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Statistical characteristics of rill cross-sectional asymmetry (RCA)The rill cross-sectional asymmetry (RCA) is a key parameter in describing rill morphology and includes the asymmetry ratio of the width (Aw) and the asymmetry ratio of the area (Aa). It reflects the differences in certain aspects of natural conditions resulting in inconsistent development speeds on both sides of a rill cross-section. The cross-section was classified as left-biased if Aw, Aa < 0, quasi-symmetrical if Aw, Aa = 0, and right skewed if Aw, Aa > 0. The left/right deflection reflects that erosion on the right happened faster than on the left, so the slope on the left is not as steep as on the right. The results of this study show that asymmetry is a common phenomenon in the cross-section of a rill. The Aw ranged from − 1.77 to 1.97, with an average value of − 0.034. There were 374 cross-sections whose RCA was less than or equal to 0, meaning that 53% of the cross-sections were right-biased. The Aa ranged from − 1.81 to 1.71, with an average of − 0.046. There were 374 cross-sections with an RCA of less than or equal to 0, meaning that 53% of the cross-sections were right-biased (Fig. 1).Figure 1Statistical characteristics of the rill cross-sectional asymmetry (RCA).Full size imageFigure 2 shows that there are four Aw groups in the interval (− 1.7, − 1.5), 53 groups in the interval (− 1.5, − 1.0), 144 groups in the interval (− 1.0, − 0.5), 173 groups in the interval (− 0.5, 0), 174 groups in the interval (0, 0.5), 120 groups in the interval (0.5, 1.0), 39 groups in the interval (1.0, 1.5), and five groups in the interval (1.5, 2). The Aa has 15 groups in the interval (− 1.8, − 1.5), 63 groups in the interval (− 1.5, − 1.0), 130 groups in the interval (− 1.0, − 0.5), 166 groups in the interval (− 0.5, 0), 161 groups in the interval (0, 0.5), 110 groups in the interval (0.5, 1.0), 53 groups in the interval (1.0, 1.5), and 14 groups in the interval (1.5, 2). The RCA of most cross-sections is concentrated in the interval (− 0.5, 0.5). This interval of Aw contains 491 cross-sections, accounting for 68.96% of the total. There are 470 cross-sections in this interval of Aa, accounting for 66.01% of the total. This indicates that, although the rill cross-section exhibits some asymmetry, the difference between both sides of the section is small (Fig. 2).Figure 2Distribution characteristics of the RCA.Full size imageThe influence of a single topographic factor on the RCACorrelation analyses of the Aw, Aa, and the slope difference on both sides (B), rill length (L), rill slope length (I), rill head catchment area (A), difference between the catchment areas of both sides (R), rill bending coefficient (K), and location of the section angle of turning of the rill (J) were carried out. The results show that the main factors that have a significant linear correlation with the Aw and the Aa are B (p < 0.01), with correlation coefficients of 0.32 and 0.22, respectively (Fig. 3). That is, the greater the difference in slope between the two sides, the more asymmetric the rill cross-section. R also has a significant linear correlation with the Aw (p < 0.05), with a correlation coefficient of 0.07. This means that the greater the difference in the catchments between the left and right sides of the rill, the greater the asymmetry of the rill cross-section. However, other topographic factors have no significant correlation with the RCA.Figure 3Correlation between rill cross-sectional asymmetry (RCA) and topographic factors.Full size imageB is the difference in slope between the left and right sides of the rill cross-section catchment area. The closer B gets to 0, the smaller the difference in slope between the left and right sides of the rill cross-section catchment area. When the catchment area slope on the right side of the cross-section is greater than that on the left side, B < 0; and when the catchment area slope on the left side of the cross-section is greater than that on the right side, B > 0. Grouping B reveals that the average RCA increases as B increases (Fig. 4). When B is (− 30, − 20), Aw is − 0.48 and Aa is − 0.38; when B is (− 20, − 10), Aw is − 0.36 and Aa is − 0.31; when B is (− 10, 0), Aw is − 0.23 and Aa is − 0.22; when B is (0, 10), Aw is 0.21 and Aa is 0.16; when B is (10, 20), Aw is 0.47 and Aa is 0.40; and when B is (20, 40), Aw is 0.31 and Aa is 0.13. These are relatively low values because this group only has two sets of cross-sections which cannot represent the characteristics of interval B. The sign of the RCA is the same as the sign of B. The directionality of the RCA is significantly affected by B. When the slope of the left catchment area is large, RCA > 0, and the rill cross-section appears to be left-biased; when the slope of the right catchment area is large, RCA < 0, and the cross-section appears to the righ-biased.Figure 4The asymmetry of different B values.Full size imageThe influence of multiple topographic factors on the RCAIn order to explore the influence of multiple topographic factors on the RCA, principal component analysis (PCA) was used to extract the main feature components of the topographic data. The PCA results show that the nine topographic factors can be reflected by two principal components at 61.84% (characteristic value: 3.117+1.211=4.328 variables) (Table 1). Therefore, the analysis of the first two principal components could reflect most of the information from all the data.Table 1 Calculation results of topographic factor principal component analysis (PCA).Full size tableThe contribution rate of the first principal component is 44.534%. The characteristic is that the factor variables have high positive loads for the four factors L, I, A, and K. L has the largest contribution rate at 88.5%, followed by A, I, and K, at 87.5%, 81.1%, and 60.2%, respectively. Therefore, the first component represents the rill slope and rill shape.The contribution rate of the second principal component is 17.303%. The characteristic is that the factor variables have high positive loads for the three factors B, J, and R. B has the largest contribution rate at 83.5%, followed by J and R, at 57.4% and 55.7%, respectively. Therefore, the second component represents the effect of the difference between the two sides of the rill.Based on the correlation between the topographic factors and the RCA of a rill cross-section in the Yuanmou dry-hot valley area, the following was observed: asymmetry in rill cross-sections is ubiquitous. The distribution range of Aw is − 1.77 to 1.97, the average value is − 0.034, and the cross-section that is right-biased accounts for 53%. A correlation analysis of the RCA and seven topographic factors shows that B has a significant positive correlation with the Aw and Aa (p < 0.01), the average RCA increases as B increases, and the directionality of the RCA is affected by B. When B > 0, RCA > 0, and the rill cross-section appears to the left; when B < 0, RCA < 0, and the cross-section appears to the right. The difference in catchment area between the sides has a significant linear correlation with the Aw (p < 0.05). Other single topographic factors have no significant correlation with the RCA. Principal component analysis and calculations show that the first principal component represents the influence of the rill slope surface and rill shape on the rill cross-sectional asymmetry. The contribution rate is 44.534%, which is characterized by a high positive load on the L, I, A, and K factors. The second principal component represents the effect of the difference between the two sides of the rill. The contribution rate is 44.534%, which is characterized by a high positive load on the B, J, and R factors. More

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Climate models need to capture a full spectrum of data from forests such as the Brazilian Amazon.Credit: Florence Goisnard/AFP/Getty

Humanity’s understanding of how forests are responding to climate change is disconcertingly fragile. Take carbon fertilization, for example — the phenomenon by which plants absorb more carbon dioxide as its concentration in the atmosphere increases. This is one of the principal mechanisms by which nature has so far saved us from the worst of climate change, but there’s little understanding of its future trajectory. In fact, researchers don’t fully understand how climate change interacts with a multitude of forest processes. Complex, unsolved questions include how climate warming affects forest health; how it affects the performance of forests as a carbon sink; and whether it alters the ecosystem services that forests provide. Forests are our life-support system, and we should be more serious about taking their pulse.Six papers in this week’s Nature provide important insights into those questions. They also underline some of the challenges that must be overcome if we are to fully understand forests’ potential in the fight against climate change. These challenges are not only in the science itself, but also relate to how forest scientists collaborate, how they are funded (especially where data collection is concerned) and how they are trained.Forest science is an amalgam of disciplines. Ecologists and plant scientists measure tree growth, soil nutrients and other parameters in thousands of forest plots around the world. Physical scientists monitor factors such as forest height and above-ground forest biomass using remote-sensing data from drones or satellites. Experimental scientists investigate how forests might behave in a warming world by artificially altering factors such as temperature or carbon dioxide levels in experimental plots. Some of the data they generate are absorbed by yet another community: the modellers, who have created dynamic global vegetation models (DGVMs). These simulate how carbon and water cycles change with climate and, in turn, inform broader earth-system and climate models of the type that feed into policymaking.Different DGVMs make different predictions about how long forests will continue to absorb anthropogenic CO2. One reason for these differences is that models are sensitive to assumptions made about the processes in forests. There are many influences — including temperature, moisture, fire and nutrients — that are generally studied in isolation. Yet they interact with each other.Not all DGVMs account for the dampening effect that a lack of soil phosphorus can have on carbon fertilization, for example. Much of central and eastern Amazonia is poor in phosphorus, and research has shown that introducing phosphorus limitation into DGVMs can cut the carbon-fertilization effect1. This week, Hellen Fernanda Viana Cunha at the National Institute for Amazonian Research in Manaus, Brazil, and her colleagues report2 a powerful experimental demonstration of how the soil’s poor phosphorus content limits carbon absorption in an old-growth Amazonian forest.Models simulating the northward spread of boreal forest as temperatures rise are also missing key drivers3, according to Roman Dial at Alaska Pacific University in Anchorage and his colleagues. They report today that a white-spruce population has migrated surprisingly far north into the Arctic tundra. To explain this, it is necessary to take into account winter winds (which facilitate long-distance dispersal) along with the availability of deep snow and soil nutrients (which promote plant growth).Models are often based on a small number of ‘functional tree types’ — for example, ‘evergreen broadleaf’ or ‘evergreen needle leaf’. These are chosen as a proxy for the behaviour of the planet’s more than 60,000 known tree species. Yet ecologists are discovering that the biology of individual species matters when it comes to a tree’s response to climate change.David Bauman at the Environmental Change Institute at the University of Oxford, UK, and his co-workers reported in May that tree mortality on 24 moist tropical plots in northern Australia has doubled in the past 35 years (and life expectancy has halved), apparently owing to the increasing dryness of the air4. But that was an average of the 81 dominant tree species: mortality rates varied substantially between species, a variation that seemed to be related to the density of their wood.Peter Reich at the Institute for Global Change Biology at the University of Michigan in Ann Arbor and his colleagues now report that modest alterations in temperature and rainfall led to varying rates of growth and survival5 for different species in southern boreal-forest trees. The species that prospered were rare.Failure to examine multiple factors simultaneously means that scientists are making findings that challenge the assumptions in models. Spring is coming earlier for temperate forests and most models assume that, by prolonging the growing season, this increases woody-stem biomass. However, observational work carried out in temperate deciduous forests by Kristina Anderson-Teixeira at the Smithsonian Conservation Biology Institute in Front Royal, Virginia, and her colleagues found no sign of this happening6.Modellers are all too aware of the need to incorporate more complexity into their models, and of the potential that increasing amounts of computing power have to assist them in this endeavour. But they need more data.Continuity problemTo obtain comprehensive, valuable data for the models, continuous, long-term observations need to be made, and that depends on the availability of long-term funding. Achieving such continuity is a problem for both remote-sensing and ground-based operations. The former can cost hundreds of millions of dollars, but the value of its long-term data sets is immense, as demonstrated by a team led by Giovanni Forzieri at the University of Florence in Italy. The authors used 20 years of satellite data to show that nearly one-quarter of the world’s intact forests have already reached their critical threshold for abrupt decline7. But even field-based data collection, which costs a pittance by comparison, struggles to achieve financial security.Important ground-based operations include the Forest Global Earth Observatory (ForestGEO), part of the Smithsonian Tropical Research Institute, which is headquartered in Washington DC. This monitors 7.5 million individual trees in plots around the world. The amount of work that goes into this monitoring is formidable. For example, at present, ForestGEO is conducting the eighth five-yearly census of a plot in Peninsular Malaysia. This involves determining the species for each of the 350,000 trees (there are some 800 species growing there) and measuring the circumference of each trunk. It will take 16 skilled people a year to measure all the trees. Delays in the provision of funding to ForestGEO have held up similar censuses at plots in countries including Papua New Guinea, Vietnam, Brunei and Ecuador.

A ForestGEO researcher making tree measurements at a forest plot in Barro Colorado Island, Panama.Credit: Jorge Aleman, STRI

The future of the plots in North Queensland, which supplied Bauman with a rare 49 years’ worth of continuous data, is uncertain. They have been monitored since the mid-1970s by the Australian public research-funding agency CSIRO — initially every two years, then, more recently, every five years. In 2019, monitoring of the plots was switched to every 50 years because of funding shortages at CSIRO, leaving scientists searching for new sources of funding.Without continuity of funding, organizations such as ForestGEO can’t equip researchers with the requisite skills or collect data over periods longer than an individual’s time in a specific post or a funder’s cycle. “We have trained people and then lost them due to job insecurity,” says Stuart Davies, who leads ForestGEO.Different groups of forest researchers are trying to address these problems. ForestGEO is coordinating the Alliance for Tropical Forest Science in an effort to make it easier to share data, and to bolster the morale and careers of the skilled technicians and scientists — many of whom live in low- and middle-income countries — who do the bulk of the data collection.But we also need more-imaginative funding mechanisms that lift long-term observational plots out of three- to five-year funding cycles. Space agencies that fund remote-sensing satellites could collaborate with other funding agencies, for example, so that earth-observation missions include a fully funded component for ground-based data collection — which is, after all, crucial for calibrating their results. Journals, too, could do more to value and incentivise the production of long-term data sets.And there is a need for more interdisciplinarity. The US Department of Energy is funding a project called NGEE–Tropics (Next-Generation Ecosystem Experiments–Tropics) in which modellers will work with empirical researchers, both observational and experimental, who study tropical forests to create a full, process-rich model of such forests. This is encouraging, and the idea could be pushed further. What is needed is an initiative that pulls the disciplines together towards a goal of building a better understanding of forest processes. Among other things, such an initiative would encourage researchers in different disciplines to take each other’s data needs into account when planning their projects.For this to work, we need to remember that the edifice of forest science relies on the long-term data that scientists wring from forests over decades. Our chances of overcoming climate change are small, but they will diminish further if we forget the basics of monitoring our home planet. More

Shotgun sequencing and generation of metagenome-assembled genomesIn our previous study, 78 Holstein Friesian dairy cows were sampled for rumen content, metagenomic shotgun sequencing was carried out, and raw Illumina sequencing reads were assembled into contigs using megahit assembler using default settings [7]. We used a pooled assembly of the original 78 samples to increase the quality of the metagenome-assembled genomes (MAGs) with the syntax: megahit [14] -t 60 -m 0.5 −1 [Illumina R1 files] −2 [Illumina R2 files]. Next, the assembled contigs were indexed using BBMap [15]: bbmap.sh threads = 60 ref = [contigs filename]. Thereafter, reads from each sample were mapped to the assembled contigs using BBTools’ bbwrap.sh script. In order to determine the depth (coverage) of each contig within each sample, the gi_summarize_bam_contig_depths tool was applied with the parameters: gi_summarize_bam_contig_depths –outputDepth depth.txt –pairedContigs paired.txt *.bam –outputDepth depth.txt –pairedContigs paired.txt.Using the depth information, metabat2 [16] was executed to bind genes together into reconstructed genomes, with parameters: metabat2 -t40 -a depth.txt.To evaluate genomic bin quality, we used the CheckM [17] tool, with parameters: checkm lineage_wf [in directory] [out directory] -x faa –genes -t10.Preparing proteomic search libraryWe generated 93 unique high-quality MAGs, and further increased our MAG database by including phyla that were not represented in our set of MAGs. In order to do so, we used the published compendium of 4,941 rumen metagenome-assembled genomes [18] and dereplicated those MAGs using dRep [19]. We then selected MAGs from phylum Spirochaetes, Actinomycetota, Proteobacteria, Firmicutes, Elusimicrobia, Bacillota, Fibrobacteres and Fusobacteria, which had the highest mean coverage in our samples as calculated using BBMap and gi_summarize_bam_contig_depths as described above [15]. This strategy minimized the false discovery rate (FDR), that would have been obtained if larger and unspecific databases would have been employed [20] and allowed the addition of 14 MAGs to our database.In order to create the proteomic search library, genes were identified along the 107 MAGs using the Prodigal tool [21], with parameters: prodigal meta and translated in silico into proteins, using the same tool. Replicates sequences were removed. Protein sequences from the hosting animal (Bos taurus) and common contaminant protein sequences (64,701 in total) were added to the proteomic search library in order to avoid erroneous target protein identification originating from the host or common contaminants. Finally, in order to subsequently assess the percentage of false-positive identifications within the proteomic search [22], the proteomic search library sequences were reversed in order and served as a decoy database.Proteomic analysisThe bacterial fraction from rumen fluid of the 12 selected animals selected from extreme feed efficiency phenotypes, were obtained at the same time as the samples analyzed for metagenomics and stored at −20 °C until extraction. To extract total proteins, a modified protocol from Deusch and Seifert was used [23]. Briefly, cell pellets were resuspended in 100 µl in 50 mM Tris-HCl (pH 7.5; 0.1 mg/ml chloramphenicol; 1 mM phenylmethylsulfonyl fluoride (PMSF)) and incubated for 10 min at 60 °C and 1200 rpm in a thermo-mixer after addition of 150 µl 20 mM Tris-HCl (pH 7.5; 2% sodium dodecyl sulfate (SDS)). After the addition of 500 µl DNAse buffer (20 mM Tris-HCl pH 7.5; 0.1 mg/ml MgCl2, 1 mM PMSF, 1 μg/ml DNAse I), the cells were lysed by ultra-sonication (amplitude 51–60%; cycle 0.5; 4 × 2 min) on ice, incubated in the thermo-mixer (10 min at 37 °C and 1,200 rpm) and centrifuged at 10,000 × g for 10 min at 4 °C. The supernatant was collected and centrifuged again. The proteins in the supernatant were precipitated by adding 20% pre-cooled trichloroacetic acid (TCA; 20% v/v). After centrifugation (12,000 × g; 30 min; 4 °C), the protein pellets were washed twice in pre-cooled (−20 °C) acetone (2 × 10 min; 12,000 × g; 4 °C) and dried by vacuum centrifugation. The protein pellet was resuspended in 2× SDS sample buffer (4% SDS (w/v); 20% glycerin (w/v); 100 mM Tris-HCl pH 6.8; a pinch of bromophenol blue, 3.6% 2‑mercaptoethanol (v/v)) by 5 min sonication bath and vortexing. Samples were incubated for 5 min at 95 °C and separated by 1D SDS-PAGE (Criterion TG 4-20% Precast Midi Gel, BIO-RAD Laboratories, Inc., USA).As previously described, after fixation and staining, each gel line was cut into 10 pieces, destained, desiccated, and rehydrated in trypsin [24]. The in-gel digest was performed by incubation overnight at 37 °C. Peptides were eluted with Aq. dest. by sonication for 15 min The sample volume was reduced in a vacuum centrifuge.Before MS analysis, the tryptic peptide mixture was loaded on an Easy-nLC II or Easy-nLC 1000 (Thermo Fisher Scientific, USA) system equipped with an in-house built 20 cm column (inner diameter 100 µm; outer diameter 360 µm) filled with ReproSil-Pur 120 C18-AQ reversed-phase material (3 µm particles, Dr. Maisch GmbH, Germany). Peptides were eluted with a nonlinear 156 min gradient from 1 to 99% solvent B (95% acetonitrile (v/v); 0.1% acetic acid (v/v)) in solvent A (0.1% acetic acid (v/v)) with a flow rate of 300 ml/min and injected online into an LTQ Orbitrap Velos or Orbitrap Velos Pro (Thermo Fisher Scientific, USA). Overview scan at a resolution of 30,000 in the Orbitrap in a range of 300-2,000 m/z was followed by 20 MS/MS fragment scans of the 20 most abundant precursor ions. Ions without detected charge state as well as singly charged ions were excluded from MS/MS analysis. Original raw spectra files were converted into the common mzXML format, in order to further process it in downstream analysis. The spectra file from each proteomic run of a given sample was searched against the protein search library, using the Comet [25] search engine with default settings.The TPP pipeline (Trans Proteomic Pipeline) [26] was used to further process the Comet [25, 27] search results and produce a protein abundance table for each sample. In detail, PeptideProphet [28] was applied to validate peptide assignments, with filtering criteria set to probability of 0.001, accurate mass binning, non-parametric errors model (decoy model) and decoy hits reporting. In addition, iProphet [28, 29] was applied to refine peptide identifications coming from PeptideProphet. Finally, ProteinProphet [28,29,30] was applied to statistically validate peptide identifications at the protein level. This was carried out using the command: xinteract -N[my_sample_nick].pep.xml -THREADS = 40 -p0.001 -l6 -PPM -OAPd -dREVERSE_ -ip [file1].pep.xml [file2].pep.xml.. [fileN].pep.xml  > xinteract.out 2  > xinteract.err. Then, TPP GUI was used in order to produce a protein table from the resulting ProtXML files (extension ipro.prot.xml).Subsequently, proteins that had an identification probability < 0.9 were also removed as well as proteins supported with less than 2 unique peptides (see Supplementary Table 1).Quantifying metagenomic presence of MAGsA reference database containing all 107 MAGs’ contigs was created (bbmap.sh command, default settings). Then, the paired-end short reads from each sample (FASTQ files) were mapped into the reference database (bbwrap.sh, default settings), producing alignment (SAM) files, which were converted into BAM format. Subsequently, a contig depth (coverage) table was produced using the command jgi_summarize_bam_contig_depths --outputDepth depth.txt --pairedContigs paired.txt *.bam. As each of the MAGs span on more than one contig, MAG depth in each sample was calculated as contig length weighted by the average depth. Finally, to account for unequal sequencing depth, each MAG depth was normalized to the number of short sequencing reads within the given sample.Correlating metagenomic and proteomic structuresIn order to compare metagenomic and proteomic structures, we first calculated the mean coding gene abundance and mean production levels of each of the 1629 detected core proteins over all 12 cows. Both mean gene abundance and mean production level were translated into ranks using the R rank function. The produced proteins were ranked in descending order and the coding genes in the gene abundance vector were reordered accordingly. The two reordered ranked vectors then plotted using the R pheatmap function, and colored using the same color scale.Selection of proteins for downstream analysisAs our goal was to analyze plasticity in microbial protein production in varying environments, e.g., as a function of host state, only MAGs that were identified in all of the 12 proteomic samples were kept for further analysis. Consequently, only proteins that were identified in at least half of the proteomic samples (e.g., in at least six samples) were selected. This last step aimed to reduce spurious correlation results. These filtering steps retained 79 MAGs coding for a total of 1,629 measurable proteins.Feed efficiency state prediction and ordinationIn order to calculate the accuracy in predicting host feed efficiency state based on the different data layers available (16S rRNA (Supplementary Table 2), metagenomics, metaproteomics), the principal component analysis (PCA) axes for all the samples based on the microbial protein production profiles were calculated. Then, twelve cycles of model building and prediction were made. Each time, the two first PCs of each of five cows along with their phenotype (efficiency state) were used to build a Support Vector Machine (SVM) [R caret package] prediction model and one sample was left out. The model was then used to perform subsequent prediction of the left-out animal phenotype (feed efficiency) by feeding the model with that animal’s first two PCs. This leave-one-out methodology was then repeated over all the samples. Finally, the prediction accuracy was determined as the percent of the cases where the correct label was assigned to the left-out sample. For the proteomics data, this procedure was applied on both the raw protein counts, and the protein production normalized based on MAG abundance, which enabled us to compare the prediction accuracies of the microbial protein production to that of the raw protein counts.Identification proteins associated with a specific host stateIn order to split the proteomics dataset into microbial proteins that tend to be produced differently as a function of the host feed efficiency states, each microbial protein profile was correlated to the sample’s host feed efficiency measure (as calculated by RFI) using the Spearman correlation (R function cor), disregarding the p value. Proteins that had a positive correlation to RFI were grouped as inefficiency associated proteins. In contrast, proteins that presented a negative correlation to RFI were grouped as efficiency associated proteins. To test for equal sizes of these two protein groups, a binomial test was performed (R function binom.test) to examine the probability to get a low number of feed efficient proteins from the overall proteins under examination, when the expected probability was set to 0.5.Functional assignment of proteinsProtein functions were assigned based on the KEGG (Kegg Encyclopedia of Genes and Genomes) [31] database. The entire KEGG genes database was compiled into a Diamond [32] search library. Then, the selected microbial proteins were searched against the database using the Diamond search tool. Significant hits (evalue < 5e-5) were further analyzed to identify the corresponding KO (KEGG Ortholog number). Annotations of glycoside hydrolases were performed using dbcan2 [33].Protein level checkerboard distribution across the feed efficiency groupsThe checkerboard distribution in protein production profiles was estimated separately within the feed efficient and inefficient animal groups. To enable the comparison between the two groups’ checkerboardness level, we chose a standardized C-score estimate (Standardized Effect Size C-score - S.E.S C-Score), based on the comparison of the observed C-score to a null-model distribution derived from simulations. The S.E.S C-score was estimated using the oecosimu function from R vegan package with 100,000 simulated null-model communities.Calculating functional redundancyThe functional redundancy within a given group of proteins was measured as the mean number of times a given KO occurred within a given group, while neglecting proteins that have not been assigned a KO level functional annotation.In order to test whether a given group of proteins exhibits more or less functional redundancy than would have been expected, a null distribution for functional redundancy was created, based on the number of proteins in the given group. A random group of proteins was drawn from the entire set, keeping the same sample size as in the tested group, and the process was repeated 100 times. Then, the functional redundancy for each random protein group was calculated. Thereafter, the null distribution was used to obtain a p value to measure the likelihood of obtaining such a value under the null.Examining functional divergenceExamining the functional divergence between the two groups of proteins, e.g. the feed efficiency and inefficiency associated proteins, was done by first counting the amount of shared functional annotations, in terms of KOs between the two groups. Thereafter, a null distribution for the expected count of KOs was built by randomly splitting in an iterative manner the proteins into groups of the same sizes and calculating the number of shared KOs. A p value for the actual count of shared proteins was obtained by ranking the actual count over the null distribution.Calculating average nearest neighbor ratio (ANN ratio)ANN Ratio analysis was carried out independently for each protein function (KO), containing more than 14 proteins with at least 5 proteins within each feed efficiency group. Initially, all proteins assigned to a given KO were split into two sets, in accordance to their feed efficiency affiliation group. Thereafter, proteins within each set were independently projected into two-dimensional space by PCA applied directly to Sequence Matrix [34]. Average nearest neighbor ratio within each set was then calculated within the minimum enclosing rectangle defined by principal component axes PC1 and PC2, as defined by Clark and Evans [35].MAG feed efficiency score calculationMicroorganism feed efficiency score was calculated for each MAG individually by first ranking each protein being produced by the given microbe along the 12 animals, based on the normalized protein production levels. Thereafter, a representative production value for the microbe in each animal was calculated as the average of the ranked (normalized) protein production levels in that animal (using R rank function). This ranking allowed us to alleviate the potential skewing effect of highly expressed proteins. The microorganism’s Feed Efficiency Score was calculated as the difference between its mean representative production value within feed efficient animals to that within feed inefficient animals. Values close to zero will reflect similar distribution between the two animal groups, positive values will indicate higher expression among efficient animals, and negative values will indicate higher expression among inefficient animals. To calculate significance, the actual feed efficiency score was compared to values in a distribution derived from a permutation based null model. Each of the permuted Feed Efficiency Scores (10,000 for each microbe) was obtained by independently shuffling each of the proteins produced by the MAG between the animals, prior to calculating the actual microorganism feed efficiency score. By positioning the absolute score value over its distribution under permuted assumptions (absolute values), we obtained a significance p value.MAG phylogenetic tree construction and phylogenetic signal estimationIn order to assess the link between phylogenetic similarity between the MAGs and their association with feed efficiency, phylogenetic tree estimating evolutionary relationships between the MAGs was constructed using the PhyloPhlAn pipeline [36]. The phylogenetic signal for Microorganism Feed Efficiency Score was estimated by providing the phylogSignal function from R phylosignal [37] package with MAGs phylogenetic tree and respective values. Pagel’s Lambda statistics was chosen for the analysis, owing to its robustness [38].Plot generationAll bar plots, scatter plots and other point plots were generated with R package ggplot2. Heatmaps were produced by either ggplot2 [39] or pheatmap [https://cran.r-project.org/web/packages/pheatmap/index.html] R packages. KEGG map was produced using the online KEGG Mapper tool [40]. Phylocorrelogram was produced with phyloCorrelogram function from R package phylosignal [37].MAG differential production analysisMAGs that contain a minimal number of proteins (50 functions) were selected for differential protein production analysis, in order to have sufficient data to perform statistical tests. For each MAG, the relative production was used in order to calculate the Jaccard pairwise dissimilarity for core protein production between feed efficient and inefficient cows using the R vegan package. Analysis of similarity between efficiency and inefficiency associated proteins for each MAG (ANOSIM) values and p values were then calculated using the same package.Predicting animal feed efficiency state according to GH family countsUsing all GH annotated proteins, a feature table that sums the count of each GH family within each sample was produced. Thereafter a leave-one-out cross-validation (LOOCV) [R caret package] was performed, each time building a Random Forest (RF) prediction model from the GH family counts and efficiency state of 11 samples, leaving one sample outside. Each one of the RF models, in its turn, was applied on the left-out animal to predict its efficiency state. Model accuracy and AUC curve were calculated based on the LOOCV performance. More