Definition of metafounders based on population structure analysis.

BACKGROUND: Limitations of the concept of identity by descent in the presence of stratification within a breeding population may lead to an incomplete formulation of the conventional numerator relationship matrix ( A ). Combining A with the genomic relationship matrix ( G ) in a single-step approach for genetic evaluation may cause inconsistencies that can be a source of bias in the resulting predictions. The objective of this study was to identify stratification using genomic data and to transfer this information to matrix A , to improve the compatibility of A and G . METHODS: Using software to detect population stratification (ADMIXTURE), we developed an iterative approach. First, we identified 2 to 40 strata ( k ) with ADMIXTURE, which we then introduced in a stepwise manner into matrix A , to generate matrix A Γ using the metafounder methodology. Improvements in consistency between matrix G and A Γ were evaluated by regression analysis and through the comparison of the overall mean and mean diagonal values of both matrices. The approach was tested on genotype and pedigree information of European and North American Brown Swiss animals (85,249). Analyses with ADMIXTURE were initially performed on the full set of genotypes (S1). In addition, we used an alternative dataset where we avoided sampling of closely related animals (S2). RESULTS: Results of the regression analyses of standard A on G were - 0.489, 0.780 and 0.647 for intercept, slope and fit of the regression. When analysing S1 data results of the regression for A Γ on G corresponding values were - 0.028, 1.087 and 0.807 for k =7, while there was no clear optimum k . Analyses of S2 gave a clear optimal k =24, with - 0.020, 0.998 and 0.817 as results of the regression. For this k differences in mean and mean diagonal values between both matrices were negligible. CONCLUSIONS: The derivation of hidden stratification information based on genotyped animals and its integration into A improved compatibility of the resulting A Γ and G considerably compared to the initial situation. In dairy breeding populations with large half-sib families as sub-structures it is necessary to balance the data when applying population structure analysis to obtain meaningful results.

The effect of the H-1 scaling factors τ and ω on the structure of H in the single-step procedure.

BACKGROUND: The single-step covariance matrix H combines the pedigree-based relationship matrix [Formula: see text] with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix [Formula: see text]. In particular, to improve convergence behavior of iterative approaches and to reduce inflation, two weights [Formula: see text] and [Formula: see text] have been introduced in the definition of [Formula: see text], which blend the inverse of a part of [Formula: see text] with the inverse of [Formula: see text]. Since the definition of this blending is based on the equation describing [Formula: see text], its impact on the structure of [Formula: see text] is not obvious. In a joint discussion, we considered the question of the shape of [Formula: see text] for non-trivial [Formula: see text] and [Formula: see text]. RESULTS: Here, we present the general matrix [Formula: see text] as a function of these parameters and discuss its structure and properties. Moreover, we screen for optimal values of [Formula: see text] and [Formula: see text] with respect to predictive ability, inflation and iterations up to convergence on a well investigated, publicly available wheat data set. CONCLUSION: Our results may help the reader to develop a better understanding for the effects of changes of [Formula: see text] and [Formula: see text] on the covariance model. In particular, we give theoretical arguments that as a general tendency, inflation will be reduced by increasing [Formula: see text] or by decreasing [Formula: see text].

Systematic genotyping of groups of cows to improve genomic estimated breeding values of selection candidates.

BACKGROUND: Extending the reference set for genomic predictions in dairy cattle by adding large numbers of cows with genotypes and phenotypes has been proposed as a means to increase reliability of selection decisions for candidates. METHODS: In this study, we explored the potential of increasing the reliability of breeding values of young selection candidates by genotyping a fixed number of first-crop daughters of each sire from one or two generations in a balanced and regular system of genotyping. Using stochastic simulation, we developed a basic population scenario that mimics the situation in dual-purpose Fleckvieh cattle with respect to important key parameters. Starting with a reference set consisting of only genotyped bulls, we extended this reference set by including increasing numbers of daughter genotypes and phenotypes. We studied the effects on model-derived reliabilities, validation reliabilities and unbiasedness of predicted values for selection candidates. We also illustrate and discuss the effects of a selected sample and an unbalanced sampling of daughters. Furthermore, we quantified the role of selection with respect to the influence on validation reliabilities and contrasted these to model-derived reliabilities. RESULTS: In the most extended design, with 200 daughters per sire genotyped from two generations, single nucleotide polymorphism (SNP) effects were estimated from a reference set of 420,000 cows and 4200 bulls. For this design, the validation reliabilities for candidates reached 80 % or more, thereby exceeding the reliabilities that were achieved in traditional progeny-testing designs for a trait with moderate to high heritability. We demonstrate that even a moderate number of 25 genotyped daughters per sire will lead to considerable improvement in the reliability of predicted breeding values for selection candidates. Our results illustrate that the strategy applied to sample females for genotyping has a large impact on the benefits that can be achieved.

Enlarging a training set for genomic selection by imputation of un-genotyped animals in populations of varying genetic architecture.

BACKGROUND: The most common application of imputation is to infer genotypes of a high-density panel of markers on animals that are genotyped for a low-density panel. However, the increase in accuracy of genomic predictions resulting from an increase in the number of markers tends to reach a plateau beyond a certain density. Another application of imputation is to increase the size of the training set with un-genotyped animals. This strategy can be particularly successful when a set of closely related individuals are genotyped. METHODS: Imputation on completely un-genotyped dams was performed using known genotypes from the sire of each dam, one offspring and the offspring's sire. Two methods were applied based on either allele or haplotype frequencies to infer genotypes at ambiguous loci. Results of these methods and of two available software packages were compared. Quality of imputation under different population structures was assessed. The impact of using imputed dams to enlarge training sets on the accuracy of genomic predictions was evaluated for different populations, heritabilities and sizes of training sets. RESULTS: Imputation accuracy ranged from 0.52 to 0.93 depending on the population structure and the method used. The method that used allele frequencies performed better than the method based on haplotype frequencies. Accuracy of imputation was higher for populations with higher levels of linkage disequilibrium and with larger proportions of markers with more extreme allele frequencies. Inclusion of imputed dams in the training set increased the accuracy of genomic predictions. Gains in accuracy ranged from close to zero to 37.14%, depending on the simulated scenario. Generally, the larger the accuracy already obtained with the genotyped training set, the lower the increase in accuracy achieved by adding imputed dams. CONCLUSIONS: Whenever a reference population resembling the family configuration considered here is available, imputation can be used to achieve an extra increase in accuracy of genomic predictions by enlarging the training set with completely un-genotyped dams. This strategy was shown to be particularly useful for populations with lower levels of linkage disequilibrium, for genomic selection on traits with low heritability, and for species or breeds for which the size of the reference population is limited.

Comparison of statistical procedures for estimating polygenic effects using dense genome-wide marker data.

In this study we compared different statistical procedures for estimating SNP effects using the simulated data set from the XII QTL-MAS workshop. Five procedures were considered and tested in a reference population, i.e., the first four generations, from which phenotypes and genotypes were available. The procedures can be interpreted as variants of ridge regression, with different ways for defining the shrinkage parameter. Comparisons were made with respect to the correlation between genomic and conventional estimated breeding values. Moderate correlations were obtained from all methods. Two of them were used to predict genomic breeding values in the last three generations. Correlations between these and the true breeding values were also moderate. We concluded that the ridge regression procedures applied in this study did not outperform the simple use of a ratio of variances in a mixed model method, both providing moderate accuracies of predicted genomic breeding values.