The effect of using genealogy-based haplotypes for genomic prediction

Background

Genomic prediction uses two sources of information: linkage disequilibrium between markers and quantitative trait loci, and additive genetic relationships between individuals. One way to increase the accuracy of genomic prediction is to capture more linkage disequilibrium by regression on haplotypes instead of regression on individual markers. The aim of this study was to investigate the accuracy of genomic prediction using haplotypes based on local genealogy information.

Methods

A total of 4429 Danish Holstein bulls were genotyped with the 50K SNP chip. Haplotypes were constructed using local genealogical trees. Effects of haplotype covariates were estimated with two types of prediction models: (1) assuming that effects had the same distribution for all haplotype covariates, i.e. the GBLUP method and (2) assuming that a large proportion (π) of the haplotype covariates had zero effect, i.e. a Bayesian mixture method.

Results

About 7.5 times more covariate effects were estimated when fitting haplotypes based on local genealogical trees compared to fitting individuals markers. Genealogy-based haplotype clustering slightly increased the accuracy of genomic prediction and, in some cases, decreased the bias of prediction. With the Bayesian method, accuracy of prediction was less sensitive to parameter π when fitting haplotypes compared to fitting markers.

Conclusions

Use of haplotypes based on genealogy can slightly increase the accuracy of genomic prediction. Improved methods to cluster the haplotypes constructed from local genealogy could lead to additional gains in accuracy.     

A computationally efficient algorithm for genomic prediction using a Bayesian model

Background

Genomic prediction of breeding values from dense single nucleotide polymorphisms (SNP) genotypes is used for livestock and crop breeding, and can also be used to predict disease risk in humans. For some traits, the most accurate genomic predictions are achieved with non-linear estimates of SNP effects from Bayesian methods that treat SNP effects as random effects from a heavy tailed prior distribution. These Bayesian methods are usually implemented via Markov chain Monte Carlo (MCMC) schemes to sample from the posterior distribution of SNP effects, which is computationally expensive. Our aim was to develop an efficient expectation–maximisation algorithm (emBayesR) that gives similar estimates of SNP effects and accuracies of genomic prediction than the MCMC implementation of BayesR (a Bayesian method for genomic prediction), but with greatly reduced computation time.

Methods

emBayesR is an approximate EM algorithm that retains the BayesR model assumption with SNP effects sampled from a mixture of normal distributions with increasing variance. emBayesR differs from other proposed non-MCMC implementations of Bayesian methods for genomic prediction in that it estimates the effect of each SNP while allowing for the error associated with estimation of all other SNP effects. emBayesR was compared to BayesR using simulated data, and real dairy cattle data with 632 003 SNPs genotyped, to determine if the MCMC and the expectation-maximisation approaches give similar accuracies of genomic prediction.

Results

We were able to demonstrate that allowing for the error associated with estimation of other SNP effects when estimating the effect of each SNP in emBayesR improved the accuracy of genomic prediction over emBayesR without including this error correction, with both simulated and real data. When averaged over nine dairy traits, the accuracy of genomic prediction with emBayesR was only 0.5% lower than that from BayesR. However, emBayesR reduced computing time up to 8-fold compared to BayesR.

Conclusions

The emBayesR algorithm described here achieved similar accuracies of genomic prediction to BayesR for a range of simulated and real 630 K dairy SNP data. emBayesR needs less computing time than BayesR, which will allow it to be applied to larger datasets.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0082-4) contains supplementary material, which is available to authorized users.     

Comparison of Bayesian models to estimate direct genomic values in multi-breed commercial beef cattle

Background

While several studies have examined the accuracy of direct genomic breeding values (DGV) within and across purebred cattle populations, the accuracy of DGV in crossbred or multi-breed cattle populations has been less well examined. Interest in the use of genomic tools for both selection and management has increased within the hybrid seedstock and commercial cattle sectors and research is needed to determine their efficacy. We predicted DGV for six traits using training populations of various sizes and alternative Bayesian models for a population of 3240 crossbred animals. Our objective was to compare alternate models with different assumptions regarding the distributions of single nucleotide polymorphism (SNP) effects to determine the optimal model for enhancing feasibility of multi-breed DGV prediction for the commercial beef industry.

Results

Realized accuracies ranged from 0.40 to 0.78. Randomly assigning 60 to 70% of animals to training (n ≈ 2000 records) yielded DGV accuracies with the smallest coefficients of variation. Mixture models (BayesB95, BayesCπ) and models that allow SNP effects to be sampled from distributions with unequal variances (BayesA, BayesB95) were advantageous for traits that appear or are known to be influenced by large-effect genes. For other traits, models differed little in prediction accuracy (~0.3 to 0.6%), suggesting that they are mainly controlled by small-effect loci.

Conclusions

The proportion (60 to 70%) of data allocated to training that optimized DGV accuracy and minimized the coefficient of variation of accuracy was similar to large dairy populations. Larger effects were estimated for some SNPs using BayesA and BayesB95 models because they allow unequal SNP variances. This substantially increased DGV accuracy for Warner-Bratzler Shear Force, for which large-effect quantitative trait loci (QTL) are known, while no loss in accuracy was observed for traits that appear to follow the infinitesimal model. Large decreases in accuracy (up to 0.07) occurred when SNPs that presumably tag large-effect QTL were over-regressed towards the mean in BayesC0 analyses. The DGV accuracies achieved here indicate that genomic selection has predictive utility in the commercial beef industry and that using models that reflect the genomic architecture of the trait can have predictive advantages in multi-breed populations.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0106-8) contains supplementary material, which is available to authorized users.     

Predicting Rotator Cuff Tears Using Data Mining and Bayesian Likelihood Ratios

Objectives

Rotator cuff tear is a common cause of shoulder diseases. Correct diagnosis of rotator cuff tears can save patients from further invasive, costly and painful tests. This study used predictive data mining and Bayesian theory to improve the accuracy of diagnosing rotator cuff tears by clinical examination alone.

Methods

In this retrospective study, 169 patients who had a preliminary diagnosis of rotator cuff tear on the basis of clinical evaluation followed by confirmatory MRI between 2007 and 2011 were identified. MRI was used as a reference standard to classify rotator cuff tears. The predictor variable was the clinical assessment results, which consisted of 16 attributes. This study employed 2 data mining methods (ANN and the decision tree) and a statistical method (logistic regression) to classify the rotator cuff diagnosis into “tear” and “no tear” groups. Likelihood ratio and Bayesian theory were applied to estimate the probability of rotator cuff tears based on the results of the prediction models.

Results

Our proposed data mining procedures outperformed the classic statistical method. The correction rate, sensitivity, specificity and area under the ROC curve of predicting a rotator cuff tear were statistical better in the ANN and decision tree models compared to logistic regression. Based on likelihood ratios derived from our prediction models, Fagan''s nomogram could be constructed to assess the probability of a patient who has a rotator cuff tear using a pretest probability and a prediction result (tear or no tear).

Conclusions

Our predictive data mining models, combined with likelihood ratios and Bayesian theory, appear to be good tools to classify rotator cuff tears as well as determine the probability of the presence of the disease to enhance diagnostic decision making for rotator cuff tears.     

Multiple-Trait Genomic Selection Methods Increase Genetic Value Prediction Accuracy

Genetic correlations between quantitative traits measured in many breeding programs are pervasive. These correlations indicate that measurements of one trait carry information on other traits. Current single-trait (univariate) genomic selection does not take advantage of this information. Multivariate genomic selection on multiple traits could accomplish this but has been little explored and tested in practical breeding programs. In this study, three multivariate linear models (i.e., GBLUP, BayesA, and BayesCπ) were presented and compared to univariate models using simulated and real quantitative traits controlled by different genetic architectures. We also extended BayesA with fixed hyperparameters to a full hierarchical model that estimated hyperparameters and BayesCπ to impute missing phenotypes. We found that optimal marker-effect variance priors depended on the genetic architecture of the trait so that estimating them was beneficial. We showed that the prediction accuracy for a low-heritability trait could be significantly increased by multivariate genomic selection when a correlated high-heritability trait was available. Further, multiple-trait genomic selection had higher prediction accuracy than single-trait genomic selection when phenotypes are not available on all individuals and traits. Additional factors affecting the performance of multiple-trait genomic selection were explored.     

Genomic relationships based on X chromosome markers and accuracy of genomic predictions with and without X chromosome markers

Background

Although the X chromosome is the second largest bovine chromosome, markers on the X chromosome are not used for genomic prediction in some countries and populations. In this study, we presented a method for computing genomic relationships using X chromosome markers, investigated the accuracy of imputation from a low density (7K) to the 54K SNP (single nucleotide polymorphism) panel, and compared the accuracy of genomic prediction with and without using X chromosome markers.

Methods

The impact of considering X chromosome markers on prediction accuracy was assessed using data from Nordic Holstein bulls and different sets of SNPs: (a) the 54K SNPs for reference and test animals, (b) SNPs imputed from the 7K to the 54K SNP panel for test animals, (c) SNPs imputed from the 7K to the 54K panel for half of the reference animals, and (d) the 7K SNP panel for all animals. Beagle and Findhap were used for imputation. GBLUP (genomic best linear unbiased prediction) models with or without X chromosome markers and with or without a residual polygenic effect were used to predict genomic breeding values for 15 traits.

Results

Averaged over the two imputation datasets, correlation coefficients between imputed and true genotypes for autosomal markers, pseudo-autosomal markers, and X-specific markers were 0.971, 0.831 and 0.935 when using Findhap, and 0.983, 0.856 and 0.937 when using Beagle. Estimated reliabilities of genomic predictions based on the imputed datasets using Findhap or Beagle were very close to those using the real 54K data. Genomic prediction using all markers gave slightly higher reliabilities than predictions without X chromosome markers. Based on our data which included only bulls, using a G matrix that accounted for sex-linked relationships did not improve prediction, compared with a G matrix that did not account for sex-linked relationships. A model that included a polygenic effect did not recover the loss of prediction accuracy from exclusion of X chromosome markers.

Conclusions

The results from this study suggest that markers on the X chromosome contribute to accuracy of genomic predictions and should be used for routine genomic evaluation.     

The importance of identity-by-state information for the accuracy of genomic selection

Background

It is commonly assumed that prediction of genome-wide breeding values in genomic selection is achieved by capitalizing on linkage disequilibrium between markers and QTL but also on genetic relationships. Here, we investigated the reliability of predicting genome-wide breeding values based on population-wide linkage disequilibrium information, based on identity-by-descent relationships within the known pedigree, and to what extent linkage disequilibrium information improves predictions based on identity-by-descent genomic relationship information.

Methods

The study was performed on milk, fat, and protein yield, using genotype data on 35 706 SNP and deregressed proofs of 1086 Italian Brown Swiss bulls. Genome-wide breeding values were predicted using a genomic identity-by-state relationship matrix and a genomic identity-by-descent relationship matrix (averaged over all marker loci). The identity-by-descent matrix was calculated by linkage analysis using one to five generations of pedigree data.

Results

We showed that genome-wide breeding values prediction based only on identity-by-descent genomic relationships within the known pedigree was as or more reliable than that based on identity-by-state, which implicitly also accounts for genomic relationships that occurred before the known pedigree. Furthermore, combining the two matrices did not improve the prediction compared to using identity-by-descent alone. Including different numbers of generations in the pedigree showed that most of the information in genome-wide breeding values prediction comes from animals with known common ancestors less than four generations back in the pedigree.

Conclusions

Our results show that, in pedigreed breeding populations, the accuracy of genome-wide breeding values obtained by identity-by-descent relationships was not improved by identity-by-state information. Although, in principle, genomic selection based on identity-by-state does not require pedigree data, it does use the available pedigree structure. Our findings may explain why the prediction equations derived for one breed may not predict accurate genome-wide breeding values when applied to other breeds, since family structures differ among breeds.     

Genomic prediction based on data from three layer lines: a comparison between linear methods

Background

The prediction accuracy of several linear genomic prediction models, which have previously been used for within-line genomic prediction, was evaluated for multi-line genomic prediction.

Methods

Compared to a conventional BLUP (best linear unbiased prediction) model using pedigree data, we evaluated the following genomic prediction models: genome-enabled BLUP (GBLUP), ridge regression BLUP (RRBLUP), principal component analysis followed by ridge regression (RRPCA), BayesC and Bayesian stochastic search variable selection. Prediction accuracy was measured as the correlation between predicted breeding values and observed phenotypes divided by the square root of the heritability. The data used concerned laying hens with phenotypes for number of eggs in the first production period and known genotypes. The hens were from two closely-related brown layer lines (B1 and B2), and a third distantly-related white layer line (W1). Lines had 1004 to 1023 training animals and 238 to 240 validation animals. Training datasets consisted of animals of either single lines, or a combination of two or all three lines, and had 30 508 to 45 974 segregating single nucleotide polymorphisms.

Results

Genomic prediction models yielded 0.13 to 0.16 higher accuracies than pedigree-based BLUP. When excluding the line itself from the training dataset, genomic predictions were generally inaccurate. Use of multiple lines marginally improved prediction accuracy for B2 but did not affect or slightly decreased prediction accuracy for B1 and W1. Differences between models were generally small except for RRPCA which gave considerably higher accuracies for B2. Correlations between genomic predictions from different methods were higher than 0.96 for W1 and higher than 0.88 for B1 and B2. The greater differences between methods for B1 and B2 were probably due to the lower accuracy of predictions for B1 (~0.45) and B2 (~0.40) compared to W1 (~0.76).

Conclusions

Multi-line genomic prediction did not affect or slightly improved prediction accuracy for closely-related lines. For distantly-related lines, multi-line genomic prediction yielded similar or slightly lower accuracies than single-line genomic prediction. Bayesian variable selection and GBLUP generally gave similar accuracies. Overall, RRPCA yielded the greatest accuracies for two lines, suggesting that using PCA helps to alleviate the “n ≪ p” problem in genomic prediction.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0057-5) contains supplementary material, which is available to authorized users.     

Genomic analysis of dominance effects on milk production and conformation traits in Fleckvieh cattle

Background

Estimates of dominance variance in dairy cattle based on pedigree data vary considerably across traits and amount to up to 50% of the total genetic variance for conformation traits and up to 43% for milk production traits. Using bovine SNP (single nucleotide polymorphism) genotypes, dominance variance can be estimated both at the marker level and at the animal level using genomic dominance effect relationship matrices. Yield deviations of high-density genotyped Fleckvieh cows were used to assess cross-validation accuracy of genomic predictions with additive and dominance models. The potential use of dominance variance in planned matings was also investigated.

Results

Variance components of nine milk production and conformation traits were estimated with additive and dominance models using yield deviations of 1996 Fleckvieh cows and ranged from 3.3% to 50.5% of the total genetic variance. REML and Gibbs sampling estimates showed good concordance. Although standard errors of estimates of dominance variance were rather large, estimates of dominance variance for milk, fat and protein yields, somatic cell score and milkability were significantly different from 0. Cross-validation accuracy of predicted breeding values was higher with genomic models than with the pedigree model. Inclusion of dominance effects did not increase the accuracy of the predicted breeding and total genetic values. Additive and dominance SNP effects for milk yield and protein yield were estimated with a BLUP (best linear unbiased prediction) model and used to calculate expectations of breeding values and total genetic values for putative offspring. Selection on total genetic value instead of breeding value would result in a larger expected total genetic superiority in progeny, i.e. 14.8% for milk yield and 27.8% for protein yield and reduce the expected additive genetic gain only by 4.5% for milk yield and 2.6% for protein yield.

Conclusions

Estimated dominance variance was substantial for most of the analyzed traits. Due to small dominance effect relationships between cows, predictions of individual dominance deviations were very inaccurate and including dominance in the model did not improve prediction accuracy in the cross-validation study. Exploitation of dominance variance in assortative matings was promising and did not appear to severely compromise additive genetic gain.     

Increased genomic prediction accuracy in wheat breeding using a large Australian panel

Key message

Genomic prediction accuracy within a large panel was found to be substantially higher than that previously observed in smaller populations, and also higher than QTL-based prediction.

Abstract

In recent years, genomic selection for wheat breeding has been widely studied, but this has typically been restricted to population sizes under 1000 individuals. To assess its efficacy in germplasm representative of commercial breeding programmes, we used a panel of 10,375 Australian wheat breeding lines to investigate the accuracy of genomic prediction for grain yield, physical grain quality and other physiological traits. To achieve this, the complete panel was phenotyped in a dedicated field trial and genotyped using a custom Axiom^TM Affymetrix SNP array. A high-quality consensus map was also constructed, allowing the linkage disequilibrium present in the germplasm to be investigated. Using the complete SNP array, genomic prediction accuracies were found to be substantially higher than those previously observed in smaller populations and also more accurate compared to prediction approaches using a finite number of selected quantitative trait loci. Multi-trait genetic correlations were also assessed at an additive and residual genetic level, identifying a negative genetic correlation between grain yield and protein as well as a positive genetic correlation between grain size and test weight.

     

Comparison of Prediction Model for Cardiovascular Autonomic Dysfunction Using Artificial Neural Network and Logistic Regression Analysis

Background

This study aimed to develop the artificial neural network (ANN) and multivariable logistic regression (LR) analyses for prediction modeling of cardiovascular autonomic (CA) dysfunction in the general population, and compare the prediction models using the two approaches.

Methods and Materials

We analyzed a previous dataset based on a Chinese population sample consisting of 2,092 individuals aged 30–80 years. The prediction models were derived from an exploratory set using ANN and LR analysis, and were tested in the validation set. Performances of these prediction models were then compared.

Results

Univariate analysis indicated that 14 risk factors showed statistically significant association with the prevalence of CA dysfunction (P<0.05). The mean area under the receiver-operating curve was 0.758 (95% CI 0.724–0.793) for LR and 0.762 (95% CI 0.732–0.793) for ANN analysis, but noninferiority result was found (P<0.001). The similar results were found in comparisons of sensitivity, specificity, and predictive values in the prediction models between the LR and ANN analyses.

Conclusion

The prediction models for CA dysfunction were developed using ANN and LR. ANN and LR are two effective tools for developing prediction models based on our dataset.     

Bayesian methods for estimating GEBVs of threshold traits

Estimation of genomic breeding values is the key step in genomic selection (GS). Many methods have been proposed for continuous traits, but methods for threshold traits are still scarce. Here we introduced threshold model to the framework of GS, and specifically, we extended the three Bayesian methods BayesA, BayesB and BayesCπ on the basis of threshold model for estimating genomic breeding values of threshold traits, and the extended methods are correspondingly termed BayesTA, BayesTB and BayesTCπ. Computing procedures of the three BayesT methods using Markov Chain Monte Carlo algorithm were derived. A simulation study was performed to investigate the benefit of the presented methods in accuracy with the genomic estimated breeding values (GEBVs) for threshold traits. Factors affecting the performance of the three BayesT methods were addressed. As expected, the three BayesT methods generally performed better than the corresponding normal Bayesian methods, in particular when the number of phenotypic categories was small. In the standard scenario (number of categories=2, incidence=30%, number of quantitative trait loci=50, h²=0.3), the accuracies were improved by 30.4%, 2.4%, and 5.7% points, respectively. In most scenarios, BayesTB and BayesTCπ generated similar accuracies and both performed better than BayesTA. In conclusion, our work proved that threshold model fits well for predicting GEBVs of threshold traits, and BayesTCπ is supposed to be the method of choice for GS of threshold traits.     

A gene frequency model for QTL mapping using Bayesian inference

Background

Information for mapping of quantitative trait loci (QTL) comes from two sources: linkage disequilibrium (non-random association of allele states) and cosegregation (non-random association of allele origin). Information from LD can be captured by modeling conditional means and variances at the QTL given marker information. Similarly, information from cosegregation can be captured by modeling conditional covariances. Here, we consider a Bayesian model based on gene frequency (BGF) where both conditional means and variances are modeled as a function of the conditional gene frequencies at the QTL. The parameters in this model include these gene frequencies, additive effect of the QTL, its location, and the residual variance. Bayesian methodology was used to estimate these parameters. The priors used were: logit-normal for gene frequencies, normal for the additive effect, uniform for location, and inverse chi-square for the residual variance. Computer simulation was used to compare the power to detect and accuracy to map QTL by this method with those from least squares analysis using a regression model (LSR).

Results

To simplify the analysis, data from unrelated individuals in a purebred population were simulated, where only LD information contributes to map the QTL. LD was simulated in a chromosomal segment of 1 cM with one QTL by random mating in a population of size 500 for 1000 generations and in a population of size 100 for 50 generations. The comparison was studied under a range of conditions, which included SNP density of 0.1, 0.05 or 0.02 cM, sample size of 500 or 1000, and phenotypic variance explained by QTL of 2 or 5%. Both 1 and 2-SNP models were considered. Power to detect the QTL for the BGF, ranged from 0.4 to 0.99, and close or equal to the power of the regression using least squares (LSR). Precision to map QTL position of BGF, quantified by the mean absolute error, ranged from 0.11 to 0.21 cM for BGF, and was better than the precision of LSR, which ranged from 0.12 to 0.25 cM.

Conclusions

In conclusion given a high SNP density, the gene frequency model can be used to map QTL with considerable accuracy even within a 1 cM region.     

Accuracy of genomic breeding values in multi-breed dairy cattle populations

Background

Two key findings from genomic selection experiments are 1) the reference population used must be very large to subsequently predict accurate genomic estimated breeding values (GEBV), and 2) prediction equations derived in one breed do not predict accurate GEBV when applied to other breeds. Both findings are a problem for breeds where the number of individuals in the reference population is limited. A multi-breed reference population is a potential solution, and here we investigate the accuracies of GEBV in Holstein dairy cattle and Jersey dairy cattle when the reference population is single breed or multi-breed. The accuracies were obtained both as a function of elements of the inverse coefficient matrix and from the realised accuracies of GEBV.

Methods

Best linear unbiased prediction with a multi-breed genomic relationship matrix (GBLUP) and two Bayesian methods (BAYESA and BAYES_SSVS) which estimate individual SNP effects were used to predict GEBV for 400 and 77 young Holstein and Jersey bulls respectively, from a reference population of 781 and 287 Holstein and Jersey bulls, respectively. Genotypes of 39,048 SNP markers were used. Phenotypes in the reference population were de-regressed breeding values for production traits. For the GBLUP method, expected accuracies calculated from the diagonal of the inverse of coefficient matrix were compared to realised accuracies.

Results

When GBLUP was used, expected accuracies from a function of elements of the inverse coefficient matrix agreed reasonably well with realised accuracies calculated from the correlation between GEBV and EBV in single breed populations, but not in multi-breed populations. When the Bayesian methods were used, realised accuracies of GEBV were up to 13% higher when the multi-breed reference population was used than when a pure breed reference was used. However no consistent increase in accuracy across traits was obtained.

Conclusion

Predicting genomic breeding values using a genomic relationship matrix is an attractive approach to implement genomic selection as expected accuracies of GEBV can be readily derived. However in multi-breed populations, Bayesian approaches give higher accuracies for some traits. Finally, multi-breed reference populations will be a valuable resource to fine map QTL.     

Prediction of haplotypes for ungenotyped animals and its effect on marker-assisted breeding value estimation

Background

In livestock populations, missing genotypes on a large proportion of animals are a major problem to implement the estimation of marker-assisted breeding values using haplotypes. The objective of this article is to develop a method to predict haplotypes of animals that are not genotyped using mixed model equations and to investigate the effect of using these predicted haplotypes on the accuracy of marker-assisted breeding value estimation.

Methods

For genotyped animals, haplotypes were determined and for each animal the number of haplotype copies (nhc) was counted, i.e. 0, 1 or 2 copies. In a mixed model framework, nhc for each haplotype were predicted for ungenotyped animals as well as for genotyped animals using the additive genetic relationship matrix. The heritability of nhc was assumed to be 0.99, allowing for minor genotyping and haplotyping errors. The predicted nhc were subsequently used in marker-assisted breeding value estimation by applying random regression on these covariables. To evaluate the method, a population was simulated with one additive QTL and an additive polygenic genetic effect. The QTL was located in the middle of a haplotype based on SNP-markers.

Results

The accuracy of predicted haplotype copies for ungenotyped animals ranged between 0.59 and 0.64 depending on haplotype length. Because powerful BLUP-software was used, the method was computationally very efficient. The accuracy of total EBV increased for genotyped animals when marker-assisted breeding value estimation was compared with conventional breeding value estimation, but for ungenotyped animals the increase was marginal unless the heritability was smaller than 0.1. Haplotypes based on four markers yielded the highest accuracies and when only the nearest left marker was used, it yielded the lowest accuracy. The accuracy increased with increasing marker density. Accuracy of the total EBV approached that of gene-assisted BLUP when 4-marker haplotypes were used with a distance of 0.1 cM between the markers.

Conclusions

The proposed method is computationally very efficient and suitable for marker-assisted breeding value estimation in large livestock populations including effects of a number of known QTL. Marker-assisted breeding value estimation using predicted haplotypes increases accuracy especially for traits with low heritability.     

Non-additive genetic variation in growth,carcass and fertility traits of beef cattle

Background

A better understanding of non-additive variance could lead to increased knowledge on the genetic control and physiology of quantitative traits, and to improved prediction of the genetic value and phenotype of individuals. Genome-wide panels of single nucleotide polymorphisms (SNPs) have been mainly used to map additive effects for quantitative traits, but they can also be used to investigate non-additive effects. We estimated dominance and epistatic effects of SNPs on various traits in beef cattle and the variance explained by dominance, and quantified the increase in accuracy of phenotype prediction by including dominance deviations in its estimation.

Methods

Genotype data (729 068 real or imputed SNPs) and phenotypes on up to 16 traits of 10 191 individuals from Bos taurus, Bos indicus and composite breeds were used. A genome-wide association study was performed by fitting the additive and dominance effects of single SNPs. The dominance variance was estimated by fitting a dominance relationship matrix constructed from the 729 068 SNPs. The accuracy of predicted phenotypic values was evaluated by best linear unbiased prediction using the additive and dominance relationship matrices. Epistatic interactions (additive × additive) were tested between each of the 28 SNPs that are known to have additive effects on multiple traits, and each of the other remaining 729 067 SNPs.

Results

The number of significant dominance effects was greater than expected by chance and most of them were in the direction that is presumed to increase fitness and in the opposite direction to inbreeding depression. Estimates of dominance variance explained by SNPs varied widely between traits, but had large standard errors. The median dominance variance across the 16 traits was equal to 5% of the phenotypic variance. Including a dominance deviation in the prediction did not significantly increase its accuracy for any of the phenotypes. The number of additive × additive epistatic effects that were statistically significant was greater than expected by chance.

Conclusions

Significant dominance and epistatic effects occur for growth, carcass and fertility traits in beef cattle but they are difficult to estimate precisely and including them in phenotype prediction does not increase its accuracy.     

Accuracy of pedigree and genomic predictions of carcass and novel meat quality traits in multi-breed sheep data assessed by cross-validation

Background

Genomic predictions can be applied early in life without impacting selection candidates. This is especially useful for meat quality traits in sheep. Carcass and novel meat quality traits were predicted in a multi-breed sheep population that included Merino, Border Leicester, Polled Dorset and White Suffolk sheep and their crosses.

Methods

Prediction of breeding values by best linear unbiased prediction (BLUP) based on pedigree information was compared to prediction based on genomic BLUP (GBLUP) and a Bayesian prediction method (BayesR). Cross-validation of predictions across sire families was used to evaluate the accuracy of predictions based on the correlation of predicted and observed values and the regression of observed on predicted values was used to evaluate bias of methods. Accuracies and regression coefficients were calculated using either phenotypes or adjusted phenotypes as observed variables.

Results and conclusions

Genomic methods increased the accuracy of predicted breeding values to on average 0.2 across traits (range 0.07 to 0.31), compared to an average accuracy of 0.09 for pedigree-based BLUP. However, for some traits with smaller reference population size, there was no increase in accuracy or it was small. No clear differences in accuracy were observed between GBLUP and BayesR. The regression of phenotypes on breeding values was close to 1 for all methods, indicating little bias, except for GBLUP and adjusted phenotypes (regression = 0.78). Accuracies calculated with adjusted (for fixed effects) phenotypes were less variable than accuracies based on unadjusted phenotypes, indicating that fixed effects influence the latter. Increasing the reference population size increased accuracy, indicating that adding more records will be beneficial. For the Merino, Polled Dorset and White Suffolk breeds, accuracies were greater than for the Border Leicester breed due to the smaller sample size and limited across-breed prediction. BayesR detected only a few large marker effects but one region on chromosome 6 was associated with large effects for several traits. Cross-validation produced very similar variability of accuracy and regression coefficients for BLUP, GBLUP and BayesR, showing that this variability is not a property of genomic methods alone. Our results show that genomic selection for novel difficult-to-measure traits is a feasible strategy to achieve increased genetic gain.     

Different models of genetic variation and their effect on genomic evaluation

Background

The theory of genomic selection is based on the prediction of the effects of quantitative trait loci (QTL) in linkage disequilibrium (LD) with markers. However, there is increasing evidence that genomic selection also relies on "relationships" between individuals to accurately predict genetic values. Therefore, a better understanding of what genomic selection actually predicts is relevant so that appropriate methods of analysis are used in genomic evaluations.

Methods

Simulation was used to compare the performance of estimates of breeding values based on pedigree relationships (Best Linear Unbiased Prediction, BLUP), genomic relationships (gBLUP), and based on a Bayesian variable selection model (Bayes B) to estimate breeding values under a range of different underlying models of genetic variation. The effects of different marker densities and varying animal relationships were also examined.

Results

This study shows that genomic selection methods can predict a proportion of the additive genetic value when genetic variation is controlled by common quantitative trait loci (QTL model), rare loci (rare variant model), all loci (infinitesimal model) and a random association (a polygenic model). The Bayes B method was able to estimate breeding values more accurately than gBLUP under the QTL and rare variant models, for the alternative marker densities and reference populations. The Bayes B and gBLUP methods had similar accuracies under the infinitesimal model.

Conclusions

Our results suggest that Bayes B is superior to gBLUP to estimate breeding values from genomic data. The underlying model of genetic variation greatly affects the predictive ability of genomic selection methods, and the superiority of Bayes B over gBLUP is highly dependent on the presence of large QTL effects. The use of SNP sequence data will outperform the less dense marker panels. However, the size and distribution of QTL effects and the size of reference populations still greatly influence the effectiveness of using sequence data for genomic prediction.     

GVCBLUP: a computer package for genomic prediction and variance component estimation of additive and dominance effects

Background

Dominance effect may play an important role in genetic variation of complex traits. Full featured and easy-to-use computing tools for genomic prediction and variance component estimation of additive and dominance effects using genome-wide single nucleotide polymorphism (SNP) markers are necessary to understand dominance contribution to a complex trait and to utilize dominance for selecting individuals with favorable genetic potential.

Results

The GVCBLUP package is a shared memory parallel computing tool for genomic prediction and variance component estimation of additive and dominance effects using genome-wide SNP markers. This package currently has three main programs (GREML_CE, GREML_QM, and GCORRMX) and a graphical user interface (GUI) that integrates the three main programs with an existing program for the graphical viewing of SNP additive and dominance effects (GVCeasy). The GREML_CE and GREML_QM programs offer complementary computing advantages with identical results for genomic prediction of breeding values, dominance deviations and genotypic values, and for genomic estimation of additive and dominance variances and heritabilities using a combination of expectation-maximization (EM) algorithm and average information restricted maximum likelihood (AI-REML) algorithm. GREML_CE is designed for large numbers of SNP markers and GREML_QM for large numbers of individuals. Test results showed that GREML_CE could analyze 50,000 individuals with 400 K SNP markers and GREML_QM could analyze 100,000 individuals with 50K SNP markers. GCORRMX calculates genomic additive and dominance relationship matrices using SNP markers. GVCeasy is the GUI for GVCBLUP integrated with an existing software tool for the graphical viewing of SNP effects and a function for editing the parameter files for the three main programs.

Conclusion

The GVCBLUP package is a powerful and versatile computing tool for assessing the type and magnitude of genetic effects affecting a phenotype by estimating whole-genome additive and dominance heritabilities, for genomic prediction of breeding values, dominance deviations and genotypic values, for calculating genomic relationships, and for research and education in genomic prediction and estimation.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-270) contains supplementary material, which is available to authorized users.     

Genomic selection using low density marker panels with application to a sire line in pigs

Background

Genomic selection has become a standard tool in dairy cattle breeding. However, for other animal species, implementation of this technology is hindered by the high cost of genotyping. One way to reduce the routine costs is to genotype selection candidates with an SNP (single nucleotide polymorphism) panel of reduced density. This strategy is investigated in the present paper. Methods are proposed for the approximation of SNP positions, for selection of SNPs to be included in the low-density panel, for genotype imputation, and for the estimation of the accuracy of genomic breeding values. The imputation method was developed for a situation in which selection candidates are genotyped with an SNP panel of reduced density but have high-density genotyped sires. The dams of selection candidates are not genotyped. The methods were applied to a sire line pig population with 895 German Piétrain boars genotyped with the PorcineSNP60 BeadChip.

Results

Genotype imputation error rates were 0.133 for a 384 marker panel, 0.079 for a 768 marker panel, and 0.022 for a 3000 marker panel. Error rates for markers with approximated positions were slightly larger. Availability of high-density genotypes for close relatives of the selection candidates reduced the imputation error rate. The estimated decrease in the accuracy of genomic breeding values due to imputation errors was 3% for the 384 marker panel and negligible for larger panels, provided that at least one parent of the selection candidates was genotyped at high-density.Genomic breeding values predicted from deregressed breeding values with low reliabilities were more strongly correlated with the estimated BLUP breeding values than with the true breeding values. This was not the case when a shortened pedigree was used to predict BLUP breeding values, in which the parents of the individuals genotyped at high-density were considered unknown.

Conclusions

Genomic selection with imputation from very low- to high-density marker panels is a promising strategy for the implementation of genomic selection at acceptable costs. A panel size of 384 markers can be recommended for selection candidates of a pig breeding program if at least one parent is genotyped at high-density, but this appears to be the lower bound.