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Pedigrees used in genetic evaluations contain errors. Because of such errors, assumptions regarding the relatedness among individuals in genetic evaluation models are wrong. Consequences of that have been investigated in earlier studies focusing on models that did not account for genomic information yet. The objective of this work was to investigate the effects of pedigree errors on the results from genetic evaluations using the single-step model, and the effect of such effects on results from validation studies with forward prediction. We used a real pedigree (n = 361,980) and real genotypes (n = 25,950) of Fleckvieh cattle, sampled in a way to provide a good consistency between pedigree and genomic relationships. Given the real pedigree and genotypes, true breeding values (TBV) were simulated to have a covariance structure equal to the matrix H assumed in a single-step model. Based on TBV, phenotypes were simulated with a heritability of 0.25. Genetic evaluations were conducted with a conventional animal model (i.e., without genomic information) and a single-step animal model under scenarios using either the correct pedigree or a pedigree containing 5%, 10%, or 20% of wrong records. Wrong records were simulated by randomly assigning wrong sires to nongenotyped females. The increasing rates of pedigree errors led to decreasing correlations between TBV and EBV and lower standard deviations of predictions. Less variation was observed because pedigree errors operate actually as a random exchange of daughters among bulls, making them look more similar to each other than they actually are. This occurs of course only when animals have progeny. Therefore, this decreased variation was more pronounced for progeny tested bulls than for young selection candidates. In a forward prediction validation scenario, the stronger decrease in variation when animals get progeny caused an apparent inflation of early predictions. This phenomenon may contribute to the usually observed problem of inflation of early predictions observed in validation studies., (The Authors. Published by Elsevier Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).)

It has been shown that single-step genomic BLUP (ssGBLUP) can be reformulated, resulting in an equivalent SNP model that includes the explicit imputation of gene contents of all ungenotyped animals in the pedigree. This reformulation reveals the underlying mechanism enabling ungenotyped animals to contribute information to genotyped animals via estimates of marker effects and consequently to the reliability of genomic predictions, a key feature generally associated with the single-step approach. Irrespective of which BLUP formulation is used for genomic prediction, with increasing numbers of genotyped animals, the marker-oriented model is recommended when calculating the reliabilities of genomic predictions. This approach has the advantage of a manageable and stable size of the model matrix that needs to be inverted to calculate analytical prediction error variances of marker effects, an advantage that also holds for prediction with the single-step model. However, when including imputed genotypes in the design matrix of marker effects, an additional imputation residual term has to be considered to account for the prediction error of imputation. We summarize some of the theoretical aspects associated with the calculation of analytical reliabilities of single-step predictions. Derivations are based on the equivalent reformulation of ssGBLUP as a marker-oriented model and the calculation of prediction error variances of marker effects. We propose 2 approximations that allow for a substantial reduction of the complexity of the matrix operations involved, while retaining most of the relevant information required for reliability calculations. We additionally provide a general framework for an implementation of single-step reliability approximation using standard animal model reliabilities as a starting point. Finally, we demonstrate the effectiveness of the proposed approach using a small example extracted from data of the routine evaluation on dual-purpose Fleckvieh (Simmental) cattle., (The Authors. Published by FASS Inc. and Elsevier Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).)

Single-step genomic evaluations have the advantage of simultaneously combining all pedigree, phenotypic, and genotypic information available. However, systems with a large number of genotyped animals have some computational challenges. In many genomic breeding programs, genomic predictions of young animals should become available for selection decisions in the shortest time possible, which requires either a very effective estimation or an approximation with negligible loss in accuracy. We investigated different procedures for predicting breeding values of young genotyped animals without setting up the full single-step system augmented for the additional genotypes. Methods were based on transmitting the information from single-step breeding values of genotyped animals that took part in the previous full run to young animals, either through genomic relationships or through a marker-based model. The different procedures were tested on real data from the April 2017 run of the German-Austrian official genomic evaluation for Fleckvieh. The data set included 62,559 genotyped animals and was used to run single-step evaluations for 23 conformation traits. A further data set comprising 1,768 young animals was used for interim prediction and we called it the validation set. The reference values for validation were the predicted breeding values of the young animals from a full single-step run containing the genotypes of all 64,327 animals. Correlations between the approximated predictions and those from the full single-step run also containing genotypes from young animals averaged 0.9932 for the best method (from 0.990 to 0.995 across traits). In conclusion, prediction of single-step breeding values for young animals can be well approximated using systems of size equal to the number of markers., (The Authors. Published by FASS Inc. and Elsevier Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).)

In a 2-step genomic system, genotypes of animals without phenotypes do not influence genomic prediction of other animals, but that might not be the case in single-step systems. We investigated the effects of including genotypes from culled bulls on the reliability of genomic predictions from single-step evaluations. Four scenarios with a constant amount of phenotypic information and increasing numbers of genotypes from culled bulls were simulated and compared with respect to prediction reliability. With increasing numbers of genotyped culled bulls, there was a corresponding increase in prediction reliability. For instance, in our simulation scenario the reliability for selection candidates was twice as large when all culled bulls from the last 4 generations were included in the analysis. Single-step evaluations imply the imputation of all nongenotyped animals in the pedigree. We showed that this imputation was increasingly more accurate as increasingly more genotypic information from the culled bulls was taken into account. This resulted in higher prediction reliabilities. The extent of the benefit from including genotypes from culled bulls might be more relevant for small populations with low levels of reliabilities., (The Authors. Published by the Federation of Animal Science Societies and Elsevier Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).)

In this study we investigate the potential of enlarging the reference population for genomic prediction in dairy cattle by routinely genotyping a random sample of the first-crop daughters of every AI bull in the breeding program. We analyzed small nuclear pedigrees, each consisting of a genotyped selection candidate and 3 generations of genotyped male ancestors. Genotypes were taken from the genomic routine evaluation of Fleckvieh cattle in Germany and Austria. The phenotypic information of a daughter of any one male in each of these pedigrees was either considered to be part of the daughter yield deviation of the corresponding sire, or was assumed to be an individually observed genotyped daughter of this sire. Daughter genotypes in this case were simulated from phased haplotypes of their sires and random maternal gametes drawn from a haplotype library. We measured the gain from genotyping daughters as the increase in model-based theoretical reliability of the genomic prediction for a putative selection candidate. We expressed the improvements as a marginal increase, corresponding to an increase in reliability at a reliability baseline level of zero, to simplify comparisons. Results were encouraging with 2 to 40% of marginal reliability increase for selection candidates depending on the assumed heritability of the trait and the number of daughters modeled to be genotyped in the design., (Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

The objective of this study was to investigate in detail the biasing effects of imputation errors on genomic predictions. Direct genomic values (DGV) of 3,494 Brown Swiss selection candidates for 37 production and conformation traits were predicted using either their observed 50K genotypes or their 50K genotypes imputed from a mimicked 6K chip. Changes in DGV caused by imputation errors were shown to be systematic. The DGV of top animals were, on average, underestimated and that of bottom animals were, on average, overestimated when imputed genotypes were used instead of observed genotypes. This pattern might be explained by the fact that imputation algorithms will usually suggest the most frequent haplotype from the sample whenever a haplotype cannot be determined unambiguously. That was empirically shown to cause an advantage for the bottom animals and a disadvantage for the top animals., (Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

This study investigated reliability of genomic predictions using medium-density (40,089; 50K) or high-density (HD; 388,951) marker sets. We developed an approximate method to test differences in validation reliability for significance. Model-based reliability and the effect of HD genotypes on inflation of predictions were analyzed additionally. Genomic breeding values were predicted for at least 1,321 validation bulls based on phenotypes and genotypes of at least 5,324 calibration bulls by means of a linear model in milk, fat, and protein yield; somatic cell score; milkability; muscling; udder, feet, and legs score as well as stature. In total, 1,485 bulls were actually HD genotyped and HD genotypes of the other animals were imputed from 50K genotypes using FImpute software. Validation reliability was measured as the coefficient of determination of the weighted regression of daughter yield deviations on predicted breeding values divided by the reliability of daughter yield deviations and inflation was evaluated by the slope of this regression. Model-based reliability was calculated from the model. Distributions for validation reliability of 50K markers were derived by repeated sampling of 50,000-marker samples from HD to test differences in validation reliability statistically. Additionally, the benefit of HD genotypes in validation reliability was tested by repeated sampling of validation groups and calculation of the difference in validation reliability between HD and 50K genotypes for the sampled groups of bulls. The mean benefit in validation reliability of HD genotypes was 0.015 compared with real 50K genotypes and 0.028 compared with 50K samples from HD affected by imputation error and was significant for all traits. The model-based reliability was, on average, 0.036 lower and the regression coefficient was 0.036 closer to the expected value with HD genotypes. The observed gain in validation reliability with HD genotypes was similar to expectations based on the number of markers and the effective number of segregating chromosome segments. Sampling error in the marker-based relationship coefficients causing overestimation of the model-based reliability was smaller with HD genotypes. Inflation of the genomic predictions was reduced with HD genotypes, accordingly. Similar effects on model-based reliability and inflation, but not on the validation reliability, were obtained by shrinkage estimation of the realized relationship matrix from 50K genotypes., (Copyright © 2014 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

An appropriate strategy to estimate variance components and breeding values in genetic models with quantitative trait loci (QTL) was developed for a dairy cattle breeding scheme by utilizing simulated data. Reliable estimates for variance components in QTL models are a prerequisite in fine-mapping experiments and for marker-assisted genetic evaluations. In cattle populations, only a small fraction of the population is genotyped at genetic markers, and only these animals are included in marker-assisted genetic evaluation models. Phenotypic information in these models are precorrected phenotypes [daughter yield deviations (DYD) for bulls, yield deviations (YD) for cows] estimated by standard animal models from the entire population. Because DYD and YD may represent different amounts of information, the problem of weighting these 2 types of information appropriately arises. To detect the best combination of phenotypes and weighting factors, a stochastic simulation for a trait representing milk yield was used. The results show that DYD models are generally optimal for estimating QTL variance components, but properties of estimates depend strongly on weighting factors. An example for the benefit in selection of using YD is shown for the selection among paternal half-sibs inheriting alternative QTL alleles. Even if QTL effects are small, marker-assisted best unbiased linear prediction can improve the selection among half-sibs, because the Mendelian sampling variance within family can be exploited, especially in DYD-YD models. Marker-assisted genetic evaluation models should also include YD for cows to ensure that marker-assisted selection improves selection even for moderate QTL effects (> or =10%). A useful strategy for practical implementation is to estimate variance components in DYD models and breeding values in DYD-YD models.