Dorian J. Garrick

Extension of the bayesian alphabet for genomic selection

BackgroundTwo Bayesian methods, BayesCπ and BayesDπ, were developed for genomic prediction to address the drawback of BayesA and BayesB regarding the impact of prior hyperparameters and treat the prior probability π that a SNP has zero effect as unknown. The methods were compared in terms of inference of the number of QTL and accuracy of genomic estimated breeding values (GEBVs), using simulated scenarios and real data from North American Holstein bulls.ResultsEstimates of π from BayesCπ, in contrast to BayesDπ, were sensitive to the number of simulated QTL and training data size, and provide information about genetic architecture. Milk yield and fat yield have QTL with larger effects than protein yield and somatic cell score. The drawback of BayesA and BayesB did not impair the accuracy of GEBVs. Accuracies of alternative Bayesian methods were similar. BayesA was a good choice for GEBV with the real data. Computing time was shorter for BayesCπ than for BayesDπ, and longest for our implementation of BayesA.ConclusionsCollectively, accounting for computing effort, uncertainty as to the number of QTL (which affects the GEBV accuracy of alternative methods), and fundamental interest in the number of QTL underlying quantitative traits, we believe that BayesCπ has merit for routine applications.

Deregressing estimated breeding values and weighting information for genomic regression analyses

BackgroundGenomic prediction of breeding values involves a so-called training analysis that predicts the influence of small genomic regions by regression of observed information on marker genotypes for a given population of individuals. Available observations may take the form of individual phenotypes, repeated observations, records on close family members such as progeny, estimated breeding values (EBV) or their deregressed counterparts from genetic evaluations. The literature indicates that researchers are inconsistent in their approach to using EBV or deregressed data, and as to using the appropriate methods for weighting some data sources to account for heterogeneous variance.MethodsA logical approach to using information for genomic prediction is introduced, which demonstrates the appropriate weights for analyzing observations with heterogeneous variance and explains the need for and the manner in which EBV should have parent average effects removed, be deregressed and weighted.ResultsAn appropriate deregression for genomic regression analyses is EBV/r2 where EBV excludes parent information and r2 is the reliability of that EBV. The appropriate weights for deregressed breeding values are neither the reliability nor the prediction error variance, two alternatives that have been used in published studies, but the ratio (1 - h2)/[(c + (1 - r2)/r2)h2] where c > 0 is the fraction of genetic variance not explained by markers.ConclusionsPhenotypic information on some individuals and deregressed data on others can be combined in genomic analyses using appropriate weighting.

Accuracy of Genomic Selection Methods in a Standard Data Set of Loblolly Pine (Pinus taeda L.)

Genomic selection can increase genetic gain per generation through early selection. Genomic selection is expected to be particularly valuable for traits that are costly to phenotype and expressed late in the life cycle of long-lived species. Alternative approaches to genomic selection prediction models may perform differently for traits with distinct genetic properties. Here the performance of four different original methods of genomic selection that differ with respect to assumptions regarding distribution of marker effects, including (i) ridge regression–best linear unbiased prediction (RR–BLUP), (ii) Bayes A, (iii) Bayes Cπ, and (iv) Bayesian LASSO are presented. In addition, a modified RR–BLUP (RR–BLUP B) that utilizes a selected subset of markers was evaluated. The accuracy of these methods was compared across 17 traits with distinct heritabilities and genetic architectures, including growth, development, and disease-resistance properties, measured in a Pinus taeda (loblolly pine) training population of 951 individuals genotyped with 4853 SNPs. The predictive ability of the methods was evaluated using a 10-fold, cross-validation approach, and differed only marginally for most method/trait combinations. Interestingly, for fusiform rust disease-resistance traits, Bayes Cπ, Bayes A, and RR–BLUB B had higher predictive ability than RR–BLUP and Bayesian LASSO. Fusiform rust is controlled by few genes of large effect. A limitation of RR–BLUP is the assumption of equal contribution of all markers to the observed variation. However, RR-BLUP B performed equally well as the Bayesian approaches.The genotypic and phenotypic data used in this study are publically available for comparative analysis of genomic selection prediction models.

Genomic prediction of simulated multibreed and purebred performance using observed fifty thousand single nucleotide polymorphism genotypes.

Genomic prediction involves characterization of chromosome fragments in a training population to predict merit. Confidence in the predictions relies on their evaluation in a validation population. Many commercial animals are multibreed (MB) or crossbred, but seedstock populations tend to be purebred (PB). Training in MB allows selection of PB for crossbred performance. Training in PB to predict MB performance quantifies the potential for across-breed genomic prediction. Efficiency of genomic selection was evaluated for a trait with heritability 0.5 simulated using actual SNP genotypes. The PB population had 1,086 Angus animals, and the MB population had 924 individuals from 8 sire breeds. Phenotypic values were simulated for scenarios including 50, 100, 250, or 500 additive QTL randomly selected from 50K SNP panels. Panels containing various numbers of SNP, including or excluding the QTL, were used in the analysis. A Bayesian model averaging method was used to simultaneously estimate the effects of all markers on the panels in MB (or PB) training populations. Estimated effects were utilized to predict genomic merit of animals in PB (or MB) validation populations. Correlations between predicted and simulated genomic merit in the validation population was used to reflect predictive ability. Panels that included QTL were able to account for 50% or more of the within-breed genetic variance when the trait was influenced by 50 QTL. The predictive power eroded as the number of QTL increased. Panels that composed the QTL and no other markers were able to account for 50% or more genetic variance even with 500 QTL. Panels that included genomic markers as well as QTL had less predictive power as the number of markers on the panel was increased. Panels that excluded the QTL and relied on markers in linkage disequilibrium (LD) to predict QTL effects performed more poorly than marker panels with QTL. Real-life situations with 50K panels that excluded the QTL could account for no more than 20% genetic variation for 50 QTL and less than 10% for 500 QTL. The difference between panels that included and excluded QTL indicates that the predictive ability of existing panels is limited by their LD. Training in PB to predict MB tended to be more predictive than training in MB to predict PB due to greater average levels of LD in PB than in MB populations. Improved across breed prediction of genomic merit will require panels with more than 50,000 markers.

Genome-Wide Association Study Identifies Loci for Body Composition and Structural Soundness Traits in Pigs

Background The recent completion of the swine genome sequencing project and development of a high density porcine SNP array has made genome-wide association (GWA) studies feasible in pigs. Methodology/Principal Findings Using Illuminas PorcineSNP60 BeadChip, we performed a pilot GWA study in 820 commercial female pigs phenotyped for backfat, loin muscle area, body conformation in addition to feet and leg (FL) structural soundness traits. A total of 51,385 SNPs were jointly fitted using Bayesian techniques as random effects in a mixture model that assumed a known large proportion (99.5%) of SNPs had zero effect. SNP annotations were implemented through the Sus scrofa Build 9 available from pig Ensembl. We discovered a number of candidate chromosomal regions, and some of them corresponded to QTL regions previously reported. We not only have identified some well-known candidate genes for the traits of interest, such as MC4R (for backfat) and IGF2 (for loin muscle area), but also obtained novel promising genes, including CHCHD3 (for backfat), BMP2 (for loin muscle area, body size and several FL structure traits), and some HOXA family genes (for overall leg action). The candidate regions responsible for body conformation and FL structure soundness did not overlap greatly which implied that these traits were controlled by different genes. Functional clustering analyses classified the genes into categories related to bone and cartilage development, muscle growth and development or the insulin pathway suggesting the traits are regulated by common pathways or gene networks that exert roles at different spatial and temporal stages. Conclusions/Significance This study is one of the earliest GWA reports on important quantitative traits in pigs, and the findings will contribute to the further biological function analysis of the identified candidate genes and potential utilization of them in marker assisted selection.

Genomic-BLUP Decoded: A Look into the Black Box of Genomic Prediction

Genomic best linear unbiased prediction (BLUP) is a statistical method that uses relationships between individuals calculated from single-nucleotide polymorphisms (SNPs) to capture relationships at quantitative trait loci (QTL). We show that genomic BLUP exploits not only linkage disequilibrium (LD) and additive-genetic relationships, but also cosegregation to capture relationships at QTL. Simulations were used to study the contributions of those types of information to accuracy of genomic estimated breeding values (GEBVs), their persistence over generations without retraining, and their effect on the correlation of GEBVs within families. We show that accuracy of GEBVs based on additive-genetic relationships can decline with increasing training data size and speculate that modeling polygenic effects via pedigree relationships jointly with genomic breeding values using Bayesian methods may prevent that decline. Cosegregation information from half sibs contributes little to accuracy of GEBVs in current dairy cattle breeding schemes but from full sibs it contributes considerably to accuracy within family in corn breeding. Cosegregation information also declines with increasing training data size, and its persistence over generations is lower than that of LD, suggesting the need to model LD and cosegregation explicitly. The correlation between GEBVs within families depends largely on additive-genetic relationship information, which is determined by the effective number of SNPs and training data size. As genomic BLUP cannot capture short-range LD information well, we recommend Bayesian methods with t-distributed priors.

Accuracies of genomic breeding values in American Angus beef cattle using K-means clustering for cross-validation

BackgroundGenomic selection is a recently developed technology that is beginning to revolutionize animal breeding. The objective of this study was to estimate marker effects to derive prediction equations for direct genomic values for 16 routinely recorded traits of American Angus beef cattle and quantify corresponding accuracies of prediction.MethodsDeregressed estimated breeding values were used as observations in a weighted analysis to derive direct genomic values for 3570 sires genotyped using the Illumina BovineSNP50 BeadChip. These bulls were clustered into five groups using K-means clustering on pedigree estimates of additive genetic relationships between animals, with the aim of increasing within-group and decreasing between-group relationships. All five combinations of four groups were used for model training, with cross-validation performed in the group not used in training. Bivariate animal models were used for each trait to estimate the genetic correlation between deregressed estimated breeding values and direct genomic values.ResultsAccuracies of direct genomic values ranged from 0.22 to 0.69 for the studied traits, with an average of 0.44. Predictions were more accurate when animals within the validation group were more closely related to animals in the training set. When training and validation sets were formed by random allocation, the accuracies of direct genomic values ranged from 0.38 to 0.85, with an average of 0.65, reflecting the greater relationship between animals in training and validation. The accuracies of direct genomic values obtained from training on older animals and validating in younger animals were intermediate to the accuracies obtained from K-means clustering and random clustering for most traits. The genetic correlation between deregressed estimated breeding values and direct genomic values ranged from 0.15 to 0.80 for the traits studied.ConclusionsThese results suggest that genomic estimates of genetic merit can be produced in beef cattle at a young age but the recurrent inclusion of genotyped sires in retraining analyses will be necessary to routinely produce for the industry the direct genomic values with the highest accuracy.

Technical note: Derivation of equivalent computing algorithms for genomic predictions and reliabilities of animal merit.

Conventional prediction of dairy cattle merit involves setting up and solving linear equations with the number of unknowns being the number of animals, typically millions, multiplied by the number of traits being simultaneously assessed. The coefficient matrix has been large and sparse and iteration on data has been the method of choice, whereby the coefficient matrix is not stored but recreated as needed. In contrast, genomic prediction involves assessment of the merit of genome fragments characterized by single nucleotide polymorphism genotypes, currently some 50,000, which can then be used to predict the merit of individual animals according to the fragments they have inherited. The prediction equations for chromosome fragments typically have fewer than 100,000 unknowns, but the number of observations used to predict the fragment effects can be one-tenth the number of fragments. The coefficient matrix tends to be dense and the resulting system of equations can be ill behaved. Equivalent computing algorithms for genomic prediction were derived. The number of unknowns in the equivalent system grows with number of genotyped animals, usually bulls, rather than the number of chromosome fragment effects. In circumstances with fewer genotyped animals than single nucleotide polymorphism genotypes, these equivalent computations allow the solving of a smaller system of equations that behaves numerically better. There were 3 solving strategies compared: 1 method that formed and stored the coefficient matrix in memory and 2 methods that iterate on data. Finally, formulas for reliabilities of genomic predictions of merit were developed.

Evidence for a major QTL associated with host response to Porcine Reproductive and Respiratory Syndrome Virus challenge

Porcine reproductive and respiratory syndrome (PRRS) causes decreased reproductive performance in breeding animals and increased respiratory problems in growing animals, which result in significant economic losses in the swine industry. Vaccination has generally not been effective in the prevention of PRRS, partially because of the rapid mutation rate and evolution of the virus. The objective of the current study was to discover the genetic basis of host resistance or susceptibility to the PRRS virus through a genome-wide association study using data from the PRRS Host Genetics Consortium PRRS-CAP project. Three groups of approximately 190 commercial crossbred pigs from 1 breeding company were infected with PRRS virus between 18 and 28 d of age. Blood samples and BW were collected up to 42 d post infection (DPI). Pigs were genotyped with the Illumina Porcine 60k Beadchip. Whole-genome analysis focused on viremia at each day blood was collected and BW gains from 0 to 21 DPI (WG21) or 42 DPI (WG42). Viral load (VL) was quantified as area under the curve from 0 to 21 DPI. Heritabilities for WG42 and VL were moderate at 0.30 and litter accounted for an additional 14% of phenotypic variation. Genomic regions associated with VL were found on chromosomes 4 and X and on 1, 4, 7, and 17 for WG42. The 1-Mb region identified on chromosome 4 influenced both WG and VL, exhibited strong linkage disequilibrium, and explained 15.7% of the genetic variance for VL and 11.2% for WG42. Despite a genetic correlation of -0.46 between VL and WG42, genomic EBV for this region were favorably and nearly perfectly correlated. The favorable allele for the most significant SNP in this region had a frequency of 0.16 and estimated allele substitution effects were significant (P < 0.01) for each group when the SNP was fitted as a fixed covariate in a model that included random polygenic effects with overall estimates of -4.1 units for VL (phenotypic SD = 6.9) and 2.0 kg (phenotypic SD = 3 kg) for WG42. Candidate genes in this region on SSC4 include the interferon induced guanylate-binding protein gene family. In conclusion, host response to experimental PRRS virus challenge has a strong genetic component, and a QTL on chromosome 4 explains a substantial proportion of the genetic variance in the studied population. These results could have a major impact in the swine industry by enabling marker-assisted selection to reduce the impact of PRRS but need to be validated in additional populations.

A whole-genome association study for pig reproductive traits

A whole-genome association study was performed for reproductive traits in commercial sows using the PorcineSNP60 BeadChip and Bayesian statistical methods. The traits included total number born (TNB), number born alive (NBA), number of stillborn (SB), number of mummified foetuses at birth (MUM) and gestation length (GL) in each of the first three parities. We report the associations of informative QTL and the genes within the QTL for each reproductive trait in different parities. These results provide evidence of gene effects having temporal impacts on reproductive traits in different parities. Many QTL identified in this study are new for pig reproductive traits. Around 48% of total genes located in the identified QTL regions were predicted to be involved in placental functions. The genomic regions containing genes important for foetal developmental (e.g. MEF2C) and uterine functions (e.g. PLSCR4) were associated with TNB and NBA in the first two parities. Similarly, QTL in other foetal developmental (e.g. HNRNPD and AHR) and placental (e.g. RELL1 and CD96) genes were associated with SB and MUM in different parities. The QTL with genes related to utero-placental blood flow (e.g. VEGFA) and hematopoiesis (e.g. MAFB) were associated with GL differences among sows in this population. Pathway analyses using genes within QTL identified some modest underlying biological pathways, which are interesting candidates (e.g. the nucleotide metabolism pathway for SB) for pig reproductive traits in different parities. Further validation studies on large populations are warranted to improve our understanding of the complex genetic architecture for pig reproductive traits.