P-value threshold of 5 × 10−8 to classify associations as significant. Here, we use our current understanding of frequently studied traits including lipid levels, height, and BMI to revisit this genome-wide significance threshold. We compare the performance of studies using the P = 5 × 10−8 threshold in terms of true and false positive rate to other multiple testing strategies: (1) less stringent P-value thresholds, (2) controlling the FDR with the Benjamini–Hochberg and Benjamini–Yekutieli procedure, and (3) controlling the Bayesian FDR with posterior probabilities. We applied these procedures to re-analyze results from the Global Lipids and GIANT GWAS meta-analysis consortia and supported them with extensive simulation that mimics the empirical data. We observe in simulated studies with sample sizes ∼20,000 and >120,000 that relaxing the P-value threshold to 5 × 10−7 increased discovery at the cost of 18% and 8% of additional loci being false positive results, respectively. FDR and Bayesian FDR are well controlled for both sample sizes with a few exceptions that disappear under a less stringent definition of true positives and the two approaches yield similar results. Our work quantifies the value of using a relaxed P-value threshold in large studies to increase their true positive discovery but also show the excess false positive rates due to such actions in modest-sized studies. These results may guide investigators considering different thresholds in replication studies and downstream work such as gene-set enrichment or pathway analysis. Finally, we demonstrate the viability of FDR-controlling procedures in GWAS.Over the last decade, GWAS meta-analyses have used a strict  P-value significance threshold for a single test from 0.05 to 0.005 , a fixed nsortium , DudbridP = 5 × 10−8 threshold a decade ago, there have been substantial experimental and methodological advances that have allowed study of many more common variants in much larger samples. The construction of denser genotype arrays  or to use posterior probabilities to control the Bayesian FDR    procedurY and the genotype jG at variant X is a p × 1 vector of covariates including the intercept, β is a p × 1 vector of covariate effects, jθ is the effect of variant j, and jε is the normally distributed error with mean 0 and variance 2jσ. This model can be applied to binary traits using a logit link function.We first consider an additive genetic model for a single continuous trait n individuals, we wish to test the null hypotheses j. m tests of which 0m null hypotheses are true. For studying multiple testing procedures, we focus on the first row of the table: R is the total number of rejected null hypotheses, V the number of null hypotheses incorrectly rejected , and S the number of null hypotheses correctly rejected (true positives). The proportion of false positives Q among all rejected hypotheses is then equal to V/R for R > 0 and set to R = 0.In a sample of Several procedures can be used to address the issue of controlling false positives when testing multiple hypotheses. In the remainder of this section we describe four such procedures, their extension to joint analysis of multiple traits, and application and assessment of these procedures in empirical and simulation studies in the context of common variant GWAS.The standard procedure to correct for multiple testing in GWAS is to control the FWER, the probability of rejecting at least one true null hypothesis:P-value thresholds often control the FWER by using the Bonferroni procedure which provides control of FWER at level α by rejecting any null hypothesis P-value:Fixed m′ ≤ m that takes into account LD.The Bonferroni criterion is conservative in two senses. One, by definition it tries to protect against making at least one mistake/false positive under the global null. The second is regarding the conservative behavior, with FWER often falling far below the desired nominal level due to correlated test statistics. This leads to loss of power. When the variants are in LD and the corresponding test statistics are correlated, one can increase the power of the Bonferroni procedure by adjusting for the effective number of independent tests  is instead defined to be equal to 1. It requires an assumption of positive regression dependence on a subset (PRDS) among the test statistics as formally defined in P-value than another must also be more likely to have no effect on the trait (i.e. truly null). For the complete set of GWAS results, PRDS is likely to be violated due to correlation among tested variants. We detail below a modification of the B–H procedure proposed by The B–H procedure, a commonly used FDR procedure that is valid when test statistics are positively correlated, is a special case of B–Y where m null hypotheses into m* < m loci by performing LD clumping on the m variants using a LD threshold of r2 > 0.1 and a maximal variant distance of 1 Mb (e.g.https://github.com/statgen/swiss). We then form a set of m* P-values using the lead variant from each locus and apply the B–H or B–Y procedures on these m* P-values.Applying the B–H or B–Y procedure to GWAS can be challenging because discoveries are counted in units of loci (clusters of nearby variants that are correlated due to LD) rather than by each individual variant. Thus, FDR-controlling procedures need to control for a subset of tested variants, typically the most strongly associated (lead) variant at each locus. Since FDR-control does not extend to a subset of the rejected null hypotheses , we adapj, let the likelihood of the observed data i.e. P < 5 × 10−8 in the observed summary statistics. This assumption can be easily relaxed, allowing for different priors among tested variants based on their functional annotations , he study  and Vj iP-values. To control the Bayesian FDR in multiple hypotheses testing at level α, we order the BFDPs for m variants from smallest to largest: k is the largest value for which: Bayesian FDR is the expected proportion of false positives among all discoveries conditional on the observed data, whereas the traditional FDR is the average Bayesian FDR over many hypothetically repeated experiments . ControlAs with the B–H and B–Y procedures, we first cluster the tested variants into loci and then apply the BFDP procedure on the lead variant for each locus.L correlated traits, there is potentially more power to detect association if the traits are analyzed together ; an alternative is to jointly analyze the L traits using multivariate test statistics and then apply the usual multiple testing procedures to the m resulting tests.In studies of j and the L traits under an extension of (1): jε is normally distributed with mean m null hypotheses of no association with any trait: Consider joint testing of the association between genetic variant  as the lead variant, we grouped all other variants that had LD threshold of r2 > 0.1 with the lead variant and within ±1 Mb of the lead variant into one locus. Next, we repeated this step on the remaining ungrouped variants until all significant variants were clustered into loci. For the adapted B–H and BFPD procedures, we first used LD clumping on all tested variants and then applied the procedures on the lead variant from each locus to obtain a set of significant loci. In the test set, we labeled loci whose lead variants had high LD (defined as r2 > 0.80) with a variant in the truth set with P < 5 × 10−8 as true positives; the remaining loci we considered false positives. We also performed sensitivity analyses on a relaxed definition of true positive which lowered the r2 threshold to 0.60, corresponding to moderate LD between test and truth variants.We evaluated the performance of the multiple testing procedures in the context of common variant GWAS by using publicly available meta-analysis results from the GLGC and the GIANT consortia. For each procedure, we calculated the empirical false discovery rate (eFDR) as the number of false positive loci in the test set V in  divided n = 188,577 to serve as the truth set and the second smallest meta-analysis  had limited power and detected few significant variants and the other  had very substantial overlap in samples with the truth set so that there was insufficient sample size differences for the truth set to well approximate the truth. Of the 2,373,282 variants analyzed in both the truth and test sets, we analyzed the 2,120,069 (89%) with MAF >5% in both sets and imputed to the HapMap 3 reference panel  served as the truth sets and the smallest meta-analyses  served as the test sets. Of the 2,282,242 variants analyzed in both meta-analyses for height, we analyzed the 2,036,404 (89%) with MAF > 5%. Of the 2,282,195 variants in both meta-analyses for BMI, we analyzed the 2,035,656 (89%) with MAF > 5% in both sets and imputed to the HapMap 3 reference panel  from the GIANT consortium . We assumed the trait value Y is inverse normalized to maintain consistency with the empirical studies, we chose the causal variant effect sizes θ from the estimated values for variants with P < 5 × 10−8 latest GLGC GWAS (the truth set), and the error term is normally distributed with mean 0 and variance equal to 1 minus the proportion of trait variance explained by the simulated causal variants. We ran association analysis with each replicate dataset using a linear regression model with no additional covariates. We took a similar approach for simulating height and BMI based on the GIANT dataset using separate generation models for the two traits. An estimated numbers of causal variants that can be detected in simulation for the five traits at different P-value thresholds of can be found in Supplementary Table S1.To mimic the GLGC test set which consisted of European cohorts, we randomly sampled 19,840 individuals from 276,791 unrelated individuals of white British ancestry in the UK BioBank dataset. For each replicate, we used the genotypes of these individuals to generate outcomes on http://lipidgenetics.org. Meta-analyses results for the GIANT Constortium are available at https://portals.broadinstitute.org/collaboration/giant/index.php/GIANT_consortium_data_files. UK Biobank genotype data are available at http://biobank.ctsu.ox.ac.uk/crystal/label.cgi?id=263.Meta-analyses results for the Global Lipids Genetics Consortium are available at https://doi.org/10.25387/g3.13211507.Supplementary material is available at figshare DOI: We applied the multiple testing procedures to HDL, LDL, TG, height, and BMI to assess their performances for different sample sizes and genetic structures.P-value thresholds to the empirical GLGC and GIANT test sets, we observed as expected that the empirical false discovery rate (eFDR) generally increased as the P-value threshold increased  for height, 18 of 19 (95%) for BMI. For the lipid traits in the GLGC test set, relaxing the threshold from P = 5 × 10−8 to P = 5 × 10−7 resulted in HDL, LDL, and TG gaining 2, 5, and 3 loci with 2, 2, and 2  being true positives. Further relaxing the threshold from P = 5 × 10−7 to P = 5 × 10−6 resulted in ≤ 56% of the additional loci being true positives for the lipid traits.For height and BMI, we identified substantially more loci by relaxing the threshold from ositives : 60 of 6ositives . FurtherP-value threshold increased for all traits  as the GLGC meta-analyses. For both traits, an increase in sample size generally led to higher proportion of true positives gained from relaxing the P-value threshold . Compared to the empirical results, B–H did a better job of controlling eFDR at the commonly used thresholds  or 123,865 (BMI). Both procedures controlled eFDR at the target FDR thresholds 5-15% for height (Supplementary Tables S6 and S7); BMI showed excess eFDR under B–H for all test sets which disappeared under the relaxed definition of true positives .We investigated whether FDR control for B–H and B–Y extended across sample sizes by using simulated datasets for height and BMI at P < 5 × 10−8. Empirical results showed that eFDR was well controlled for height and BMI at target Bayesian FDR thresholds 1-25% but poorly controlled for lipid traits  and unadjusted (5 × 10−8) for testing three traits. For the multivariate tests, the P = 5 × 10−8 and P = 5 × 10−7 thresholds had identical eFDR of 0%. Between the three sets of thresholds, the multivariate analysis had the lowest eFDR as well as the highest proportion of true positive discoveries when relaxing the P-value thresholds. For both the B–H and BFDP procedures, multivariate tests had lower eFDR than the univariate tests but only the multivariate B–H procedure controlled the eFDR at target thresholds 5-15%.In empirical results (Supplementary Table S9), the P = 5 × 10−8 threshold had the lowest eFDR for all three sets of tests. Consistent with empirical results, multivariate tests had the lowest eFDR at all three P-value thresholds and better true positive rate for relaxing thresholds compared with the univariate tests. For the B–H and BFDP procedure, both univariate and multivariate tests controlled the eFDR at target thresholds 5-15%.In simulation results (Supplementary Table S10), the 2 > 0.80 with a genome-wide significant (P < 5 × 10−8) variant in the truth set. We chose this strict criterion to avoid underestimating the number of false positives in our analysis but it likely led to overestimation of eFDR. To assess the impact of this, we repeated our simulation analyses using a relaxed definition of true positives by lowering the LD threshold requirement to 0.60 and the P-value requirement to 5 × 10−7 (Supplementary Table S5). As expected, under this relaxed definition we observed fewer false positives and occurrences of excess eFDR largely disappeared as well. For example, simulation results for height using the BFDP procedure at FDR thresholds of 10% and 15% showed eFDR of 13% and 17% under the strict definition and 10% and 14% under the relaxed definition.We defined true positives in the test set strictly as loci whose lead variants had LD threshold of rIn addition to our LD-based definitions, we used physical distance to define loci and true positives. We grouped variants within ±1Mb of the lead variants into loci and defined true positives as loci whose lead variants were within ±50kb of a genome-wide significant variant in the truth set. The analyses results (Supplementary Table S11) showed that the distance-based definitions led to smaller numbers of true and false positives for all traits and multiple testing procedures.P-value thresholds and other multiple testing procedures. Although the standard procedure for identifying significant associations in common variant GWAS is to use a P-value threshold of 5 × 10−8, relaxing the significance criteria, whether through use of less stringent P-value thresholds or controlling for alternative error rate measures such as FDR (depending on the target threshold) increases the number of identified loci. We demonstrated that a substantial proportion of the additional loci identified by relaxed P-value thresholds are true positives, with larger proportions of true positives in analysis of larger samples.In this paper, we leverage the sequentially growing nature of GWAS meta-analyses to evaluate true and false positive rate of P-value thresholds are often used to generate the list of loci for replication, the expected true and false discovery rates under different thresholds have not been quantified. We showed by simulation for common variant GWAS with sample size > 100,000 that 90-93% of additional discoveries with P-values between 5 × 10−8 and 5 × 10−7 were true positives, representing true associations that would be lost under a more stringent threshold. However, for more modest sample sizes , our simulation showed that only 77-87% of additionally discovered loci with P-values between 5 × 10−8 and 5 × 10−7 were true positives. Here, investigators should exercise caution when relaxing the significance threshold for replication studies as the increase to replicated associations may not outweigh the excess false discovery rate.GWAS identify trait-associated variants and loci based on association analysis of millions of variants. The identified loci are often further validated in replication studies before being used for statistical and functional analyses to identify causal genes, variants, and mechanisms. Although relaxed P-value threshold of 5 × 10−8 is appropriate in both large and modest-sized studies to generate a highly accurate list of associated loci. However, such threshold may be unhelpfully conservative for analyses where including (many) more true loci at the cost of (a few) more false positives is acceptable such as gene-set enrichment or pathway analysis. In these situations, a relaxed threshold of 5 × 10−7 may be better served to prioritize GWAS results for downstream analyses.For follow-up studies such as constructing animal models where the per-locus cost of follow-up is high, a stringent Materials and Methods) provided approximate control of the empirical estimate of FDR (eFDR) for the tested traits and samples at target thresholds 5-25%. The B–Y procedure is far too conservative in GWAS as the correction factor which removes assumptions on the dependency structure of test statistics is unnecessary under the adapted B–H procedure which forms independent test statistics using the lead variants from each locus.FDR-control is an appropriate choice for practitioners who are willing to tolerate some proportion of false positive discoveries as long as it can be controlled below a target threshold. At equal thresholds, controlling the FDR is less conservative than controlling the FWER and thus expands the GWAS-identified set of associated loci for downstream analysis, especially for highly polygenic traits. We showed that the B–H procedure adapted for GWAS  as discussed in A Our analysis is based on five anthropometric and lipid traits which obviously do not fully reflect the wide range of phenotypes studied in GWAS. However, our simulated traits do represent different levels of polygenicity ranging from HDL with 89 causal variants and some larger effect sizes  to height with 1100 causal variants and generally smaller effect sizes, covering a wide range of genetic architectures for quantitative phenotypes.Our analysis is also limited to studies of European-origin individuals. Further work using test and truth sets with non-European samples would be welcome to confirm that our findings are applicable more generally.We relied on publicly available meta-analyses results from the GLGC and GIANT consortia for our empirical and simulation studies. However, imputation qualities were not provided for these datasets, which raises the concern that our analyses would have missed the effects of poorly imputed variants. Since we restricted our analyses to ∼2 million HapMap3 common variants with consistently high imputation r-squared across past studies, we believe our results were not substantially affected by variation in imputation quality.n = 8,816), we observed well-controlled eFDR for the B–H procedure as expected. However, in larger test sets , we observed noticeable excess in eFDR which disappeared in simulations. This is likely because the sample size differences between the larger empirical test sets and the approximate truth set is small enough that the “truths” may no longer be accurate. When this occurs, false positive discovery in the test set can become biased since a false positive in the test set may be discovered (and thus become a true positive) in a subsequent study larger than the truth set. In simulated datasets where the truth was known, the eFDR was well-controlled.We defined true and false positive discoveries in our empirical analysis using the largest, most recent common variant GWAS which we called the truth sets. Since our empirical test set came from the same sequential set of meta-analyses as the truth set, the samples in our test set were a complete subset of those in the truth set. Although this procedure did not guarantee the (unknown) list of loci truly associated with each tested trait, the truth sets served as reasonable approximations when there were considerable sample size differences between the truth and test sets. When we repeated our analysis for smaller test sets  and so could not easily investigate how our results would have changed depending on whether GC is or is not applied.Association results on the same samples may differ owing to changes in quality control and/or statistical analysis. For example, some studies may choose not to apply genomic control which can then lead to inflated Although our results showed only modest differences between multivariate and univariate tests in terms of multiple testing corrections, we only considered the case of three correlated traits as opposed to the tens to thousands of traits that might simultaneously be tested in metabolomics or imaging studies. With many traits, combining univariate tests but not adjusting for multiple traits will surely lead to excess false positive discoveries (as even our limited results demonstrated), whereas adjusting for hundreds of traits may be overly conservative. Here, multivariate tests may represent an attractive option.In this study, we focused on common variants (MAF > 5%). This allowed us to construct likely highly accurate truth sets of loci based on serial common variant GWAS for anthropometric and lipid traits to facilitate the evaluation of different procedures for multiple testing corrections. We plan next to consider multiple testing in the context of rare variant analysis  which neP-value thresholds, B–H and B–Y for FDR control, and BFDP for Bayesian FDR control. We have shown that for studies based on large samples, using a less stringent P-value threshold of 5 × 10−7 or use of FDR-controlling procedure (B–H) at target threshold of 5% substantially increases the number of true positive discoveries that can be used in downstream analyses while only modestly increasing false positives compared with the commonly used 5 × 10−8P-value threshold. The latter threshold remains the preferred choice for modest-sized studies or when a stringently curated list of loci is desired. Finally, we show that FDR-control largely extends across sample sizes with a few exceptions that disappear under a relaxed definition of true positives and FDR-controlling procedures can be similarly applied to large and modest-sized studies.In this study, we evaluated the performance of four procedures for multiple testing corrections in the context of common variant GWAS:


Spatial trends represent an obstacle to genetic evaluation in maize breeding. Spatial analyses can correct spatial trends, which allow for an increase in selective accuracy. The objective of this study was to compare the spatial (SPA) and non-spatial (NSPA) models in diallel multi-environment trial analyses in maize breeding. The trials consisted of 78 inter-populational maize hybrids, tested in four environments , with three replications, under a randomized complete block design. The SPA models accounted for autocorrelation among rows and columns by the inclusion of first-order autoregressive matrices (AR1 ⊗ AR1). Then, the rows and columns factors were included in the fixed and random parts of the model. Based on the Bayesian information criteria, the SPA models were used to analyze trials E3 and E4, while the NSPA model was used for analyzing trials E1 and E2. In the joint analysis, the compound symmetry structure for the genotypic effects presented the best fit. The likelihood ratio test showed that some effects changed regarding significance when the SPA and NSPA models were used. In addition, the heritability, selective accuracy, and selection gain were higher when the SPA models were used. This indicates the power of the SPA model in dealing with spatial trends. The SPA model exhibits higher reliability values and is recommended to be incorporated in the standard procedure of genetic evaluation in maize breeding. The analyses bring the parents 2, 10 and 12, as potential parents in this microregion. Zea mays L.) is the most cultivated crop worldwide [Maize  in maize breeding –15. The In diallel analyses, the REML/BLUP procedure allows the estimation of additive and dominance genetic variances, as well as the narrow- and broad-sense heritabilities –26. In ae), composed of the correlated error (ξ) and, the independent random error (η) [e = ξ+η. For MET analyses, Smith et al. [In diallel MET analyses, there are many sources of variation . As mainrror (η) , 41, wheh et al. , 42 proph et al.  and soybh et al.  breedingThe two-stage analysis can present some issues, such as convergence failure and high computational demand, owing to the large amount of data . SelectiThere are several studies regarding diallel designs in maize breeding , 48–50, 1), which were widely adopted in the region, were used as checks , with no reciprocal crossing, was implemented . The genThe trials were carried out during the 2018 winter season at four locations in the southwestern Goiás State, Brazil: the environments, E1 and E2, in the municipality of Jataí, and the environments, E3 and E4, in the municipalities of Caiapônia and Mineiros, respectively. The planting and harvesting dates, geographic coordinates, altitudes, average temperatures, and precipitation data for each environment are presented in S3 Table and S1 Fig in -1. Agricultural practices for maize crops in Brazil [2.According to Alvares et al. , the wean Brazil  were adoTo evaluate the grain yield (GY) trait, the ears at physiological maturity were harvested and shelled. Then, the grain weight and grain moisture percentage were recorded, and the GY trait was calculated at 13% moisture. All phenotypic measurements were taken from the middle rows, leaving the two border rows.The estimation of variance components and the prediction of genotypic values for the GY trait were made using the REML/BLUP procedure , 17, accy is the vector of phenotypic data, τ is the vector of replications and checks (assumed to be fixed) added to the general mean, ug is the vector of the GCA effect (assumed as random), us is the vector of the SCA effect (assumed as random), and e is the vector of residuals (random). Uppercase letters refer to the incidence matrices for these effects.The individual analyses, considering the randomized complete block design with one observation per plot, was given by the following equation:e N; where R refers to the residual variance matrix. Models accounting for different residual variance structures considering the correlations among observations (rows and columns) were tested.In this model, y is the vector of phenotypic data, τ is the vector of block-locations-checks combinations (assumed to be fixed), which comprises the effects of environment, replication within the environment, and checks added to the overall mean; ug is the vector of additive genetic effects (assumed as random); us is the vector of dominant genetic effects (assumed as random); uge is the vector of the interaction between additive genetic effects and environments (random), use is the vector of the interaction between dominance genetic effects and environments (random), and e is the vector of residuals (random). Uppercase letters refer to the incidence matrices for these effects.The joint analysis, considering the randomized complete block design with one observation per plot and four environments, was performed using the following equation:eN; where R refers to the residual variance matrix. Models accounting for different residual variance structures considering the correlations among observations (rows and columns) were tested.In this model: SPA and NSPA analyses were performed for comparison purposes.In the individual analyses, the residual (co)variance structure could account for heterogeneity within the trial. The best fitted models were tested by the inclusion or the absence of the spatial information (given by rows and columns) in the fixed and random parts of the model. The joint analysis accounted for heterogeneity across environments in residual and genetic (co)variance matrices in two different ways: (i) by assuming spatially independent observations and (ii) by allowing spatial autocorrelations among observations, indexed by rows and columns.AR1) for rows (Σr(ρr)) and columns (Σc(ρc)). There are three possible models beyond the NSPA model (Ir is the identity matrix of rows (r × r), and Ic is the identity matrix of columns (c × c). The baseline model did not consider any correlations among the rows and columns. The following two residual structures account for the correlation among rows (M2) and columns (M3), respectively, by the inclusion of the AR1 structure. M2 and M3 contemplate the residual structure as xAR1, or, Σx, represent first-order autoregressive correlation matrix, for x (row or column).The presence of autocorrelation among rows and columns was considered by the inclusion of first-order autoregressive matrices  was included in the fixed and random parts of the model. First, the selected residual structure (MRx) of each trial was adopted as the first model, named Mx.1. Second, we tested the presence of fixed linear effects for rows and columns (Mx.2 and Mx.3). Third, we tested the presence of random linear effects for rows and columns (Mx.4 and Mx.5). Finally, the measurement error was added to the random part of the model (Mx.6).The fixed part of the model (rows and columns) deals with rows and columns as covariates, and was developed as a regression of the phenotypic responses as a function of the row and column positions. In the random part of the model, the rows and columns effects were included to quantify the variability among rows and columns. Finally, we also tested the inclusion of an independent error regarding the measurement error, which is an independent residual variance, Five different genetic variance structures were tested across different environments: diagonal (DIAG), compound symmetry (CS), heterogeneous correlation (CORH), and factor analytic of first (FA1) and second (FA2) orders.c) [LogL (LogLc), as follows:LogLc is the corrected LogL by p is the number of random parameters, q is the number of fixed parameters, and n is the model’s degrees of freedom.To select the best-fit model, the conditional Bayesian information criterion (BICc)  was usedLogLR is the logarithm of the maximum residual likelihood function of the reduced model. For the LRT test, chi-square statistics with 1 degree of freedom and 5% probability of Type I error were considered.The variances of the random effects were assessed using the likelihood ratio test (LRT) as follows :LRT=−22) heritability (given by the additive genetic variance among hybrids) were estimated for each trial using the following equations [The additive genetic variance (quations –66:σ^A2) heritability, were estimated considering the four environments in a joint analysis using the following equations [In addition to the genetic parameters by each trial, the additive genetic variance (quations –66:σ^Arg) and the overall mean (μg) for the GY trait was also calculated as follows:In addition, the genotypic correlation across environments , and D is the number of selected interpopulational hybrids (10).The correlations among the NSPA and SPA models were evaluated using the Pearson correlation coefficient. Cohen’s Kappa coefficient (K)  was applAfter selecting the individual and joint SPA models, further analyses were conducted using the NSPA model to expose the relative importance of the SPA model. Therefore, all analyses performed under the spatial approach were also re-made under a non-spatial approach, considering the independence among rows and columns.All statistical analyses were carried out using ASReml v.4.1 , ASReml-In trials E1 and E2, the NSPA model (MR1), which did not consider any correlation among the rows, and among the columns, was the best fitted model . In triaThe E1, E2, and E3 trials did not consider any other effect beyond the selected residual in the previous step; the E4 trial was the only trial that considered the inclusion of a linear effect of rows (M3.2), which improved the model’s goodness-of-fit .BICc in the previous steps. In the joint analysis, the genetic (additive and dominance effects) covariance matrix was also modeled. The compound symmetry model (CS) was assigned as the best-fit model  from NSPA to SPA analyses. First, the NSPA analyses presented broad-sense heritability estimates of approximately 5%. For SPA analysis, the broad-sense heritability estimates were split per environment, and their values varied according to each environment, from 4% (E1 and E3) to over 7% (E4). Compared to the individual analysis, the broad-sense heritability decreased from 13% in trial E1 to 4.8% in joint analysis, but in trial E4, it increased from 6.6% to 7.5%. The genotypic correlation across environments increased from 0.71, in NSPA analysis, to 0.75, in SPA analysis.We contrasted the additive and dominance genetic effects by NSPA and SPA analyses, in each trial, to check the differences when the spatial information was used. Considering the three best parents selected, the same selected parents were observed in trials E1 and E2  . The top ten genetic materials were compared and detached. The E3 and E4 trials presented different crossings into the top 10 dominance genetic values. The Pearson correlation coefficients were equal to 1.0 in the E1 and E2 trials, while in the E3 and E4 trials, they were higher than 0.8  reinforce the importance of this analysis. It was observed that the spatial information was useful for selecting different parents and interpopulational hybrids using SPA over NSPA analyses. In addition, using the Pearson correlation coefficient demonstrates the existence of different genetic materials when contrasting NSPA and SPA analyses, and the Cohen’s Kappa coefficient, which focuses on the selected genetic materials, confirms the difference among the selected.th position in SPA analyses. As demonstrated, the spatial trend corrections affected the additive and dominance genetic effects and must be considered by the breeder in breeding program strategies. The selection will be made based on these genotypic, additive genetic, and dominance genetic effects values, and their accuracy will directly affect the subsequent cycles of the breeding process.By observing the differences between the additive and dominance genetic effects, some interesting conclusions can be drawn for use in maize breeding programs. For instance, in trial E1, the H10,12, from the best parents (by additive effects) also presented a high dominance genetic effect; however, in trial E2, this effect was negative, demonstrating the presence of dominance by environment interaction effect, and its importance to calculate it. P6, which showed one of the lowest additive genetic effects, when combined with P12 (one of the highest additive genetic effects) presented one of the highest dominance genetic effects. These characteristics were observed in all the trials. In trial E3, a significant difference was noted between variance estimates and genetic parameter values from NSPA and SPA analyses, which demonstrates the importance of the SPA analyses in this study. Focusing on P3 and P12 as an example, the P3 was into three better parents in NSPA analyses, and decreased significantly in SPA analyses, while P12 arose from a median rank (in NSPA) to the third better in SPA analyses. Following, when looking into the dominance genetic effects just of the same two parents cross , it was in the top 10 in the NSPA analyses, and dropped to the 16Identifying the best genetic material is the main goal of any breeding program. The main goal of this study was to identify the best potential parents and their combinations to form heterotic groups. The interpretation individually and jointly brings the parents 2, 10 and 12, as potential parents in this microregion composted by the four environments. Overall, they presented a high additive genetic effect  and a high dominance genetic effect (seem to be contrasting and complementary), which would be very interesting in a hybrid composition, as the heterosis effect is expected in maize.In this way, this study highlighted the importance of considering the dependence among rows and columns when required for specific trials and applied all additional information into the joint analysis, combined with the best genetic covariance structure. The adoption of SPA analyses led to better results, as observed in BICc, selective accuracy, heritability, and selection gains. This study confirmed the importance of SPA diallel MET analyses in maize breeding, which is a pioneer in the literature.The adoption of MET permits a better understanding of the genetic effect, as it enables the breeder to account for the GxE interaction effect. This makes it possible to isolate the genetic effect or further explore the GxE interaction effect, depending on the goal. In addition, the diallel matching design enriches the study as it accesses the effects within the genotypic effect, both additive and dominance genetic effects, by crossing all parents among themselves. We found that the SPA analyses maximize the selective accuracy when compared to NSPA analyses, confirming the superiority of the SPA models. In addition, the LRT confirmed that the mismodeling process can lead to the misinterpretation of model effects, where some significant effects can be considered non-significant due to inappropriate analyses.Based on the fitted information, it was possible to identify the genotypes with the highest potential for future heterotic groups that can be used as potential commercial hybrids. The parents 2, 10 and 12, were indicated as potential parents in this microregion. Owing to their high additive genetic effects, bringing favorable genes to the future parental lines, their positive combination, given by the dominance genetic effect, will be expressed as a strong heterosis in future hybrids.S1 File(DOCX)Click here for additional data file.S1 Dataset(TXT)Click here for additional data file.


The breeding scheme in the Rubia Gallega cattle population is based upon traits measured in farms and slaughterhouses. We have developed a ssGWAS by backsolving the SNP effects after implementing a ssGBLUP. The results showed an apparent heterogeneity of the additive genetic variance across the genome. Some of the genomic regions explaining the most of this additive variance were shared across traits, indicating the presence of pleiotropic effects, which were reflected in their genetic correlations.NCK1, MSTN, KCNA3, LCORL, NCAPG, and RIN3.The breeding scheme in the Rubia Gallega cattle population is based upon traits measured in farms and slaughterhouses. In recent years, genomic evaluation has been implemented by using a ssGBLUP (single-step Genomic Best Linear Unbiased Prediction). This procedure can reparameterized to perform ssGWAS (single-step Genome Wide Association Studies) by backsolving the SNP (single nucleotide polymorphisms) effects. Therefore, the objective of this study was to identify genomic regions associated with the genetic variability in growth and carcass quality traits. We implemented a ssGBLUP by using a database that included records for Birth Weight , Weaning Weight , Cold Carcass Weight , Fatness  and Conformation . The pedigree included 464,373 individuals, 2449 of which were genotyped. After a process of filtering, we ended up using 43,211 SNP markers. We used the GBLUP and SNPBLUP model equivalences to obtain the effects of the SNPs and then calculated the percentage of variance explained by the regions of the genome between 1 Mb. We identified 7 regions of the genome for CCW; 8 regions for BW, WW, FAT and 9 regions for CON, which explained the percentage of variance above 0.5%. Furthermore, a number of the genome regions had pleiotropic effects, located at: BTA1 (131–132 Mb), BTA2 (1–11 Mb), BTA3 (32–33 Mb), BTA6 (36–38 Mb), BTA16 (24–26 Mb), and BTA 21 (56–57 Mb). These regions contain, amongst others, the following candidate genes:  The Rubia Gallega is one of the most important breeds of local cattle in Spain’s specialized in meat production, renowned for its meat quality. Currently, the census of the population stands at around 40,000 individuals, and its herd book was established in the 1960s. The Rubia Gallega breeding program started in 1990. The average performance of the breed implies a good growth rate 1200) and low feed conversion rate (~5), with a 60% carcass yield and a calving interval slightly higher than 400 days 00 and lo. The objSince 2018, genomic selection (GS) under a single-step approach or ssGBLUP  has beenIn this sense, Wang et al.  developeThis study aims to identify genomic regions associated with the genetic variability in growth and carcass quality traits in the Rubia Gallega breed by carrying out GWAS analyses based on predictions obtained by ssGBLUP. Following this procedure, the other objectives of this study were: (1) to identify candidate genes that could contain causal mutations, explaining the important percentage of the genetic variability of the traits and (2) to study the degree of similitude between the distribution of the additive genetic variance across the analyzed traits to characterize pleiotropic regions between them.The datasets used in the study contained phenotypic information and pedigree, collected by ACRUGA . The phenotypic data included 327,350 records for the BW, 83,818 for WW, 91,621 for CCW, 91,609 for CON and 91,475 for FAT see . CON wasWe used the Axiom Bovine platform from ThermoFisher Scientific, Waltham, MA, USA to genotype 2455 individuals. Among them, 688 were genotyped with the Axiom_BovMDv2 and 1767 with the Axiom_BovMDv3. The files were merged using PLINK v1.19 . We carrb) included in the model were: the age of the animal, in days, as a covariate; the age of the mother at birth, split into six categories  and sex . The variances of the random effects wereThe model of analysis for traits BW, CCW, CON, and FAT was the followingFor all models and traits, VanRaden  as6)G=G=H is thP effect :(10)σ^u,www.ensembl.org, Accessed on 25 March 2021), which contains the latest version of the bovine genome, Bos Taurus (ARS-UCD1.2), to identify the genes present in those regions.Firstly, we estimated the variance components by the restricted maximum likelihood (REML) , using tThe estimates of variance components are shown in The results on the GWAS for each of the traits are shown in The large proportion of the phenotypic variance explained by additive genetic effects defines the moderate to high heritabilities obtained. The estimates of heritabilities are in accordance with the estimates obtained for other populations ,17,18. TThe results acquired from the ssGWAS show that the additive genetic variance obtained is not homogeneously distributed along the genome. Moreover, some regions explain a greater proportion compared to others. The presence of pleiotropy was confirmed when we analyzed the genomic regions of the genome accounting for the percentage of additive genetic variance above 0.5% see . FurtherMyostatin (MSTN) gene. The MTSN gene is a growth differentiation factor associated with beef cattle’s double-muscled phenotype [MTSN gene [There are two genomic regions, located on chromosomes BTA2 and BTA6, that were highlighted in previous studies  as suscehenotype , causinghenotype . This sthenotype ,26. PrevTSN gene  are segrTSN gene . HoweverTSN gene .Leucine Aminopeptidase 3 (LAP3), FAM184B, DDB1 and CUL4 associated factor 16 (DCAF16), Ligand Dependent Nuclear Receptor Corepressor Like (LCORL), and Non-SMC Condensin I Complex Subunit G (NCAPG). The DCAF16 mediates the processes of ubiquitination and proteasome-dependent degradation of nuclear proteins [NCAPG is a gene involved in cell division and mitotic chromosome condensation [DCAF16-NCAPG regions have been associated with average daily gain in beef cattle [NCAPG has been associated with postnatal growth and cold carcass weight in cattle [LAP3 and FAM184B have been associated with growth and carcass traits [The second featured genomic region is on chromosome BTA6, between 36986502 and 37463048 base pairs. In this region, there are a number of candidate genes such as proteins , and NCAensation . The DCAf cattle . NCAPG hn cattle ,35, fat n cattle . Furthers traits ,40.Cytoplasmic protein (NCK1). NCK1 is a protein-coding gene located in the cytoplasm and involved in translation regulation processes [Potassium Voltage-Gated Channel Subfamily A Member 3 (KCNA3), which encodes a member of the voltage-gated potassium channel involved in the proliferation and activation of the T-cells [Dual Specifity Phosphatase 10 (DUSP10), a dual specificity protein that inhibits members of the MAP (Mitogen-activated protein) kinase family, associated with the proliferation and differentiation of cells [DUSP10 is associated with beef cattle’s growth traits, as average daily gain and carcass weight [Ras and Rab Interactor 3 (RIN3) and Legumain (LGMN). RIN3 is a Ras interaction-interference effector protein that binds to RAB5 to exchange GDP (Guanosine triphosphate) for free GTP (Guanosine diphosphate) [LGMN is a protein-coding gene for a cysteine protease with specificity for hydrolysis of asparaginyl bonds, involved in regulating the processing of MHC class II antigen proteins in the lysosomal or endosomal systems [LGMN is associated with adipose tissue expression changes, significant for meat quality in beef cattle [Further on, on chromosome BTA1 (between 131853658 and 132433521 base pairs), we identified the candidate gene rocesses , associarocesses . On chro T-cells . On chroof cells . DUSP10 s weight ,47. Finaosphate) ,49, and osphate) . LGMN is systems . MoreoveFrom the results we obtained, we observed heterogeneity in the additive genetic variability across the genome. These results could serve as the basis for the modification of future procedures of genomic assessment in the Rubia Gallega population. At present, the implementation of genomic assessment is in the initial phases, and it uses the GBLUP procedure, following the procedure by VanRaden . HoweverFurthermore, the GBLUP procedure weights each SNP marker’s information to calculate the genomic relationship matrix . NonetheThe results of this study confirm the moderate to high heritability of growth and carcass quality traits in beef cattle populations. They also show that the additive genetic variation is heterogeneously distributed across the genome. Finally, it was observed that the genomic regions explaining most of the additive genetic variance are shared among the traits due to pleiotropy.


Adult height inspired the first biometrical and quantitative genetic studies and is a test-case trait for understanding heritability. The studies of height led to formulation of the classical polygenic model, that has a profound influence on the way we view and analyse complex traits. An essential part of the classical model is an assumption of additivity of effects and normality of the distribution of the residuals. However, it may be expected that the normal approximation will become insufficient in bigger studies. Here, we demonstrate that when the height of hundreds of thousands of individuals is analysed, the model complexity needs to be increased to include non-additive interactions between sex, environment and genes. Alternatively, the use of log-normal approximation allowed us to still use the additive effects model. These findings are important for future genetic and methodologic studies that make use of adult height as an exemplar trait. Since the dawn of biometry and genetics, human height has served as a model, exemplar quantitative trait. Studies of adult height have shaped a classical biometric and quantitative genetic approach to inheritance –3. NowadAn important part of our view of height is an assumption of additivity of effects that is explicitly made in early works and is justified by a “physiological” argument: “stature is not a simple element, but a sum of the accumulated lengths or thicknesses of more than a hundred bodily parts” . One shoAdditivity implies normality, and the adult height serves as an empirical example of a normally distributed biological trait in textbooks on statistics –15. FurtThus, from studies of adult height, we know that an “ideal” quantitative trait results from a sum of the individual contribution of different influences, and it has a normal distribution of residuals  , 17; aduAt the same time, it is well-understood that additivity of effects and normal distribution of residuals is only an approximation to the distribution of height in human populations. Practically, we notice several peculiarities in the distribution of adult height  data  to indivEach of the six analysis groups was stratified by sex; within these 12 sub-groups we have excluded individuals who deviated from the mean by 4.75 standard deviations or more . In total, 32 people were excluded according to this criterion. Supplementary Table Throughout this manuscript, we use “height” for height in centimeters, while “log-height” is used for the base-10 logarithm of height.p value in the GIANT univariate analysis. We observed that rs9404952:G > A (NC_000006.11:g.29804165 G > A) was neither genotyped nor imputed in the UKB. Three SNPs—rs1420023:C > A,G,T (NC_000012.11:g.12876111 C > D), rs1659127:G > A,C,T (NC_000016.9:g.14388305 G > H), rs7567851:G > A,C (NC_000002.11:g.178684720 G > M)—were genotyped and imputed in UKB with alleles different between direct genotyping and imputations. We therefore excluded these three SNPs from analysis because of ambiguity. From the residual 419 SNPs we have selected 305 that satisfied all of the following criteria: had imputation quality in UKB greater than 0.9; had univariate p value less than 5 × 10−10 in GIANT analysis of Wood et al.; had EAF difference less than 5% between six above defined UKB groups and “250 K GWAS Meta-analysis” of Wood et al. [We considered 697 SNPs associated with height, reported in Wood et al. The SNPs were clustered in 423 loci, with a locus defined as one or multiple jointly associated SNPs located within a 1-Mb window [d et al.  was utilp < 10−8 in the Yengo analysis. We used the same procedure, as described above, to load data and define a polygenic score.For the purposes of analysing epistasis we also constructed an “updated” PGHS based on 712 loci (3290 SNPs) reported in Yengo et al. . That stAlthough GWAS conducted by Yengo et al.  is more Using data on 370 thousand white British individuals we estimated a linear mixed model of height that included sex, PGHS, year of birth, year of visit to the assessment centre (five levels), household income, analysis group (six levels) and ten first principal components of genetic variation as fixed effects and assessment centre code and genotyping batch as random effects. From the predicted height we then have subtracted estimated effects of sex and PGHS, after which the resulting predictor was centred and scaled to have mean zero and variance of one. The linear mixed model was estimated using the R package “lme4” .To generate Fig. Within each of the six analysis groups we computed median polygenic score and median residual predictor. To generate Fig. PGHS is the vector of PGHS values, g1,…,gn are the vectors of genotypes of loci included in PGHS, μ is an intercept and β1 is a scaling factor (both estimated from the data) and a1, …, an are the weights fixed at the values corresponding to the estimates of additive effects obtained by previously published studies.We formalise the additive models asThe epistatic model is formalised asβ2. This is made possible by assuming that all pairwise interaction effects are proportional to the products of the published additive genetic effects from the linear model.Thus our epistatic model only considers the dominance and pairwise epistatic interactions and estimates these effects through a single parameter, Height, Sex, PGHS are vectors of height, sex and PGHS values correspondingly, RP1 to RP16 are the vectors of the residual predictor components as described above, μ and β1 to β18 are the corresponding regression coefficients, and ɛ is the vector of residuals. The proportion of variance of height explained by the additive model was estimated as the relative decrease in the variance of height after subtracting observed from the values predicted by the additive model. The proportion of variance of height explained by the multiplicative model was estimated as the relative decrease in the variance of height after subtracting observed from the exponentiated value of the predicted log-height . For each allele frequency 1 million independent simulations were performed. The equality of distributions of Z-test statistics obtained for height and log-height was tested with Kolmogorov–Smirnov test.For minor allele frequencies 0.01, 0.05, 0.1, 0.5 we generated random vectors of genotypes  distributed according to Hardy–Weinberg equilibrium. We then tested the association of these random genotypes with the residuals of height and log-height, obtained for 369,153 individuals of European (white) descent. The residuals were obtained from a regression model including sex, PGHS, and RP as independent variables and the statistical strength of association was characterised by the To analyse the transferability of height prediction models between groups of different origin we generated linear height and log-height prediction models using British people of white descent born in England as a training set. The models included sex, PGHS, income  and age  as independent variables. Groups where height and log-height were predicted were defined either as described above  or defined by Ethnic background (UKB field 21000). Supplementary Table lm function from R package ‘stats’ [We used the  ‘stats’  to fit l ‘stats’  as imple ‘stats’ .For ratios, the confidence interval (CI) was computed using Fieller’s theorem . The tesFirst, we reviewed anthropological literature concerned with the study of the distribution of height in different populations and collected the data on the mean height, its standard deviation, and sample size where it was possible. Across different populations, we studied how the mean height relates to the SD and CV and analysed effects of sex.p < 0.001), while only 6% of the variance of the CV (p = 0.08).In the analysis of 50 populations  we obserp = 0.9). The slope in this model was 1.080 that differs significantly from 1 (p = 0.003). This observation supports multiplicative contribution of sex to the height variance.To determine whether male and female mean height are related multiplicatively or additively, we regressed the mean male height on the mean female height Fig. . We usedThus, when we study a range of diverse human populations, both SD and effects of sex scale up with increased mean—a behaviour, not expected from a normal, but common for a log-normal distribution .p < 10−100 for English, p < 10−50 for all-but-English), in people with higher PGHS  and those with higher value of the residual predictor  , are clear and significant.p = 10−12 for English, and p = 4 × 10−6 for all-but-English), the sex by residual predictor interaction was next significant , and interaction between polygenic score and the residual predictor was weaker although still significant . We have also tested for the effects of epistasis. In quantitative genetics, the term “epistasis” implies any deviation from additivity  of genetic effects of different loci [p = 1.32 × 10−2 for all, p = 2.02 × 10−2 for English, and p = 0.346 for all-but-English). We speculated that our polygenic score is probably too weak to detect epistasis, and updated it to include 3290 SNPs from 712 loci [p = 4 × 10−7 for all, p = 2 × 10−4 for English, and p = 2 × 10−4 for all-but-English).We next have used individual-level UK Biobank data to explore all pairwise interactions between sex, polygenic score, and the residual predictor. The interactions were introduced into the model as a product between corresponding variables, for example, the interaction between sex  and PGHS was defined as sex*PGHS. We observed significant and replicable interactions between all three factors . Thus, logarithmic transformation both stabilises the variance and allows us to use a simpler model for the mean.The observations of increased effects of various predictors and of the SD with the mean, the effects of interactions, and variance heterogeneity we observed for adult height lead us to try an alternative, log-normal, approximation .Furthermore, we explored how well height predictive models trained in people born in England translate to people born elsewhere .The multiplicative model of height predicts that at the extremes, people will be taller than predicted by an additive model, while in the centre, the additive model will overestimate the height. When we compare the observed distribution of height with the normal and log-normal, we observe that with a single exception both approximations provide an excellent fit to the data  height data, analysis of heterogeneous populations, and analysis of the extremes of height. These findings are important for future genetic and methodologic studies that make use of adult height as an exemplar trait.Several independent lines of evidence support our conclusion about the presence of multiplicative effects and potential role of log-normal approximation for height. For example, the fact that variation of height is different between human populations, while the coefficient of variation is rather stable, has been documented in socioeconomic and anthropological literature , 33, leaOur findings may be discussed in context of measurement theory . This thAs we detailed in the Introduction, prehaps, with the exception of sex, the multiplicative effects of other factors, such as genes and environment, on height were not appreciated before. We believe that this may be explained by the fact that the multiplicative effects are very small and their discovery asked for the sample sizes that were out of reach until very recent. In contrast to the traits that are well-known to be distributed log-normally , the within-population coefficient of variation of adult height is small —as soonAlthough given the small CV the normal and log-normal approximations of height may be almost equivalent, still, some differences in statistical properties may be expected. Indeed, the use of log-normal approximation improves the model fit to the data, although it does that by very little (the difference in the proportion of variance explained is less than 0.1%). The predictions from the two models are also essentially the same . Assuming that the distribution of height in mega-cohorts is better approximated by the log-normal rather than normal distribution, with even larger sample sizes, both Gene by Sex as well as Gene by Gene interactions will become significant for genetic variants with progressively smaller effects. Hence, if one were to keep the model simple, one would likely have to turn to log-normal approximation.What may be expected in the future, when many millions of samples could be analysed? From our analysis it follows that while the use of log-normal approximation is expected to lead to better prediction, on population level the gain is very small. At the same time, deviation may be pronounced for individuals at the edges of distribution. We do not expect that the use of either normal or log-normal approximation will lead to large differences in type 1 or type 2 error. However, with progressively larger sample sizes the epistatic effects will become detectable for individual variants. At the moment, under normal approximation, we can already detect the gene by sex interaction for the lead SNP rs143384:G > A (The question whether one should use normal or log-normal approximation to study human height depends much on the scientific question being asked. As we demonstrated, for prediction of means, as well as in the context of heritability estimation and GWAS we expect that differences are negligible. However, if one aims to study interactions and aims to predict variation of height, the difference between using normal and log-normal approximation will be substantial.Thus, as far as we can see, our discovery mainly has a conceptual value and may guide better interpretation of the results of analysis of big data. As we demonstrate, a study of big height data under an additive model demonstrated variance heterogeneity and interactions. Variance heterogeneity across genotypes is often interpreted as evidence of possible interactions –27 or enOn a side note, we would like to reflect on the fact that most anthropometric traits, such as height, weight, body mass index, are well approximated by a log-normal distribution with male having greater mean and hence greater variance. This may be one of the explanations of the “greater male variability” in physical characteristics, first noted by Darwin: “several studies had been conducted to demonstrate that variability was indeed more characteristic of males … The biological evidence overwhelmingly favoured males as the more variable sex … The cause of the greater general variability in the male sex, than in the female is unknown” .To conclude, we analysed adult height using summary-level data from a variety of world populations and big individual-level UK Biobank data. Our analysis shows that when the height of hundreds of thousands of adults is analysed, the non-additive interactions can be detected. This leads to increased model complexity and a “breakdown” of the classical example of the classical quantitative genetics. This apparent breakdown could, however, be avoided, and the additivity assumption could be kept if the log-normal approximation is used. We speculate that future increase in the volumes of available data will eventually force us to further review the assumptions about distribution of adult height and the model of its control.Our findings are important for the field of quantitative and complex trait genetics, because new methods are often tested using adult height, and the findings for height are often extrapolated and have profound effects on the ways we look at and study other traits.Supplementary MaterialSupplementary Tables


The lowering genotyping cost is ushering in a wider interest and adoption of genomic prediction and selection in plant breeding programs worldwide. However, improper conflation of historical and recent linkage disequilibrium between markers and genes restricts high accuracy of genomic prediction (GP). Multiple ancestors may share a common haplotype surrounding a gene, without sharing the same allele of that gene. This prevents parsing out genetic effects associated with the underlying allele of that gene among the set of ancestral haplotypes. We present “Parental Allele Tracing, Recombination Identification, and Optimal predicTion”  approach that utilizes marker data to allow for a rapid identification of lines carrying specific alleles, increases the accuracy of genomic relatedness and diversity estimates, and improves genomic prediction. Leveraging identity-by-descent relationships, PATRIOT showed an improvement in GP accuracy by 16.6% relative to the traditional rrBLUP method. This approach will help to increase the rate of genetic gain and allow available information to be more effectively utilized within breeding programs. Glycine max L. Merr.; Crop domestication has caused extreme genetic bottleneck, with a reduction in genetic diversity in domesticated crops compared to wild ancestors including in soybean  is becoming mainstream in mid- to large breeding programs , as it uCurrent genomic selection models are predominantly based on IBS relationships between lines and utilize historic LD between markers and the trait of interest, as well as pedigree-based relatedness . ModificWhile previous efforts have relied on using haplotypes based on observed LD between markers, we explore an alternative approach of tracking the parental source of each allele. Two main distinctions between the approaches should be noted: (1) our approach does not assume any previous evidence of haplotypes or LD, instead utilizing markers which could only have been inherited from exactly one of the direct parents to define IBD segments, and (2) individuals which would otherwise have the same estimated effect from a shared haplotype can now be assigned different estimated effects due to tracking exactly which ancestral line a haplotype was inherited from.We test an approach hereafter named “Parental Allele Tracing, Recombination Identification, and Optimal predicTion” (PATRIOT) that utilizes raw marker data for tracking IBD inheritance of chromosome segments, enabling the rapid identification of lines carrying specific alleles, increasing the accuracy of genomic relatedness and diversity estimates, and improving genomic prediction and selection performance. Using the SoyNAM population , which ihttps://npgsweb.ars-grin.gov/gringlobal/search. The pedigree information used in this study is provided in Pedigrees for public breeding lines tested in the Uniform Soybean Tests were recorded based on reporting in their last year of testing in the Northern testsSNP marker data for 5,149 soybean nested association mapping (SoyNAM) RILs, as well as their parents, were downloaded from SoyBase,Soybase.orgWe identified 868 accessions within the National Plant Germplasm System (NPGS) soybean collection wherein both parent and progeny were genotyped with the SoySNP50k SNP set, including near-isogenic lines derived from backcrossing schema. SNP marker data for all accessions in the GRIN database were downloaded from 1, and OH2), and 2013 . Additionally, SoyNAM RIL provided by Dr. George Graef was used to evaluate the performance of individual gene tracking for several qualitative traits .Phenotypic records for the SoyNAM recombinant inbred line mapping population were downloaded from SoyBase (see Footnote 7), including yield, plant height, lodging, oil, and protein. Replicated entries’ phenotypic records from within a single environment were used to calculate BLUP for those lines, while unreplicated entries were incorporated using the raw phenotypic values. The “Corrected Strain” column was used to connect phenotypes with genotypic records. Phenotypic records were available from 2011 (IL and NE), 2012 .Prepare a master marker file for progeny and parents which have been genotyped with the same marker panel.Within each progeny, identify markers which could only have been inherited from one of the parents. Name those markers by their parental source and rename the remaining markers as “Parent A and Parent B.”Impute ambiguous markers if they are flanked on either side by alleles inherited from the same parent. This often requires going more than one marker away to get to a marker which is known to be inherited from a specific parent.The workflow can be translated into the following algorithm:For each marker position, calculate the difference between the average phenotype of lines which inherited that marker from each parent and the location mean.To allow the nominal data created in steps 1–4 to be utilized for genomic prediction in linear regression-based approaches , we created what we call an allele effect estimator. This requires the addition of three extra steps (5–7):α):jα is the allele effect estimate for ancestral allele source j, ijy is the phenotype for the ith line containing the ancestral allele source j, n is the total number of lines which inherited ancestral allele j, and μ is the population phenotypic mean.If there are eight different sources of alleles at a specific locus, there will be eight different estimates (one for each source). This process needs to be repeated separately for every location and trait. However, the same file of ancestral allele sources can be used regardless of environment or trait. The difference between the average phenotype of lines containing a specific ancestral allele and the location mean is the allele effect estimate (AEE or Create a new matrix (AEE matrix) by replacing the parental source of each locus with the estimated AEE for that parent at that locus. Markers for which parentage could not be differentiated are replaced with the average AEE of the two possible parents at that locus.Within the context of genomic selection, replace the raw marker file  with the AEE matrix .In this way, separate allele effect estimates are created for each parental source of an allele. For loci whose ancestral source could not be determined , the average of the two parental allelic differential estimators were used. Since each AEE is generated in a separate calculation, the AEE value is not regressed toward the mean to account for multiple regression. Instead, these values replace the marker representation as an input to GS models that evaluate the performance of this new approach . They alAs a proof of concept, tracing of chromosome segment inheritance within the pedigree of soybean cultivar “Rend” was performed. After ensuring consistency between expected results and the outputs, chromosome tracing was performed on the remainder of the 868/50K panel. Following completion of the single-generation tracing pipeline, the multi-generation tracing script was run on traced lines to allow visualization of multiple generations of inheritance and recombination.T, I, R, W1, and Dt2 loci, those lines for which the immediate flanking markers were assigned to the same parental allele source were used to evaluate the accuracy of allele calling with PATRIOT IBD tracking.In addition to the 868/50K panel, SoyNAM project parents and RILs were investigated with the chromosome tracing pipeline. The A/B genotype representation data available from SoyBase were utilized to impute chromosomal segments. Even with a sparse marker coverage, recombination events were still identifiable . For SoyTo expand on the usefulness of the chromosome tracing pipeline outlined in Traditional rrBLUP performance was evaluated using mixed.solve, a function in R package “rrBLUP” . The rrBvia two approaches. For the first approach, we measure the correlation between predicted phenotypes and the observed phenotype in the testing set (lines not used to train the model). Improvement in genomic prediction accuracy was calculated by dividing the correlation between observed and predicted values using PATRIOT by the correlation between observed and predicted values using rrBLUP. In the second approach, we compared the mean phenotype of the testing lines with top 10% predicted phenotypes using PATRIOT and rrBLUP, and divide the mean of PATRIOT-selected lines by the mean of rrBLUP-selected lines to determine the improvement in genomic selection effectiveness. This second approach was then modified to compare the top 5% of lines for the 2012 OH1 yield test to gain further insight into where differences in model performance were most significant.The performance of PATRIOT and rrBLUP was evaluated with For the 868/50Kpanel, 13.14% of all SNPs were unassigned to a specific parent. For the SoyNAM panel, 6.78% of all SNPs were unassigned to a specific parent. Using the SoyNAM panel marker data after PATRIOT IBD tracing and imputation, we examined the rates of recombination throughout the genome. Of the 5,149 RILs examined, we found total recombinations per line ranged from 10 to 557, with an average of 50.9 recombinations per line. The percentage of chromosomes that were inherited intact from one parent or another was 18.3% . A total of 5,011 RILs inherited at least one intact chromosome from a parent.Phytophthora root rot (PRR) resistance locus Rps1 , as a long introgression (shown in green) on chromosome 3 from Kingwa . This allele is then transmitted from Williams 82 to Resnik  in a smaller chromosomal segment around Rps1k. However, the resistance allele was not passed on to Resnik’s progeny, Rend . Resnik is therefore more suitable than Rend to breed for Phytophthora resistance. Chromosomal tracing over multiple generations allows presence/absence characterization for the Rps1k allele without the need for allele-specific markers and can reduce the need for phenotyping in disease nurseries, as allele state is known by virtue of IBD. Chromosomal segments were traced in the 868/50K panel using the PATRIOT framework. To demonstrate the PATRIOT workflow, we traced the inheritance of the major cus Rps1 . WilliamRps1k is greatly reduced in Resnik, indicating recombination during the cross of Asgrow 31274×Williams 82, and (ii) a segment of the soft red “AmbiguousParentage” class appears in the progeny, which indicates that recombination occurs somewhere within this region, but could not be delimited between two adjacent markers due to multiple markers being alike by state in the parents. This occurs in Asgrow 3127  on chromosome 3, separating large segments inherited from Williams and Essex.Recombination events can be visually identified when examining multiple generations within Rps1k example is provided, the PATRIOT framework is applicable to trace chromosomal regions and for IBD characterization of important genes through generations, as well as to visualize nearby recombination events. In addition, While the −1 in rrBLUP GS) Similar results were found for other traits, and can be found in To examine the relative effectiveness of rrBLUP with PATRIOT (PATRIOT GS) compared to traditional rrBLUP (rrBLUP GS), yield predictions for 16 environments from each model were generated using the same randomized testing set for each model. Results from the two GS approaches are presented in 1 environment, which showed a large increase in GP accuracy (+39.5%) but only slight increase in genomic selection effectiveness (+3.8%). When examining the bottom 10% of predicted lines (rather than top 10% as before), the genomic selection effectiveness was 52.7% greater using PATRIOT than rrBLUP. This finding, coupled with smaller average absolute error terms using PATRIOT, suggests that the GP accuracy increase came from decreased error terms (PATRIOT prediction was closer to the observed phenotype than was rrBLUP prediction) throughout the full range of phenotypes, allowing for better rankings. Indeed, using a 5% selection level for high GEBVs using PATRIOT resulted in a 29.8% increase in average observed phenotype compared to rrBLUP in the 2012 OH1 set.To help explain the cause of the difference in performance improvement between genomic prediction accuracy (+16.6%) and genomic selection effectiveness , we further examined the yield predictions from the 2012 OHSome of the earlier efforts in soybean chromosomal tracing involved RFLP markers, as researchers traced chromosome segments in 67 genotypes through generations . The traThe genome tracing of large segments through multiple generations enables breeders to follow genes of interest throughout the pedigrees of modern lines . This alWhile IBD can be traced in many released public cultivars on the basis of markers from the SoySNP50K chip in soybean, applicability to breeding programs during the development of new pure lines requires a cost-effective genotyping system to allow genotyping of these lines at an earlier stage of development. This can be achieved by utilizing a smaller, less expensive genotyping array such as the SoyNAM6K BeadChip  to genotThe PATRIOT framework facilitates the identification of lines for breeding purposes that have favorable genes linked in coupling, as well as in situations where breaking the linkage drag is imperative. For example, SCN resistance from PI494182 was determined to carry a risk of linkage drag . LikewisMuch like genome-wide association studies (GWAS), genomic prediction models rely on the association between markers and QTL. However, the association between marker and QTL decays in subsequent generations, leading to reduced accuracy without retraining of the model . With thThe prediction accuracy is expected to decay much more slowly with chromosome tracing because the linkage between marker and QTL decays only when recombination occurs, rather than with changing founder allele frequency at a given locus. Furthermore, multi-generation tracing allows the preservation of information on lineage-specific marker association which can better model the differences in genes linked to a particular marker or set of markers. This concept can be elucidated with a hypothetical example with following conditions: (1) diploid organism, (2) single gene controlling the trait of interest, (3) trait of interest causes 1 unit increase in phenotype, (4) SNP marker is known and is 1cM away from the gene, and (5) wild population. In this scenario, the genetic information is given in With the incidence rate of the desirable allele, we can expect 0.5 unit phenotype level due to the causal gene. If the “A” allele of the SNP was selected, the total proportion selected will only be 50% but the phenotype level will only be 0.6units above the wild-type baseline. However, if the population was intermated after genotyping, and parental tracking for each progeny, marker–gene region can be tracked and therefore QTL effect can be accurately estimated by replication of the parental segment. These steps will ensure that with 1cM marker–gene linkage, the progeny after intermating can show 0.99 unit of phenotype level without model retraining.This does not mean retraining or recalculation of SNP effects is not needed when IBD is used, but the decay in predictive ability is less. Other factors can also reduce the frequency of retraining. According to The multi-generation chromosome segment tracing aspect of PATRIOT can also be used as a tool to connect QTL mapping studies among related populations. In addition to tracing chromosomal regions within a pedigree, this framework can be used to connect linkage mapping studies using related lines as parents by tracing QTL regions identified in related parents in separate studies to their ancestral sources. This allows for a meta-analysis to utilize the increased power which comes from having multiple mapping populations with common ancestry to map marker–trait associations.However, there are challenges to the PATRIOT framework. In crosses where parents share large runs of IBS or IBD based on marker data, it is difficult to determine which parent is contributing each allele to the progeny. However, if these runs are IBD, the effect on allele estimation is equivalent, regardless of which parent is assigned to the allele. Additionally, a surprising number of singleton marker calls suggests that either double recombination is occurring at a much higher rate than previously believed, or that the reference genome assembly order does not agree with the true marker order. Increased marker density can overcome some of these challenges. Likewise, uncertain regions can be assigned new allele effect classes. For example, Williams 82 (PI518671) has 3,399 out of 42,080 markers which could not be assigned with certainty to a specific parent (Williams or Kingwa). To circumvent this challenge, each of these markers was assigned a new parent class of “PI518671” when tracking segments passed on to progeny but continue to use AEEs based on the average AEE of parents Williams and Kingwa when predicting its own performance.PATRIOT genomic prediction accuracy for yield using all populations was greater than the calculated marker-based heritability of the trait in 13 of 16 environments , suggestThe fact that this high level of prediction accuracy was possible with a 6K SNP chip in the SoyNAM populations suggest significant potential cost savings, as the cost of genotyping at this density is less expensive than growing and phenotyping in replicated field plots . More geWhile our genomic prediction models utilized only the immediate parents for calculating allele effect estimates, it is possible to expand the method by combining with the multi-generation IBD tracing script. This approach has an added benefit of bridging the gap between populations that do not share a direct parent but share ancestors in previous generations. By doing so, an increased number of lines can be used for allele effect estimation, further improving the accuracy of these values.IBD-based genomic selection has the clear potential to improve selection accuracy over existing genomic selection approaches. However, there is a trade-off due to the significant increase in computational time . While tThe PATRIOT pipeline provides a framework for identifying, tracking, and applying IBD information to increase effectiveness of genomic selection under SNP-based models. Tracking IBD with PATRIOT enables pedigree-based gene tracking through generations, which can be useful for parental selection, as well as for predicting phenotypes for monogenic and oligogenic traits. Relatedness metrics within breeding populations can also be improved due to the specification of IBD allele sharing rather than IBS. The IBD information also works to improve genomic prediction and selection results. This improvement was shown in first-cycle genomic prediction but should provide additional benefits in later cycles due to the donor-specific allele effect estimation, which does not suffer from the problem of population shift between training and testing sets. The large and consistent benefit shown suggests that chromosome tracing is a quick and efficient way to increase the accuracy of genomic selection models, with no additional cost beyond modestly increased computational time.https://github.com/SoylabSingh/PATRIOT, https://soybase.org/SoyNAM/index.php, and https://soybase.org/snps/.Publicly available datasets were analyzed in this study. These datasets can be found at: JS conceptualized the project with AS and conducted the statistical analysis with suggestions from AS and DL. JS and AS prepared the first draft. All authors contributed to the article and approved the submitted version.Authors sincerely appreciate the funding support from Iowa Soybean Association, R. F. Baker Center for Plant Breeding, Bayer Chair in Soybean Breeding, and USDA CRIS project (IOW04714). Part of JS graduate assistance was provided by the NSF NRT (graduate fellowship).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Fertility and reproductive performance are key drivers of dairy farm profitability. Hence, reproduction traits have been included in a large majority of worldwide dairy cattle selection indexes. The reproductive traits are lowly heritable but can be improved through direct genetic selection. However, most scientific studies and dairy cattle breeding programs have focused solely on the genetic effects of the dam (GED) on reproductive performance and, therefore, ignored the contribution of the service sire in the phenotypic outcomes. This study aimed to investigate the service sire effects on female reproductive traits in Holstein cattle from a genomic perspective. Genetic parameter estimation and genome-wide association studies (GWAS) were performed for the genetic effect of service sire (GESS) on conception rate (CR), 56-day non-return rate (NRR56), calving ease (CE), stillbirth (SB), and gestation length (GL). Our findings indicate that the additive genetic effects of both sire and dam contribute to the phenotypic variance of reproductive traits measured in females , and these two genetic effects are positively correlated for SB (0.1394) and GL (0.7871). Interestingly, the breeding values for GESS on insemination success traits (CR and NRR56) are unfavorably and significantly correlated with some production, health, and type breeding values (ranging from −0.449 to 0.274), while the GESS values on calving traits  are usually favorably associated with those traits (ranging from −0.493 to 0.313). One hundred sixty-two significant single-nucleotide polymorphisms (SNPs) and their surrounding protein-coding genes were identified as significantly associated with GESS and GED, respectively. Six genes overlapped between GESS and GED for calving traits and 10 genes overlapped between GESS for success traits and calving traits. Our findings indicate the importance of considering the GESS when genetically evaluating the female reproductive traits in Holstein cattle. In recent decades, the genetic selection for functional traits, including reproductive performance, has received great emphasis in dairy cattle selection indexes, aiming to achieve more balanced and sustainable breeding goals . Female The determination of the genetic effect of service sire (GESS) on reproductive traits relies on genetic and genomic analyses, including the estimation of genetic parameters and genome-wide association studies (GWAS). Previous studies have identified interesting genomic regions associated with SCR, as reviewed by 1) and used in this study. The reproductive traits include CR , NRR56 , CE , SB , and GL (in days). The last insemination before a positive pregnancy diagnosis in each parity was considered as pregnancy. Furthermore, the cows with calving records but without a positive pregnancy diagnosis were considered pregnant when last inseminated before calving. Insemination records that had the next insemination within 1–17 days or had neither insemination nor calving records after that time period were excluded from the NRR56 calculation. CE and SB were directly coded from raw data after excluding ambiguous records (3%) caused by mis-recording. GL records lower than 260 and greater than 302 days were also deleted. A descriptive summary for each trait after data editing is shown in Records of birth dates, insemination events, pregnancy diagnoses, and calving information collected in 39 farms  from 1987 to 2020 were extracted from the AfiFarm software  and a sub-validation population  for assessing the accuracy of genotype imputation as the concordance rate of imputed SNPs. Only SNPs with imputation accuracy greater than 90% were kept for further analyses. Furthermore, SNPs with minor allele frequency lower than 0.05, unknown chromosome or genome position, and extreme deviation from the Hardy–Weinberg equilibrium  were removed. After data editing, 109,274 SNPs located in the autosomes and pseudo-autosomal regions of the X chromosome were retained in the dataset.A total of 3,477 Holstein bulls were genotyped with the Illumina BovineSNP50 BeadChip  containing 54,609 single-nucleotide polymorphism (SNP) markers. These genotypes were imputed to the Illumina 150K Bovine Beadchip  using the BEAGLE v5.1 software  and a reThe variance and covariance components for each reproductive trait were estimated using the AI-REML algorithm implemented in the DMUAI module of the DMU v6 software . A previy represents the vector of phenotypic observations , β is the vector of fixed effects included in the model, in which different systematic effects were fitted for each trait . All of the fixed effects significantly (P < 0.05) influenced the dependent variables  and were identified based on mixed model analysis using the PROC MIXED function implemented in the SAS software ; um and uf are the vectors of the random animal effects accounted by GESS and GED, respectively; pem and pef are the vectors of the random permanent environmental effects of the service sire and dam, respectively; hym is the vector of the random herd–year–month effects; e is the vector of the random residual effects; and, X, Z1, W1, W2 and Z2 are the corresponding incidence matrices. We assumed that:where with:m,f is the genetic covariance of service sire and dam; A is the additive genetic relationship matrix among the animals; and I is an identity matrix. For calving traits, the model could be considered as an improved sire–dam model that assumes that the GESS has a genetic covariance with the GED. Compared to the traditional evaluation models of calving traits that only consider the animal effect, the current model includes both service sire and dam effects in the female reproductive performance phenotypes through GESS and GED, respectively. Differently from direct and maternal  effects usually assumed to be correlated, this was not the case for the genetic components of service sire and dam in the current study. Therefore, the GESS heritability estimates were calculated as follows:where and the repeatability estimates were calculated as follows:The GED repeatability was estimated in the same way but replacing The standard error of the heritability and repeatability estimates, respectively, were calculated using the Delta method . A Wald p-values were corrected for multiple testing by calculating the false discovery rate (FDR) .The “Fixed and random model Circulating Probability Unification” (FarmCPU) R package  was usedte (FDR)  at the 5te (FDR)  were use3) was used to identify important trait–QTL associations previously reported in the literature.Positional genes located at up to 200 kb upstream and downstream of the significant SNPs were identified using the BiomaRt package . This 20The descriptive statistics of the five reproductive traits evaluated are shown in The (co)variance components, heritability, and genetic correlations for GESS and GED for all five reproduction traits are shown in For calving traits, the heritability estimates of GESS are lower than the GED for CE (0.004 ± 0.001 vs. 0.029 ± 0.002) and similar for GL (0.102 ± 0.001 vs. 0.102 ± 0.000) but higher for SB (0.078 ± 0.010 vs. 0.008 ± 0.001). Both GESS and GED show low heritability for SB and CE, though a moderate estimation was observed for GL. Except for the GED for SB (0.021 ± 0.002) and GL (0.116 ± 0.004), the repeatabilities were almost equal to the corresponding heritabilities. Each cow has only one calving record in each parity, which results in poor consistency among repeated data. The low heritability estimates of SB and CE indicate that these traits might benefit more from genomic information. A S-MGS model was used to evaluate calving traits in previous studies, which resulted in low heritability for CE and SB (0.07–0.13) . The S-MSPP1) regulate both tissue and embryonic growth . The correlation coefficient was considerably high in GL, whereas that in CE was low and non-significant . The results indicate the homogeneity between the GESS and the GED for SB and GL. The genetic covariances of the insemination traits between the effects of service bull and dams were usually ignored in previous studies , and the overlapped QTL regions are listed in The estimated breeding values obtained from former genetic estimation with accuracy above 10% were used for DRP calculation. Hence, the EBV of 2,996 and 1,147 individuals were used in GWAS for GESS and GED, respectively. The detailed information of the genomic regions and candidate genes for GESS and GED for the five reproductive traits are summarized in BMP4) and early embryogenesis . CTCFL gene detected in the present study. Although previous studies have attempted to identify candidate genes related to GESS on success traits (BMP4 (bone morphogenetic protein 4) was previously indicated as a candidate gene for spermatogenesis  was reported to regulate mouse embryonic stem cell differentiation to trophoblast-like cells  in our study are consistent with previous genomic studies of calving traits focused on BTA18 . Furthermore, we also mapped these SNPs to the Animal QTL Database (see Text Footnote 3) and subsequently found that some of them were located in QTLs associated with related traits . For GED on success traits, 86 nearby protein-coding genes located 200 kb upstream and downstream of significant SNPs were mapped. Particularly, SMAD4 has been reported to be linked to embryogenesis and folliculogenesis in mice , sulfotransferase activity (GO:0008146), and cyclin-dependent protein kinase holoenzyme complex (GO:0000307). These categories include functionable genes named CCNG2 and CKS2 (GO:0000307), LIMS2 (GO:0001889 and GO:0061351), MYO7B, WWOX (GO:0005902), SMYD3, TFB2M (GO:0008170), F2RL1, and F2RL2 (GO:0070493) as previously discussed. In addition, the enrichment analysis for GED showed main terms such as CXCR3 chemokine receptor binding (GO:0048248), homophilic cell adhesion via plasma membrane adhesion molecules (GO:0007156), and synapse pruning (GO:0098883), including CXCL10 (GO:0048248), PCDHA13 (GO:0007156), and C1QB (GO:0098883). Therefore, our findings provide further evidence of the possible genetic mechanism of GESS and GED on reproductive performance in Holstein cattle.The enriched GO terms and KEGG pathways that passed the criteria of the Benjamini–Hochberg-corrected Generally, only the GED for reproduction performance is analyzed in genetic evaluations, though research including the current study have shown the need to dissect GESS . CompareBMP4 and CTCFL for success traits and WWOX, TFB2M, and SMYD3 for calving traits) are suggested as important candidate genes for GESS according to positional and functional analyses. As GESS and GED are lowly heritable, genomic prediction might be a promising alternative for breeding schemes aiming to improve fertility performance in dairy cattle.The GESS on reproductive traits is heritable, with a similar genetic variance to the GED. Moreover, the approximate genetic correlation among the GESS and production, health, and type traits is unfavorable for the success traits (CR and NRR56) but favorable for the calving traits . A total of 100 and 62 significant SNPs were detected to be associated with GESS and GED on those five reproductive traits, respectively. Among them, five genes .ZC and YW conceived the study. ZC and LB designed the analyses, discussed the results, and drafted the manuscript. ZC performed all the data analyses and the data curation of genotype. ZC, HL, and RS prepared the phenotypic files. YC assisted with the modeling analyses. LL and GG provided support for the collection of raw data. All authors have read and approved the final version of the manuscript.LL is employed by Beijing Dairy Cattle Center. GG is employed by Beijing Sunlon Livestock Development Company Limited. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.