KnockoffZoom: a flexible method that localizes causal variants at multiple resolutions by testing the conditional associations of genetic segments of decreasing width, while provably controlling the false discovery rate. Our method utilizes artificial genotypes as negative controls and is equally valid for quantitative and binary phenotypes, without requiring any assumptions about their genetic architectures. Instead, we rely on well-established genetic models of linkage disequilibrium. We demonstrate that our method can detect more associations than mixed effects models and achieve fine-mapping precision, at comparable computational cost. Lastly, we apply KnockoffZoom to data from 350k subjects in the UK Biobank and report many new findings.In the statistical analysis of genome-wide association data, it is challenging to precisely localize the variants that affect complex traits, due to linkage disequilibrium, and to maximize power while limiting spurious findings. Here we report on  GWAS analysis currently relies mostly on linear mixed models, which do not account for linkage disequilibrium (LD) between tested variants. Here, Sesia et al. propose KnockoffZoom, a non-parametric statistical method for the simultaneous discovery and fine-mapping of causal variants, assuming only that LD is described by hidden Markov models (HMMs). However, it has been challenging to translate these findings into actionable knowledge2. As a step in this direction, we present a new statistical method that improves our ability to resolve the location of causal variants.Since the sequencing of the human genome, there have been massive efforts to identify genetic variants that affect phenotypes of medical relevance. By genotyping single-nucleotide polymorphisms (SNPs) in large genome-wide association studies (GWAS), thousands of associations with different traits and diseases have been discovered8. Nonetheless, this still tests marginal independence because it does not account for linkage disequilibrium (LD)10. Thus, it cannot distinguish causal SNPs from uninteresting nearby variants, since neither are independent of the phenotype. This limitation becomes concerning as we focus on polygenic traits and rely on larger samples; in this setting, it has been observed that most variants are correlated with the phenotype, although only a fraction of them may be important11. Therefore, most null hypotheses of no association should be rejected2, which is a rather uninformative conclusion. The awareness that marginal testing is insufficient has led to the heuristic practice of post hoc aggregation (clumping) of associated loci in LD12, and to the development of fine mapping13. Fine-mapping methods refine marginally significant loci and discard associated but noncausal SNPs by accounting for LD, often within a Bayesian perspective17. However, this two-step approach switches models and assumptions in the middle of the analysis, obfuscating the interpretation of the findings and possibly invalidating type-I error guarantees. Moreover, as LD makes more noncausal variants appear marginally associated with the trait in larger samples, fine-mapping tools face an increasingly complicated task refining wider regions.The analysis of GWAS data started by testing SNP-by-SNP hypotheses of marginal independence with the trait (not accounting for the rest of the genome) using univariate regression. Today, the leading approaches employ a linear mixed model (LMM) that includes a random term approximating the effects of other variants in distant lociknockoffs18, which can account for LD genome wide without heuristic post processing, while controlling the false-discovery rate (FDR)19. The only assumption of knockoffs is that LD is adequately described by hidden Markov models (HMMs) that have been successfully employed in many areas of genetics23, Moreover, since knockoffs do not require any model linking genotypes to phenotypes, they seamlessly apply to both quantitative and qualitative traits. In fact, the general validity of knockoffs for GWAS has been explored and discussed before29.An alternative solution is suggested by recent advances in statistics, notably KnockoffZoom: a new method that leverages knockoffs to address the current difficulties in locus discovery and fine mapping. KnockoffZoom searches for causal variants across the genome and reports SNPs (or groups thereof) that distinctly influence the trait accounting for the effects of all others. This is carried out by testing the conditional association of predefined groups of SNPs at multiple resolutions, ranging from that of locus discovery to that of fine mapping, while probably controlling the FDR. This work involves some key innovations. First, we develop algorithms to analyze the data at multiple levels of resolution, in order to maximize power in the presence of LD without pruning the variants24. Second, we improve the computational efficiency and apply our method to a large dataset, the UK Biobank30—a previously unfeasible task.Here we present KnockoffZoom tests stricter conditional hypotheses: a variant is null if it is independent of the trait conditionally on all other variants, including its neighbors (Methods). Suppose that we believed a multivariate linear model realistically describes the inheritance of the trait31, then, a conditional hypothesis would be non-null if the corresponding variant had a nonzero coefficient. Generally, in the absence of unmeasured confounders or feedback effects of the phenotype onto the genome, our tests lead to the discovery of causal variants. In particular, we can separate markers that have a distinct effect on the phenotype from those whose associations are merely due to LD.In the marginal analysis, a variant is null if its allele distribution is independent of the phenotype. By contrast, t tests in multivariate linear regression. In that case, F tests may be preferable. Analogously, we group variants that are too similar for their distinct effects to be discerned, and test whether the trait is independent of all of them, conditional on the other groups. A group is null if it only contains SNPs that are independent of the phenotype, conditional on the others. Concretely, we define contiguous blocks at multiple resolutions by partitioning the genome via adjacency-constrained hierarchical clustering32. We adopt the r2 computed by PLINK12 as a similarity measure for the SNPs, and cut the dendrogram at different heights, see Fig. KnockoffZoom, as long as the groups are determined before looking at the phenotype data. In particular, contiguity is not necessary; we have adopted it because it corresponds to the idea that researchers want to localize causal variants within a genomic segment, and because it produces interpretable results when some of the genetic variation is not genotyped. In addition, contiguity tends to yield higher power when we assume an HMM for the distribution of the genotypes (Supplementary Methods).LD makes conditional null hypotheses challenging to reject, for the same reason why colinearity reduces the power of To balance power and resolution, we consider increasingly refined partitions , at each resolution. The FDR is a meaningful error rate for complex traits34, but its control is challenging35. We overcome this difficulty with knockoffs. These are carefully engineered synthetic variables that can act as negative controls because they are exchangeable with the genotypes and reproduce the spurious associations that we want to winnow37. Constructing knockoffs requires specifying the distribution of the genotypes, which we approximate as an HMM. In this paper, we implement the fastPHASE21 HMM . With the UK Biobank data, for which the haplotypes have been phased23, we accelerate this algorithm further by avoiding implicit re-phasing (Supplementary Methods).We can mathematically prove that knockoff filter36. As a predictive model, we adopt efficient implementations of sparse linear and logistic regression designed for massive datasets38, although other methods could be easily incorporated18. Thus, we can exploit the power of variable selection techniques that would otherwise offer no statistical guarantees31. This methodology is detailed in the “Methods”. A schematic of our workflow is shown in Supplementary Fig. https://msesia.github.io/knockoffzoom. The computational cost  with the current HMM by fitting separate models and generating knockoffs independently for each population.Our inferences rely on a model for the distribution of the genotypes, which requires some approximation. The HMM implemented hereKnockoffZoom identifies them exactly while controlling the FDR. In practice, one could impute the missing variants and then analyze them as if they were measured. However, while meaningful for marginal tests, this would not be useful to study conditional association because imputed variants contain no information about any phenotype beyond that carried by the genotyped SNPs. In fact, the imputed values are conditionally independent of any phenotype given the genotyped SNPs, since they are a function of the SNP data and of an LD model estimated from a separate panel of independent individuals. Therefore, without strict modeling assumptions . We simulate traits using a linear model with Gaussian errors: 2500 causal variants are on chromosomes 1–22, clustered in evenly spaced 0.1-Mb-wide groups of 5 . Therefore, these simulations are unrealistic only with regard to the conditional distribution of the trait given the genotypes, about which KnockoffZoom makes no assumptions. Thus, we explicitly demonstrate our robustness to model misspecification, including the possible presence of some population structure, and the lower accuracy of the HMM for rarer variants  below 0.05, for the marginal hypotheses.Locus discovery: We apply KnockoffZoom because its findings are distinct and count as false positives if causal variants are not included. In comparison, distinct LMM discoveries are more difficult to define. Following the typical approach, we clump together nearby significant variants with PLINK, using standard parameters8 , while its power is comparable to that of the oracle. Our method reports more precise discoveries, while the BOLT-LMM discoveries become wider as the signal strength increases, as anticipated from Fig. p value threshold is substantially less powerful.Figure KnockoffZoom and BOLT-LMM at higher resolutions. Above, the aggressive LMM clumping strategy is informed by the known locations of the regions containing causal variants, to ensure that each is reported at most once. However, this information is generally unavailable, and the scientists must determine which discoveries are important. Therefore, we set out to find as many distinct associations as possible, applying KnockoffZoom at multiple resolutions, and interpreting the PLINK clumps as distinct findings, without consolidation. Figure KnockoffZoom results at each resolution , we separately fine-map each associated region with either CAVIAR14 or SUSIE17. We aggressively clump the LMM findings to ensure that they are distinct, as in Fig. Fine mapping: After applying BOLT-LMM  and the same knockoffs as in the simulations. Our discoveries are compared with the BOLT-LMM findings in Table 41 and other covariates in the predictive model (Methods). The results remain stable if we ignore the principal components (Supplementary Table KnockoffZoom misses very few of the BOLT-LMM discoveries (see Methods about glaucoma) and reports many additional findings (Supplementary Table 8 (Supplementary Table 8.Findings: We study four continuous traits and five diseases in the UK Biobank (Supplementary Table https://msesia.github.io/knockoffzoom/ukbiobank); see Fig. KnockoffZoom at low resolution (0.226 Mb) for different traits in Supplementary Table We usually obtain fewer findings at higher resolutions, since these conditional hypotheses are more challenging, but there are exceptions. Some exceptions may be due to multiple nearby signals  are replicated, at the cost of lower power, while the BH procedure does not control the FDR. See Supplementary Table The results are summarized in Table 44. The enrichment among five relevant terms is highly significant , rs72650673 , and rs1029388 . Many other discoveries are in coding regions and may plausibly localize a direct functional effect on the trait , obtaining 525 cases and 349,594 controls. We apply KnockoffZoom using sparse logistic regression, and report the results in Fig. We highlight with an example that our framework is not tied to any model for the dependence of phenotypes on genotypes, or to any specific data analysis tool. Therefore, we simulate an imbalanced case–control study where BOLT-LMM is known to failKnockoffZoom is randomized: its output depends on random variables that are not part of the data, in this case the knockoffs. Even though we have not done it here, it is possible to re-sample the knockoffs and obtain different sets of discoveries, each controlling the FDR24. However, it is not yet clear how to best combine these while preserving the FDR control. This is challenging in theory and it should be studied further. Meanwhile, we have repeated our analyses using a different set of knockoffs in Supplementary Table KnockoffZoom. Instead, the variability in KnockoffZoom typically involves either completely new loci (near the FDR threshold) or finer-grained details (multiple distinct discoveries within the same locus) that cannot be detected by BOLT-LMM.Like many other modern statistical methods, https://msesia.github.io/knockoffzoom) has a modular structure that accommodates many options, reflecting the flexibility of KnockoffZoom. Users may experiment with different importance measures: for example, one can incorporate prior information, such as summary statistics from other studies. Similarly, there are many ways of defining the LD blocks: leveraging genomic annotations is a promising direction.Our software  ∈ {0, 1, 2}p for each individual. We assume that the pairs n subjects are independently sampled from some distribution PXY. The goal is to infer how PY∣X depends on X, testing the conditional hypotheses defined below, without assuming anything else about this likelihood, or restricting the sizes of n and p. Later, we will describe how we can achieve this by leveraging prior knowledge of the genotype distribution PX. Now, we formally define the hypotheses.We observe a phenotype p} into L blocks, for some L ≤ p. For any g ≤ L, we say that the gth group of variables Y is independent of Gg). We denote by PY∣X is a linear model, 39). In general, we want to select a subset 24, which only considered the variables one by one. Our hypotheses are better suited for the analysis of GWAS data because they allow us to deal with LD without pruning the variants (Supplementary Methods). As a comparison, the null statement of the typical hypothesis in a GWAS is that Y is marginally independent of Xj, for a given SNP j.Let Knockoffs18 solve the problem defined above if PX is known and tractable, as explained below. The idea is to augment the data with synthetic variables, one for each genetic variant. We know that the knockoffs are null because we create them without looking at Y. Moreover, we construct them so that they behave similarly to the SNPs in null groups, and can serve as negative controls. The original work considered explicitly only the case of a trivial partition p singletons18, but we extend it for our problem by leveraging some previous work along this direction39. Formally, we say that X for a partition p} if two conditions are satisfied: (1) Y is independent of X; (2) the joint distribution of Xj : j ∈ G} is swapped with PX18. In the Supplementary Methods, we develop algorithms to generate powerful group knockoffs when PX is an HMM, the parameters of which are fitted on the available data using fastPHASE21; see Supplementary Note gth group in Tg and Xj: j ∈ Gg} and 38 for Y given X and Xj and λCV tuned by cross-validation. These statistics are designed to detect sparse signals in a generalized linear model—a popular approximation of the distribution of Y in a GWAS31. Our power may be affected if this model is misspecified, but our inferences remain valid. A variety of other tools could be used to compute more flexible or powerful statistics, perhaps by incorporating prior knowledge18. Finally, we combine the importance measures into test statistics Wg through an antisymmetric function, e.g., 18. The appropriate threshold for FDR control is calculated by the knockoff filter36. Further details about the test statistics are given in Supplementary Note entclass1pt{minimaq if there are fewer than 1∕q findings to be made. Usually, this is not a problem for the analysis of complex traits, where many loci are significant. However, this may explain why, at level q = 0.1, we report none of the 5 discoveries obtained by BOLT-LMM for glaucoma in Table 36, at the cost of losing the provable FDR guarantee.As currently implemented, our procedure has no power at the nominal FDR level 8). We leverage these covariates by including them in the predictive model for the KnockoffZoom test statistics, along with the top five principal components of the genetic matrix. We fit a sparse regression model on the augmented matrix of explanatory variables m covariates, the genotypes, and their knockoff copies, respectively. The coefficients for Z are not regularized, and we ignore them in the final computation of the test statistics.We control for the sex, age, and squared age of the subjects to increase power , among our 350,119 individuals. The final SNP count is 591,513. A few subjects withdrew consent and we removed their observations from the analysis.We consider 430,287 genotyped and phased subjects with British ancestry. According to the UK Biobank, 147,718 of these have at least one close relative in the dataset; we keep one from each of the 60,169 familial groups, chosen to minimize the missing phenotypes. This yields 350,119 unrelated subjects. We only analyze biallelic SNPs with minor allele frequency above 0.1% and in Hardy–Weinberg equilibrium (10The effect sizes of the causal variants are heterogeneous, with relative values chosen uniformly at random across clusters so that the ratio between the smallest and the largest is 1/19. The causal variables in the model are standardized, so rarer variants have stronger effects.Peer Review FileSupplementary Information


Genomic selection (GS) is becoming popular in animals’ genetic development. We, therefore, investigated the single-step genomic best linear unbiased prediction (ssGBLUP) as tool for GS, and compared its efficacy with the traditional pedigree BLUP (pedBLUP) method.M1) and ii) correlation using inverse of coefficient matrix from the mixed-model equations (rM2). Then, we compared these accuracies by overall population, info-type , and bull-types .A total of 9,952 males born between 1997 and 2018 under Hanwoo proven-bull selection program was studied. We analyzed body weight at 12 months and carcass weight (kg), backfat thickness, eye muscle area, and marbling score traits. About 7,387 bulls were genotyped using Illumina 50K BeadChip Arrays. Multiple-trait animal model analyses were performed using BLUPF90 software programs. Breeding value accuracy was calculated using two methods: i) Pearson’s correlation of genomic estimated breeding value (GEBV) with EBV of all animals  at population level. However, rM2 from both BLUP models varied noticeably across info-types and bull-types. The ssGBLUP estimates of rM2 in PHEN, GEN, and PH+ GEN ranged between 0.51 and 0.63, 0.66 and 0.70, and 0.68 and 0.73, respectively. In YBULL, CBULL, and PBULL, the rM2 estimates ranged between 0.54 and 0.57, 0.55 and 0.62, and 0.70 and 0.74, respectively. The pedBLUP based rM2 estimates were also relatively lower than ssGBLUP estimates. At the population level, we found an increase in accuracy by 2.0% to 4.5% among traits. Traits in PHEN were least influenced by ssGBLUP (0% to 2.0%), whereas the highest positive changes were in GEN (8.1% to 10.7%). PH+GEN also showed 6.5% to 8.5% increase in accuracy by ssGBLUP. However, the highest improvements were found in bull-types .The rA noticeable improvement by ssGBLUP was observed in this study. Findings of differential responses to ssGBLUP by various bulls could assist in better selection decision making as well. We, therefore, suggest that ssGBLUP could be used for GS in Hanwoo proven-bull evaluation program. At that time, the main aim of such model adoption was to exploit the existing correlations among traits more efficiently, and thus obtain a better breeding value (BV) profile on animals under such evaluation schemes. Of note, even after the adoption of such advanced and complex models in PT and PGT, there remained other limiting factors with pedBLUP evaluation, such as greater demands for high-quality pedigrees, and the dependence on the number of phenotypes available– especially more records from those of the close relatives. The PGT program, which performs sire performances through the evaluation of its own progenies, is generally known to be an expensive animal improvement scheme due to the higher generation intervals, and its prerequisites for more information from relatives such as progenies, in order to ensure an adequate evaluation accuracy of sires. In PGT, through pedBLUP, an earlier selection of animals was not only difficult but also often required progenies to be sacrificed in the evaluation of most economic traits. Nonetheless, the lack of perfect evaluation accuracy was also an issue with PGT. Yet, animal breeders were limited to choose such expensive breeding tools as possible better alternatives (e.g. genotype-based technologies) were not feasible enough to be implemented economically.In 1980s, the Hanwoo performance test (PT) and progeny test (PGT) programs were adopted in the Korean National Evaluation System to assist Hanwoo proven bull selection program. Over time newer breeding tools were utilized for Hanwoo evaluations so that more desirable improvements in phenotypes could be achieved. With more phenotypes being available by 2009, the decade-long older traditional pedigree-based best linear unbiased prediction (pedBLUP) evaluation, Fortunately, over the past decades, the advancement in animal genotyping technologies has made it competitive and more cost-effective. Nowadays, the development in statistical approaches related to genotype-based analyses also made it possible to resolve many of above limitations with pedBLUP. With genotypes, animal BVs can also be estimated easily and more reliably. Note that selection based on animal’s genomic information, also known as genomic selection  through a genomic relationship matrix (GRM), which is based on the genotype information of the animals and using a GBLUP method. For GBLUPs, two widely-used methods are also available, p method . The sinWe observed that there has been a great momentum for the large scale implementation of GBLUP and GS in various livestock species in the recent years ,6. This In this study, yearling weight and carcass trait measures were recorded on the males of Hanwoo cattle that were raised under Korean National Improvement System. A total of 9,952 bulls, born between 1997 to 2018 under proven-bull selection program, were recorded for phenotypes. Phenotyped bulls were considered to be in one of three categories such as those of young male calves , young candidate bulls  and, progeny tested bull (PBULL). All CBULL bulls were recorded for yearling weight at 12 months of age (WT12) for PT program. Carcass traits studied in this study were carcass weight (CWT), backfat thickness (BFT), eye muscle area (EMA) and marbling score (MS). Details on recorded animals are presented in Genotypic data on 7,387 Hanwoo males were generated in two batches using a high-density Illumina BovineSNP50K BeadChip  array as per the standard protocol. Then, two genotype datasets were combined into one based on common autosomal SNPs , followed by a population-based genotype imputation step using FImpute 2.0 software package . That imi.e. PEDIG [A pedigree on studied animals was collected from Korea Animal Improvement Association (KAIA). The pedigree, related to animals with phenotypes and genotypes, included 67,802 animals and extended up to the maximum of 14 ancestral generations. A total of 19,260 animals were found as inbred in the dataset. This pedigree also included 1,393 sires, 46,202 dams, and 516 full-sib family groups (with an average family size of 2.1). Note that about 95% of the inbred animals showed lower inbreeding rates (0% to 5%). Although the highest inbreeding coefficient in the study was 0.31, the average coefficients in the whole population and within the inbred animals were 0.004 and 0.015, respectively. We also calculated the average relatedness of all animals using the pedigree data. Mainly, two software packages, e. PEDIG  and CFC e. PEDIG  were usei.e. BLT and BTS. The fixed effect of BLT was fitted with WT12, whereas BTS with carcass traits only. The fixed covariate of age at slaughter was also fitted with carcass traits. As for fitting random effects, the additive genetic effect of the animal was the only random genetic component in the model. We, then, estimated animal BVs and standard errors of prediction (SEP) using BLUPf90 software package [y = Xb + Zu + e, where y is the vector of traits, b is the vector of fixed effects and covariates, u is the vector of random effects (additive genetic), e is the vector of random residual effect, and X and Z are the respective design matrices relating observations to the fixed and random effects b and u. The variance structure of u and e were assumed as var (u) = G0 ⊗ A, var (e) = R0 ⊗ I, where G0, A, R0, and I were the additive genetic (co)variance matrix between traits, the pedigree relationship matrix, the residual (co)variance matrix between traits and the identity matrix, respectively.A conventional BLUP method  based mu package . The mix−1, the ssGBLUP used an H−1 [The estimation of GEBV was performed by ssGBLUP method through fitting factors as described for pedBLUP analysis. However, instead of an Ad an H−1  matrix, G is a genomic relationship matrix, τ and ω are adjustment for G and A respectively. Following VanRaden [where VanRaden , G was cpi is the allele frequency at locus i in all genotyped animals, G towards the A matrix [D is weight for each locus (I if same variance assumed), W is a design matrix as follows:Where constant  that sumG and H matrices were derived using software default parameter settings for τ (0.05) and ω (0.05) by PREGSF90 at runtime. Finally, animal BV solutions and their SEPs were estimated by BLUPF90 using appropriate options for the software runs.Both Theoretically, the accuracy of (G)EBVs are referred to as the correlation between estimated (genomic) breeding values of animals and their respective true breeding values (TBV), where TBV is generally unknown for any given population . As a rerM1 = CorEBV,GEBV, where rM1 was a Pearson’s product-moment correlation coefficient between the GEBV and EBV, which we could easily obtain through ssGBLUP and pedBLUP models in this study, respectively. A possible advantage of this approach would be the ability to compare the current outcomes with other studies that were already available. Another benefit of this estimate was the ability of an overall assessment for the expected accuracy of animals, where all available samples was considered at a time, and without further differentiation for number of information available. In other words, the accuracy of estimation could be interpreted on a population level.The first estimate of the accuracy of GEBVs is also referred to as the prediction accuracy of the model, where GEBVs derived through ssGBLUP are directly compared with EBVs from pedBLUP for all animals. This method of estimation was based on the report from Daetwyler et al , in whicM2 and PEV in the equation denoted the accuracy and error-variance estimates for each animal, respectively. Note that each PEV estimate can be directly obtained for all individuals from the inverse of the coefficient matrix of the mixed model equation i.e. the MME matrix, as shown earlier by [i.e. VA or additive genetic variance of each trait, was estimated separately through REML method for the same dataset but excluding genotype information by REMLF90 [M2 measures for respective traits were compared to animals based on the type of bulls, level of pedigree relatedness, and type of information available on animals, e.g. phenotyped or genotyped animals etc.Contrarily, the second type of accuracy was calculated at each individual level. In this method, the prediction error variance (PEV) of both EBV and GEBV were estimated for each animal and the respective trait. Such PEVs were then used for the calculation of accuracy for each EBV and GEBV estimates per animal, respectively, using the equation, rM2=-PEVVA. Trlier by . For PEV REMLF90  softwareGenetic parameters and correlation on traits were also reported in the study. For these estimates, the estimation of variance and covariance components were carried out using the same dataset and an animal model fitting of the same set of fixed and random effects as described above under the model description for pedBLUP evaluation. The approximation of (co)variance components were obtained through a REML approach using REML90 software. Total phenotypic variance was calculated as i.e. standard deviation) alongside the higher variation in their phenotypic data. The same animal subset conversely showed relatively higher averages and lower variations for all carcass traits than those of PH+GEN, especially in their BF and MS traits. It is found that phenotypic measures in the present study were either in general agreement with a few earlier reports on Hanwoo cattle [Descriptive statistics on five phenotypic traits according to info-type such as PH+GEN (both phenotyped and genotyped), and PHEN (phenotyped only) are presented in o cattle ,18 or dio cattle ,20. We a2) and correlation estimates for five traits are given in 2 estimates of WT12 and CWT were 0.26 and 0.35, respectively. Moderate to higher h2 estimates were observed in EMA (0.44), BFT (0.46), and MS (0.56) traits as well. Genetic (rg) and phenotypic correlations (rp) of WT12 were the highest with CWT (rg: 0.70 and rp: 0.71). CWT was moderately correlated with EMA (rg: 0.55). The rg between EMA and BFT was negative, i.e. −0.24. The MS-rg was low and positive with CWT and EMA, but low and negative with WT12 and BFT. However, all rp estimates were positive except for the rg between BFT and MS traits.Heritability (hM1 and rM2), using the population dataset, are shown in M1 estimates  were generally higher among traits and showed less variability, i.e. 0.90 to 0.96. This rM1 of MS was the lowest among all five traits, whereas the highest for WT12 and EMA. The rM2 estimates (derived from the coefficient matrix of MME), in contrast, had a higher variability range (0 to 0.95), which also showed noticeably lower averages (0.40 to 0.45) in all traits. Those averages among five traits and between two evaluation methods (ssGBLUP and pedBLUP) were generally not the same but close and demonstrated a slight improvement of 2% to 4.5% by ssGBLUP over pedBLUP. For traits under concern, MS had the lowest average rM2 estimates, which was also the highest improvement by ssGBLUP according to whole population. Both BFT and EMA realized over 3% increment in BV accuracy by ssGBLUP, and WT12 had the lowest improvement by 2%. The overall performance of ssGBLUP at the population level, therefore, to be considered as some improvement over the pedBLUP evaluation.The accuracy estimates of single-step genomic evaluations using two earlier described approaches , followed by PH+GEN (0.91 to 0.93) and GEN (0.89 to 0.92) group estimates. Although these estimates (rM1) were somewhat similar among three info-types, there was some noticeable differences in rM2 estimates among these animal categories, irrespective of ssGBLUP or pedBLUP estimates. The average rM2 within info-types were also significantly lower than the average rM1 estimates across all methods of evaluation. Unlike rM1 estimates, the rM2 estimates indicated relatively higher accuracy in PH+GEN bulls, bulls that provided both genotypic and phenotypic information to the models of interest. It is also clear that the accuracy ranges in PH+GEN bulls were narrower, and all estimates were relatively higher (M2 estimates in PH+GEN group were found as the narrowest (0.43 to 0.92), which also indicated about relatively larger lower and upper bounds of estimate as compared to those of either PHEN (0.23 to 0.82) or GEN (0.32 to 0.93) estimates; which also concurred with other traits. Both evaluation models showed similar patterns in this manner. As far as the improvement by ssGBLUP was concerned, the rM2 estimates indicated some none-to-little positive changes (0% to 2%) among the BV estimates of all studied traits. This indicated that PHEN bulls, even if they were included and evaluated under ssGBLUP, were unable to capture much of the benefits from the single-step method. This further emphasized the importance of type of information in the dataset. In this regard, we found substantial improvements in accuracy within GEN and PH+GEN bulls. Both these later bull categories (with genotype information) obtained GEBVs which were seemingly more reliable by 8.1%–10.7% and 6.5%–8.5%, respectively, to their pedigree based EBVs. Regarding trait BV responses to ssGBLUP evaluation, the GEBV estimates of BFT, MS, and EMA showed more reliability improvements than was obtained by WT12  but have genotypes. Additionally, i.e. mainly in PT and PGT) and under info-type categories in the study, could vary distinctly by distribution of estimates among them. PGT bull accuracies in GEN and PH+GEN mostly appeared in small clusters both at the lower and higher end of estimates. However, PT bulls showed less clusters and estimates were spread at wider ranges. The relatively lesser spread of estimates outside the 1:1 regression line fewer in PHEN category for PT and PGT also reflected their similarities across traits. Another important finding  was 0.70 to 0.74 and the highest in the study. GEBV accuracy of other two bull-types were somewhat similar though which were 0.55 to 0.62 in YBULL, and 0.54 to 0.57 in CBULL. The pedBLUP-based mean accuracies were also lower than those based on ssGBLUP in all traits. Due to the very similar patterns in ssGBLUP and pedBLUP accuracies across bull-types, it was obvious that the improvements by ssGBLUP over pedBLUP would differ across bull-types as well. We, therefore, observed substantial differences in improvements across bull-types. Interestingly, YBULL which gained a lowest accuracy in ssGBLUP for all traits also showed the most positive improvements in accuracy by +21.3% to +35.7%. Accuracy improvement in CBULL remained moderate between +3.3% and +12.2% across traits. PBULL, in contrast, that obtained the highest rM2 by ssGBLUP also showed the lowest positive changes in accuracy (2.8% to 6.1%) with respect to pedBLUP. It was also clearly observed that improvements in accuracy by traits was different among bull-types. Among traits, MS showed most positive improvements by 6.1% to 35.7% by ssGBLUP, followed by 4.3% to 34.1% in EMA and 4.3% to 31.7% in BFT. Improvements in CWT and WT12 by ssGBLUP were also noticeably higher , EMA (0.44), BF (0.48), and MS9 (0.58) using pedigree BLUP dataset. Little disagreements were observed from Choi et al [2 in yearling weight (0.25), carcass weight (0.29), longissimus muscle area (0.38), and backfat thickness (0.45), but a slightly higher in MS (0.62), which could be due to their relatively larger datasets. We also found subtle differences with Park et al [2 for yearling weight (0.30), backfat (0.50) and MS9 (0.63) or with slightly lower h2 for carcass weight (0.30), but with a similar EMA (0.42). The h2 of CWT in Hanwoo from earlier reports [2 in this study was deemed consistent with Hwang et al [2 for IMF as 0.55 and 0.69, using GRM and NRM, respectively. They reported that residual variances increased by GRM based method, whereas BV variance increased by NRM based method. That could be equally applicable for correlation estimates. Overall, there were no great differences among estimates across studies.For genetic parameters estimates, this study coincided with Shin et al , who repoi et al  with therk et al  with the reports –26 was ang et al  Lee and ng et al . Such sung et al  showed hIn this study, we analyzed five important beef traits in Hanwoo cattle and compared the evaluation accuracy of these traits with respect to pedBLUP and ssGBLUP. Our aim in this study was to analyze the impact of both pedigree and genomic information driven prediction methods on the BV estimation among several bull categories, which were raised under the proven bull selection program. As it has been stated earlier, since the implementation of GS in Korea for Hanwoo proven bull selection is very recent, the practical impact on different animal groups is yet to be understood properly. Also note that GS has been widely applied in dairy cattle and proved to be successful. For beef cattle evaluation, however, this has not been tested extensively so far, and there are very limited resources to compare. This indicates that it would be equally challenging to verify outcomes in the light of beef cattle, given that GS under implementation can also differ significantly among breeds and as per breeding objectives.With various model accuracies, in general, the present study revealed a noticeable increase in the BV accuracy by ssGBLUP when compared to pedBLUP evaluation. Different animal groups as well as traits also reported differently in this manner. Our report observed the improvement by genomic model to be as high as 35% for MS in YBULL. Some earlier reports on Hanwoo cattle also concurred with the present study. A recent ssGBLUP study in Hanwoo cattle by Shin et al  presentei.e. low to medium rM2, had also been mostly benefited by ssGBLUP. Our results on bull-type comparisons were also equally appealing and displayed similar patterns as with info-types. We found that the most benefited bull-type was YBULL with an accuracy improvement between 21.3% to 35.7% by ssGBLUP among the five traits. The responses in CBULL and PBULL were somewhat lower (2.8% to 12.2%) among traits but not negligible. Especially the lower improvement rates for PBULL was neither unexpected, as even with a pedBLUP proven bulls would capture most of the heritable genetic variances due to their large progeny pools in the dataset. Therefore, any improvement by ssGBLUP to PBULL, even if it is small, would be considered as significant. When both info-type and bull-types were investigated together, it was not surprising to find that most YBULL and CBULL were also GEN or PH+GEN bulls. With this it became more obvious that the higher GEBV accuracies in such genotyped young or candidate bulls were desired, as the inclusion of genotype information to the model (through GRM) could predict animal BVs with increased accuracy [In this study, we also reported the differences in the animal evaluations based on certain classification such as info-type or bull-type. Evidently, some distinct responses from animals’ accuracies due to info-types were clearly noticeable with ssGBLUP and not so much with pedBLUP. Not only that, the average accuracy for most info-types were uplifted by ssGBLUP, the baseline estimates also improved, and therefore, it decreased the spread between the lowest and highest estimates. For instance, we showed the lowest estimate in PH+GEN with ssGBLUP was higher by +0.15 points than pedBLUP, so as by +0.34 in GEN. Further investigation of the results  revealedaccuracy ,30. Resuaccuracy .M2 estimates. This might indicate that those of closely related animals were benefited by ssGBLUP. In this regard, some earlier reports agreeably showed evidences for the positive association between closely related animals and their higher GEBV accuracies [With animal relatedness, we noticed some relationships between relatedness and rcuracies ,32. Nonecuracies  could obcuracies  emphasizWe already mentioned that adoption of GS is very recent in Hanwoo cattle development. Currently, GS is performed at a limited scale in the Hanwoo Proven Bull Selection Program. To better illustrate, we can summarize the proven-bull selection program into four subsequent phases such as i) production of young bull-calves by design mating of PBULL and adult cows from various designated farms; ii) selection and procurement of some of those young bull-calves as young candidate bulls and performance testing; iii) production of progeny from (by design mating) using performance-tested young bulls and adult cows from designated farms, and iv) selection of those performance-tested young bulls as proven bulls via progeny testing. GS is performed between phase 1 and 2, when young (candidate) bulls are to be procured from a pool of young calves . Previously, a pedigree index, assisted by an appearance inspection process, was the main tool for young (candidate) bulls’ selection. Now, through GS, as soon as the genotype of all those young males are known, their GEBVs are calculated through summation of total SNP effects. Note that these SNP markers effects are rather based on their parents NGE which were performed earlier through a multi-step GBLUP method. Also, the direct genetic value (DGV) or GEBV is used instead of an EBV to calculate performance index of animals in various phases of bull selection. However, the selection of the young males is a very important step as they will become the proven bulls for the next generations. Therefore, the selection of the candidate (bull) pool is now more reliable and accurate than before due to GS in young males. It is also possible to avoid all additional testing steps  and select animals much earlier in their lifetime; thereby, reducing generation intervals as well as the cost of animal productions.Although the current GS is an upgrade to the earlier methods, the real benefits from GS deemed rather limited. Firstly, the recent practice of GS in Hanwoo is limited by scale. To reap the full benefit from GS, it could be used in Hanwoo preselection processes, such as PT and PGT phases. This might increase the genetic gains in major selection traits at a much-desired extent, especially in MS. Secondly, the multi-step GBLUP based GS approach itself poses some technical limitation. This is because the Hanwoo reference population that is used in this purpose is very small (if compared with other cattle breeds). For a multi-step GBLUP, a larger reference population for bull evaluation is essential . NonetheThe ssGBLUP is generally appreciated because of its unified framework for more accurate genomic evaluations of animals. To date, its application in many species also produced better results. Our results were largely in agreement with these previous studies as well, where ssGBLUP performed noticeably better than pedBLUP. Increase in accuracy through ssGBLUP was also substantial in most of bull sub-groups, especially to those without phenotypes. As young bulls are the next generation of parents, future selection decisions based on ssGBLUP is deemed promising as baseline accuracies were significantly improved in this study. Differences in traits improvement regarding ssGBLUP were also indicated in our outcomes. We also provided evidence how the currently implemented multi-step GBLUP based GS in Hanwoo might face challenges. We believe that this study provided strong evidence for the success of ssGBLUP in Hanwoo national evaluation as a tool for GS.


Phasianus colchicus, over four generations. Pheasants were reared in captivity but bred from adults that lived in the wild and hence, were subject to selection on survival. Pheasant chicks are precocial and were reared without parents, enabling us to standardize environmental and parental care effects. We constructed a pedigree based on 15 microsatellite loci and implemented animal models to estimate heritability. We found moderate heritabilities for discrimination learning and inhibitory control (h2 = 0.17–0.23) but heritability for spatial ability was low (h2 = 0.09). Genetic correlations among-traits were largely positive but characterized by high uncertainty and were not statistically significant. Principle component analysis of the genetic correlation matrix estimate revealed a leading component that explained 69% of the variation, broadly in line with expectations under a general intelligence model of cognition. However, this pattern was not apparent in the phenotypic correlation structure which was more consistent with a modular view of animal cognition. Our findings highlight that the expression of cognitive traits is influenced by environmental factors which masks the underlying genetic structure.To understand the evolution of cognitive abilities, we need to understand both how selection acts upon them and their genetic (co)variance structure. Recent work suggests that there are fitness consequences for free-living individuals with particular cognitive abilities. However, our current understanding of the heritability of these abilities is restricted to domesticated species subjected to artificial selection. We investigated genetic variance for, and genetic correlations among four cognitive abilities: inhibitory control, visual and spatial discrimination, and spatial ability, measured on >450 pheasants,  Cognitive traits are crucial determinants of animals’ abilities to adapt to changing environments. For cognitive traits to evolve they must be underpinned by a genetic component. Using quantitative genetics in a nondomesticated system, we show that the basic abilities to inhibit behavior and learn about visual and spatial cues are moderately heritable. This heritability, coupled with fitness consequences of individual differences now demonstrated across several species, highlights the evolutionary potential for basic cognitive abilities. Understanding the genetic underpinnings of cognitive abilities provides insights into how cognitive traits are structured and have evolved. General cognitive abilities  underpin critical behaviors, such as foraging , mate chDrosophila melanogaster, h2 = 0.08, Apis melifera capensis, h2 = 0.39–0.54, Gallus gallus), discrimination learning, an aspect of associative learning  showed no heritable component   , Drosophila melanogaster, Parus major), found little support for a genetic component of variation  and used animal models  in four generations of pheasants  and collected a blood sample for genotyping. Birds were individually marked and in July/August, we released them into the wild where they had access to supplementary feeding stations containing wheat and were subject to natural hazards, for example, predation and disease, but where no anthropogenic hunting took place. In the following March, prior to the birds’ first breeding season, we captured and housed surviving birds in breeding groups and collected their eggs (see Adult breeding) which were artificially incubated and hatched to produce the next generation. In year 1, pheasant chicks were purchased from a commercial game dealer on the day of their hatching. In years 2 and 4, the chicks were hatched from eggs collected from our captive breeding adults. In year 3, due to an incubator malfunction and low hatching success of eggs from our captive breeding adults, 80% of chicks were purchased.This study took place over 4 years from May 2014 to July 2017 at North Wyke Research Farm, Devon, UK . In the May of each year, we reared ~200 newly hatched pheasant without parents in identical housing enclosures for 9–10 weeks while we tested their individual cognitive performances .We assessed inhibitory control using the detour reach paradigm in which subjects are required to retrieve a food reward from behind a transparent barrier . Birds wLearning tasks for details).The three remaining tasks  involved foraging grids (38 cm × 14 cm × 4 cm) containing circular wells (diameter 2.8 cm), 1.2 cm apart, from which individuals could acquire mealworm rewards by pecking through crepe paper. The apparatus for discrimination tasks contained only two wells and for the spatial ability task, the apparatus contained 10 wells . During a test trial, if the first peck was to the rewarded well it was scored as “correct” and the bird was allowed to consume the food reward before being presented with a new set of wells. If the first peck was to a blocked unrewarded well, it was scored as “incorrect” and these wells were removed and promptly replaced with a new set of wells. The location of the rewarded well was pseudorandomized between trials so that it was not in the same location (closest or furthest well) for more than three consecutive trials. There were 10 trials within a session and individuals received 5 sessions. Our measure of performance was the number of correct trials within a session.To assess spatial discrimination performances, we used the same two-well apparatus as that in the visual discrimination task (above), but instead of encircling each well with a particular color, both wells were unmarked and identical, differing only in their location on the apparatus e.g., . The corIndividuals were required to locate a single rewarded well among 10 (2 × 5 grid) unmarked wells. The reward location remained consistent for each individual but the location was counterbalanced across individuals within years; for half of the individuals, the reward was located on the second row (furthest from the bird), second well from the bird’s left, and for the other half of the birds, it was located in the second row, second well from the right. Birds received four training sessions prior to testing in which all 10 wells were uncovered and the location of the rewarded well was visible to ensure that they had experienced the rewarded location. During a test session, all wells were covered with crepe paper and the number of incorrect choices made before locating the rewarded well was recorded. We considered new incorrect choices only and ignored repeated incorrect choices because repeats were not recorded in all years, and thus, learning measures were comparable across years. Therefore, there were a total of nine incorrect choices per trial. There were two trials within a session and individuals received eight sessions. Our measure of performance was the number of incorrect choices within a session.In the March of each year, we recaptured surviving pheasants that had been released in the previous year using baited funnel traps that were checked three times per day. Caught pheasants were housed in outdoor pens which contained multiple shelters, food hoppers, water, and branches for perching. In years 1 and 2, individuals from our released population (for which we had genetic information) were housed in single-male multiple-female groups of either two, three, or four females and in year 3, we had larger groupings of ~15 individuals with approximately 4:1 ratio of females:males. The social composition of pens was held constant while eggs were collected daily until the end of April. Collected eggs were artificially incubated as a single batch in a Brinsea OvaEasy 580 incubator. After 25 days of incubation, hatched chicks were randomly allocated to one of four identical rearing houses (described above). Hence, we were unaware of which chicks had hatched from which egg and therefore from which adult housing pen they came.Pedigree Information). DNA was extracted from blood samples and using data from 15 microsatellite markers , we used Colony software . Candidate parents were those individuals that we captured and housed in captivity from whom we collected eggs and had taken blood samples from as chicks (years 1–4) or as adults (year 4).In each year, blood samples were collected when the birds were approximately 10 weeks old, the day before their release into the wild. In year 4, we also collected blood samples from adults held temporarily in captivity that we had not previously reared because these individuals formed the majority of our breeding adults. Across years, we had genetic information for 50% of mothers and 61% of fathers that we housed in captivity during the study ; so, we keep the present description brief. First, a series of univariate mixed models  were compared (using AIC and Likelihood ratio tests) to test for the presence of additive genetic variance in each cognitive trait. Then, estimates of genetic variance were extracted from animal models and scaled by the phenotypic variance (VP) to yield estimated heritabilities (proportion of variance explained by additive genetic component VA), which we present with associated estimated SE. For univariate models of visual discrimination, spatial discrimination, and spatial ability , we employed a random regression strategy for modeling additive genetic and permanent environment effects across repeated sessions . For inhibitory control, there was only a single measure of performance; so, this was used following a square root transformation to better approach the assumption of Gaussian errors. The assumption of Gaussian errors was used in all models and appeared reasonable based on visual inspection of residuals. Fixed effects of sex, rearing group (house/year combination), mean test order, and (where appropriate) session number were included as fixed effects. For each trait, we also calculated the coefficient of variation (the square-root of the VA component divided by the (observed) phenotypic mean; CVA = √VA/µ), as an alternative standardization of genetic variance  and then to characterize its genetic component (G) . Treating spatial discrimination as a trait with repeated measures (as per univariate models), we were unable to obtain stable convergence of multivariate models from this data set. Consequently, to reduce the number of parameters, we elected to use the mean observed phenotype (across three sessions) for each individual as the measure of performance. ID was then estimated in a four-trait multivariate mixed model with; fixed effects on each trait as described for univariate models; a random effect (intercept) of individual identity on each trait; random slopes on session for visual discrimination and spatial ability variances pertain to performance at final observation); and observation level  variances fixed to zero for those traits with a single observation . The latter is imposed since among- and within-individual variance cannot be partitioned from a single observation per individual. Similarly, as visual discrimination and spatial ability were not recorded at the same observations, observation level  covariance between these traits is undefined in the data structure and so was not modeled. Pairwise phenotypic correlation estimates (rP) were obtained from this model and the among-trait correlation structure explored using eigen decomposition. We then used multivariate animal models to partition ID into genetic G and nongenetic components to estimate the corresponding set of between trait genetic correlations (rG) and subject these to eigen decomposition. In the current context the eigen decompositions of among-individual phenotypic and genetic correlation structures are equivalent to principle component analyses (PCA) and allow us to determine if correlation structure is consistent with a single underlying latent variable, analogous to a general intelligence model of cognition. Note that all response variables were scaled so that positive values represent good performance. For example, we reversed the performance scores for the inhibitory control and spatial ability tasks by subtracting the number of errors made from the maximum number of errors. This means that under a general intelligence model, correlations among cognitive traits are predicted to be uniformly positive in ID and/or G.All analyses were conducted in R version 3.6.1 . An anim package . Detailevariance . This isBirds were habituated to human observation and were subject to minimal handling. All procedures were adopted to mitigate stress during cognitive testing and birds could choose whether or not to participate in tasks. Birds were reared at a lower density than that recommended by DEFRA’s code of practice . During AIC and LRT univariate model comparisons). Thus, the preferred model (lowest AIC score) included additive genetic effects for all traits. For inhibitory control that was observed only once, the animal model was a significantly better fit than the null model . For all other traits, there was evidence of among-individual variance in average performance  and in variation in rate of performance change over repeat sessions . For visual discrimination, stepwise addition of the random genetic intercept (Model 3) and slope (Model 4) led to significantly improved model fits, providing evidence of significant genetic variance that is itself a function of session. For spatial ability, a similar conclusion is statistically supported given that Model 4  is a significantly better fit than Model 3 . We note that while Model 3 is not actually significantly better than Model 2, Model 4 is . Thus, the influence of individual genetic merit here only becomes apparent when it is allowed to vary across sessions. Finally, for spatial discrimination, stepwise additions result in significant improvement from Models 0 to 3, providing evidence of among-individual variance in random intercept (Model 1 vs. Model 0), slope of regression on session , and additive genetic variance (Model 3 vs. Model 2). We encountered problems reaching the asreml default convergence criteria for Model 4. Nonetheless, given apparent stability of model log-likelihood and parameter estimates after several thousand iterations, we chose to accept the solution as valid. Based on this, there is no statistical support for dependence of additive genetic merit on session . Despite the lack of significant genetic slope variance in spatial discrimination, we decided for consistency to estimate heritability and repeatability under a “final” model of Model 4 for all traits with repeat measures. Given scaling of the session variable (see earlier), we calculated these using random intercept variances only such that estimates pertain to the final observed session in each case. Heritability of inhibitory control was estimated under Model 1.Likelihood ratio tests (LRT) and comparison of AIC scores across univariate model formulation support the presence of additive genetic variance in all four traits , 0.33 (0.08), and 0.17 (0.03), respectively /VP). Across traits, genetics explained between 9% and 23% of the variation. There were moderate heritabilities  of both discrimination tasks , and lower estimates for inhibitory control (17%) and spatial ability (9%)   and found they were very similar such that the choice of final model here is of little consequence , h2 = 0.22 (0.11), CVA = 0.13). We also checked how the square root transformation of inhibitory control influenced final estimates (relative to modeling untransformed data) by refitting Model 1 on the observed data scale. This yielded estimates of h2 = 0.12 (0.10) and CVA = 0.39. The significance and magnitude of fixed effects varied across task performances. These effects are not directly relevant to hypotheses being tested but are reported in full in the supplemental materials , as are the estimated variance components under final models of each trait (see Repeatabilities (with SE) for ity (9%) . The coe10–0.30) . Note thrait see .213 = 23.711, P = 0.034; Supplementary Information 6—PCA, The four-trait mixed model provided evidence of some significant among-individual correlation structure among cognitive performance traits , we did manage to estimate the genetic-variance correlation matrix among inhibitory control, visual discrimination, and spatial ability in a trivariate formulation of the random regression animal model. Based on comparison to a reduced model in which all cross-trait genetic correlation terms were set to zero, there is no evidence for significant genetic correlation among these traits . Similarly, bivariate models of spatial discrimination and each of the other traits provided no evidence of significant genetic correlation structure . The lack of significant genetic correlations was despite point estimates of the genetic correlations that were strongly positive in some  cases .While we were unable to estimate l) cases . Eigen dA) are being increasingly advocated for behavioral studies. However, these are only comparable across studies if traits are measured on ratio scale with an objective zero point  phenotypic correlation structure among traits. Principle component analysis however was not consistent with a strong leading general intelligence factor. Nor was there evidence of significant genetic correlations among traits, although this may be partly due to low statistical power. Towards the end of our Discussion, we make some cautious interpretation of qualitative patterns in both observed phenotypic  and genetic covariance structures. We consider what these patterns may mean for responses to selection on cognitive traits and argue that comparing both the phenotypic and genetic correlations is important for our understanding of factors that maintain individual variation in cognitive traits.We found evidence of additive genetic variation underpinning all four cognitive traits in pheasants, although estimated heritabilities were low to moderate in all cases. Discrimination of visual and spatial cues had the largest genetic components, compared with inhibitory control and  spatial ability. Investigations of (additive) genetic variance for specific cognitive traits are rare and limited to a few taxa . As notero point . This isPoecile gambeli] and North Island robins, [Petroica longipes]) and thus, these species are expected to have been strongly selected for better spatial memory over generations. Although pheasants do not cache food items, they likely have a strong spatial dimension to their lives including movement between territories and feeders, return to resource-rich areas, and memory of refuges. Speculatively, if strong directional selection has acted on spatial ability in pheasants, this might have eroded standing genetic variation contributing to the low heritability estimate  is similar to estimates obtained for visual learning in insects  but highestimate .The heritability estimate for inhibitory control was low to moderate (0.17) with relatively high uncertainty  though still marginally significant based on likelihood ratio tests. Estimates obtained from animal models are often more conservative than other methods in which common environment effects are difficult to control for  phenotypic correlation structure  model of cognition as applied to variation at the among-individual level. That is because under such a model, we would expect all traits to load strongly (and in the same direction) onto a dominant first principle component  in which visual learning ability did not positively correlate with inhibitory control   phenotypic correlation matrix revealed no single dominant leading vector, with each of the four axes explaining between 18 and 35% of the variation. This is inconsistent with a general intelligence omponent . The moromponent  providin control . Convers control  and Austorsalis) , a generG is actually consistent with the general intelligence model of cognition (rG > 0.66), albeit not a statistically significant one. For instance, the discrimination tasks exhibited positive genetic correlation (rG = 0.66), which is not surprising given both tasks required individuals to discriminate between two cues. It is therefore intuitive that both tasks would involve similar cognitive processes, such as comparable working memory capacity and levels of attention. However, despite being genetically correlated, they were not phenotypically correlated (r < 0.01). Similar considerations apply to the spatial tasks, which we had expected to covary both phenotypically and genetically because both tasks assessed an individuals’ ability to learn about and respond differently to different locations. The phenotypic correlations between these traits was low (r = 0.23), while the genetic correlation estimate was almost 1 (but highly uncertain). More generally the apparently poor correspondence between phenotypic and genetic correlation estimates may simply arise because of high uncertainty in the latter. However, to the extent that apparent differences are real, they also suggest that environmental factors may differentially affect how individual cognitive abilities are expressed, thus masking a genetic basis of variation that is common to the different cognitive traits. We do know, for instance, that recent negative social experiences are related to poorer performances on the spatial discrimination tasks in adult pheasants  inferences from phenotypic patterns. As a final note, although psychometric tasks aim to test a single, discrete cognitive ability, performance in such tasks is likely the result of various interacting cognitive processes , each of which may be influenced by the expression of multiple genetic loci. This makes it difficult to isolate which trait or suite of traits are actually heritable because genetic variance detected in task performances could be due to any or all of these factors see . Additioaraa029_suppl_Supplementary_Information_1Click here for additional data file.araa029_suppl_Supplementary_Information_2Click here for additional data file.


Triticum aestivum L.). In total, eight latent factors including grain yield, architecture, flag leaf‐related traits, grain minerals, yellow rust, two types of stem rust, and leaf rust were identified as common sources of the observed phenotypes. The genetic component of the factor scores for each latent variable was fed into a Bayesian network to obtain a trait structure reflecting the genetic interdependency among traits. Three directed paths were consistently identified by two Bayesian network algorithms. Flag leaf‐related traits influenced leaf rust, and yellow rust and stem rust influenced grain yield. Additional paths that were identified included flag leaf‐related traits to minerals and minerals to architecture. This study shows that data‐driven exploratory factor analysis can reveal smaller dimensional common latent phenotypes that are likely to give rise to numerous observed field phenotypes without relying on prior biological knowledge. The inferred genomic latent factor structure from the Bayesian network provides insights for plant breeding to simultaneously improve multiple traits, as an intervention on one trait will affect the values of focal phenotypes in an interrelated complex trait system.Inferring trait networks from a large volume of genetically correlated diverse phenotypes such as yield, architecture, and disease resistance can provide information on the manner in which complex phenotypes are interrelated. However, studies on statistical methods tailored to multidimensional phenotypes are limited, whereas numerous methods are available for evaluating the massive number of genetic markers. Factor analysis operates at the level of latent variables predicted to generate observed responses. The objectives of this study were to illustrate the manner in which data‐driven exploratory factor analysis can map observed phenotypes into a smaller number of latent variables and infer a genomic latent factor network using 45 agro‐morphological, disease, and grain mineral phenotypes measured in synthetic hexaploid wheat lines ( Grain yield in wheat is influenced by several agro‐morphological traits. However, successfully incorporating yield‐promoting agro‐morphological traits in breeding programs to improve genetic gains requires detailed knowledge of the interrelationships between and among traits. The second objective was to determine a trait network structure among the genomic latent factors using a Bayesian network. This is an essential task because breeding programs often aim to improve multiple correlated traits concurrently. Knowledge of directed trait networks accounting for the genetic interdependency among traits can improve the understanding of the manner in which the selection of one phenotype may increase or decrease the observation of another phenotype, providing additional insight beyond associations  and diverse accessions of cultivated durum wheat (Triticum turgidum L.), was used in this study. These plant materials were shared by the International Winter Wheat Improvement Program in Turkey and are available at http://www.iwwip.org. Pedigree information and other details on these lines were reported previously  and tested for multiple traits for use in a breeding program.A diversity panel of 2.2We analyzed 16 agronomic‐, 16 grain mineral‐, and 13 wheat rust‐related phenotypes in the current study. Agronomic traits including grain yield (GY), harvest index (HI), biomass weight (BMWT), grain volume weight (GVWT), flag leaf length (FLL), flag leaf width (FLW), flag leaf area (FLA), rachis break (RB), sterile spikelet (SP), spike length (SL), seeds per spike (SPS), spikelet number (SN), fertile spikelet (FS), spike weight (SW), grain weight per spike (GPS), and spike harvest index (SHI) were measured using previously described standard procedures ji is the effect of the jth block within the ith replication; kc is the kth check; gl(ji) is the effect of the lth noncheck genotypes (tested entries) within the jth incomplete block of the ith replication; and ijklε is the residual.The experiments were conducted across several locations in Turkey and one location in Kenya in 2017. The experimental design was an alpha lattice design with two replications , parameters Λ and Ѱ were estimated by maximizing the log‐likelihood of L using the R package psych  were sampled from the conditional distribution of p  and e~N, respectively. Here, G is a n × n genomic relationship matrix, I is a n × n identity matrix, Σg and Σe are variance–covariance matrices of additive genetic effect and residuals, respectively, and ⊗ is the Kronecker product. The G matrix was set as WW′/2∑j=1mpj(1‐pj), where W is the centered marker incidence matrix taking the values of 0 − 2pj for zero copies of the reference allele, 1 − 2pj for one copy of the reference allele, 2 − 2pj for two copies of the reference allele, and jp is the allele frequency at marker j = 1,…, m .A Bayesian multi‐trait genomic best linear unbiased prediction model was applied to partition inferred latent variables into genetic and environmental components. 2.7The posterior means of genetic values of latent variables obtained from the Bayesian multi‐trait genomic best linear unbiased prediction model were used to examine the manner in which the traits are interrelated using a Bayesian network. A Bayesian network is a graphical representation of the conditional independence among random variables based on a directed acyclic graph , is an important foliar fungal disease of wheat that causes major yield loss (Bhatta et al., Foliar diseases such as yellow rust, caused by Several studies have reported negative associations between grain minerals and architecture‐related traits. A larger number of seeds per spike and kernel size in wheat is associated with lower grain mineral accumulation in the grain, which is mainly attributed to the grain mineral dilution effect (Bhatta, Baenziger, et al., 5This study demonstrates that data‐driven latent variable analysis can reveal the underlying structure of phenotypes on a smaller dimensional scale. Thus, determining the genetic effects of correlated traits by factor analysis is an efficient approach for learning the minimum set of core factors contributing to high‐dimensional observed phenotypes. Additionally, by reconstructing a more general structure of genomic latent factors from observed phenotypes using a Bayesian network, a clearer picture of trait interdependency can be obtained, which is useful for developing breeding and management strategies for crops such as wheat.The authors declare that they have no competing interests.MM, MB, WH, and GM conceived the study. MM and HY analyzed the data. MM drafted the manuscript. WH, MB, HY, and GM revised the manuscript. GM supervised and directed the study. All the authors read and approved the manuscript.