Fast computation of the eigensystem of genomic similarity matrices.

The computation of a similarity measure for genomic data is a standard tool in computational genetics. The principal components of such matrices are routinely used to correct for biases due to confounding by population stratification, for instance in linear regressions. However, the calculation of both a similarity matrix and its singular value decomposition (SVD) are computationally intensive. The contribution of this article is threefold. First, we demonstrate that the calculation of three matrices (called the covariance matrix, the weighted Jaccard matrix, and the genomic relationship matrix) can be reformulated in a unified way which allows for the application of a randomized SVD algorithm, which is faster than the traditional computation. The fast SVD algorithm we present is adapted from an existing randomized SVD algorithm and ensures that all computations are carried out in sparse matrix algebra. The algorithm only assumes that row-wise and column-wise subtraction and multiplication of a vector with a sparse matrix is available, an operation that is efficiently implemented in common sparse matrix packages. An exception is the so-called Jaccard matrix, which does not have a structure applicable for the fast SVD algorithm. Second, an approximate Jaccard matrix is introduced to which the fast SVD computation is applicable. Third, we establish guaranteed theoretical bounds on the accuracy (in [Formula: see text] norm and angle) between the principal components of the Jaccard matrix and the ones of our proposed approximation, thus putting the proposed Jaccard approximation on a solid mathematical foundation, and derive the theoretical runtime of our algorithm. We illustrate that the approximation error is low in practice and empirically verify the theoretical runtime scalings on both simulated data and data of the 1000 Genome Project.

Moving beyond heritability in the search for coral adaptive potential.

Global environmental change is happening at unprecedented rates. Coral reefs are among the ecosystems most threatened by global change. For wild populations to persist, they must adapt. Knowledge shortfalls about corals' complex ecological and evolutionary dynamics, however, stymie predictions about potential adaptation to future conditions. Here, we review adaptation through the lens of quantitative genetics. We argue that coral adaptation studies can benefit greatly from "wild" quantitative genetic methods, where traits are studied in wild populations undergoing natural selection, genomic relationship matrices can replace breeding experiments, and analyses can be extended to examine genetic constraints among traits. In addition, individuals with advantageous genotypes for anticipated future conditions can be identified. Finally, genomic genotyping supports simultaneous consideration of how genetic diversity is arrayed across geographic and environmental distances, providing greater context for predictions of phenotypic evolution at a metapopulation scale.

Weighted genomic prediction for growth and carcass-related traits in Nelore cattle.

This study aimed to assess the impact of differential weighting in genomic regions harboring candidate causal loci on the genomic prediction accuracy and dispersion for growth and carcass-related traits in Nelore cattle. The dataset contained 168 793 phenotypic records for adjusted weight at 450 days of age (W450), 83 624 for rib eye area (REA), 24 480 for marbling (MAR) and 82 981 for subcutaneous backfat thickness (BFT) and rump fat thickness (RFT). The pedigree harbored information from 244 254 animals born between 1977 and 2016, including 6283 sires and 50 742 dams. Animals (n = 7769) were genotyped with the low-density panel (Clarifide® Nelore 3.0), and the genotypes were imputed to a panel containing 735 044 markers. A linear animal model was applied to estimate the genetic parameters and to perform the weighted single-step genome-wide association study (WssGWAS). A total of seven models for genomic prediction were evaluated combining the SNP weights obtained in the iterations of the WssGWAS and the candidate QTL. The heritability estimated for W450 (0.35) was moderate, and for carcass-related traits, the estimates were moderate for REA (0.27), MAR (0.28) and RFT (0.28), and low for BFT (0.18). The prediction accuracy for W450 incorporating reported QTL previously described in the literature along with different SNPs weights was like those described for the default ssGBLUP model. The use of the ssGWAS to weight the SNP effects displayed limited advantages for the REA prediction accuracy. Comparing the ssGBLUP with the BLUP model, a meaningful improvement in the prediction accuracy from 0.09 to 0.63 (700%) was observed for MAR. The highest prediction accuracy was obtained for BFT and RFT in all evaluated models. The application of information obtained from the WssGWAS is an alternative to reduce the genomic prediction dispersion for growth and carcass-related traits, except for MAR. Furthermore, the results obtained herein pointed out that is possible to improve the prediction accuracy and reduce the genomic prediction dispersion for growth and carcass-related traits in young animals.

Genomic Prediction of Resistance to Tan Spot, Spot Blotch and Septoria Nodorum Blotch in Synthetic Hexaploid Wheat.

Genomic prediction combines molecular and phenotypic data in a training population to predict the breeding values of individuals that have only been genotyped. The use of genomic information in breeding programs helps to increase the frequency of favorable alleles in the populations of interest. This study evaluated the performance of BLUP (Best Linear Unbiased Prediction) in predicting resistance to tan spot, spot blotch and Septoria nodorum blotch in synthetic hexaploid wheat. BLUP was implemented in single-trait and multi-trait models with three variations: (1) the pedigree relationship matrix (A-BLUP), (2) the genomic relationship matrix (G-BLUP), and (3) a combination of the two matrices (A+G BLUP). In all three diseases, the A-BLUP model had a lower performance, and the G-BLUP and A+G BLUP were statistically similar (p ≥ 0.05). The prediction accuracy with the single trait was statistically similar (p ≥ 0.05) to the multi-trait accuracy, possibly due to the low correlation of severity between the diseases.

An unbiased kinship estimation method for genetic data analysis.

Accurate estimate of relatedness is important for genetic data analyses, such as heritability estimation and association mapping based on data collected from genome-wide association studies. Inaccurate relatedness estimates may lead to biased heritability estimations and spurious associations. Individual-level genotype data are often used to estimate kinship coefficient between individuals. The commonly used sample correlation-based genomic relationship matrix (scGRM) method estimates kinship coefficient by calculating the average sample correlation coefficient among all single nucleotide polymorphisms (SNPs), where the observed allele frequencies are used to calculate both the expectations and variances of genotypes. Although this method is widely used, a substantial proportion of estimated kinship coefficients are negative, which are difficult to interpret. In this paper, through mathematical derivation, we show that there indeed exists bias in the estimated kinship coefficient using the scGRM method when the observed allele frequencies are regarded as true frequencies. This leads to negative bias for the average estimate of kinship among all individuals, which explains the estimated negative kinship coefficients. Based on this observation, we propose an unbiased estimation method, UKin, which can reduce kinship estimation bias. We justify our improved method with rigorous mathematical proof. We have conducted simulations as well as two real data analyses to compare UKin with scGRM and three other kinship estimating methods: rGRM, tsGRM, and KING. Our results demonstrate that both bias and root mean square error in kinship coefficient estimation could be reduced by using UKin. We further investigated the performance of UKin, KING, and three GRM-based methods in calculating the SNP-based heritability, and show that UKin can improve estimation accuracy for heritability regardless of the scale of SNP panel.

Predictive assessment of single-step BLUP with linear and non-linear similarity RKHS kernels: A case study in chickens.

Single-step GBLUP (ssGBLUP) to obtain genomic prediction was proposed in 2009. Many studies have investigated ssGBLUP in genomic selection in animals and plants using a standard linear kernel (similarity matrix) called genomic relationship matrix (G). More general kernels should allow capturing non-additive effects as well, whereas GBLUP is based on additive gene action. In this study, we generalized ssBLUP to accommodate two non-linear kernels, the averaged Gaussian kernel (AK) and the recently developed arc-cosine deep kernel (DK). We evaluated the methodology using body weight (BW) and hen-housing production (HHP) traits, recorded on a sample of phenotyped and genotyped commercial broiler chickens. There were, thus, different ssGBLUP models corresponding to G, AK and DK. We used random replication of training (TRN) and testing (TST) layouts at different genotyping rates (20%, 40%, 60% and 80% of all birds) in three selective genotyping scenarios. The selections were genotyping the youngest individuals in the pedigree (YS), random genotyping (RS) and genotyping based on parent average (PA). Predictive abilities were measured using rank correlations between the observed and the predictive phenotypic values in TST for each random partition. Prediction accuracy was influenced by the type of kernel when a large proportion of birds was genotyped. An advantage of non-linear kernels (AK and DK) was more apparent when 60 and 80% of birds had been genotyped. For BW, the lowest rank correlations were obtained with G (0.093 ± 0.015 using RS by 20% genotyped individuals) and the highest values with DK (0.320 ± 0.016 in the PA setting with 80% genotyped individuals). For HHP, the lowest and highest rank correlations were obtained by AK with 20% and 80% genotyped individuals, 0.071 ± 0.016 (in RS) and 0.23 ± 0.016 (in PA) respectively. Our results indicated that AK and DK are more effective than G when a large proportion of the target population is genotyped. Our expectation is that ssGBLUP with AK or DK models can perform even better than G when non-additive genetic effects influence the underlying variability of complex traits.

Inferring trait-specific similarity among individuals from molecular markers and phenotypes with Bayesian regression.

Modeling covariance structure based on genetic similarity between pairs of relatives plays an important role in evolutionary, quantitative and statistical genetics. Historically, genetic similarity between individuals has been quantified from pedigrees via the probability that randomly chosen homologous alleles between individuals are identical by descent (IBD). At present, however, many genetic analyses rely on molecular markers, with realized measures of genomic similarity replacing IBD-based expected similarities. Animal and plant breeders, for example, now employ marker-based genomic relationship matrices between individuals in prediction models and in estimation of genome-based heritability coefficients. Phenotypes convey information about genetic similarity as well. For instance, if phenotypic values are at least partially the result of the action of quantitative trait loci, one would expect the former to inform about the latter, as in genome-wide association studies. Statistically, a non-trivial conditional distribution of unknown genetic similarities, given phenotypes, is to be expected. A Bayesian formalism is presented here that applies to whole-genome regression methods where some genetic similarity matrix, e.g., a genomic relationship matrix, can be defined. Our Bayesian approach, based on phenotypes and markers, converts prior (markers only) expected similarity into trait-specific posterior similarity. A simulation illustrates situations under which effective Bayesian learning from phenotypes occurs. Pinus and wheat data sets were used to demonstrate applicability of the concept in practice. The methodology applies to a wide class of Bayesian linear regression models, it extends to the multiple-trait domain, and can also be used to develop phenotype-guided similarity kernels in prediction problems.

ICGRM: integrative construction of genomic relationship matrix combining multiple genomic regions for big dataset.

BACKGROUND: Genomic prediction is an advanced method for estimating genetic values, which has been widely accepted for genetic evaluation in animal and disease-risk prediction in human. It estimates genetic values with genome-wide distributed SNPs instead of pedigree. The key step of it is to construct genomic relationship matrix (GRM) via genome-wide SNPs; however, usually the calculation of GRM needs huge computer memory especially when the SNP number and sample size are big, so that sometimes it will become computationally prohibitive even for super computer clusters. We herein developed an integrative algorithm to compute GRM. To avoid calculating GRM for the whole genome, ICGRM freely divides the genome-wide SNPs into several segments and computes the summary statistics related to GRM for each segment that requires quite few computer RAM; then it integrates these summary statistics to produce GRM for whole genome. RESULTS: It showed that the computer memory of ICGRM was reduced by 15 times (from 218Gb to 14Gb) after the genome SNPs were split into 5 to 200 parts in terms of the number of SNPs in our simulation dataset, making it computationally feasible for almost all kinds of computer servers. ICGRM is implemented in C/C++ and freely available via https://github.com/mingfang618/CLGRM. CONCLUSIONS: ICGRM is computationally efficient software to build GRM and can be used for big dataset.

A mating advice system in dairy cattle incorporating genomic information.

This study investigated the effects of alternative mating programs that incorporate genomic information on expected progeny herd performance and inbreeding, as well as methods to include un-genotyped animals in such mating programs. A total of 54,535 Holstein-Friesian cattle with imputed high-density genotypes (547,650 SNP after edits) were available. First, to quantify the accuracy of imputing un-genotyped animals (often an issue in populations), a sub-population of 729 genotyped animals had their genotypes masked, and their allele dosages were imputed, using linear regression exploiting information on genotyped relatives. The reference population for imputation included all genotyped animals, excluding the 729 selected animals and their sires, dams, and grandsires, and had either (1) their sires' genotypes, (2) their dams' genotypes (3) both their sires' and their dams' genotypes, or (4) both their sires' and maternal grandsires' genotypes introduced into the reference population. The correlations between true genotypes and the imputed allele dosages ranged from 0.58 (sire only) to 0.68 (both sire and dam). A herd of 100 cows was then simulated (1,000 replicates) from the sub-population of 729 imputed animals. The top 10 bulls from the genotyped population, based on their total genetic merit index (TMI) were selected to be used as sires. Three mating allotment methods were investigated: (1) random mating, (2) sequential mating based on maximizing only the expected TMI of the progeny, and (3) linear programming to maximize a generated index constructed to maximize genetic merit and minimize expected progeny inbreeding as well as intra- and inter-progeny variability in genetic merit. Relationships among candidate parents were calculated using either the pedigree relationship matrix or the genomic relationship matrix; the latter was constructed using either the true genotypes of both parents or the true genotypes of the sire plus the imputed allele dosages of the dam. Using the genomic co-ancestry estimates resulted in lower average herd expected genomic inbreeding levels compared with using the pedigree-based co-ancestry estimates. Additionally, if the dams were not genotyped, using their imputed allele dosages also resulted in lower average herd expected inbreeding levels compared with using the pedigree co-ancestry estimates. The inter-progeny coefficient of variation for selected traits, milk and fertility, estimated breeding values were reduced by 12 to 65% using the linear programing method compared with sequential mating.

Genetic evaluation of test-day milk yields from smallholder dairy production systems in Kenya using genomic relationships.

Efforts to improve dairy production in smallholder farming systems of East Africa over the past decade have had limited impact because of the lack of records on performance to guide targeted breeding programs. Estimates of genetic parameters in these systems are lacking. Using data generated through a project ("Germplasm for Dairy Development in East Africa") in Kenya and a genomic relationship matrix from genotypic records, we examined the potential impact of different models handling contemporary groups or herd effects on estimates of genetic parameters using a fixed regression model (FRM) for test-day (TD) milk yields, and the covariance structure for TD milk yield at various stages of lactation for animals using a random regression model (RRM). Models in which herd groups were defined using production levels derived from the data fitted the data better than those in which herds were grouped depending on management practices or were random. Lactation curves obtained for animals under different production categories did not display the typical peak yield characteristic of improved dairy systems in developed countries. Heritability estimates for TD milk yields using the FRM varied greatly with the definition of contemporary herd groups, ranging from 0.05 ± 0.03 to 0.27 ± 0.05 (mean ± standard error). The analysis using the RRM fitted the data better than the FRM. The heritability estimates for specific TD yields obtained by the RRM were higher than those obtained by the FRM. Genetic correlations between TD yields were high and positive for measures within short consecutive intervals but decreased as the intervals between TD increased beyond 60 d and became negative with intervals of more than 5 mo. The magnitude of the genetic correlation estimates among TD records indicates that using TD milk records beyond a 60-d interval as repeated measures of the same trait for genetic evaluation of animals on smallholder farms would not be optimal. Although each individual smallholder farmer retains only a few animals, using the genomic relationship between animals to link the large number of farmers operating under specified environments provides a sufficiently large herd-group for which a breeding program could be developed.

Genome variants associated with RNA splicing variations in bovine are extensively shared between tissues.

BACKGROUND: Mammalian phenotypes are shaped by numerous genome variants, many of which may regulate gene transcription or RNA splicing. To identify variants with regulatory functions in cattle, an important economic and model species, we used sequence variants to map a type of expression quantitative trait loci (expression QTLs) that are associated with variations in the RNA splicing, i.e., sQTLs. To further the understanding of regulatory variants, sQTLs were compare with other two types of expression QTLs, 1) variants associated with variations in gene expression, i.e., geQTLs and 2) variants associated with variations in exon expression, i.e., eeQTLs, in different tissues. RESULTS: Using whole genome and RNA sequence data from four tissues of over 200 cattle, sQTLs identified using exon inclusion ratios were verified by matching their effects on adjacent intron excision ratios. sQTLs contained the highest percentage of variants that are within the intronic region of genes and contained the lowest percentage of variants that are within intergenic regions, compared to eeQTLs and geQTLs. Many geQTLs and sQTLs are also detected as eeQTLs. Many expression QTLs, including sQTLs, were significant in all four tissues and had a similar effect in each tissue. To verify such expression QTL sharing between tissues, variants surrounding (±1 Mb) the exon or gene were used to build local genomic relationship matrices (LGRM) and estimated genetic correlations between tissues. For many exons, the splicing and expression level was determined by the same cis additive genetic variance in different tissues. Thus, an effective but simple-to-implement meta-analysis combining information from three tissues is introduced to increase power to detect and validate sQTLs. sQTLs and eeQTLs together were more enriched for variants associated with cattle complex traits, compared to geQTLs. Several putative causal mutations were identified, including an sQTL at Chr6:87392580 within the 5th exon of kappa casein (CSN3) associated with milk production traits. CONCLUSIONS: Using novel analytical approaches, we report the first identification of numerous bovine sQTLs which are extensively shared between multiple tissue types. The significant overlaps between bovine sQTLs and complex traits QTL highlight the contribution of regulatory mutations to phenotypic variations.

Evaluating the accuracy of genomic prediction of growth and wood traits in two Eucalyptus species and their F1 hybrids.

BACKGROUND: Genomic prediction is a genomics assisted breeding methodology that can increase genetic gains by accelerating the breeding cycle and potentially improving the accuracy of breeding values. In this study, we use 41,304 informative SNPs genotyped in a Eucalyptus breeding population involving 90 E.grandis and 78 E.urophylla parents and their 949 F1 hybrids to develop genomic prediction models for eight phenotypic traits - basic density and pulp yield, circumference at breast height and height and tree volume scored at age three and six years. We assessed the impact of different genomic prediction methods, the composition and size of the training and validation set and the number and genomic location of SNPs on the predictive ability (PA). RESULTS: Heritabilities estimated using the realized genomic relationship matrix (GRM) were considerably higher than estimates based on the expected pedigree, mainly due to inconsistencies in the expected pedigree that were readily corrected by the GRM. Moreover, the GRM more precisely capture Mendelian sampling among related individuals, such that the genetic covariance was based on the true proportion of the genome shared between individuals. PA improved considerably when increasing the size of the training set and by enhancing relatedness to the validation set. Prediction models trained on pure species parents could not predict well in F1 hybrids, indicating that model training has to be carried out in hybrid populations if one is to predict in hybrid selection candidates. The different genomic prediction methods provided similar results for all traits, therefore either GBLUP or rrBLUP represents better compromises between computational time and prediction efficiency. Only slight improvement was observed in PA when more than 5000 SNPs were used for all traits. Using SNPs in intergenic regions provided slightly better PA than using SNPs sampled exclusively in genic regions. CONCLUSIONS: The size and composition of the training set and number of SNPs used are the two most important factors for model prediction, compared to the statistical methods and the genomic location of SNPs. Furthermore, training the prediction model based on pure parental species only provide limited ability to predict traits in interspecific hybrids. Our results provide additional promising perspectives for the implementation of genomic prediction in Eucalyptus breeding programs by the selection of interspecific hybrids.

A comparison of identity-by-descent and identity-by-state matrices that are used for genetic evaluation and estimation of variance components.

The genetic covariance matrix conditional on pedigree is proportional to the pedigree-based additive relationship matrix (PARM), which is twice the matrix of identity-by-descent (IBD) probabilities. In genomic prediction, IBD probabilities in the PARM, which are expected genetic similarities between relatives that are derived from the pedigree, are substituted by realized similarities that are derived from genotypes to obtain a genomic additive relationship matrix (GARM). Different definitions of similarity lead to different GARMs, and two commonly used GARMS are the matrix G, which is based on an allele substitution effect model, and the matrix T, which is based on an allele effect model. We show that although the two matrices T and G are not proportional, they give identical predictions of differences between breeding values. When genomic information is used for variance component estimation, the GARM Gx is computed from genotype covariates that have been standardized to have unit variance. That approach is equivalent to fitting a random regression model using the same standardized covariates. We show that under Hardy-Weinberg and linkage equilibria (LE) that the genetic variance is kσγ2, where σγ2 is the variance of a randomly sampled element from the vector of k substitution effects. However, if linkage disequilibrium (LD) has been generated through selection, covariances between genotypes at different loci will be negative, and therefore, the additive genetic variance will be lower than kσγ2. When the GARM Gx is assumed to be proportional to the genetic covariance matrix, the parameter being estimated is kσγ2. We have demonstrated by simulation that kσγ2 overestimates the additive genetic variance when LD is generated by selection. We argue that unlike the PARM, GARMs are not proportional to a genetic covariance matrix conditional on the observed causal genotypes. The objective here is to recognize the difference between these covariance matrices and its implications.

Accuracy of genomic breeding value prediction for intramuscular fat using different genomic relationship matrices in Hanwoo (Korean cattle).

OBJECTIVE: Intramuscular fat is one of the meat quality traits that is considered in the selection strategies for Hanwoo (Korean cattle). Different methods are used to estimate the breeding value of selection candidates. In the present work we focused on accuracy of different genotype relationship matrices as described by forni and pedigree based relationship matrix. METHODS: The data set included a total of 778 animals that were genotyped for BovineSNP50 BeadChip. Among these 778 animals, 72 animals were sires for 706 reference animals and were used as a validation dataset. Single trait animal model (best linear unbiased prediction and genomic best linear unbiased prediction) was used to estimate the breeding values from genomic and pedigree information. RESULTS: The diagonal elements for the pedigree based coefficients were slightly higher for the genomic relationship matrices (GRM) based coefficients while off diagonal elements were considerably low for GRM based coefficients. The accuracy of breeding value for the pedigree based relationship matrix (A) was 13% while for GRM (GOF, G05, and Yang) it was 0.37, 0.45, and 0.38, respectively. CONCLUSION: Accuracy of GRM was 1.5 times higher than A in this study. Therefore, genomic information will be more beneficial than pedigree information in the Hanwoo breeding program.

Implementation of genomic recursions in single-step genomic best linear unbiased predictor for US Holsteins with a large number of genotyped animals.

The objectives of this study were to develop and evaluate an efficient implementation in the computation of the inverse of genomic relationship matrix with the recursion algorithm, called the algorithm for proven and young (APY), in single-step genomic BLUP. We validated genomic predictions for young bulls with more than 500,000 genotyped animals in final score for US Holsteins. Phenotypic data included 11,626,576 final scores on 7,093,380 US Holstein cows, and genotypes were available for 569,404 animals. Daughter deviations for young bulls with no classified daughters in 2009, but at least 30 classified daughters in 2014 were computed using all the phenotypic data. Genomic predictions for the same bulls were calculated with single-step genomic BLUP using phenotypes up to 2009. We calculated the inverse of the genomic relationship matrix GAPY(-1) based on a direct inversion of genomic relationship matrix on a small subset of genotyped animals (core animals) and extended that information to noncore animals by recursion. We tested several sets of core animals including 9,406 bulls with at least 1 classified daughter, 9,406 bulls and 1,052 classified dams of bulls, 9,406 bulls and 7,422 classified cows, and random samples of 5,000 to 30,000 animals. Validation reliability was assessed by the coefficient of determination from regression of daughter deviation on genomic predictions for the predicted young bulls. The reliabilities were 0.39 with 5,000 randomly chosen core animals, 0.45 with the 9,406 bulls, and 7,422 cows as core animals, and 0.44 with the remaining sets. With phenotypes truncated in 2009 and the preconditioned conjugate gradient to solve mixed model equations, the number of rounds to convergence for core animals defined by bulls was 1,343; defined by bulls and cows, 2,066; and defined by 10,000 random animals, at most 1,629. With complete phenotype data, the number of rounds decreased to 858, 1,299, and at most 1,092, respectively. Setting up GAPY(-1) for 569,404 genotyped animals with 10,000 core animals took 1.3h and 57 GB of memory. The validation reliability with APY reaches a plateau when the number of core animals is at least 10,000. Predictions with APY have little differences in reliability among definitions of core animals. Single-step genomic BLUP with APY is applicable to millions of genotyped animals.

Short communication: Multi-trait estimation of genetic parameters for milk protein composition in the Danish Holstein.

Genetic parameters were estimated for the major milk proteins using bivariate and multi-trait models based on genomic relationships between animals. The analyses included, apart from total protein percentage, αS1-casein (CN), αS2-CN, ß-CN, κ-CN, α-lactalbumin, and ß-lactoglobulin, as well as the posttranslational sub-forms of glycosylated κ-CN and αS1-CN-8P (phosphorylated). Standard errors of the estimates were used to compare the models. In total, 650 Danish Holstein cows across 4 parities and days in milk ranging from 9 to 481d were selected from 21 herds. The multi-trait model generally resulted in lower standard errors of heritability estimates, suggesting that genetic parameters can be estimated with high accuracy using multi-trait analyses with genomic relationships for scarcely recorded traits. The heritability estimates from the multi-trait model ranged from low (0.05 for ß-CN) to high (0.78 for κ-CN). Genetic correlations between the milk proteins and the total milk protein percentage were generally low, suggesting the possibility to alter protein composition through selective breeding with little effect on total milk protein percentage.

Technical note: Equivalent genomic models with a residual polygenic effect.

Routine genomic evaluations in animal breeding are usually based on either a BLUP with genomic relationship matrix (GBLUP) or single nucleotide polymorphism (SNP) BLUP model. For a multi-step genomic evaluation, these 2 alternative genomic models were proven to give equivalent predictions for genomic reference animals. The model equivalence was verified also for young genotyped animals without phenotypes. Due to incomplete linkage disequilibrium of SNP markers to genes or causal mutations responsible for genetic inheritance of quantitative traits, SNP markers cannot explain all the genetic variance. A residual polygenic effect is normally fitted in the genomic model to account for the incomplete linkage disequilibrium. In this study, we start by showing the proof that the multi-step GBLUP and SNP BLUP models are equivalent for the reference animals, when they have a residual polygenic effect included. Second, the equivalence of both multi-step genomic models with a residual polygenic effect was also verified for young genotyped animals without phenotypes. Additionally, we derived formulas to convert genomic estimated breeding values of the GBLUP model to its components, direct genomic values and residual polygenic effect. Third, we made a proof that the equivalence of these 2 genomic models with a residual polygenic effect holds also for single-step genomic evaluation. Both the single-step GBLUP and SNP BLUP models lead to equal prediction for genotyped animals with phenotypes (e.g., reference animals), as well as for (young) genotyped animals without phenotypes. Finally, these 2 single-step genomic models with a residual polygenic effect were proven to be equivalent for estimation of SNP effects, too.

Accounting for genetic architecture in single- and multipopulation genomic prediction using weights from genomewide association studies in pigs.

We studied the effect of including GWAS results on the accuracy of single- and multipopulation genomic predictions. Phenotypes (backfat thickness) and genotypes of animals from two sire lines (SL1, n = 1146 and SL3, n = 1264) were used in the analyses. First, GWAS were conducted for each line and for a combined data set (both lines together) to estimate the genetic variance explained by each SNP. These estimates were used to build matrices of weights (D), which was incorporated into a GBLUP method. Single population evaluated with traditional GBLUP had accuracies of 0.30 for SL1 and 0.31 for SL3. When weights were employed in GBLUP, the accuracies for both lines increased (0.32 for SL1 and 0.34 for SL3). When a multipopulation reference set was used in GBLUP, the accuracies were higher (0.36 for SL1 and 0.32 for SL3) than in single-population prediction. In addition, putting together the multipopulation reference set and the weights from the combined GWAS provided even higher accuracies (0.37 for SL1, and 0.34 for SL3). The use of multipopulation predictions and weights estimated from a combined GWAS increased the accuracy of genomic predictions.

The effect of including genomic relationships in the estimation of genetic parameters of functional traits in pigs.

The term functionality in animal breeding is used for traits that increase the efficiency of production by lowering the input cost, such as animal health and leg weakness related to longevity. The main objective of the study was to investigate the impact of genomic information, in a multivariate variance component analysis, on some of these traits. In addition, the effect of the inclusion was studied by testing the model's prediction ability based on best linear unbiased estimates for fixed and random effects. The material in this study consists of phenotypes from 76,683 animals, of which 4933 animals are genotyped. The heritabilities for front leg conformation, stayability, osteochondrosis and arched back, estimated using the traditional pedigree, were found to be between 0.12 and 0.29. When using the combined genomic and pedigree relationship matrix, the heritabilities were between 0.14 and 0.36. The results show that the combined relationship matrix can be used for the estimation of (co)variance components, and that the predictive ability of the model in this study marginally increases with the inclusion of genomic information.

Genomic additive and dominance variance of milk performance traits.

Milk performance traits are likely influenced by both additive and non-additive (e.g. dominance) genetic effects. Genetic variation can be partitioned using genomic information. The objective of this study was to estimate genetic variance components of production and milk component traits (e.g. acetone, fatty acids), which are particularly important for milk processing or which can provide information on the health status of cows. A genomic relationship approach was applied to phenotypic and genetic information of 1295 Holstein cows for estimating additive genetic and dominance variance components. Most of the 17 investigated traits were mainly affected by additive genetic effects, but protein content and casein content also showed a significant contribution of dominance. The ratio of dominance to additive variance was estimated as 0.64 for protein content and 0.56 for casein content. This ratio was highest for SCS (1.36) although dominance was not significant. Dominance effects were negligible in other moderately heritable milk traits.