How complicated is the relationship between a protein’s sequence and its function? High-order epistatic interactions among residues are thought to be pervasive, making a protein’s function difficult to predict or understand from its sequence. Most prior studies, however, used methods that misinterpret measurement errors, small local idiosyncracies around a designated wild-type sequence, and global nonlinearity in the sequence-function relationship as rampant high-order interactions. Here we present a simple new method to jointly estimate global nonlinearity and specific epistatic interactions across a protein’s genotype-phenotype map. Our reference-free approach calculates the effect of each amino acid state or combination by averaging over all genotypes that contain it relative to the global average. We show that this method is more accurate than any alternative approach and is robust to measurement error and partial sampling. We reanalyze 20 combinatorial mutagenesis experiments and find that main and pairwise effects, together with a simple form of global nonlinearity, account for a median of 96% of total variance in the measured phenotype (and > 92% in every case), and only a tiny fraction of genotypes are strongly affected by epistasis at third or higher orders. The genetic architecture is also sparse: the number of model terms required to explain the vast majority of phenotypic variance is smaller than the number of genotypes by many orders of magnitude. The sequence-function relationship in most proteins is therefore far simpler than previously thought, and new, more tractable experimental approaches, combined with reference-free analysis, may be sufficient to explain it in most cases. If we had a comprehensive understanding of a protein’s sequence-function relationship, we could predict the functional and evolutionary consequences of any mutation or novel amino acid sequence. Whether such knowledge is possible in practice depends on the extent of epistatic interactions. If all residues in a protein act independently, then knowing the effects of point mutations on any genetic background would suffice to predict the function of any possible sequence, and any mutation’s evolutionary fate would be independent of the genetic context in which it occurs. A simple genetic architecture like this could be easily inferred using moderate-throughput experiments. At the opposite extreme, extensive high-order epistasis would cause each mutation to have idiosyncratic effects that depend absolutely on the particular sequence background into which it is introduced. In that case, assessing the protein’s genetic architecture would require exhaustive assessment of every possible genotype, and the evolutionary accessibility of all mutations would change with every sequence substitution that occurs.Deep mutational scanning (DMS) methods to characterize large libraries of protein variants have recently made it possible to assess the complexity of the sequence-function relationship, but studies to date disagree on the complexity of the sequence-function relationship. Some report extensive high-order interactions –7, whileThese discrepancies may reflect the use of different methods to characterize epistasis. Two aspects of widely used approaches can yield overestimates of amino acid interactions. First, most studies to date have analyzed mutational data using reference-based models, which designate a single sequence as the reference against which all effects are measured: the main effects of mutations are estimated by introducing each one into a single reference genotype, and epistatic interactions are calculated as the deviation of a protein variant containing several mutations from the sum of the lower order effects. A concern is that technical noise or small epistatic idiosyncracies in measurement of the reference genotype or low-order variants can propagate into estimates of higher-order effect terms, causing spurious higher-order interactions to be inferred . Second,We therefore developed a method that does not suffer from these sources of error and used it to systematically reexamine existing datasets. Advances have been made in both potential areas of concern, but currently available methods still have critical limitations. Fourier analysis , 29—alsoExisting methods to address nonspecific epistasis also have limitations. Sometimes molecular phenotypes can be measured or transformed onto a scale that is not strongly affected by nonspecific epistasis, such as free energy of binding within the dynamic range of assay measurement , 35, 36.Here we develop and implement a straightforward formulation of reference-free analysis that is applicable to any number of states, and we couple it in a joint estimation procedure with an effective model of nonspecific epistasis. We first explain our approach and compare its desirable properties to existing approaches. We then use it to reanalyze 20 previously published combinatorial mutagenesis experiments on proteins with diverse functions, and we use the results to assess the complexity of the sequence-function relationship. Finally, we explore strategies to infer sequence-function relationships when only a fraction of possible genotypes can be experimentally sampled.Our method of reference-free analysis defines the causal factors in a protein’s genetic architecture as sequence states rather than mutations. This structure allows it to describe the genetic causes of phenotypic variation across the ensemble of all genotypes. In reference-based and background-averaged analyses, the determinants of genetic architecture are mutations—changes from the reference state to a different state—rather than the states themselves. Proteins containing a reference state therefore have no genetic determinant for that state at any site or for any combination across sites that includes even one reference state. For example, the “wildtype” sequence contains the reference state at all sites: it has no mutations, so it manifests no main effects or epistatic interactions at all. All the single-step neighbors of the reference are each subject to one main effect, but they contain no combinations of mutations, so they cannot be affected by epistasis at any order. Two-step mutants are subject to one pairwise epistatic effect each but cannot be affected by higher-order epistasis, and so on. In fact, all these “low-order” genotypes are proteins too, and their genetic architecture is just as interesting and complex as protein sequences distant from the wild-type.Reference-free analysis (RFA) allows all genotypes to provide equally important evidence about the global genetic architecture. RFA takes an ANOVA-like approach in which every sequence state at every site is a causal factor that can potentially affect the functional phenotype, and all such factors can interact with each other. A combinatorial DMS study represents a full factorial experiment from which all possible causal factors and all possible interactions can be quantified . In the To incorporate nonspecific epistasis, we use a generalized linear model in which each protein’s phenotype is a nonlinear function of its genetic score—the sum of the specific effects of the states and their combinations in the protein’s sequence . To incoRFA has several desirable features. Setting aside the link function for simplicity of explanation, the RFA model at each order explains the maximum amount of phenotypic variance across all measured genotypes that could possibly be explained by any linear model of the same order . ConsideReference-free analysis contrasts with reference-based analysis (RBA), which defines each effect in the model using single measurements rather than averages. The RBA zero-order term is the phenotype of the designated reference sequence; this estimator is a good predictor in the local neighborhood of the reference but is less accurate across sequence space than the global average. The first-order RBA term for each state is the difference between the one mutant that contains that state and the reference sequence, and each higher-order term is the difference between the one mutant containing a combination of states and the sum of the estimated lower-order effects. These are good predictors of the effects of introducing each state or combination into the reference background, but they are suboptimal estimators across the set of all genotypes. RFA also differs from background-averaged analysis (BA), which designates a particular state as the reference at each site; the main effect of each amino acid is defined as the average difference in phenotype of the set of variants containing that state and the set of variants containing the reference state at the same site.The structure of RFA has several additional advantages. First, the mapping from reference-free effects to phenotype is intuitive. Each variant’s genetic score is a simple sum of the effects of its sequence states and combinations. This contrasts with BA and prior implementations of Fourier analysis, where the genetic score of each variant is a complicated weighted sum of every term in the entire model, including the terms for states and combinations that the variant does not contain . Second,If we had precise phenotypic measurement for every possible variant, we could exactly compute the effects of genetic states and combinations as they are encoded in any of the formalisms. In reality, experimental data are always affected by measurement noise, and in large libraries some variants typically go unmeasured. RFA is designed to perform well in the face of both these challenges.To assess the performance of RFA versus RBA and BA when measurements are noisy, we simulated phenotypic measurements using a known genetic architecture and normally distributed measurement error. We then estimated the genetic architecture from these data and compared the estimated model terms to the true values under each approach . We founWhen data are incomplete, the model terms of RFA and BA can still be estimated using regression because each term is averaged over many particular genotypes, and the phenotypes of unmeasured variants can then be predicted from the estimated model. In both cases, terms estimated by regression should converge to the true effects as sample size increases, and the estimates are unbiased when variants are sampled without bias .  and a four-site, 20-state experiment in which the 80 main effects account for 92% of phenotypic variance (ParB). The additive effects of individual amino acids therefore account for the majority of genetic variation in protein function in most cases.We first assessed the extent to which main effects alone explain the genetic architecture by fitting a truncated first-order reference-free model, with the sigmoid link function to incorporate nonspecific epistasis. Using cross-validation to estimate the fraction of phenotypic variance explained, we found that the first-order model achieves a median out-of-sample ur cases . There iur cases , Fig. S1R2 of 0.96 and a minimum of 0.92 across all datasets . The small fraction of phenotypic variance unexplained by the third-order model represents some combination of fourth- and higher-order epistasis, measurement noise, and limitations in the sigmoid link function to accurately capture nonspecific epistasis.When second-order terms are included, virtually all genetic variance is explained, with a median cross-validation datasets . Adding Although high-order epistasis is negligible for the majority of genotypes, there could still be a subset of genotypes shaped by strong high-order epistasis. To address this possibility, we analyzed the residuals of the second-order model, which represent the sum of all higher-order epistatic interactions and measurement noise. Genotypes with a residual greater than 20% of the phenotype range were considered candidates for strong higher-order epistasis , althougThese data establish that protein sequence-function relationships are surprisingly simple: estimating just additive effects and pairwise interactions, coupled with a simple model of nonspecific epistasis, is sufficient for high-accuracy phenotypic prediction across the entire ensemble of protein variants. Third- and higher-order interactions are not completely absent, but these effects are typically weak, and each one affects a small number of genotypes.R2 was calculated. We found that RBA’s accuracy is dramatically lower than RFA’s: The median R2 across datasets is less than 0.2 at all orders, leaving the vast majority of genetic variance to be explained by higher-order epistasis  to a designated wild-type and all single, double, and triple mutants; the phenotypes of other genotypes were then predicted using the best-fit model parameters, and the pistasis . The frapistasis , Fig. S2A and B). For the first-order reference-free models, using the link function improves the median out-of-sample R2 from 0.59 to 0.92. With second-order models, the sigmoid link function improves the median R2 from 0.87 to 0.96. With third-order models, median R2 improves from 0.95 to 0.98.We next characterized the effect of incorporating nonspecific epistasis in the 20 datasets by comparing the results of RFA with and without the sigmoid link function. We found that incorporating nonspecific epistasis dramatically improves phenotype prediction, increases the variance attributable to main and low-order epistatic effects, and reduces that attributed to high-order specific epistasis , A and BR2 when the sigmoid link function is used is tightly correlated with the fraction of genotypes at or beyond the phenotype bounds . We calculated each protein’s T90 by ranking all the effects in the protein’s genetic architecture by their contribution to phenotypic variance, constructing increasingly complex RFA models by sequentially including each effect term, and estimating the predictive accuracy of each model using cross-validation , in which the mutated sites were specifically chosen to be enriched for epistatic interactions  declines approximately linearly as the number of possible genotypes rises (30 genotypes and the same number of possible model terms), the expected T90 is less than 10,000 terms.We found that genetic architecture is very sparse . T90 ranractions . T90 inces rises . This reEven though only a small fraction of terms is important in proteins’ genetic architecture, finding them may be challenging. Experimentally analyzing exhaustive libraries is intractable for more than a small number of sites. A critical question is therefore whether genetic architecture can be estimated by a sparse learning approach that characterizes a relatively small random sample of possible genotypes and uses penalized regression to estimate from these data the most important effects in the genetic model .R2, and determined the minimum sample size required for R2 of 0.9  and the number of genotypes that must be sampled to achieve this level of explanation (N90) , in which just ten main effects explain 90% of the variance but 16,000 genotypes—about 25% of the total—must be sampled to find them.We explored several factors that might determine the required sampling density: the total number of genotypes in the sequence space, the sparseness of the architecture, and the fraction of genotypes with phenotypes in the dynamic range of measurement. First, the genetic model for a larger sequence space entails more potential terms at every epistatic order, so estimating it might require sampling a larger library. We found that tionship . Second,on (N90) . An extrN90 and the fraction of variants in the dynamic range  and the fraction of variants in dynamic range (a) are therefore the key factors that determine how well a genetic architecture can be reconstructed by random sampling. To quantify the effects of these factors, we modeled N90 as a function of N and a across the datasets  is es, and its fractional occupancy is (1 + es–)–1. This relationship is analogous to the Boltzmann equation, with s taking on the role of –∆G, the Gibbs free energy difference between the states, expressed in units of kT. When s equals 0, the functional and nonfunctional states are equally populated, and the phenotype is midway between the upper and lower bounds. An amino acid that increases the score by 2.3 always causes a ten-fold increase in the relative occupancy of the measurable functional state, corresponding to an apparent ∆∆G of –1.4 kcal/mol at 37°C. This relationship holds across proteins, functions, and assay systems, which all display the same scaling relationship between a variant’s genetic score and its phenotype, mediated via the probability of occupying the functional state.A benefit of combining the sigmoid link function with RFA is that specific genetic effects can then be expressed in simple terms that are comparable across datasets . The sig16 antibodies . The vast majority of variants in this library are at or near the lower bound of detectable binding; as a result, the average genetic score is –7.8, corresponding to just 0.04% occupancy of the measurable functional state . Even the highest genetic score in the entire library is only 2.6 — 93% occupancy of the functional state. Main effects at three key sites explain the most phenotypic variance: Substituting any of these from the ancestral to derived state increases the genetic score by between 4.2 and 5.2, corresponding to an increase in relative occupancy of the functional state by 70- to 180-fold and a ∆∆G of 2 to 3 kcal/mol each. Other sites make modest contributions: The five next-largest effects each change the genetic score by about 1  when mutated back to the ancestral state, shifting the relative occupancy by 36% each, but reducing the absolute occupancy to just 8% when all five change together. There is virtually no specific epistasis in this genetic architecture .Here we define RFA and state its key properties. A detailed exposition with proofs is provided in q states at each of n sites, but RFA can also be applied when the number of states varies among sites. Let g denote a genotype, y(g) its phenotype, and G the set of all genotypes. The global average phenotype is denotedWe consider a simple genotype space defined by y across G. RFA decomposes the phenotype into the contribution of individual states and their interactions. The first-order effect of state s at site i is the difference between the average phenotype of the subset of genotypes sharing that state  its order, and the summation involves all nonzero-order effects. An effect of order k affects the phenotype of one in every qk genotypes. The expression above therefore states that the amount of phenotypic variance attributable to an effect is the square of its magnitude, normalized by the fraction of genotypes it affects.where A corollary of the definition of reference free effects is that the first-order effects of all states at a site sum to zero:We call this the zero-mean property. The second-order effects of all state-pairs in one site-pair also sum to zero, as do all higher-order effects at a combination of sites.ω, reference-free effects of order k computed from these measurements have an error of varianceWhen individual phenotypes are subject to measurement error of variance ω and is miniscule when k is small relative to n. Therefore, reference-free effects can be robustly determined from noisy phenotypic measurements, thanks to the averaging of effects over large numbers of genotypes. By contrast, the error associated with reference-based effects of order k is 2kω, which is always greater than ω and typically too large to distinguish effects from errors when k > 2. The error associated with background-averaged effects of order k is (2q)k/qn× ω, which is greater than the error for reference-free effects of the same order and exceeds ω as k increases.By definition k, we modelWhen measurement is incomplete, reference-free effects can be inferred by regression. To infer the effects in a truncated model that contains terms of order up to ϵ(g) is the sum of all higher-order effects and measurement noise. Regression estimates are obtained by minimizing the sum of squared errors across the set of sampled genotypes (G∗):where the error ϵ(g) is unbiased—equals zero when averaged across all genotypes. This in turn derives from the zero-mean property, which implies that the net phenotypic contribution of any order of effects is zero when averaged across all genotypes; unmodeled higher-order interactions do not bias the regression because they appear as noise to lower-order models.Because RFA minimizes the sum of squared errors across all genotypes, the regression estimates converge to the true values as more genotypes are sampled. Furthermore, the regression estimates are unbiased provided that genotypes are randomly missing. This is because s). We model the link function by a sigmoid that is defined by two parameters, L and U, which represent the lower and upper bound of phenotype:We account for nonspecific epistasis by assuming that the effects of sequence states are transformed by a global link function into the observed phenotype . The netR2 in cross-validation. Except for four datasets, cross-validation was performed by randomly partitioning genotypes into training and test sets. For the three datasets with 48 or fewer genotypes and the CR9114-B dataset where only 81 genotypes are above the lower phenotype bound, cross-validation was performed by leaving out each measurement replicate in turn. The R package lbfgs was used for numerical optimization. All scripts for inference and analysis are available on GitHub (github.com/whatdoidohaha/RFA).Reference-free effects and nonspecific epistasis were jointly inferred by L1-regularized regression. The optimal L1 penalty was determined by maximizing the out-of-sample R2.To jointly infer reference-based effects and nonspecific epistasis, we devised a two-step approach. This was necessary because reference-based analysis is incompatible with regression. For example, regression infers a first-order model by assigning values to the effects of point mutations that best predict the phenotype for both point and higher-order mutants. However, the effect of a point mutation is defined solely by the phenotype of the one variant that contains only that mutation; the regression estimate can be far from true depending on the exact phenotypes of higher-order mutants. For each candidate set of nonspecific epistasis parameters, we computed the reference-based effects on genetic score that exactly recapitulate the phenotypes of mutants up to model order. The effects were then used to predict the phenotype for higher-order mutants. We only predicted higher-order mutants for which all relevant lower-order effects are measured; for example, when a point mutant is missing, any double or higher-order mutant involving that mutation was excluded from prediction. This procedure was repeated for different values of nonspecific epistasis parameters, resulting in values that maximize the Background-averaged analysis was originally developed only for binary state spaces. To implement it for spaces with more than two states per site, we extended the recursive matrix formalism of ref.  and implr2 > 0.9 between replicates) is available for at least 40% of possible genotypes was included for analysis. Several datasets were edited as follows.We systematically mined the literature for mutagenesis experiments with a combinatorially complete design. Among the many datasets comprising fewer than 100 genotypes, we chose three datasets where high-order epistasis has been reported. Any larger dataset in which precise measurement (2+ dataset, in which epistasis accounts for the greatest fraction of phenotypic variance, is presented here.The methyl-parathion hydrolase activity  was meas75—the antibiotics concentration that reduces the growth rate by 75%—was reported in logarithmic scale, set arbitrarily as –2 when the variant is unviable at any concentration. We reverted the logarithm, making IC75 equal to 0 when the variant is unviable.The original dihydrofolate reductase dataset  includesThe hemagglutinin study  characteIn the avGFP dataset , fluoresr2 is less than 0.9 for the NBS dataset, only the parS dataset was analyzed. The absolute fitness of each variant was inferred by comparing the read count before and after the bulk competition assay. Variants with the pre-competition read count fewer than 15 were excluded, resulting in 42.2% coverage of the 160,000 possible genotypes—down from 97.0% in the original study.The ParB study  measuresr2 is greater than 0.9. Variants with a pre-competition read count fewer than 100 were excluded, resulting in 68.6% coverage of the 160,000 possible genotypes—down from 93.4% in the original study.The extent of measurement noise in the GB1 dataset  could noSupplement 1


Hordeum vulgare L.) plant genetic resources from the German Federal Ex situ Genebank for Agricultural and Horticultural Crops (IPK) and of 1,089 accessions from the International Center for Agriculture Research in the Dry Areas (ICARDA) genebank. Based on prediction abilities for each trait, three scenarios for predictive characterization were compared: 1) a benchmark scenario, where test and training sets only contain ICARDA accessions, 2) across-genebank predictions using IPK as training and ICARDA as test set, and 3) integrated genebank predictions that include IPK with 30% of ICARDA accessions as a training set to predict the rest of ICARDA accessions. Within the population of ICARDA accessions, prediction abilities were low to moderate, which was presumably caused by a limited number of accessions used to train the model. Interestingly, ICARDA prediction abilities were boosted up to ninefold by using training sets composed of IPK plus 30% of ICARDA accessions. Pervasive genotype × environment interactions (GEIs) can become a potential obstacle to train robust genome-wide prediction models across genebanks. This suggests that the potential adverse effect of GEI on prediction ability was counterbalanced by the augmented training set with certain connectivity to the test set. Therefore, across-genebank predictions hold the promise to improve the curation of the world’s genebank collections and contribute significantly to the long-term development of traditional genebanks toward biodigital resource centers.Genome-wide prediction is a powerful tool in breeding. Initial results suggest that genome-wide approaches are also promising for enhancing the use of the genebank material: predicting the performance of plant genetic resources can unlock their hidden potential and fill the information gap in genebanks across the world and, hence, underpin prebreeding programs. As a proof of concept, we evaluated the power of across-genebank prediction for extensive germplasm collections relying on historical data on flowering/heading date, plant height, and thousand kernel weight of 9,344 barley ( The Seeds of Discovery initiative, which aims to promote the effective use of PGR, has characterized 37% and 66% of International Maize and Wheat Improvement Center (CIMMYT) and International Center for Agriculture Research in the Dry Areas (ICARDA) wheat genebank accessions, respectively, using sequencing-based diversity array technology  are a valuable source of diversity that provides the basis for developing disease-resistant, nutrient-dense, and climate-resilient crop varieties . HoweverDArTseq; .Systematic valorization of the produced genomic data has made rapid advances in subsequent genomic studies and breeding purposes. In combination with the genomic profile, genebank’s comprehensive historical phenotypic data, accumulated over the years, provided useful information about genetic gaps in collections . DiffereTo fill this gap, we integrated our study data across the two important barley collections maintained at ICARDA and IPK. Prior to applying genomic prediction, a strategic pipeline to curate the non-orthogonal historical data was implemented for the IPK collection . The samField experiments for 16,554 ICARDA barley accessions were performed from 1983 to 2012 in Tel Hadya, Syria  and from 2016 to 2019 in Merchouch, Morocco   startingPhenotypic data from IPK included information on 6,957 spring and 2,387 winter barley accessions collected from the IPK campus . Spring barley subpopulation included 4,425 six-rowed and 2,532 two-rowed accessions. Winter subpopulations included 1,901 and 486 accessions of six-rowed and two-rowed accessions, respectively . FT was Phenotypic data analyses for the ICARDA collection were performed following the methods specified for the IPK genebank . Analysem-dimensional vector of phenotypic records, n-dimensional vector of genotypic effects, l-dimensional vector of year effects, s-dimensional vector of genotype-by-year interaction effects, where genotype .Model 1 was also used for the outlier test with slightly different assumptions, that is, treating outliers . A data outliers .PstI and MspI (New England Biolabs) restriction enzymes, and sequencing was performed with Illumina HiSeq 2500. Read mapping and variant calling were performed essentially as described by http://www.novocraft.com/products/novosort/). Variant calling was performed with bcftools  based on the Euclidean distances computed from markers. PCoA was performed using the “ecodist” R package (version 2.0.9).For genomic predictions, 27 ICARDA accessions having phenotypic information but belonging to the 2RF row-type group were excluded because this row type did not exist among IPK accessions. Row-type 2RF comprises barley accessions in which each spikelet contains two rows of seeds, the two outer rows of seeds being larger and more prominent, forming ridges along the length of the spikelet. The inner seeds may be smaller or less developed. The distinction between the two-rowed and 2RF classifications is based on the level of detail provided about the seed arrangement within the spikelet on the barley head. Among the genotyped ICARDA accessions, 1,071, 1,057, and 1,081 accessions were phenotyped for HD, PH, and TKW, respectively. For IPK, 9,341, 9,298, and 7,575 genotyped accessions had BLUEs for FT, PH, and TKW, respectively. Three different genome-wide prediction models were applied: 1) genomic best linear unbiased prediction GBLUP; , 2) exteThe GBLUP model exploits the additive effects of all markers and has the following form:n-dimensional vector of BLUEs obtained from the phenotypic data analyses, k-dimensional vector of fixed effects including covariates (if any) and the intercept, n-dimensional random vector of (additive) genetic values, and where The EGBLUP model is an extension of the GBLUP model by considering additive-by-additive epistatic effects between all pairs of markers:n-dimensional random vector of additive-by-additive genetic values, while all other notations are the same as in the GBLUP model. The epistatic covariance matrix was calculated as follows , we decided not to treat them as a separate group to predict the facultative ICARDA accessions, but instead, we opted for the following scenarios:Scenario 2c: Using winter IPK accessions to predict ICARDA facultative accessions.Scenario 2d: Using spring IPK accessions to predict ICARDA facultative accessions.Scenario 2e: Pooling together winter and spring IPK accessions to predict ICARDA facultative accessions.In this approach, the same sub-scenarios described in scenario 2 were implemented with a slight adjustment of the training sets. The phenotypic records of 30% of ICARDA accessions were integrated with the respective phenotypic records of the IPK dataset to predict the rest of ICARDA accessions. Twenty random samplings were considered and performed separately.For each scenario, each of the three genomic prediction models was implemented twice, one ignoring the row-type subgroup information and the other modeling the row type as a fixed covariate. The influence of the row type on the prediction ability was investigated by comparing the prediction abilities that resulted from these two cases. For all three scenarios, the prediction ability was estimated as the correlation between the observed and predicted values of all accessions in the test set. In addition, the prediction ability for each row-type subgroup was also calculated separately. The standard error was estimated using a bootstrap approach with 1,000 samplings.Linear mixed models combined with rigorous quality assessment were implemented for historical IPK data and described in detail in recent works . Brieflyvs. sowing date (spring types), used to express this trait. Moreover, no significant average differences were observed between IPK and ICARDA genebanks regarding PH and TKW .Regarding BLUEs, wide phenotypic variation was observed in each growth class for both genebank collections Figure 1The genetic structure of ICARDA and IPK collections was investigated through a PCoA based on the Euclidean distance matrix estimated using 27,610 SNPs. At first glance, the accessions derived from the ICARDA genebank seem to occupy a relatively small area of IPK diversity space. However, this result should be interpreted carefully since only 1,116 genotyped ICARDA accessions were used in this analysis  with those within ICARDA genebank prediction used as a benchmark scenario (GBLUP). With few exceptions , prediction abilities were higher using the integrated across-genebank training dataset than within the ICARDA genebank Table 2.Genebanks are considered a reservoir of untapped genetic diversity for potential climate-relevant traits and improved adaptation to various biotic and abiotic stresses . PhenotyGenome-wide predictions for ICARDA accessions were conducted at two levels: predictions within and across genebanks. Within the ICARDA genebank Figure 3On a large scale, we observed that the IPK genebank covers most of the neutral molecular diversity existent among the portion genotyped of the ICARDA collection Figure 2Genetic resources are vital for future food security. The deployment of advanced technologies would provide an unprecedented opportunity to profit from the immense natural diversity stored in genebanks. Following the successful proof-of-concept implementation of genome-wide predictions within genebank accessions , we expahttp://dx.doi.org/10.5447/ipk/2023/8).All relevant phenotypic data presented in the study are included in the YJ and JR designed the study and edited the manuscript. SE and YJ performed the data analysis. SE wrote the manuscript. ZK and AA provided the material and reviewed the manuscript. AS, YZ, MM, and NS reviewed and edited the manuscript. MM, NS, and AH generated and possessed genomic data. MH prepared variant matrices. All authors contributed to the article and approved the submitted version.


Medicago sativa). The model plant Medicago truncatula, a close relative of alfalfa was used to study the genetic control of resistance towards a new Verticillium alfalfae isolate. The accidental introduction of pathogen strains through global trade is a threat to crop production and such new strains might also be better adapted to global warming. Isolates of V. alfalfae were obtained from alfalfa fields in Iran and characterized. The Iranian isolate AF1 was used in a genome-wide association study (GWAS) involving 242 accessions from the Mediterranean region. Root inoculations were performed with conidia at 25°C and symptoms were scored regularly. Maximum Symptom Score and Area under Disease Progess Curve were computed as phenotypic traits to be used in GWAS and for comparison to a previous study with French isolate V31.2 at 20°C. This comparison showed high correlation with a shift to higher susceptibility, and similar geographical distribution of resistant and susceptible accessions to AF1 at 25°C, with resistant accessions mainly in the western part. GWAS revealed 30 significant SNPs linked to resistance towards isolate AF1. None of them were common to the previous study with isolate V31.2 at 20°C. To confirm these loci, the expression of nine underlying genes was studied. All genes were induced in roots following inoculation, in susceptible and resistant plants. However, in resistant plants induction was higher and lasted longer. Taken together, the use of a new pathogen strain and a shift in temperature revealed a completely different genetic control compared to a previous study that demonstrated the existence of two major QTLs. These results can be useful for Medicago breeding programs to obtain varieties better adapted to future conditions.Verticillium wilt is a major threat to many crops, among them alfalfa ( However, thanks to their innate immunity system, disease is rather the exception than the rule, at least in undisturbed environments. Disease resistance in plants has been described as qualitative  disease resistance  and quanPlants’ defense mechanisms and pathogens’ pathogenicity have undergone a series of adaptive changes during co-evolution. When a pathogen overcomes preformed defense structures, the plant’s innate immune system is activated by recognition of conserved pathogen-associated molecular patterns (PAMPs) also named microbe-associated molecular patterns (MAMPs)  or damagAs adaptive response pathogens evolved to produce and release effectors into the host plant cells which suppress PTI/MTI. The plants’ response was to adapt their immune system by recruiting a second layer of defense that directly or indirectly detects pathogen effectors through plant resistance (R) proteins leading to Effector-Triggered Immunity (ETI) .Recognition of the pathogen through perception of PAMPs/MAMPs, in the case of PTI/MTI or effectors, in the case of ETI, is followed by cascades of signaling pathways such as ion fluxes and phosphorylation of proteins  leading This fragile balance between plants resistance and pathogens’ virulence is more and more threatened by anthropogenic factors such as global trade. The exchange of seeds and plants worldwide has led to the spread of pathogens in areas where they were absent before and to which local plants may not have evolved resistance mechanisms.Verticillium spp. This disease is one of the most destructive fungal diseases in the world and affects more than 200 different hosts, among them many economically important crops  taking advantage of the international MtHapMap project  for 2 weeks and the mycelium was harvested by filtration and stored at −20°C.DNA was extracted from frozen mycelium using the CTAB protocol . The quaV. alfalfae) and NoF/NoNuR   . The ITSlfalfae)  were use2.1.3Small disks (0.8 cm) of mycelium were punched from the border of 2-week-old cultures and inoculated in the center of Petri dishes containing 15 ml PDA. The diameter of the colony was measured at regular intervals for 2 weeks at 20°C, 25°C, and 28°C in the dark.After 14 days, 20 mL of sterile water was added to every culture and the surface of the mycelium was rubbed gently with a bent Pasteur pipette to release the conidia. The conidia were collected and their concentration was determined under the microscope with a Malassez counting chamber.The study was performed in three independent experiments including two independent blocks through augmented split-plot design where the whole-plot factor was assigned to temperature (three separate incubators) and split-plot factor was assigned to the fungal strains. In each experiment three Petri dishes were used per strain per condition.The linear mixed model was used to analyze the effect of temperature on hyphal growth and sporulation as follows:j design matrix for the q random effects of experiments .where Y is the response vector  X is the N x p design matrix for the p fixed factor including the grand mean of the trait , temperatures and the different strains, and Z represents N x qV. alfalfae isolates. The least square means (LSmeans)  was performed using the lmer function of the lmerTest package  of the RLSmeans)  for each2.22.2.1Medicago truncatula accessions was selected based on the number of available seeds (The MtHapMap collection was multiplied in our greenhouse in 2014 for a GWAS study at 20°C . A set o®-7 diameter 33cm) and seedlings were grown in a phytotron with 25°C day/23°C night and a photoperiod of 16h.They were scarified manually with sandpaper and incubated at 5°C in Petri dishes between layers of moist filter paper for 2–3 days, then were transferred to room temperature for 24h. Germinated seeds were transplanted into Jiffy substrate  and Area Under the Disease Progress Curves (AUDPC) respectively.In total, 8,442 inoculated plants were assessed through an augmented block design with three independent experiments for all 242 accessions; 4 accessions  were included in each block as check lines to evaluate the block effects. Each experiment contained 6–12 plants per accession, while the check accessions were consistently six plants per block.2.2.2For data analysis the Mixed Linear Model (MLM) approach was applied. Estimated breeding values corresponding to the traits (AUDPC and MSS) were calculated as BLUEs (Best Linear Unbiased Estimation) through the following mixed linear model:The BLUEs were extracted from the model to be used for genome-wide association mapping.Data transformation was deployed whenever it was needed to homogenize variances and normalize residuals of the ANOVAs.V. alfalfae isolate.Multiple mean comparisons were performed using Tukey (pairwise comparisons) tests at p-value ≤ 0.05 using the cld function of the multcomp R package to group the accessions with regard to their response to inoculation with the selected Iranian 2) was calculated through the variance components method on raw phenotypic data while the blocks and repeats were regarded as fixed effects and the accession regarded as random effect.The broad sense heritability  and were filtered with a minimum allele frequency (MAF) of 5% and minimum count to 200, which resulted in 5,671,743 SNPs retained.To fine map the genomic regions of was used . Single M. truncatula individuals. The kinship matrix (K matrix) was computed from a 840K LD-pruned SNP dataset. Both matrices have been described earlier by A total of five GWAS statistical models were tested including General Linear Model (GLM) without any correction for population structure (naive model), GLM Q-Model with Q-matrix as correction for population structure and three Mixed Linear Models  with K-matrix and/or Q-matrix respectively as correction for kinship relationships and population structure. The population structure (Q matrix) is based on population admixture proportions of For all models, the Q-Q plot was plotted to evaluate which was the best fitted model for this study. Manhattan plots were computed to illustrate the association of SNPs with AUDPC and MSS.For plotting the Manhattan graph the association score of SNPs was calculated through p-values of all SNPs as follows - log10.To correct for multiple testing, Bonferroni and False Discovery Rate (FDR) corrections were used. Multiple testing adjustment was conducted at α = 0.05.2.32.3.1M. truncatula in a previous study . Primers for quantitative real-time PCR (qRT-PCR) were designed using the primer3plus web interface for primer3 . For each candidate gene, primer pairs were designed based on exon-exon junction and were examined for primer stability (https://www.ncbi.nlm.nih.gov/tools/primer-blast/) and specific amplification through blast on the M. truncatula A17 genome . The primer pairs for qRT-PCR were selected based on the results of primer efficiency tests with a mix of cDNA from all conditions and time points  and pooled into a resistant and a susceptible group for each harvesting time. Total RNA was extracted using 200 mg of frozen root tissue samples following the TRIzol method (Invitrogen). After DNase I treatment (Promega) RNA quality was analyzed by NanoDrop nd-1000 Spectrophotometer and subsequently purified by the LiCl precipitation method .15 primer following the manufacturer’s instructions.cDNA was synthesized from one microgram of pure RNA with the ImProm-II ™ Reverse Transcription System kit  using Oligo (dT)® mix qPCR 2X Lo-Rox Kit  in the QuantStudio™ 6 Flex Real-Time PCR System (Applied Biosystems). At least two technical replicates were run for all samples.qRT-PCR was performed with the EurobioGreenThe reaction consisted of one step of 95°C for 3 min for cDNA denaturation, followed by 40 cycles of denaturation and annealing/polymerization . To assess the quality of qRT-PCR reactions the melting curve was implemented at the end of the reaction . In order select the primers for gene expression studies we checked primer efficiency with a dilution series of an equimolar mix of cDNA from mock-inoculated and inoculated roots of the susceptible and resistant plants.T values were extracted through Design & Analysis software (V.2.4.3). Relative gene expression levels were analyzed by the comparative CT method  and V. nonalfalfae-specific (NoF/NoNuR) primers. Amplification with AlfF/AlfD1r resulted in a band of the expected size of 1060 bp . Inversely, PCR with the V. non-alfalfae specific primers amplified only DNA from strain LPP0323 but not from Iranian isolates and the French strain V31.2 (data not shown).Putative  1060 bp  for ten In contrast to the French isolate, discoloration and formation of dark sections (black resting structures) were observed for the Iranian isolates and they occurred more frequently at 25°C than at 20°C.To investigate vegetative and reproductive features of the Iranian isolates, hyphal growth and the amount of produced conidia were examined at three different temperatures Figure 2V. alfalfae isolates and the French strain V31.2 on PDA medium showed similar behavior for all isolates with linear growth for up to two weeks. Growth was best at 25°C and very poor at 28°C  after 3 weeks. A wide range of variation in the response, typical for quantitative traits, was observed among the 242 M. truncatula accessions, as shown by Area Under Disease Progress Curve (AUDPC) and Maximum Symptom Score (MSS) values (Ten-day-old ) values 6.Broad sense heritability (H2) values for AUDPC and MSS were 0.719 and 0.724 respectively; the correlation between AUDPC and MSS was 0.96.M. truncatula response towards Iranian V. alfalfae.These results show that the population and the phenotype scoring method are suitable to implement a genome-wide association study in order to investigate the genetic architecture of  , glycoside hydrolase family 1 protein (Medtr4g023000), pathogenesis-related thaumatin family protein (Medtr8g075550), and finally a hypothetical protein without known function (Medtr1g087500).They encode proteins such as Rho-like GTP-binding protein (Medtr8g075240), casein kinase I-like protein (Medtr1g042280), MATH domain protein (Medtr1g042160), proteasome subunit alpha type-7-A protein (Medtr8g075320), osmosensor histidine kinase (Medtr8g075340), 3-hydroxyisobutyrate dehydrogenase-like 1V. alfalfae AF1 versus control condition, at early  and intermediate (96 hpi) time points. In order to erase individual differences due to the genetic background, pools of the most resistant and the most susceptible accessions were used for RNA extraction . They showed a very early induction at 4 hpi in both susceptible and resistant plants which decreased thereafter. Expression returned to basic levels in susceptible plants but stayed at induced levels for at least 24h in the resistant plants , Medtr1g042160 (MATH domain protein) and Medtr1g087500 . They also exhibited very early induction at 4 hpi in both susceptible and resistant plants which was higher in resistant plants, but compared to genes of the first group their maximum expression was at 24 hpi and their induction lasted until 96 hpi , and exhibited induction at 4 hpi in resistant plants which increased until 96 hpi whereas in susceptible plants only a weak induction at 24h was observed  and Medtr8g075550 (pathogenesis-related thaumatin family protein) exhibited strong induction at 24 hpi which decreased thereafter in resistant plants. In susceptible plants the expression was induced weakly only for Medtr8g075550, at 24h and even slightly suppressed for both genes at 96hpi , there was still a high correlation between the current study at 25°C and the previous one at 20°C , but wit to 20°C . Studies to 20°C . Howeveri.e. resistant accessions are located in western regions of the Mediterranean basin while the susceptible ones are located in the eastern parts  calculated values for both traits  suggests that their variability is linked to a combination of genetic and environmental factors with a higher contribution of genetic variance.The continuous distribution of AUDPC and MSS scores through the panel of M. truncatula resistance towards the Iranian V. alfalfae isolate through genome-wide association mapping.Taken together, the range of phenotypic variation of the plants’ response to the pathogen and high heritability indicated that population and traits are suitable for studying the genetic architecture of GWAS evaluates the statistical significance of the association between quantitative differences of a particular phenotype and specific genetic polymorphisms in a set of genetically distinct individuals . A firstV. alfalfae strain V31.2 on chromosome 7 as well as QTLs on chromosomes 2 and 6. The major QTL on chromosome 7 was later confirmed by GWAS through co-localisation of 11 and 4 different SNPs respectively related to AUDPC and MSS (versus 20°C) revealed a higher number of loci and did not show overlap with the Mazurier study (2018) except for the locus on chromosome 1 with a common candidate gene Medtr1g042160 encoding a MATH domain protein. A comparison between the two studies also showed that five resistant accessions in the previous study , with more than 90% identity, though the coverage was low for three among them.The high synteny between hizobium . A studyhizobium  and suggloci detected by GWAS, we selected genes in the areas 10 kb upstream and downstream of all significant SNPs. This distance is based on data on linkage disequilibrium and recombination rates described for M. truncatula in a previous study  on chromosome 1 which was detected through AUDPC was common to the previous study with the French strain at 20°C . This geloci on chromosomes 1, 4, 7 and 8 was studied in roots of susceptible and resistant plants after root inoculation.In addition to the MATH gene, expression of eight other genes from These genes encode proteins mainly related to signaling and defense in stress resistance.M. truncatula roots inoculated with AF1, to a higher level in resistant plants compared to susceptible ones. Kinases through phosphorylation of their targets participate in many signaling pathways, as do GTP-binding proteins, and have putative roles in phytohormone signaling and defense against biotic stress  in common, which corresponds to about 1% overlap between the two studies. Due to the high number of candidate genes and the small contribution of each locus to resistance, it did not seem reasonable to go further for functional studies.Taken together, the expression patterns of these genes, te genes . Our preM. truncatula and V. alfalfae. However, the results show that such combined effects can completely change the genetic architecture of plant disease resistance and should be a warning to breeders and institutions that control exchange of plant material.In addition, since two variables (temperature and pathogen strain) have been changed, it is not possible to separate their effects on the outcome of the interaction between The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.AF performed all experiments, analyzed the data and wrote a first draft of the manuscript. CB contributed substantially to the data analysis and interpretation and critically revised the manuscript. AE contributed to collecting the samples and acquisition of funding, and revised the manuscript. MM provided phenotypic data and interpretation of data. MG contributed to collecting and identifying the samples. LG contributed substantially to the conception and design of the work and supervised statistical analysis and interpretation of data. MR conceived and supervised the project, contributed to acquire funding, and revised the manuscript. All authors contributed to the article and approved the submitted version.


Skin damage is a trait of economic and welfare importance that results from social interactions between animals. These interactions may produce wound signs on the gilt’s skin as a result of damage behavior , biting syndromes , and swine inflammation and necrosis syndrome. Although current selection for traits that are affected by social interactions primarily focuses on improving direct genetic effects, combined selection on direct and social genetic effects could increase genetic gain and avoid a negative response to selection in cases of competitive behavior. The objectives of this study were to (1) estimate variance components for combined skin damage (CSD), with or without accounting for social genetic effects, (2) investigate the impact of including genomic information on the prediction accuracy, bias, and dispersion of CSD estimated breeding values, and (3) perform a single-step genome-wide association study (ssGWAS) of CSD under a classical and a social interaction model.Our results show that CSD is heritable and affected by social genetic effects. Modeling CSD with social interaction models increased the total heritable variance relative to the phenotypic variance by three-fold compared to the classical model. Including genomic information increased the prediction accuracy of direct, social, and total estimated breeding values for purebred sires by at least 21.2%. Bias and dispersion of estimated breeding values were reduced by including genomic information in classical and social interaction models but remained present. The ssGWAS did not identify any single nucleotide polymorphism that was significantly associated with social or direct genetic effects for CSD.Combined skin damage is heritable, and genetic selection against this trait will increase the welfare of animals in the long term. Combined skin damage is affected by social genetic effects, and modeling this trait with a social interaction model increases the potential for genetic improvement. Including genomic information increases the prediction accuracy of estimated breeding values and reduces their bias and dispersion, although some biases persist. The results of the genome-wide association study indicate that CSD has a polygenic architecture and no major quantitative trait locus was detected. Skin damage is a trait of economic and welfare importance in pigs. Damaging animal behavior and syndromes such as tail and ear biting can negatively affect the skin health of pigs, reducing animal welfare and the health status of the herd through an increase in disease susceptibility and inflammation of respiratory organs –3. When Different forms of damaging behavior and syndromes that affect skin quality result from animal interactions. Environmental factors such as limited access to food and space, availability of environmental enrichment , 2, 4, aFor traits that are affected by social interactions, the phenotype of an individual can be expressed as a combination of environmental and heritable effects, with the heritable effect partitioned into direct and social components –11. The Direct and social genetic effects can be understood as different traits that are expressed in the same phenotype that can be either genetically correlated or not , 12. TheApart from a potentially greater heritable variance when accounting for social genetic effects, the genetic gain for traits that are affected by social interactions can also be increased by a higher prediction accuracy of estimated breeding values. Including genomic information for the estimation of DBV and SBV can increase the prediction accuracy because the Mendelian sampling terms and the relationships between individuals are better estimated . MoreoveThe objectives of this study were to (1) estimate variance components for combined skin damage in pigs, with or without accounting for social genetic effects, (2) investigate the impact of including genomic information on the prediction accuracy, bias, and dispersion of CSD estimated breeding values, and (3) perform a single-step genome-wide association study (ssGWAS) of combined skin damage under a classical and a social interaction model.Animal Care and Use Committee approval was not needed because the data were obtained from a pre-existing genetic program database.Combined skin damage (CSD) was defined as the combination of wound signs on the gilt’s skin as a result of damage behavior , biting syndromes , and swine inflammation and necrosis syndrome. Although tail biting is frequently used as an indicator of damage behavior in pigs , 4, 18, A population of F1 gilts born between 2015 and 2020 on five multiplier farms in Germany was evaluated for CSD. This population consisted of 46,340 gilts produced by 278 sires and 5101 dams. Of these 278 sires, 119 had progeny on two to five farms, whereas the remaining were present on a single multiplier farm. Sires originated from two purebred dam lines that were based on the Landrace and Large White breeds (D1 and D2), whereas dams were from three purebred dam lines that were based on two Landrace and one Large White populations  or from a two-way cross (D1D3). Therefore, phenotyped gilts belonged to five F1 lines: D1D2, D1D3, D1(D1D3), D2D3, and D2(D1D3). Gilts were evaluated from the start of the finishing phase when pen groups were formed with the goal of reducing body weight variation within a pen. The pen groups were composed of 10.7 ± 0.7 individuals at the end of the finishing phase and did not consider animals that died, that were culled, or that were removed due to rare cases of extreme biting behavior. Feed was provided ad libitum to all animals in the study. A summary of the population for each farm is in Table At the end of the finishing phase (148.8 ± 13.4 days), eight trained scorers phenotyped the gilts for CSD in a binary format: 1 if the combination of skin wounds prevented the sale of the animal to the regular market at a full price and 2 if animals were successfully sold with minimum or no wound signs or culled for an unrelated reason. Gilts in the same pen were phenotyped on the same day and by the same scorer.p-value for the Hardy–Weinberg equilibrium test smaller than 10−7, or that were located on the sex chromosomes. No animals were excluded due to a low call rate. After quality control, within-line imputation of missing genotypes was performed with the FImpute v3 software  and a social interaction model [Model (2)] that accounted for both direct and social genetic effects:en mates , 13. Thesoftware  with a p] and a sIn Model (2), the total heritable variance relative to the phenotypic variance . In ssGBLUP, the inverse of the relationship matrix  for Model (2). Estimates of total breeding values were calculated as:The group of validation sires included 30 young sires that had at least ten phenotyped progeny born after October 2019, but that had no progeny information before that, whereas the group of validation gilts included 14,710 young phenotyped animals born after October 2019. Validation was performed for DBV for Model (1) and for DBV, SBVThe linear regression (LR) method was used to obtain validation statistics . In thisp-values that were calculated as:p-value smaller than the significance level of 5% adjusted by multiple testing via Bonferroni correction, i.e., 0.05/m, where m is the total number of SNPs in the analysis. All analyses were performed using the POSTGSF90 software [A single-step genome-wide association study was performed to identify quantitative trait loci (QTL) that are statistically associated with the direct and social genetic components of CSD. With breeding values estimated based on the complete dataset, SNP effects were derived from DBV in Model (1) and from DBV and SBV in Model (2), using the formulas presented by VanRaden  and Strasoftware .p > 0.05), which indicates that the incidence of CSD in this population was likely not associated with body weight or weight variation within pen groups.The percentage of pigs with CSD averaged 4.3% but ranged from 0.3 to 10.3% across farms  was low at 0.03, whereas the estimate of the total heritable variance relative to the phenotypic variance in Model 2) was three-fold greater, at 0.10 , in addition to the direct effect, we estimated the social genetic effect, which is close to the animal’s genetic ability to damage others . Using classical animal models, Breuer et al.  scored tResults from modeling pig skin damage with social interaction models are still scarce. Using social interaction models, Van der Zande  evaluateIn this study, we validated DBV in Model (1) and DBV, SBV, and TBV in Model (2) with the LR method . The benEstimates of the prediction accuracy of breeding values estimated using pedigree-BLUP (no genomics) ranged from 0.06 to 0.13  presented the smallest bias, with or without genomic information (− 0.04 vs. − 0.08). Overall, including genomic information reduced biases, but it remained present for both models. Regression coefficients measuring the dispersion of estimated breeding values ranged from 0.23 to 0.70 with BLUP and from 0.59 to 1.00 with ssGBLUP. Including genomic information significantly reduced the overdispersion of estimated breeding values, especially for TBV in Model (2), which presented a large overdispersion with BLUP (0.23) but became non-dispersed with ssGBLUP (1.00).Our results show that when validation is done on a group of sires, adding genomic information increases the prediction accuracy of all estimated breeding values , with a minimum relative increase of 21.2%. The highest prediction accuracy was obtained for estimates of DBV in Model (2) with ssGBLUP (0.25). However, in spite of the slightly lower prediction accuracy of estimates of TBV (0.18) compared to DBV (0.25) in Model (2), selecting on estimates of TBV is expected to increase the genetic gain per generation. For instance, based on the formulas by Ellen et al. , with a Estimates of prediction accuracy, bias, and dispersion of gilt breeding values are in Table It is important to note that the higher prediction accuracy when validating on a group of gilts compared to a group of sires could be due to the availability of the gilts’ own phenotypes and, therefore, a more accurate estimation of SBV. In addition, with validation on gilts, the number of pen mates (N) used to estimate TBV was considered to be a known parameter. The LR method relies on estimating breeding values with complete and partial datasets, where the phenotypic information of validation animals in the partial dataset is unavailable. In this study, the TBV of gilts were estimated with a known variable N with both partial and whole datasets. However, one might argue that the number of animals within a pen (N) is unknown for the estimation of breeding values with a partial dataset. To evaluate the impact of N in the validation results, we compared estimates of TBV calculated with known N to those using a constant N (10.7). This indeed caused a decrease in the prediction accuracy from 0.30 to 0.26, although the correlation between estimates of TBV from these two scenarios was high, at 0.98. In spite of these results, estimates of TBV were always more accurate than estimates of DBV and SBV.The bias of estimated breeding values ranged from − 0.09 to 0.18 for DBV and SBV but was greatly increased for estimates of TBV from Model (2) (− 1.03). In contrast, while estimates of DBV and SBV were more over-dispersed (0.49–0.88), estimates of TBV from Model (2) were virtually non-dispersed . Although accuracy is the most interesting measurement, unbiased estimated breeding values will ensure fair comparisons between selection candidates . Biases The dataset used in this study may be one of the largest datasets for pig damage behavior in the literature, but it has important limitations. One limitation is that only gilts were scored for CSD. Males and females may differ when it comes to behavior , 44, whip-values for SNP effects. Overall, no direct or social SNP effects were significantly associated with CSD. The absence of significant associations in our study can be explained by factors such as low heritability, small sample size, and small effective population size [Figure ion size . Combiniion size  evaluateion size .Fig. 1MaManhattan plots for the total genetic variance explained by windows of 20 adjacent SNPs are shown in Fig. Combined skin damage in group-housed pigs is a heritable trait, and genetic selection against this trait will increase the welfare of animals in the long term. Combined skin damage is affected by social genetic effects, and modeling it with social interaction models increases the total heritable variance relative to the phenotypic variance by three-fold compared to classical models. The inclusion of genomic information increases the prediction accuracy of estimates of purebred sires’ DBV, SBV, and TBV by at least 21.2% on a relative basis. Bias and dispersion are also reduced by including genomic information for both the classical and social interaction models, but some biases remained. A genome-wide association study did not identify SNPs that were significantly associated with social or direct genetic components of CSD, indicating its polygenic architecture. Although results from this study point to a higher potential of selection against CSD using social interaction models, further research on CSD recorded using more than two categories, as done here, and on male or mixed-sex populations with more dynamic pen group structures is still needed. Future research should also focus on validating phenotypic trends from selection against CSD at the TBV level.