Impacts of both reference population size and inclusion of a residual polygenic effect on the accuracy of genomic prediction

Background

The purpose of this work was to study the impact of both the size of genomic reference populations and the inclusion of a residual polygenic effect on dairy cattle genetic evaluations enhanced with genomic information.

Methods

Direct genomic values were estimated for German Holstein cattle with a genomic BLUP model including a residual polygenic effect. A total of 17,429 genotyped Holstein bulls were evaluated using the phenotypes of 44 traits. The Interbull genomic validation test was implemented to investigate how the inclusion of a residual polygenic effect impacted genomic estimated breeding values.

Results

As the number of reference bulls increased, both the variance of the estimates of single nucleotide polymorphism effects and the reliability of the direct genomic values of selection candidates increased. Fitting a residual polygenic effect in the model resulted in less biased genome-enhanced breeding values and decreased the correlation between direct genomic values and estimated breeding values of sires in the reference population.

Conclusions

Genetic evaluation of dairy cattle enhanced with genomic information is highly effective in increasing reliability, as well as using large genomic reference populations. We found that fitting a residual polygenic effect reduced the bias in genome-enhanced breeding values, decreased the correlation between direct genomic values and sire''s estimated breeding values and made genome-enhanced breeding values more consistent in mean and variance as is the case for pedigree-based estimated breeding values.     

Estimation of (co)variances for genomic regions of flexible sizes: application to complex infectious udder diseases in dairy cattle

Background

Multi-trait genomic models in a Bayesian context can be used to estimate genomic (co)variances, either for a complete genome or for genomic regions (e.g. per chromosome) for the purpose of multi-trait genomic selection or to gain further insight into the genomic architecture of related traits such as mammary disease traits in dairy cattle.

Methods

Data on progeny means of six traits related to mastitis resistance in dairy cattle (general mastitis resistance and five pathogen-specific mastitis resistance traits) were analyzed using a bivariate Bayesian SNP-based genomic model with a common prior distribution for the marker allele substitution effects and estimation of the hyperparameters in this prior distribution from the progeny means data. From the Markov chain Monte Carlo samples of the allele substitution effects, genomic (co)variances were calculated on a whole-genome level, per chromosome, and in regions of 100 SNP on a chromosome.

Results

Genomic proportions of the total variance differed between traits. Genomic correlations were lower than pedigree-based genetic correlations and they were highest between general mastitis and pathogen-specific traits because of the part-whole relationship between these traits. The chromosome-wise genomic proportions of the total variance differed between traits, with some chromosomes explaining higher or lower values than expected in relation to chromosome size. Few chromosomes showed pleiotropic effects and only chromosome 19 had a clear effect on all traits, indicating the presence of QTL with a general effect on mastitis resistance. The region-wise patterns of genomic variances differed between traits. Peaks indicating QTL were identified but were not very distinctive because a common prior for the marker effects was used. There was a clear difference in the region-wise patterns of genomic correlation among combinations of traits, with distinctive peaks indicating the presence of pleiotropic QTL.

Conclusions

The results show that it is possible to estimate, genome-wide and region-wise genomic (co)variances of mastitis resistance traits in dairy cattle using multivariate genomic models.     

A low-marker density implementation of genomic selection in aquaculture using within-family genomic breeding values

Background

Genomic selection can increase genetic gain within aquaculture breeding programs, but the high costs related to high-density genotyping of a large number of individuals would make the breeding program expensive. In this study, a low-cost method using low-density genotyping of pre-selected candidates and their sibs was evaluated by stochastic simulation.

Methods

A breeding scheme with selection for two traits, one measured on candidates and one on sibs was simulated. Genomic breeding values were estimated within families and combined with conventional family breeding values for candidates that were pre-selected based on conventional BLUP breeding values. This strategy was compared with a conventional breeding scheme and a full genomic selection program for which genomic breeding values were estimated across the whole population. The effects of marker density, level of pre-selection and number of sibs tested and genotyped for the sib-trait were studied.

Results

Within-family genomic breeding values increased genetic gain by 15% and reduced rate of inbreeding by 15%. Genetic gain was robust to a reduction in marker density, with only moderate reductions, even for very low densities. Pre-selection of candidates down to approximately 10% of the candidates before genotyping also had minor effects on genetic gain, but depended somewhat on marker density. The number of test-individuals, i.e. individuals tested for the sib-trait, affected genetic gain, but the fraction of the test-individuals genotyped only affected the relative contribution of each trait to genetic gain.

Conclusions

A combination of genomic within-family breeding values, based on low-density genotyping, and conventional BLUP family breeding values was shown to be a possible low marker density implementation of genomic selection for species with large full-sib families for which the costs of genotyping must be kept low without compromising the effect of genomic selection on 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.     

Genomic selection requires genomic control of inbreeding

Background

In the past, pedigree relationships were used to control and monitor inbreeding because genomic relationships among selection candidates were not available until recently. The aim of this study was to understand the consequences for genetic variability across the genome when genomic information is used to estimate breeding values and in managing the inbreeding generated in the course of selection on genome-enhanced estimated breeding values.

Methods

These consequences were measured by genetic gain, pedigree- and genome-based rates of inbreeding, and local inbreeding across the genome. Breeding schemes were compared by simulating truncation selection or optimum contribution selection with a restriction on pedigree- or genome-based inbreeding, and with selection using estimated breeding values based on genome- or pedigree-based BLUP. Trait information was recorded on full-sibs of the candidates.

Results

When the information used to estimate breeding values and to constrain rates of inbreeding were either both pedigree-based or both genome-based, rates of genomic inbreeding were close to the desired values and the identical-by-descent profiles were reasonably uniform across the genome. However, with a pedigree-based inbreeding constraint and genome-based estimated breeding values, genomic rates of inbreeding were much higher than expected. With pedigree-instead of genome-based estimated breeding values, the impact of the largest QTL on the breeding values was much smaller, resulting in a more uniform genome-wide identical-by-descent profile but genomic rates of inbreeding were still higher than expected based on pedigree relationships, because they measure the inbreeding at a neutral locus not linked to any QTL. Neutral loci did not exist here, where there were 100 QTL on each chromosome. With a pedigree-based inbreeding constraint and genome-based estimated breeding values, genomic rates of inbreeding substantially exceeded the value of its constraint. In contrast, with a genome-based inbreeding constraint and genome-based estimated breeding values, marker frequencies changed, but this change was limited by the inbreeding constraint at the marker position.

Conclusions

To control inbreeding, it is necessary to account for it on the same basis as what is used to estimate breeding values, i.e. pedigree-based inbreeding control with traditional pedigree-based BLUP estimated breeding values and genome-based inbreeding control with genome-based estimated breeding values.     

Deregressing estimated breeding values and weighting information for genomic regression analyses

Background

Genomic 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.

Methods

A 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.

Results

An 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.

Conclusions

Phenotypic information on some individuals and deregressed data on others can be combined in genomic analyses using appropriate weighting.     

Long-term response to genomic selection: effects of estimation method and reference population structure for different genetic architectures

Background

Genomic selection has become an important tool in the genetic improvement of animals and plants. The objective of this study was to investigate the impacts of breeding value estimation method, reference population structure, and trait genetic architecture, on long-term response to genomic selection without updating marker effects.

Methods

Three methods were used to estimate genomic breeding values: a BLUP method with relationships estimated from genome-wide markers (GBLUP), a Bayesian method, and a partial least squares regression method (PLSR). A shallow (individuals from one generation) or deep reference population (individuals from five generations) was used with each method. The effects of the different selection approaches were compared under four different genetic architectures for the trait under selection. Selection was based on one of the three genomic breeding values, on pedigree BLUP breeding values, or performed at random. Selection continued for ten generations.

Results

Differences in long-term selection response were small. For a genetic architecture with a very small number of three to four quantitative trait loci (QTL), the Bayesian method achieved a response that was 0.05 to 0.1 genetic standard deviation higher than other methods in generation 10. For genetic architectures with approximately 30 to 300 QTL, PLSR (shallow reference) or GBLUP (deep reference) had an average advantage of 0.2 genetic standard deviation over the Bayesian method in generation 10. GBLUP resulted in 0.6% and 0.9% less inbreeding than PLSR and BM and on average a one third smaller reduction of genetic variance. Responses in early generations were greater with the shallow reference population while long-term response was not affected by reference population structure.

Conclusions

The ranking of estimation methods was different with than without selection. Under selection, applying GBLUP led to lower inbreeding and a smaller reduction of genetic variance while a similar response to selection was achieved. The reference population structure had a limited effect on long-term accuracy and response. Use of a shallow reference population, most closely related to the selection candidates, gave early benefits while in later generations, when marker effects were not updated, the estimation of marker effects based on a deeper reference population did not pay off.     

The effect of genomic information on optimal contribution selection in livestock breeding programs

Background

Long-term benefits in animal breeding programs require that increases in genetic merit be balanced with the need to maintain diversity (lost due to inbreeding). This can be achieved by using optimal contribution selection. The availability of high-density DNA marker information enables the incorporation of genomic data into optimal contribution selection but this raises the question about how this information affects the balance between genetic merit and diversity.

Methods

The effect of using genomic information in optimal contribution selection was examined based on simulated and real data on dairy bulls. We compared the genetic merit of selected animals at various levels of co-ancestry restrictions when using estimated breeding values based on parent average, genomic or progeny test information. Furthermore, we estimated the proportion of variation in estimated breeding values that is due to within-family differences.

Results

Optimal selection on genomic estimated breeding values increased genetic gain. Genetic merit was further increased using genomic rather than pedigree-based measures of co-ancestry under an inbreeding restriction policy. Using genomic instead of pedigree relationships to restrict inbreeding had a significant effect only when the population consisted of many large full-sib families; with a half-sib family structure, no difference was observed. In real data from dairy bulls, optimal contribution selection based on genomic estimated breeding values allowed for additional improvements in genetic merit at low to moderate inbreeding levels. Genomic estimated breeding values were more accurate and showed more within-family variation than parent average breeding values; for genomic estimated breeding values, 30 to 40% of the variation was due to within-family differences. Finally, there was no difference between constraining inbreeding via pedigree or genomic relationships in the real data.

Conclusions

The use of genomic estimated breeding values increased genetic gain in optimal contribution selection. Genomic estimated breeding values were more accurate and showed more within-family variation, which led to higher genetic gains for the same restriction on inbreeding. Using genomic relationships to restrict inbreeding provided no additional gain, except in the case of very large full-sib families.     

Accuracy of direct genomic breeding values for nationally evaluated traits in US Limousin and Simmental beef cattle

Background

In national evaluations, direct genomic breeding values can be considered as correlated traits to those for which phenotypes are available for traditional estimation of breeding values. For this purpose, estimates of the accuracy of direct genomic breeding values expressed as genetic correlations between traits and their respective direct genomic breeding values are required.

Methods

We derived direct genomic breeding values for 2239 registered Limousin and 2703 registered Simmental beef cattle genotyped with either the Illumina BovineSNP50 BeadChip or the Illumina BovineHD BeadChip. For the 264 Simmental animals that were genotyped with the BovineHD BeadChip, genotypes for markers present on the BovineSNP50 BeadChip were extracted. Deregressed estimated breeding values were used as observations in weighted analyses that estimated marker effects to derive direct genomic breeding values for each breed. For each breed, genotyped individuals were clustered into five groups using K-means clustering, with the aim of increasing within-group and decreasing between-group pedigree relationships. Cross-validation was performed five times for each breed, using four groups for training and the fifth group for validation. For each trait, we then applied a weighted bivariate analysis of the direct genomic breeding values of genotyped animals from all five validation sets and their corresponding deregressed estimated breeding values to estimate variance and covariance components.

Results

After minimizing relationships between training and validation groups, estimated genetic correlations between each trait and its direct genomic breeding values ranged from 0.39 to 0.76 in Limousin and from 0.29 to 0.65 in Simmental. The efficiency of selection based on direct genomic breeding values relative to selection based on parent average information ranged from 0.68 to 1.28 in genotyped Limousin and from 0.51 to 1.44 in genotyped Simmental animals. The efficiencies were higher for 323 non-genotyped young Simmental animals, born after January 2012, and ranged from 0.60 to 2.04.

Conclusions

Direct genomic breeding values show promise for routine use by Limousin and Simmental breeders to improve the accuracy of predicted genetic merit of their animals at a young age and increase response to selection. Benefits from selecting on direct genomic breeding values are greater for breeders who use natural mating sires in their herds than for those who use artificial insemination sires. Producers with unregistered commercial Limousin and Simmental cattle could also benefit from being able to identify genetically superior animals in their herds, an opportunity that has in the past been limited to seed stock animals.     

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.     

Allele coding in genomic evaluation

Background

Genomic data are used in animal breeding to assist genetic evaluation. Several models to estimate genomic breeding values have been studied. In general, two approaches have been used. One approach estimates the marker effects first and then, genomic breeding values are obtained by summing marker effects. In the second approach, genomic breeding values are estimated directly using an equivalent model with a genomic relationship matrix. Allele coding is the method chosen to assign values to the regression coefficients in the statistical model. A common allele coding is zero for the homozygous genotype of the first allele, one for the heterozygote, and two for the homozygous genotype for the other allele. Another common allele coding changes these regression coefficients by subtracting a value from each marker such that the mean of regression coefficients is zero within each marker. We call this centered allele coding. This study considered effects of different allele coding methods on inference. Both marker-based and equivalent models were considered, and restricted maximum likelihood and Bayesian methods were used in inference.

Results

Theoretical derivations showed that parameter estimates and estimated marker effects in marker-based models are the same irrespective of the allele coding, provided that the model has a fixed general mean. For the equivalent models, the same results hold, even though different allele coding methods lead to different genomic relationship matrices. Calculated genomic breeding values are independent of allele coding when the estimate of the general mean is included into the values. Reliabilities of estimated genomic breeding values calculated using elements of the inverse of the coefficient matrix depend on the allele coding because different allele coding methods imply different models. Finally, allele coding affects the mixing of Markov chain Monte Carlo algorithms, with the centered coding being the best.

Conclusions

Different allele coding methods lead to the same inference in the marker-based and equivalent models when a fixed general mean is included in the model. However, reliabilities of genomic breeding values are affected by the allele coding method used. The centered coding has some numerical advantages when Markov chain Monte Carlo methods are used.     

Accounting for trait architecture in genomic predictions of US Holstein cattle using a weighted realized relationship matrix

Background

Genomic BLUP (GBLUP) can predict breeding values for non-phenotyped individuals based on the identity-by-state genomic relationship matrix (G). The G matrix can be constructed from thousands of markers spread across the genome. The strongest assumption of G and consequently of GBLUP is that all markers contribute equally to the genetic variance of a trait. This assumption is violated for traits that are controlled by a small number of quantitative trait loci (QTL) or individual QTL with large effects. In this paper, we investigate the performance of using a weighted genomic relationship matrix (wG) that takes into consideration the genetic architecture of the trait in order to improve predictive ability for a wide range of traits. Multiple methods were used to calculate weights for several economically relevant traits in US Holstein dairy cattle. Predictive performance was tested by k-means cross-validation.

Results

Relaxing the GBLUP assumption of equal marker contribution by increasing the weight that is given to a specific marker in the construction of the trait-specific G resulted in increased predictive performance. The increase was strongest for traits that are controlled by a small number of QTL (e.g. fat and protein percentage). Furthermore, bias in prediction estimates was reduced compared to that resulting from the use of regular G. Even for traits with low heritability and lower general predictive performance (e.g. calving ease traits), weighted G still yielded a gain in accuracy.

Conclusions

Genomic relationship matrices weighted by marker realized variance yielded more accurate and less biased predictions for traits regulated by few QTL. Genome-wide association analyses were used to derive marker weights for creating weighted genomic relationship matrices. However, this can be cumbersome and prone to low stability over generations because of erosion of linkage disequilibrium between markers and QTL. Future studies may include other sources of information, such as functional annotation and gene networks, to better exploit the genetic architecture of traits and produce more stable predictions.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0100-1) contains supplementary material, which is available to authorized users.     

Dynamics of long-term genomic selection

Background

Simulation and empirical studies of genomic selection (GS) show accuracies sufficient to generate rapid gains in early selection cycles. Beyond those cycles, allele frequency changes, recombination, and inbreeding make analytical prediction of gain impossible. The impacts of GS on long-term gain should be studied prior to its implementation.

Methods

A simulation case-study of this issue was done for barley, an inbred crop. On the basis of marker data on 192 breeding lines from an elite six-row spring barley program, stochastic simulation was used to explore the effects of large or small initial training populations with heritabilities of 0.2 or 0.5, applying GS before or after phenotyping, and applying additional weight on low-frequency favorable marker alleles. Genomic predictions were from ridge regression or a Bayesian analysis.

Results

Assuming that applying GS prior to phenotyping shortened breeding cycle time by 50%, this practice strongly increased early selection gains but also caused the loss of many favorable QTL alleles, leading to loss of genetic variance, loss of GS accuracy, and a low selection plateau. Placing additional weight on low-frequency favorable marker alleles, however, allowed GS to increase their frequency earlier on, causing an initial increase in genetic variance. This dynamic led to higher long-term gain while mitigating losses in short-term gain. Weighted GS also increased the maintenance of marker polymorphism, ensuring that QTL-marker linkage disequilibrium was higher than in unweighted GS.

Conclusions

Losing favorable alleles that are in weak linkage disequilibrium with markers is perhaps inevitable when using GS. Placing additional weight on low-frequency favorable alleles, however, may reduce the rate of loss of such alleles to below that of phenotypic selection. Applying such weights at the beginning of GS implementation is important.     

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.     

Persistence of accuracy of genome-wide breeding values over generations when including a polygenic effect

Background

When estimating marker effects in genomic selection, estimates of marker effects may simply act as a proxy for pedigree, i.e. their effect may partially be attributed to their association with superior parents and not be linked to any causative QTL. Hence, these markers mainly explain polygenic effects rather than QTL effects. However, if a polygenic effect is included in a Bayesian model, it is expected that the estimated effect of these markers will be more persistent over generations without having to re-estimate the marker effects every generation and will result in increased accuracy and reduced bias.

Methods

Genomic selection using the Bayesian method, ''BayesB'' was evaluated for different marker densities when a polygenic effect is included (GWpEBV) and not included (GWEBV) in the model. Linkage disequilibrium and a mutation drift balance were obtained by simulating a population with a Ne of 100 over 1,000 generations.

Results

Accuracy of selection was slightly higher for the model including a polygenic effect than for the model not including a polygenic effect whatever the marker density. The accuracy decreased in later generations, and this reduction was stronger for lower marker densities. However, no significant difference in accuracy was observed between the two models. The linear regression of TBV on GWEBV and GWpEBV was used as a measure of bias. The regression coefficient was more stable over generations when a polygenic effect was included in the model, and was always between 0.98 and 1.00 for the highest marker density. The regression coefficient decreased more quickly with decreasing marker density.

Conclusions

Including a polygenic effect had no impact on the selection accuracy, but showed reduced bias, which is especially important when estimates of genome-wide markers are used to estimate breeding values over more than one generation.     

Genome-wide association study of insect bite hypersensitivity in two horse populations in the Netherlands

Background

Insect bite hypersensitivity is a common allergic disease in horse populations worldwide. Insect bite hypersensitivity is affected by both environmental and genetic factors. However, little is known about genes contributing to the genetic variance associated with insect bite hypersensitivity. Therefore, the aim of our study was to identify and quantify genomic associations with insect bite hypersensitivity in Shetland pony mares and Icelandic horses in the Netherlands.

Methods

Data on 200 Shetland pony mares and 146 Icelandic horses were collected according to a matched case–control design. Cases and controls were matched on various factors (e.g. region, sire) to minimize effects of population stratification. Breed-specific genome-wide association studies were performed using 70 k single nucleotide polymorphisms genotypes. Bayesian variable selection method Bayes-C with a threshold model implemented in GenSel software was applied. A 1 Mb non-overlapping window approach that accumulated contributions of adjacent single nucleotide polymorphisms was used to identify associated genomic regions.

Results

The percentage of variance explained by all single nucleotide polymorphisms was 13% in Shetland pony mares and 28% in Icelandic horses. The 20 non-overlapping windows explaining the largest percentages of genetic variance were found on nine chromosomes in Shetland pony mares and on 14 chromosomes in Icelandic horses. Overlap in identified associated genomic regions between breeds would suggest interesting candidate regions to follow-up on. Such regions common to both breeds (within 15 Mb) were found on chromosomes 3, 7, 11, 20 and 23. Positional candidate genes within 2 Mb from the associated windows were identified on chromosome 20 in both breeds. Candidate genes are within the equine lymphocyte antigen class II region, which evokes an immune response by recognizing many foreign molecules.

Conclusions

The genome-wide association study identified several genomic regions associated with insect bite hypersensitivity in Shetland pony mares and Icelandic horses. On chromosome 20, associated genomic regions in both breeds were within 2 Mb from the equine lymphocyte antigen class II region. Increased knowledge on insect bite hypersensitivity associated genes will contribute to our understanding of its biology, enabling more efficient selection, therapy and prevention to decrease insect bite hypersensitivity prevalence.     

Impact of prior specifications in ashrinkage-inducing Bayesian model for quantitative trait mapping and genomic prediction

Background

In quantitative trait mapping and genomic prediction, Bayesian variable selection methods have gained popularity in conjunction with the increase in marker data and computational resources. Whereas shrinkage-inducing methods are common tools in genomic prediction, rigorous decision making in mapping studies using such models is not well established and the robustness of posterior results is subject to misspecified assumptions because of weak biological prior evidence.

Methods

Here, we evaluate the impact of prior specifications in a shrinkage-based Bayesian variable selection method which is based on a mixture of uniform priors applied to genetic marker effects that we presented in a previous study. Unlike most other shrinkage approaches, the use of a mixture of uniform priors provides a coherent framework for inference based on Bayes factors. To evaluate the robustness of genetic association under varying prior specifications, Bayes factors are compared as signals of positive marker association, whereas genomic estimated breeding values are considered for genomic selection. The impact of specific prior specifications is reduced by calculation of combined estimates from multiple specifications. A Gibbs sampler is used to perform Markov chain Monte Carlo estimation (MCMC) and a generalized expectation-maximization algorithm as a faster alternative for maximum a posteriori point estimation. The performance of the method is evaluated by using two publicly available data examples: the simulated QTLMAS XII data set and a real data set from a population of pigs.

Results

Combined estimates of Bayes factors were very successful in identifying quantitative trait loci, and the ranking of Bayes factors was fairly stable among markers with positive signals of association under varying prior assumptions, but their magnitudes varied considerably. Genomic estimated breeding values using the mixture of uniform priors compared well to other approaches for both data sets and loss of accuracy with the generalized expectation-maximization algorithm was small as compared to that with MCMC.

Conclusions

Since no error-free method to specify priors is available for complex biological phenomena, exploring a wide variety of prior specifications and combining results provides some solution to this problem. For this purpose, the mixture of uniform priors approach is especially suitable, because it comprises a wide and flexible family of distributions and computationally intensive estimation can be carried out in a reasonable amount of time.     

Different genomic relationship matrices for single-step analysis using phenotypic,pedigree and genomic information

Background

The incorporation of genomic coefficients into the numerator relationship matrix allows estimation of breeding values using all phenotypic, pedigree and genomic information simultaneously. In such a single-step procedure, genomic and pedigree-based relationships have to be compatible. As there are many options to create genomic relationships, there is a question of which is optimal and what the effects of deviations from optimality are.

Methods

Data of litter size (total number born per litter) for 338,346 sows were analyzed. Illumina PorcineSNP60 BeadChip genotypes were available for 1,989. Analyses were carried out with the complete data set and with a subset of genotyped animals and three generations pedigree (5,090 animals). A single-trait animal model was used to estimate variance components and breeding values. Genomic relationship matrices were constructed using allele frequencies equal to 0.5 (G05), equal to the average minor allele frequency (GMF), or equal to observed frequencies (GOF). A genomic matrix considering random ascertainment of allele frequencies was also used (GOF*). A normalized matrix (GN) was obtained to have average diagonal coefficients equal to 1. The genomic matrices were combined with the numerator relationship matrix creating H matrices.

Results

In G05 and GMF, both diagonal and off-diagonal elements were on average greater than the pedigree-based coefficients. In GOF and GOF*, the average diagonal elements were smaller than pedigree-based coefficients. The mean of off-diagonal coefficients was zero in GOF and GOF*. Choices of G with average diagonal coefficients different from 1 led to greater estimates of additive variance in the smaller data set. The correlation between EBV and genomic EBV (n = 1,989) were: 0.79 using G05, 0.79 using GMF, 0.78 using GOF, 0.79 using GOF*, and 0.78 using GN. Accuracies calculated by inversion increased with all genomic matrices. The accuracies of genomic-assisted EBV were inflated in all cases except when GN was used.

Conclusions

Parameter estimates may be biased if the genomic relationship coefficients are in a different scale than pedigree-based coefficients. A reasonable scaling may be obtained by using observed allele frequencies and re-scaling the genomic relationship matrix to obtain average diagonal elements of 1.     

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

Background

Genomic 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.

Methods

Deregressed 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.

Results

Accuracies 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.

Conclusions

These 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.     

X-inactivation informs variance-based testing for X-linked association of a quantitative trait

Background

The X chromosome plays an important role in human diseases and traits. However, few X-linked associations have been reported in genome-wide association studies, partly due to analytical complications and low statistical power.

Results

In this study, we propose tests of X-linked association that capitalize on variance heterogeneity caused by various factors, predominantly the process of X-inactivation. In the presence of X-inactivation, the expression of one copy of the chromosome is randomly silenced. Due to the consequent elevated randomness of expressed variants, females that are heterozygotes for a quantitative trait locus might exhibit higher phenotypic variance for that trait. We propose three tests that build on this phenomenon: 1) A test for inflated variance in heterozygous females; 2) A weighted association test; and 3) A combined test. Test 1 captures the novel signal proposed herein by directly testing for higher phenotypic variance of heterozygous than homozygous females. As a test of variance it is generally less powerful than standard tests of association that consider means, which is supported by extensive simulations. Test 2 is similar to a standard association test in considering the phenotypic mean, but differs by accounting for (rather than testing) the variance heterogeneity. As expected in light of X-inactivation, this test is slightly more powerful than a standard association test. Finally, test 3 further improves power by combining the results of the first two tests. We applied the these tests to the ARIC cohort data and identified a novel X-linked association near gene AFF2 with blood pressure, which was not significant based on standard association testing of mean blood pressure.

Conclusions

Variance-based tests examine overdispersion, thereby providing a complementary type of signal to a standard association test. Our results point to the potential to improve power of detecting X-linked associations in the presence of variance heterogeneity.