Genome-wide Breeding Values Research Articles

Genetic characterization of carrot root shape and size using genome-wide association analysis and genomic-estimated breeding values

Key messageThe principal phenotypic determinants of market class in carrot—the size and shape of the root—are under primarily additive, but also highly polygenic, genetic control.The size and shape of carrot roots are the primary determinants not only of yield, but also market class. These quantitative phenotypes have historically been challenging to objectively evaluate, and thus subjective visual assessment of market class remains the primary method by which selection for these traits is performed. However, advancements in digital image analysis have recently made possible the high-throughput quantification of size and shape attributes. It is therefore now feasible to utilize modern methods of genetic analysis to investigate the genetic control of root morphology. To this end, this study utilized both genome wide association analysis (GWAS) and genomic-estimated breeding values (GEBVs) and demonstrated that the components of market class are highly polygenic traits, likely under the influence of many small effect QTL. Relatively large proportions of additive genetic variance for many of the component phenotypes support high predictive ability of GEBVs; average prediction ability across underlying market class traits was 0.67. GWAS identified multiple QTL for four of the phenotypes which compose market class: length, aspect ratio, maximum width, and root fill, a previously uncharacterized trait which represents the size-independent portion of carrot root shape. By combining digital image analysis with GWAS and GEBVs, this study represents a novel advance in our understanding of the genetic control of market class in carrot. The immediate practical utility and viability of genomic selection for carrot market class is also described, and concrete guidelines for the design of training populations are provided.

Bayesian QTL analyses using pedigreed families of an outcrossing species, with application to fruit firmness in apple

Proof of concept of Bayesian integrated QTL analyses across pedigree-related families from breeding programs of an outbreeding species. Results include QTL confidence intervals, individuals' genotype probabilities and genomic breeding values. Bayesian QTL linkage mapping approaches offer the flexibility to study multiple full sib families with known pedigrees simultaneously. Such a joint analysis increases the probability of detecting these quantitative trait loci (QTL) and provide insight of the magnitude of QTL across different genetic backgrounds. Here, we present an improved Bayesian multi-QTL pedigree-based approach on an outcrossing species using progenies with different (complex) genetic relationships. Different modeling assumptions were studied in the QTL analyses, i.e., the a priori expected number of QTL varied and polygenic effects were considered. The inferences include number of QTL, additive QTL effect sizes and supporting credible intervals, posterior probabilities of QTL genotypes for all individuals in the dataset, and QTL-based as well as genome-wide breeding values. All these features have been implemented in the FlexQTL(™) software. We analyzed fruit firmness in a large apple dataset that comprised 1,347 individuals forming 27 full sib families and their known ancestral pedigrees, with genotypes for 87 SSR markers on 17 chromosomes. We report strong or positive evidence for 14 QTL for fruit firmness on eight chromosomes, validating our approach as several of these QTL were reported previously, though dispersed over a series of studies based on single mapping populations. Interpretation of linked QTL was possible via individuals' QTL genotypes. The correlation between the genomic breeding values and phenotypes was on average 90 %, but varied with the number of detected QTL in a family. The detailed posterior knowledge on QTL of potential parents is critical for the efficiency of marker-assisted breeding.

Unraveling the genetic architecture of environmental variance of somatic cell score using high-density single nucleotide polymorphism and cow data from experimental farms

In recent years, it has been shown that not only is the phenotype under genetic control, but also the environmental variance. Very little, however, is known about the genetic architecture of environmental variance. The main objective of this study was to unravel the genetic architecture of the mean and environmental variance of somatic cell score (SCS) by identifying genome-wide associations for mean and environmental variance of SCS in dairy cows and by quantifying the accuracy of genome-wide breeding values. Somatic cell score was used because previous research has shown that the environmental variance of SCS is partly under genetic control and reduction of the variance of SCS by selection is desirable. In this study, we used 37,590 single nucleotide polymorphism (SNP) genotypes and 46,353 test-day records of 1,642 cows at experimental research farms in 4 countries in Europe. We used a genomic relationship matrix in a double hierarchical generalized linear model to estimate genome-wide breeding values and genetic parameters. The estimated mean and environmental variance per cow was used in a Bayesian multi-locus model to identify SNP associated with either the mean or the environmental variance of SCS. Based on the obtained accuracy of genome-wide breeding values, 985 and 541 independent chromosome segments affecting the mean and environmental variance of SCS, respectively, were identified. Using a genomic relationship matrix increased the accuracy of breeding values relative to using a pedigree relationship matrix. In total, 43 SNP were significantly associated with either the mean (22) or the environmental variance of SCS (21). The SNP with the highest Bayes factor was on chromosome 9 (Hapmap31053-BTA-111664) explaining approximately 3% of the genetic variance of the environmental variance of SCS. Other significant SNP explained less than 1% of the genetic variance. It can be concluded that fewer genomic regions affect the environmental variance of SCS than the mean of SCS, but genes with large effects seem to be absent for both traits.

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

BackgroundIt 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.MethodsThe 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.ResultsWe 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.ConclusionsOur 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.

Using the Pareto principle in genome-wide breeding value estimation

Genome-wide breeding value (GWEBV) estimation methods can be classified based on the prior distribution assumptions of marker effects. Genome-wide BLUP methods assume a normal prior distribution for all markers with a constant variance, and are computationally fast. In Bayesian methods, more flexible prior distributions of SNP effects are applied that allow for very large SNP effects although most are small or even zero, but these prior distributions are often also computationally demanding as they rely on Monte Carlo Markov chain sampling. In this study, we adopted the Pareto principle to weight available marker loci, i.e., we consider that x% of the loci explain (100 - x)% of the total genetic variance. Assuming this principle, it is also possible to define the variances of the prior distribution of the 'big' and 'small' SNP. The relatively few large SNP explain a large proportion of the genetic variance and the majority of the SNP show small effects and explain a minor proportion of the genetic variance. We name this method MixP, where the prior distribution is a mixture of two normal distributions, i.e. one with a big variance and one with a small variance. Simulation results, using a real Norwegian Red cattle pedigree, show that MixP is at least as accurate as the other methods in all studied cases. This method also reduces the hyper-parameters of the prior distribution from 2 (proportion and variance of SNP with big effects) to 1 (proportion of SNP with big effects), assuming the overall genetic variance is known. The mixture of normal distribution prior made it possible to solve the equations iteratively, which greatly reduced computation loads by two orders of magnitude. In the era of marker density reaching million(s) and whole-genome sequence data, MixP provides a computationally feasible Bayesian method of analysis.

Genomic selection in loblolly pine - from lab to field

Background Tree breeding is logistically complex and expensive, and breeders have long sought to use molecular markers to accelerate breeding. A candidate gene approach based on testing for association between the presence of DNA sequence variation in or near candidate genes, and phenotypic variation in a population has long been explored [1,2]. However, using candidate gene approach (QTLs) has not been successful in breeding [3,4]. QTL-trait associations detected in one genetic background are often not observed in other families, because of recombination of genes during the segregation and low levels of linkage disequilibrium in the population. A new technology called genomic selection (GS) is revolutionizing dairy cattle breeding. In GS, marker effects are first estimated in a large training population (>500) with both phenotypic and genotypic data. Subsequently, estimated marker effects are used to predict breeding values in validation populations for which marker genotypes but not phenotypes are available [4]. Several dairy cattle breeding companies now routinely use GS to select and market bulls. The success of GS in cattle breeding is largely based on bovine genome sequencing and discovery of thousands of SNP markers. GS application, if successful, will have a great impact on forest tree breeding because of their complex and logistically difficult breeding programs. Although, there have been several simulation studies examining the effective population size, linkage disequilibrium, and heritability on the predicted accuracy of GS in tree breeding [5], GS has not yet been demonstrated for forest trees using empirical markers data, mainly due to lack of sufficient dense markers. Methods Biallelic SNP markers provided by the CTGN project (http://dendrome.ucdavis.edu/ctgn/) were used for genotyping. A population of 149 cloned full-sib offspring of loblolly pine (Pinus taeda L.) was phenotyped. Fitting 3406 informative SNP markers simultaneously, we estimated genome-wide breeding values and compared them with breeding values based on pedigree model. Variances explained by the marker additive and dominant effects were obtained.

Hierarchical likelihood opens a new way of estimating genetic values using genome-wide dense marker maps

BackgroundGenome-wide dense markers have been used to detect genes and estimate relative genetic values. Among many methods, Bayesian techniques have been widely used and shown to be powerful in genome-wide breeding value estimation and association studies. However, computation is known to be intensive under the Bayesian framework, and specifying a prior distribution for each parameter is always required for Bayesian computation. We propose the use of hierarchical likelihood to solve such problems.ResultsUsing double hierarchical generalized linear models, we analyzed the simulated dataset provided by the QTLMAS 2010 workshop. Marker-specific variances estimated by double hierarchical generalized linear models identified the QTL with large effects for both the quantitative and binary traits. The QTL positions were detected with very high accuracy. For young individuals without phenotypic records, the true and estimated breeding values had Pearson correlation of 0.60 for the quantitative trait and 0.72 for the binary trait, where the quantitative trait had a more complicated genetic architecture involving imprinting and epistatic QTL.ConclusionsHierarchical likelihood enables estimation of marker-specific variances under the likelihoodist framework. Double hierarchical generalized linear models are powerful in localizing major QTL and computationally fast.

The use of communal rearing of families and DNA pooling in aquaculture genomic selection schemes

BackgroundTraditional family-based aquaculture breeding programs, in which families are kept separately until individual tagging and most traits are measured on the sibs of the candidates, are costly and require a high level of reproductive control. The most widely used alternative is a selection scheme, where families are reared communally and the candidates are selected based on their own individual measurements of the traits under selection. However, in the latter selection schemes, inclusion of new traits depends on the availability of non-invasive techniques to measure the traits on selection candidates. This is a severe limitation of these schemes, especially for disease resistance and fillet quality traits.MethodsHere, we present a new selection scheme, which was validated using computer simulations comprising 100 families, among which 1, 10 or 100 were reared communally in groups. Pooling of the DNA from 2000, 20000 or 50000 test individuals with the highest and lowest phenotypes was used to estimate 500, 5000 or 10000 marker effects. One thousand or 2000 out of 20000 candidates were preselected for a growth-like trait. These pre-selected candidates were genotyped, and they were selected on their genome-wide breeding values for a trait that could not be measured on the candidates.ResultsA high accuracy of selection, i.e. 0.60-0.88 was obtained with 20000-50000 test individuals but it was reduced when only 2000 test individuals were used. This shows the importance of having large numbers of phenotypic records to accurately estimate marker effects. The accuracy of selection decreased with increasing numbers of families per group.ConclusionsThis new selection scheme combines communal rearing of families, pre-selection of candidates, DNA pooling and genomic selection and makes multi-trait selection possible in aquaculture selection schemes without keeping families separately until individual tagging is possible. The new scheme can also be used for other farmed species, for which the cost of genotyping test individuals may be high, e.g. if trait heritability is low.

Optimum contribution selection using traditional best linear unbiased prediction and genomic breeding values in aquaculture breeding schemes

The aim of this study was to compare genetic gain for a traditional aquaculture sib breeding scheme with breeding values based on phenotypic data (TBLUP) with a breeding scheme with genome-wide (GW) breeding values. Both breeding schemes were closed nuclei with discrete generations modeled by stochastic simulation. Optimum contribution selection was applied to restrict pedigree-based inbreeding to either 0.5 or 1% per generation. There were 1,000 selection candidates and a sib test group of either 4,000 or 8,000 fish. The number of selected dams and sires to create full sib families in each generation was determined from the optimum contribution selection method. True breeding values for a trait were simulated by summing the number of each QTL allele and the true effect of each of the 1,000 simulated QTL. Breeding values in TBLUP were predicted from phenotypic and pedigree information, whereas genomic breeding values were computed from genetic markers whose effects were estimated using a genomic BLUP model. In generation 5, genetic gain was 70 and 74% greater for the GW scheme than for the TBLUP scheme for inbreeding rates of 0.5 and 1%. The reduction in genetic variance was, however, greater for the GW scheme than for the TBLUP scheme due to fixation of some QTL. As expected, accuracy of selection increased with increasing heritability (e.g., from 0.77 with a heritability of 0.2 to 0.87 with a heritability of 0.6 for GW, and from 0.53 and 0.58 for TBLUP in generation 5 with sib information only). When the trait was measured on the selection candidate compared with only on sibs and the heritability was 0.4, accuracy increased from 0.55 to 0.69 for TBLUP and from 0.83 to 0.86 for GW. The number of selected sires to get the desired rate of inbreeding was in general less in GW than in TBLUP and was 33 for GW and 83 for TBLUP (rate of inbreeding 1% and heritability 0.4). With truncation selection, genetic gain for the scheme with GW breeding values was nearly twice as large as a scheme with traditional BLUP breeding values. The results indicate that the benefits of applying GW breeding values compared with TBLUP are reduced when contributions are optimized. In conclusion, genetic gain in aquaculture breeding schemes with optimized contributions can increase by as much as 81% by applying genome-wide breeding values compared with traditional BLUP breeding values.

EM algorithm for Bayesian estimation of genomic breeding values

BackgroundIn genomic selection, a model for prediction of genome-wide breeding value (GBV) is constructed by estimating a large number of SNP effects that are included in a model. Two Bayesian methods based on MCMC algorithm, Bayesian shrinkage regression (BSR) method and stochastic search variable selection (SSVS) method, (which are called BayesA and BayesB, respectively, in some literatures), have been so far proposed for the estimation of SNP effects. However, much computational burden is imposed on the MCMC-based Bayesian methods. A method with both high computing efficiency and prediction accuracy is desired to be developed for practical use of genomic selection.ResultsEM algorithm applicable for BSR is described. Subsequently, we propose a new EM-based Bayesian method, called wBSR (weighted BSR), which is a modification of BSR incorporating a weight for each SNP according to the strength of its association to a trait. Simulation experiments show that the computational time is much reduced with wBSR based on EM algorithm and the accuracy in predicting GBV is improved by wBSR in comparison with BSR based on MCMC algorithm. However, the accuracy of predicted GBV with wBSR is inferior to that with SSVS based on MCMC algorithm which is currently considered to be a method of choice for genomic selection.ConclusionsEM-based wBSR method proposed in this study is much advantageous over MCMC-based Bayesian methods in computational time and can predict GBV more accurately than MCMC-based BSR. Therefore, wBSR is considered a practical method for genomic selection with a large number of SNP markers.

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

BackgroundWhen 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.MethodsGenomic 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.ResultsAccuracy 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.ConclusionsIncluding 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.

The Accuracy of Genomic Selection in Norwegian Red Cattle Assessed by Cross-Validation

Genomic Selection (GS) is a newly developed tool for the estimation of breeding values for quantitative traits through the use of dense markers covering the whole genome. For a successful application of GS, accuracy of the prediction of genomewide breeding value (GW-EBV) is a key issue to consider. Here we investigated the accuracy and possible bias of GW-EBV prediction, using real bovine SNP genotyping (18,991 SNPs) and phenotypic data of 500 Norwegian Red bulls. The study was performed on milk yield, fat yield, protein yield, first lactation mastitis traits, and calving ease. Three methods, best linear unbiased prediction (G-BLUP), Bayesian statistics (BayesB), and a mixture model approach (MIXTURE), were used to estimate marker effects, and their accuracy and bias were estimated by using cross-validation. The accuracies of the GW-EBV prediction were found to vary widely between 0.12 and 0.62. G-BLUP gave overall the highest accuracy. We observed a strong relationship between the accuracy of the prediction and the heritability of the trait. GW-EBV prediction for production traits with high heritability achieved higher accuracy and also lower bias than health traits with low heritability. To achieve a similar accuracy for the health traits probably more records will be needed.

Reducing dimensionality for prediction of genome-wide breeding values

Partial least square regression (PLSR) and principal component regression (PCR) are methods designed for situations where the number of predictors is larger than the number of records. The aim was to compare the accuracy of genome-wide breeding values (EBV) produced using PLSR and PCR with a Bayesian method, 'BayesB'. Marker densities of 1, 2, 4 and 8 Ne markers/Morgan were evaluated when the effective population size (Ne) was 100. The correlation between true breeding value and estimated breeding value increased with density from 0.611 to 0.681 and 0.604 to 0.658 using PLSR and PCR respectively, with an overall advantage to PLSR of 0.016 (s.e = 0.008). Both methods gave a lower accuracy compared to the 'BayesB', for which accuracy increased from 0.690 to 0.860. PLSR and PCR appeared less responsive to increased marker density with the advantage of 'BayesB' increasing by 17% from a marker density of 1 to 8Ne/M. PCR and PLSR showed greater bias than 'BayesB' in predicting breeding values at all densities. Although, the PLSR and PCR were computationally faster and simpler, these advantages do not outweigh the reduction in accuracy, and there is a benefit in obtaining relevant prior information from the distribution of gene effects.

The impact of single nucleotide polymorphism selection on prediction of genomewide breeding values

The study focuses on the impact of different sets of single nucleotide polymorphisms (SNPs) selected from the available data set on prediction of genomewide breeding values (GBVs) of animals. Correlations between breeding values estimated as additive polygenic effects (EBVs) and GBVs as well as correlations between true breeding values (TBVs) and GBVs are used as major criteria for the comparison of different SNP selection schemes and GBV estimation models.The analysed data is the simulated data set from the XII QTL Workshop. In the analysis five different SNP data sets are considered. For prediction of EBVs a standard mixed animal model is applied, whereas GBVs are defined as the sum of additive effects of SNPs estimated for the different SNP data sets using model 1 with fixed SNPs effects, model 2 with fixed SNPs effects and a random additive polygenic effect, model 3 with a random effects of uncorrelated SNP genotypes.The additive polygenic and residual variance components estimated by the EBV model amount to 1.36 and 3.12, respectively. Differences between models are expressed by comparing the ranking of individuals based on EBV and on GBV and by correlations. Among 100 individuals with the highest EBVs, depending on a model and a data set, there are only between 11 and 37 individuals with the highest GBVs. The highest correlation between GBV and EBV amounts to 0.787 and is observed for model 3 with 3,328 SNPs selected based on their minor allele frequency, the lowest correlation of 0.519 is attributed to model 2 with 300 SNPs. Correlations between GBV estimates obtained from different models with the same number of SNPs range between 0.916 and 0. 998, whereas correlations between different SNP data sets using the same model fall under 0.850.These results indicate that successful application of high throughoutput SNP genotyping technologies for prediction of breeding values is a very promising approach, but before the method can be routinely applied further methodological improvements regarding model construction and SNP selection are required.

A Bayesian QTL linkage analysis of the common dataset from the 12thQTLMAS workshop

To compare the power of various QTL mapping methodologies, a dataset was simulated within the framework of 12th QTLMAS workshop. A total of 5865 diploid individuals was simulated, spanning seven generations, with known pedigree. Individuals were genotyped for 6000 SNPs across six chromosomes. We present an illustration of a Bayesian QTL linkage analysis, as implemented in the special purpose software FlexQTL. Most importantly, we treated the number of bi-allelic QTL as a random variable and used Bayes Factors to infer plausible QTL models. We investigated the power of our analysis in relation to the number of phenotyped individuals and SNPs. We report clear posterior evidence for 12 QTL that jointly explained 30% of the phenotypic variance, which was very close to the total of included simulation effects, when using all phenotypes and a set of 600 SNPs. Decreasing the number of phenotyped individuals from 4665 to 1665 and/or the number of SNPs in the analysis from 600 to 120 dramatically reduced the power to identify and locate QTL. Posterior estimates of genome-wide breeding values for a small set of individuals were given. We presented a successful Bayesian linkage analysis of a simulated dataset with a pedigree spanning several generations. Our analysis identified all regions that contained QTL with effects explaining more than one percent of the phenotypic variance. We showed how the results of a Bayesian QTL mapping can be used in genomic prediction.

Comparison of accuracy of genome-wide and BLUP breeding value estimates in sib based aquaculture breeding schemes

This study compared the accuracy for genome-wide breeding values (GWEBV) with traditional BLUP breeding values estimated from phenotypic performance of sibs (BLUPEBV) in a typical sib based aquaculture breeding scheme. The breeding schemes were closed nuclei with 1000 selection candidates from 100 families in each generation G1 to G5. Phenotypes were recorded on sibs of the selection candidates. Both selection candidates and their recorded sibs were genotyped using dense SNP genotyping technology and marker effects estimated from the sibs were used to predict GWEBV of the selection candidates. With 40 sibs, accuracy in G3 was 0.54 for BLUPEBV compared to 0.78 for GWEBV (marker density 0.5 N e / M), i.e. a relative increase of 44%. When the number of sibs for the GWEBV scheme decreased from 40 to 20 sibs, accuracy decreased by 7% in G3. Both for BLUPEBV and GWEBV breeding schemes, the effect of heritability on accuracy was small and accuracy increased around 4% when increasing heritability from 0.2 to 0.4. Contrary to expectations differences in accuracy between BLUPEBV and GWEBV were the same for the low (0.2) and high (0.4) heritability, which may be due to the large number of phenotypic records used. When records were only available in generation G1, accuracy of GWEBV decreased over generations and was 0.66 in G1, 0.57 in G2 and 0.51 in G3 with 40 sibs and marker density 0.5 N e / M. Accuracy increased with increased marker density for GWEBV, but the increase was small when marker density increased from 0.5 to 1.0 N e / M except when the test group size was increased from 20 to 40, indicating that with a higher marker density a higher number of phenotypes is needed. Increasing the size of the genome (1000 cM vs. 2000 cM) decreased the accuracy for the GWEBV breeding values but increased the accuracy for the BLUPEBV breeding values. Overall, accuracy was up to 33% higher for GWEBV than for BLUPEBV for the studied scenarios because both between and within family genetic variances are utilized when estimating genome-wide breeding values. The results indicate that aquaculture breeding companies can increase the accuracy of selection when using genomic selection in a typical sib based aquaculture breeding scheme.

Effects of the number of markers per haplotype and clustering of haplotypes on the accuracy of QTL mapping and prediction of genomic breeding values

The aim of this paper was to compare the effect of haplotype definition on the precision of QTL-mapping and on the accuracy of predicted genomic breeding values. In a multiple QTL model using identity-by-descent (IBD) probabilities between haplotypes, various haplotype definitions were tested i.e. including 2, 6, 12 or 20 marker alleles and clustering base haplotypes related with an IBD probability of > 0.55, 0.75 or 0.95. Simulated data contained 1100 animals with known genotypes and phenotypes and 1000 animals with known genotypes and unknown phenotypes. Genomes comprising 3 Morgan were simulated and contained 74 polymorphic QTL and 383 polymorphic SNP markers with an average r2 value of 0.14 between adjacent markers. The total number of haplotypes decreased up to 50% when the window size was increased from two to 20 markers and decreased by at least 50% when haplotypes related with an IBD probability of > 0.55 instead of > 0.95 were clustered. An intermediate window size led to more precise QTL mapping. Window size and clustering had a limited effect on the accuracy of predicted total breeding values, ranging from 0.79 to 0.81. Our conclusion is that different optimal window sizes should be used in QTL-mapping versus genome-wide breeding value prediction.

A fast algorithm for BayesB type of prediction of genome-wide estimates of genetic value

Genomic selection uses genome-wide dense SNP marker genotyping for the prediction of genetic values, and consists of two steps: (1) estimation of SNP effects, and (2) prediction of genetic value based on SNP genotypes and estimates of their effects. For the former step, BayesB type of estimators have been proposed, which assume a priori that many markers have no effects, and some have an effect coming from a gamma or exponential distribution, i.e. a fat-tailed distribution. Whilst such estimators have been developed using Monte Carlo Markov chain (MCMC), here we derive a much faster non-MCMC based estimator by analytically performing the required integrations. The accuracy of the genome-wide breeding value estimates was 0.011 (s.e. 0.005) lower than that of the MCMC based BayesB predictor, which may be because the integrations were performed one-by-one instead of for all SNPs simultaneously. The bias of the new method was opposite to that of the MCMC based BayesB, in that the new method underestimates the breeding values of the best selection candidates, whereas MCMC-BayesB overestimated their breeding values. The new method was computationally several orders of magnitude faster than MCMC based BayesB, which will mainly be advantageous in computer simulations of entire breeding schemes, in cross-validation testing, and practical schemes with frequent re-estimation of breeding values.