, let (x_{i,j,k} ) be the abundance of OTU k at sampling day i in microcosm j. As there are three replicates, we have that ( j= 1,2,3). If the underlying network was created by Pearson correlation, we denote the day mean ( x_{i,.,k} ) as the average over the replicates, this is:$$begin{aligned} x_{i,.,k}= frac{x_{i,1,k}+x_{i,2,k}+x_{i,3,k}}{3}. end{aligned}$$ (2) The time series mean of OTU k, (x_{.,.,k} ) is the mean of these daily means over all sampling days,$$begin{aligned} x_{.,.,k} = frac{sum _{i=1}^{N}x_{i,.,k}}{N}, end{aligned}$$ (3) where N denotes the number of sampling days. Furthermore, we have the associated standard deviation (sigma _k) as given by:$$begin{aligned} sigma _k =sqrt{ frac{1}{N}sum _{i=1}^{N}left( x_{i,.,k}-x_{.,.,k}right) ^2}. end{aligned}$$ (4) The z-value of the abundance of OTU k at day i is then:$$begin{aligned} z_{i,k} = frac{x_{i,.,k}-x_{.,.,k}}{sigma _k}. end{aligned}$$ (5) This value is used in the mapping of the node sizes and colours. The node for OTU k at sampling day i has the size ( a+bcdot left| z_{i,k}right| ), where a and b are constants. Furthermore, the same node is coloured: Black if ( z_{i,k} < -1 ). This indicates that the OTU that day had a lower abundance than the average. Grey if (-1 le z_{i,k} le 1 ). This indicates that the OTU that day had about the same abundance as the average. Orange if ( z_{i,k} > 1 ). This indicates that the OTU that day had a higher abundance than the average.

Furthermore, the edge colour are dependent on the product of the two participating nodes. Hence, the edge between OTU k and OTU l at day i will have the colour:

Red if ( z_{i,k}cdot z_{i,l} < -0.3 ). This shows a contribution to a negative interaction. Gray if (-0.3 le z_{i,k}cdot z_{i,l} le 0.3 ). This shows no major contribution of neither a positive nor negative interaction. Blue if (z_{i,k}cdot z_{i,l} > 0.3 ). This shows a contribution to a positive interaction.

Our approach is motivated by the fact that the Pearson correlation ( rho _{k,l} ) of the day means of OTU k and OTU l is given by:$$begin{aligned} rho _{k,l} = frac{1}{N} sum _{i=1}^{N} z_{i,k}cdot z_{i,l}. end{aligned}$$
(6)
For the Spearman correlation, the visualization is based on the rank of each of the OTU abundance values in a sample. Hence, instead of using the raw abundances ( x_{i,j,k} ) in the calculation of the day mean, the ranks ( r_{i,j,k} ) are used instead, and all subsequent calculations and mappings are the same. In a scenario when there is only one replicate, the quantity ( rho _{k,l} ) would then be the Spearman correlation of the abundances of OTU k and OTU l. More