Using whole-genome sequence data to predict quantitative trait phenotypes in Drosophila melanogaster

Predicting organismal phenotypes from genotype data is important for plant and animal breeding, medicine, and evolutionary biology. Genomic-based phenotype prediction has been applied for single-nucleotide polymorphism (SNP) genotyping platforms, but not using complete genome sequences. Here, we report genomic prediction for starvation stress resistance and startle response in Drosophila melanogaster, using ～2.5 million SNPs determined by sequencing the Drosophila Genetic Reference Panel population of inbred lines. We constructed a genomic relationship matrix from the SNP data and used it in a genomic best linear unbiased prediction (GBLUP) model. We assessed predictive ability as the correlation between predicted genetic values and observed phenotypes by cross-validation, and found a predictive ability of 0.239±0.008 (0.230±0.012) for starvation resistance (startle response). The predictive ability of BayesB, a Bayesian method with internal SNP selection, was not greater than GBLUP. Selection of the 5% SNPs with either the highest absolute effect or variance explained did not improve predictive ability. Predictive ability decreased only when fewer than 150,000 SNPs were used to construct the genomic relationship matrix. We hypothesize that predictive power in this population stems from the SNP-based modeling of the subtle relationship structure caused by long-range linkage disequilibrium and not from population structure or SNPs in linkage disequilibrium with causal variants. We discuss the implications of these results for genomic prediction in other organisms.     

Mixed Model Methods for Genomic Prediction and Variance Component Estimation of Additive and Dominance Effects Using SNP Markers

We established a genomic model of quantitative trait with genomic additive and dominance relationships that parallels the traditional quantitative genetics model, which partitions a genotypic value as breeding value plus dominance deviation and calculates additive and dominance relationships using pedigree information. Based on this genomic model, two sets of computationally complementary but mathematically identical mixed model methods were developed for genomic best linear unbiased prediction (GBLUP) and genomic restricted maximum likelihood estimation (GREML) of additive and dominance effects using SNP markers. These two sets are referred to as the CE and QM sets, where the CE set was designed for large numbers of markers and the QM set was designed for large numbers of individuals. GBLUP and associated accuracy formulations for individuals in training and validation data sets were derived for breeding values, dominance deviations and genotypic values. Simulation study showed that GREML and GBLUP generally were able to capture small additive and dominance effects that each accounted for 0.00005–0.0003 of the phenotypic variance and GREML was able to differentiate true additive and dominance heritability levels. GBLUP of the total genetic value as the summation of additive and dominance effects had higher prediction accuracy than either additive or dominance GBLUP, causal variants had the highest accuracy of GREML and GBLUP, and predicted accuracies were in agreement with observed accuracies. Genomic additive and dominance relationship matrices using SNP markers were consistent with theoretical expectations. The GREML and GBLUP methods can be an effective tool for assessing the type and magnitude of genetic effects affecting a phenotype and for predicting the total genetic value at the whole genome level.     

Genomic prediction using imputed whole-genome sequence data in Holstein Friesian cattle

Background

In contrast to currently used single nucleotide polymorphism (SNP) panels, the use of whole-genome sequence data is expected to enable the direct estimation of the effects of causal mutations on a given trait. This could lead to higher reliabilities of genomic predictions compared to those based on SNP genotypes. Also, at each generation of selection, recombination events between a SNP and a mutation can cause decay in reliability of genomic predictions based on markers rather than on the causal variants. Our objective was to investigate the use of imputed whole-genome sequence genotypes versus high-density SNP genotypes on (the persistency of) the reliability of genomic predictions using real cattle data.

Methods

Highly accurate phenotypes based on daughter performance and Illumina BovineHD Beadchip genotypes were available for 5503 Holstein Friesian bulls. The BovineHD genotypes (631,428 SNPs) of each bull were used to impute whole-genome sequence genotypes (12,590,056 SNPs) using the Beagle software. Imputation was done using a multi-breed reference panel of 429 sequenced individuals. Genomic estimated breeding values for three traits were predicted using a Bayesian stochastic search variable selection (BSSVS) model and a genome-enabled best linear unbiased prediction model (GBLUP). Reliabilities of predictions were based on 2087 validation bulls, while the other 3416 bulls were used for training.

Results

Prediction reliabilities ranged from 0.37 to 0.52. BSSVS performed better than GBLUP in all cases. Reliabilities of genomic predictions were slightly lower with imputed sequence data than with BovineHD chip data. Also, the reliabilities tended to be lower for both sequence data and BovineHD chip data when relationships between training animals were low. No increase in persistency of prediction reliability using imputed sequence data was observed.

Conclusions

Compared to BovineHD genotype data, using imputed sequence data for genomic prediction produced no advantage. To investigate the putative advantage of genomic prediction using (imputed) sequence data, a training set with a larger number of individuals that are distantly related to each other and genomic prediction models that incorporate biological information on the SNPs or that apply stricter SNP pre-selection should be considered.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0149-x) contains supplementary material, which is available to authorized users.     

Accuracy of genomic selection for a sib-evaluated trait using identity-by-state and identity-by-descent relationships

Background

GBLUP (genomic best linear unbiased prediction) uses high-density single nucleotide polymorphism (SNP) markers to construct genomic identity-by-state (IBS) relationship matrices. However, identity-by-descent (IBD) relationships can be accurately calculated for extremely sparse markers. Here, we compare the accuracy of prediction of genome-wide breeding values (GW-BV) for a sib-evaluated trait in a typical aquaculture population, assuming either IBS or IBD genomic relationship matrices, and by varying marker density and size of the training dataset.

Methods

A simulation study was performed, assuming a population with strong family structure over three subsequent generations. Traditional and genomic BLUP were used to estimate breeding values, the latter using either IBS or IBD genomic relationship matrices, with marker densities ranging from 10 to ~1200 SNPs/Morgan (M). Heritability ranged from 0.1 to 0.8, and phenotypes were recorded on 25 to 45 sibs per full-sib family (50 full-sib families). Models were compared based on their predictive ability (accuracy) with respect to true breeding values of unphenotyped (albeit genotyped) sibs in the last generation.

Results

As expected, genomic prediction had greater accuracy compared to pedigree-based prediction. At the highest marker density, genomic prediction based on IBS information (IBS-GS) was slightly superior to that based on IBD information (IBD-GS), while at lower densities (≤100 SNPs/M), IBD-GS was more accurate. At the lowest densities (10 to 20 SNPs/M), IBS-GS was even outperformed by the pedigree-based model. Accuracy of IBD-GS was stable across marker densities performing well even down to 10 SNPs/M (2.5 to 6.1% reduction in accuracy compared to ~1200 SNPs/M). Loss of accuracy due to reduction in the size of training datasets was moderate and similar for both genomic prediction models. The relative superiority of (high-density) IBS-GS over IBD-GS was more pronounced for traits with a low heritability.

Conclusions

Using dense markers, GBLUP based on either IBD or IBS relationship matrices proved to perform better than a pedigree-based model. However, accuracy of IBS-GS declined rapidly with decreasing marker densities, and was even outperformed by a traditional pedigree-based model at the lowest densities. In contrast, the accuracy of IBD-GS was very stable across marker densities.     

A simple method to separate base population and segregation effects in genomic relationship matrices

Background

Genomic selection and estimation of genomic breeding values (GBV) are widely used in cattle and plant breeding. Several studies have attempted to detect population subdivision by investigating the structure of the genomic relationship matrix G. However, the question of how these effects influence GBV estimation using genomic best linear unbiased prediction (GBLUP) has received little attention.

Methods

We propose a simple method to decompose G into two independent covariance matrices, one describing the covariance that results from systematic differences in allele frequencies between groups at the pedigree base (G_A^*) and the other describing genomic relationships (G_S) corrected for these differences. Using this decomposition and F_st statistics, we examined whether observed genetic distances between genotyped subgroups within populations resulted from the heterogeneous genetic structure present at the base of the pedigree and/or from breed divergence. Using this decomposition, we tested three models in a forward prediction validation scenario on six traits using Brown Swiss and dual-purpose Fleckvieh cattle data. Model 0 (M0) used both components and is equivalent to the model using the standard G-matrix. Model 1 (M1) used G_S only and model 2 (M2), an extension of M1, included a fixed genetic group effect. Moreover, we analyzed the matrix of contributions of each base group (Q) and estimated the effects and prediction errors of each base group using M0 and M1.

Results

The proposed decomposition of G helped to examine the relative importance of the effects of base groups and segregation in a given population. We found significant differences between the effects of base groups for each breed. In forward prediction, differences between models in terms of validation reliability of estimated direct genomic values were small but predictive power was consistently lowest for M1. The relative advantage of M0 or M2 in prediction depended on breed, trait and genetic composition of the validation group. Our approach presents a general analogy with the use of genetic groups in conventional animal models and provides proof that standard GBLUP using G yields solutions equivalent to M0, where base groups are considered as correlated random effects within the additive genetic variance assigned to the genetic base.     

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 effect of high-density genotypic data and different methods on joint genomic prediction: A case study in large white pigs

Joint genomic prediction (GP) is an attractive method to improve the accuracy of GP by combining information from multiple populations. However, many factors can negatively influence the accuracy of joint GP, such as differences in linkage disequilibrium phasing between single nucleotide polymorphisms (SNPs) and causal variants, minor allele frequencies and causal variants’ effect sizes across different populations. The objective of this study was to investigate whether the imputed high-density genotype data can improve the accuracy of joint GP using genomic best linear unbiased prediction (GBLUP), single-step GBLUP (ssGBLUP), multi-trait GBLUP (MT-GBLUP) and GBLUP based on genomic relationship matrix considering heterogenous minor allele frequencies across different populations (wGBLUP). Three traits, including days taken to reach slaughter weight, backfat thickness and loin muscle area, were measured on 67 276 Large White pigs from two different populations, for which 3334 were genotyped by SNP array. The results showed that a combined population could substantially improve the accuracy of GP compared with a single-population GP, especially for the population with a smaller size. The imputed SNP data had no effect for single population GP but helped to yield higher accuracy than the medium-density array data for joint GP. Of the four methods, ssGLBUP performed the best, but the advantage of ssGBLUP decreased as more individuals were genotyped. In some cases, MT-GBLUP and wGBLUP performed better than GBLUP. In conclusion, our results confirmed that joint GP could be beneficial from imputed high-density genotype data, and the wGBLUP and MT-GBLUP methods are promising for joint GP in pig breeding.     

Genomic and pedigree-based prediction for leaf,stem, and stripe rust resistance in wheat

Key message

Genomic prediction for seedling and adult plant resistance to wheat rusts was compared to prediction using few markers as fixed effects in a least-squares approach and pedigree-based prediction.

Abstract

The unceasing plant-pathogen arms race and ephemeral nature of some rust resistance genes have been challenging for wheat (Triticum aestivum L.) breeding programs and farmers. Hence, it is important to devise strategies for effective evaluation and exploitation of quantitative rust resistance. One promising approach that could accelerate gain from selection for rust resistance is ‘genomic selection’ which utilizes dense genome-wide markers to estimate the breeding values (BVs) for quantitative traits. Our objective was to compare three genomic prediction models including genomic best linear unbiased prediction (GBLUP), GBLUP A that was GBLUP with selected loci as fixed effects and reproducing kernel Hilbert spaces-markers (RKHS-M) with least-squares (LS) approach, RKHS-pedigree (RKHS-P), and RKHS markers and pedigree (RKHS-MP) to determine the BVs for seedling and/or adult plant resistance (APR) to leaf rust (LR), stem rust (SR), and stripe rust (YR). The 333 lines in the 45th IBWSN and the 313 lines in the 46th IBWSN were genotyped using genotyping-by-sequencing and phenotyped in replicated trials. The mean prediction accuracies ranged from 0.31–0.74 for LR seedling, 0.12–0.56 for LR APR, 0.31–0.65 for SR APR, 0.70–0.78 for YR seedling, and 0.34–0.71 for YR APR. For most datasets, the RKHS-MP model gave the highest accuracies, while LS gave the lowest. GBLUP, GBLUP A, RKHS-M, and RKHS-P models gave similar accuracies. Using genome-wide marker-based models resulted in an average of 42% increase in accuracy over LS. We conclude that GS is a promising approach for improvement of quantitative rust resistance and can be implemented in the breeding pipeline.

     

Invited review: efficient computation strategies in genomic selection

The purpose of this study is review and evaluation of computing methods used in genomic selection for animal breeding. Commonly used models include SNP BLUP with extensions (BayesA, etc), genomic BLUP (GBLUP) and single-step GBLUP (ssGBLUP). These models are applied for genomewide association studies (GWAS), genomic prediction and parameter estimation. Solving methods include finite Cholesky decomposition possibly with a sparse implementation, and iterative Gauss–Seidel (GS) or preconditioned conjugate gradient (PCG), the last two methods possibly with iteration on data. Details are provided that can drastically decrease some computations. For SNP BLUP especially with sampling and large number of SNP, the only choice is GS with iteration on data and adjustment of residuals. If only solutions are required, PCG by iteration on data is a clear choice. A genomic relationship matrix (GRM) has limited dimensionality due to small effective population size, resulting in infinite number of generalized inverses of GRM for large genotyped populations. A specific inverse called APY requires only a small fraction of GRM, is sparse and can be computed and stored at a low cost for millions of animals. With APY inverse and PCG iteration, GBLUP and ssGBLUP can be applied to any population. Both tools can be applied to GWAS. When the system of equations is sparse but contains dense blocks, a recently developed package for sparse Cholesky decomposition and sparse inversion called YAMS has greatly improved performance over packages where such blocks were treated as sparse. With YAMS, GREML and possibly single-step GREML can be applied to populations with >50 000 genotyped animals. From a computational perspective, genomic selection is becoming a mature methodology.     

Multi-generation genomic prediction of maize yield using parametric and non-parametric sparse selection indices

Genomic prediction models are often calibrated using multi-generation data. Over time, as data accumulates, training data sets become increasingly heterogeneous. Differences in allele frequency and linkage disequilibrium patterns between the training and prediction genotypes may limit prediction accuracy. This leads to the question of whether all available data or a subset of it should be used to calibrate genomic prediction models. Previous research on training set optimization has focused on identifying a subset of the available data that is optimal for a given prediction set. However, this approach does not contemplate the possibility that different training sets may be optimal for different prediction genotypes. To address this problem, we recently introduced a sparse selection index (SSI) that identifies an optimal training set for each individual in a prediction set. Using additive genomic relationships, the SSI can provide increased accuracy relative to genomic-BLUP (GBLUP). Non-parametric genomic models using Gaussian kernels (KBLUP) have, in some cases, yielded higher prediction accuracies than standard additive models. Therefore, here we studied whether combining SSIs and kernel methods could further improve prediction accuracy when training genomic models using multi-generation data. Using four years of doubled haploid maize data from the International Maize and Wheat Improvement Center (CIMMYT), we found that when predicting grain yield the KBLUP outperformed the GBLUP, and that using SSI with additive relationships (GSSI) lead to 5–17% increases in accuracy, relative to the GBLUP. However, differences in prediction accuracy between the KBLUP and the kernel-based SSI were smaller and not always significant.Subject terms: Quantitative trait, Genetic models     

Genomic prediction based on data from three layer lines using non-linear regression models

Background

Most studies on genomic prediction with reference populations that include multiple lines or breeds have used linear models. Data heterogeneity due to using multiple populations may conflict with model assumptions used in linear regression methods.

Methods

In an attempt to alleviate potential discrepancies between assumptions of linear models and multi-population data, two types of alternative models were used: (1) a multi-trait genomic best linear unbiased prediction (GBLUP) model that modelled trait by line combinations as separate but correlated traits and (2) non-linear models based on kernel learning. These models were compared to conventional linear models for genomic prediction for two lines of brown layer hens (B1 and B2) and one line of white hens (W1). The three lines each had 1004 to 1023 training and 238 to 240 validation animals. Prediction accuracy was evaluated by estimating the correlation between observed phenotypes and predicted breeding values.

Results

When the training dataset included only data from the evaluated line, non-linear models yielded at best a similar accuracy as linear models. In some cases, when adding a distantly related line, the linear models showed a slight decrease in performance, while non-linear models generally showed no change in accuracy. When only information from a closely related line was used for training, linear models and non-linear radial basis function (RBF) kernel models performed similarly. The multi-trait GBLUP model took advantage of the estimated genetic correlations between the lines. Combining linear and non-linear models improved the accuracy of multi-line genomic prediction.

Conclusions

Linear models and non-linear RBF models performed very similarly for genomic prediction, despite the expectation that non-linear models could deal better with the heterogeneous multi-population data. This heterogeneity of the data can be overcome by modelling trait by line combinations as separate but correlated traits, which avoids the occasional occurrence of large negative accuracies when the evaluated line was not included in the training dataset. Furthermore, when using a multi-line training dataset, non-linear models provided information on the genotype data that was complementary to the linear models, which indicates that the underlying data distributions of the three studied lines were indeed heterogeneous.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0075-3) contains supplementary material, which is available to authorized users.     

Comparing genomic prediction accuracy from purebred,crossbred and combined purebred and crossbred reference populations in sheep

Background

The accuracy of genomic prediction depends largely on the number of animals with phenotypes and genotypes. In some industries, such as sheep and beef cattle, data are often available from a mixture of breeds, multiple strains within a breed or from crossbred animals. The objective of this study was to compare the accuracy of genomic prediction for several economically important traits in sheep when using data from purebreds, crossbreds or a combination of those in a reference population.

Methods

The reference populations were purebred Merinos, crossbreds of Border Leicester (BL), Poll Dorset (PD) or White Suffolk (WS) with Merinos and combinations of purebred and crossbred animals. Genomic breeding values (GBV) were calculated based on genomic best linear unbiased prediction (GBLUP), using a genomic relationship matrix calculated based on 48 599 Ovine SNP (single nucleotide polymorphisms) genotypes. The accuracy of GBV was assessed in a group of purebred industry sires based on the correlation coefficient between GBV and accurate estimated breeding values based on progeny records.

Results

The accuracy of GBV for Merino sires increased with a larger purebred Merino reference population, but decreased when a large purebred Merino reference population was augmented with records from crossbred animals. The GBV accuracy for BL, PD and WS breeds based on crossbred data was the same or tended to decrease when more purebred Merinos were added to the crossbred reference population. The prediction accuracy for a particular breed was close to zero when the reference population did not contain any haplotypes of the target breed, except for some low accuracies that were obtained when predicting PD from WS and vice versa.

Conclusions

This study demonstrates that crossbred animals can be used for genomic prediction of purebred animals using 50 k SNP marker density and GBLUP, but crossbred data provided lower accuracy than purebred data. Including data from distant breeds in a reference population had a neutral to slightly negative effect on the accuracy of genomic prediction. Accounting for differences in marker allele frequencies between breeds had only a small effect on the accuracy of genomic prediction from crossbred or combined crossbred and purebred reference populations.     

Pre-selecting markers based on fixation index scores improved the power of genomic evaluations in a combined Yorkshire pig population

Combining different swine populations in genomic prediction can be an important tool, leading to an increased accuracy of genomic prediction using single nucleotide polymorphism (SNP) chip data compared with within-population genomic. However, the expected higher accuracy of multi-population genomic prediction has not been realized. This may be due to an inconsistent linkage disequilibrium (LD) between SNPs and quantitative trait loci (QTL) across populations, and the weak genetic relationships across populations. In this study, we determined the impact of different genomic relationship matrices, SNP density and pre-selected variants on prediction accuracy using a combined Yorkshire pig population. Our objective was to provide useful strategies for improving the accuracy of genomic prediction within a combined population. Results showed that the accuracy of genomic best linear unbiased prediction (GBLUP) using imputed whole-genome sequencing (WGS) data in the combined population was always higher than that within populations. Furthermore, the use of imputed WGS data always resulted in a higher accuracy of GBLUP than the use of 80K chip data for the combined population. Additionally, the accuracy of GBLUP with a non-linear genomic relationship matrix was markedly increased (0.87% to 15.17% for 80K chip data, and 0.43% to 4.01% for imputed WGS data) compared with that obtained with a linear genomic relationship matrix, except for the prediction of XD population in the combined population using imputed WGS data. More importantly, the application of pre-selected variants based on fixation index (Fst) scores improved the accuracy of multi-population genomic prediction, especially for 80K chip data. For BLUP|GA (BLUP approach given the genetic architecture), the use of a linear method with an appropriate weight to build a weight-relatedness matrix led to a higher prediction accuracy compared with the use of only pre-selected SNPs for genomic evaluations, especially for the total number of piglets born. However, for the non-linear method, BLUP|GA showed only a small increase or even a decrease in prediction accuracy compared with the use of only pre-selected SNPs. Overall, the best genomic evaluation strategy for reproduction-related traits for a combined population was found to be GBLUP performed with a non-linear genomic relationship matrix using variants pre-selected from the 80K chip data based on Fst scores.     

Comparison on genomic predictions using three GBLUP methods and two single-step blending methods in the Nordic Holstein population

Background

A single-step blending approach allows genomic prediction using information of genotyped and non-genotyped animals simultaneously. However, the combined relationship matrix in a single-step method may need to be adjusted because marker-based and pedigree-based relationship matrices may not be on the same scale. The same may apply when a GBLUP model includes both genomic breeding values and residual polygenic effects. The objective of this study was to compare single-step blending methods and GBLUP methods with and without adjustment of the genomic relationship matrix for genomic prediction of 16 traits in the Nordic Holstein population.

Methods

The data consisted of de-regressed proofs (DRP) for 5 214 genotyped and 9 374 non-genotyped bulls. The bulls were divided into a training and a validation population by birth date, October 1, 2001. Five approaches for genomic prediction were used: 1) a simple GBLUP method, 2) a GBLUP method with a polygenic effect, 3) an adjusted GBLUP method with a polygenic effect, 4) a single-step blending method, and 5) an adjusted single-step blending method. In the adjusted GBLUP and single-step methods, the genomic relationship matrix was adjusted for the difference of scale between the genomic and the pedigree relationship matrices. A set of weights on the pedigree relationship matrix (ranging from 0.05 to 0.40) was used to build the combined relationship matrix in the single-step blending method and the GBLUP method with a polygenetic effect.

Results

Averaged over the 16 traits, reliabilities of genomic breeding values predicted using the GBLUP method with a polygenic effect (relative weight of 0.20) were 0.3% higher than reliabilities from the simple GBLUP method (without a polygenic effect). The adjusted single-step blending and original single-step blending methods (relative weight of 0.20) had average reliabilities that were 2.1% and 1.8% higher than the simple GBLUP method, respectively. In addition, the GBLUP method with a polygenic effect led to less bias of genomic predictions than the simple GBLUP method, and both single-step blending methods yielded less bias of predictions than all GBLUP methods.

Conclusions

The single-step blending method is an appealing approach for practical genomic prediction in dairy cattle. Genomic prediction from the single-step blending method can be improved by adjusting the scale of the genomic relationship matrix.     

Comparison of joint versus purebred genomic evaluation in the French multi-breed dairy goat population

Background

All progeny-tested bucks from the two main French dairy goat breeds (Alpine and Saanen) were genotyped with the Illumina goat SNP50 BeadChip. The reference population consisted of 677 bucks and 148 selection candidates. With the two-step approach based on genomic best linear unbiased prediction (GBLUP), prediction accuracy of candidates did not outperform that of the parental average. We investigated a GBLUP method based on a single-step approach, with or without blending of the two breeds in the reference population.

Methods

Three models were used: (1) a multi-breed model, in which Alpine and Saanen breeds were considered as a single breed; (2) a within-breed model, with separate genomic evaluation per breed; and (3) a multiple-trait model, in which a trait in the Alpine was assumed to be correlated to the same trait in the Saanen breed, using three levels of between-breed genetic correlations (ρ): ρ = 0, ρ = 0.99, or estimated ρ. Quality of genomic predictions was assessed on progeny-tested bucks, by cross-validation of the Pearson correlation coefficients for validation accuracy and the regression coefficients of daughter yield deviations (DYD) on genomic breeding values (GEBV). Model-based estimates of average accuracy were calculated on the 148 candidates.

Results

The genetic correlations between Alpine and Saanen breeds were highest for udder type traits, ranging from 0.45 to 0.76. Pearson correlations with the single-step approach were higher than previously reported with a two-step approach. Correlations between GEBV and DYD were similar for the three models (within-breed, multi-breed and multiple traits). Regression coefficients of DYD on GEBV were greater with the within-breed model and multiple-trait model with ρ = 0.99 than with the other models. The single-step approach improved prediction accuracy of candidates from 22 to 37% for both breeds compared to the two-step method.

Conclusions

Using a single-step approach with GBLUP, prediction accuracy of candidates was greater than that based on parent average of official evaluations and accuracies obtained with a two-step approach. Except for regression coefficients of DYD on GEBV, there were no significant differences between the three models.     

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.     

Modeling Epistasis in Genomic Selection

Modeling epistasis in genomic selection is impeded by a high computational load. The extended genomic best linear unbiased prediction (EG-BLUP) with an epistatic relationship matrix and the reproducing kernel Hilbert space regression (RKHS) are two attractive approaches that reduce the computational load. In this study, we proved the equivalence of EG-BLUP and genomic selection approaches, explicitly modeling epistatic effects. Moreover, we have shown why the RKHS model based on a Gaussian kernel captures epistatic effects among markers. Using experimental data sets in wheat and maize, we compared different genomic selection approaches and concluded that prediction accuracy can be improved by modeling epistasis for selfing species but may not for outcrossing species.     

Genomic best linear unbiased prediction method including imprinting effects for genomic evaluation

Background

Genomic best linear unbiased prediction (GBLUP) is a statistical method used to predict breeding values using single nucleotide polymorphisms for selection in animal and plant breeding. Genetic effects are often modeled as additively acting marker allele effects. However, the actual mode of biological action can differ from this assumption. Many livestock traits exhibit genomic imprinting, which may substantially contribute to the total genetic variation of quantitative traits. Here, we present two statistical models of GBLUP including imprinting effects (GBLUP-I) on the basis of genotypic values (GBLUP-I1) and gametic values (GBLUP-I2). The performance of these models for the estimation of variance components and prediction of genetic values across a range of genetic variations was evaluated in simulations.

Results

Estimates of total genetic variances and residual variances with GBLUP-I1 and GBLUP-I2 were close to the true values and the regression coefficients of total genetic values on their estimates were close to 1. Accuracies of estimated total genetic values in both GBLUP-I methods increased with increasing degree of imprinting and broad-sense heritability. When the imprinting variances were equal to 1.4% to 6.0% of the phenotypic variances, the accuracies of estimated total genetic values with GBLUP-I1 exceeded those with GBLUP by 1.4% to 7.8%. In comparison with GBLUP-I1, the superiority of GBLUP-I2 over GBLUP depended strongly on degree of imprinting and difference in genetic values between paternal and maternal alleles. When paternal and maternal alleles were predicted (phasing accuracy was equal to 0.979), accuracies of the estimated total genetic values in GBLUP-I1 and GBLUP-I2 were 1.7% and 1.2% lower than when paternal and maternal alleles were known.

Conclusions

This simulation study shows that GBLUP-I1 and GBLUP-I2 can accurately estimate total genetic variance and perform well for the prediction of total genetic values. GBLUP-I1 is preferred for genomic evaluation, while GBLUP-I2 is preferred when the imprinting effects are large, and the genetic effects differ substantially between sexes.     

Improving the accuracy of genomic prediction in Chinese Holstein cattle by using one-step blending

Background

The one-step blending approach has been suggested for genomic prediction in dairy cattle. The core of this approach is to incorporate pedigree and phenotypic information of non-genotyped animals. The objective of this study was to investigate the improvement of the accuracy of genomic prediction using the one-step blending method in Chinese Holstein cattle.

Findings

Three methods, GBLUP (genomic best linear unbiased prediction), original one-step blending with a genomic relationship matrix, and adjusted one-step blending with an adjusted genomic relationship matrix, were compared with respect to the accuracy of genomic prediction for five milk production traits in Chinese Holstein. For the two one-step blending methods, de-regressed proofs of 17 509 non-genotyped cows, including 424 dams and 17 085 half-sisters of the validation cows, were incorporated in the prediction model. The results showed that, averaged over the five milk production traits, the one-step blending increased the accuracy of genomic prediction by about 0.12 compared to GBLUP. No further improvement in accuracies was obtained from the adjusted one-step blending over the original one-step blending in our situation. Improvements in accuracies obtained with both one-step blending methods were almost completely contributed by the non-genotyped dams.

Conclusions

Compared with GBLUP, the one-step blending approach can significantly improve the accuracy of genomic prediction for milk production traits in Chinese Holstein cattle. Thus, the one-step blending is a promising approach for practical genomic selection in Chinese Holstein cattle, where the reference population mainly consists of cows.     

Estimating Additive and Non-Additive Genetic Variances and Predicting Genetic Merits Using Genome-Wide Dense Single Nucleotide Polymorphism Markers

Non-additive genetic variation is usually ignored when genome-wide markers are used to study the genetic architecture and genomic prediction of complex traits in human, wild life, model organisms or farm animals. However, non-additive genetic effects may have an important contribution to total genetic variation of complex traits. This study presented a genomic BLUP model including additive and non-additive genetic effects, in which additive and non-additive genetic relation matrices were constructed from information of genome-wide dense single nucleotide polymorphism (SNP) markers. In addition, this study for the first time proposed a method to construct dominance relationship matrix using SNP markers and demonstrated it in detail. The proposed model was implemented to investigate the amounts of additive genetic, dominance and epistatic variations, and assessed the accuracy and unbiasedness of genomic predictions for daily gain in pigs. In the analysis of daily gain, four linear models were used: 1) a simple additive genetic model (MA), 2) a model including both additive and additive by additive epistatic genetic effects (MAE), 3) a model including both additive and dominance genetic effects (MAD), and 4) a full model including all three genetic components (MAED). Estimates of narrow-sense heritability were 0.397, 0.373, 0.379 and 0.357 for models MA, MAE, MAD and MAED, respectively. Estimated dominance variance and additive by additive epistatic variance accounted for 5.6% and 9.5% of the total phenotypic variance, respectively. Based on model MAED, the estimate of broad-sense heritability was 0.506. Reliabilities of genomic predicted breeding values for the animals without performance records were 28.5%, 28.8%, 29.2% and 29.5% for models MA, MAE, MAD and MAED, respectively. In addition, models including non-additive genetic effects improved unbiasedness of genomic predictions.