Transmission ratio distortion regions in the context of genomic evaluation and their effects on reproductive traits in cattle

Transmission ratio distortion (TRD), which is a deviation from Mendelian expectations, has been associated with basic mechanisms of life such as sperm and ova fertility and viability at developmental stages of the reproductive cycle. In this study different models including TRD regions were tested for different reproductive traits [days from first service to conception (FSTC), number of services, first service nonreturn rate (NRR), and stillbirth (SB)]. Thus, in addition to a basic model with systematic and random effects, including genetic effects modeled through a genomic relationship matrix, we developed 2 additional models, including a second genomic relationship matrix based on TRD regions, and TRD regions as a random effect assuming heterogeneous variances. The analyses were performed with 10,623 cows and 1,520 bulls genotyped for 47,910 SNPs, 590 TRD regions, and several records ranging from 9,587 (FSTC) to 19,667 (SB). The results of this study showed the ability of TRD regions to capture some additional genetic variance for some traits; however, this did not translate into higher accuracy for genomic prediction. This could be explained by the nature of TRD itself, which may arise in different stages of the reproductive cycle. Nevertheless, important effects of TRD regions were found on SB (31 regions) and NRR (18 regions) when comparing at-risk versus control matings, especially for regions with allelic TRD pattern. Particularly for NRR, the probability of observing nonpregnant cow increases by up to 27% for specific TRD regions, and the probability of observing stillbirth increased by up to 254%. These results support the relevance of several TRD regions on some reproductive traits, especially those with allelic patterns that have not received as much attention as recessive TRD patterns.

Genomic evaluation of feed efficiency in US Holstein heifers

There is growing interest in improving feed efficiency traits in dairy cattle. The objectives of this study were to estimate the genetic parameters of residual feed intake (RFI) and its component traits [dry matter intake (DMI), metabolic body weight (MBW), and average daily gain (ADG)] in Holstein heifers, and to develop a system for genomic evaluation for RFI in Holstein dairy calves. The RFI data were collected from 6,563 growing Holstein heifers (initial body weight = 261 ± 52 kg; initial age = 266 ± 42 d) for 70 d, across 182 trials conducted between 2014 and 2022 at the STgenetics Ohio Heifer Center (South Charleston, OH) as part of the EcoFeed program, which aims to improve feed efficiency by genetic selection. The RFI was estimated as the difference between a heifer's actual feed intake and expected feed intake, which was determined by regression of DMI against midpoint MBW, age, and ADG across each trial. A total of 61,283 SNPs were used in genomic analyses. Animals with phenotypes and genotypes were used as training population, and 4 groups of prediction population, each with 2,000 animals, were selected from a pool of Holstein animals with genotypes, based on their relationship with the training population. All traits were analyzed using univariate animal model in DMU version 6 software. Pedigree information and genomic information were used to specify genetic relationships to estimate the variance components and genomic estimated breeding values (GEBV), respectively. Breeding values of the prediction population were estimated by using the 2-step approach: deriving the prediction equation of GEBV from the training population for estimation of GEBV of prediction population with only genotypes. Reliability of breeding values was obtained by approximation based on partitioning a function of the accuracy of training population GEBV and magnitudes of genomic relationships between individuals in the training and prediction population. Heifers had DMI (mean ± SD) of 8.11 ± 1.59 kg over the trial period, with growth rate of 1.08 ± 0.25 kg/d. The heritability estimates (mean ± SE) of RFI, MBW, DMI, and growth rate were 0.24 ± 0.02, 0.23 ± 0.02, 0.27 ± 0.02, and 0.19 ± 0.02, respectively. The range of genomic predicted transmitted abilities (gPTA) of the training population (-0.94 to 0.75) was higher compared with the range of gPTA (-0.82 to 0.73) of different groups of prediction population. Average reliability of breeding values from the training population was 58%, and that of prediction population was 39%. The genomic prediction of RFI provides new tools to select for feed efficiency of heifers. Future research should be directed to find the relationship between RFI of heifers and cows, to select individuals based on their lifetime production efficiencies.

Single-step SNPBLUP evaluation in six German beef cattle breeds

The implementation of genomic selection for six German beef cattle populations was evaluated. Although the multiple-step implementation of genomic selection is the status quo in most national dairy cattle evaluations, the breeding structure of German beef cattle, coupled with the shortcoming and complexity of the multiple-step method, makes single step a more attractive option to implement genomic selection in German beef cattle populations. Our objective was to develop a national beef cattle single-step genomic evaluation in five economically important traits in six German beef cattle populations and investigate its impact on the accuracy and bias of genomic evaluations relative to the current pedigree-based evaluation. Across the six breeds in our study, 461,929 phenotyped and 14,321 genotyped animals were evaluated with a multi-trait single-step model. To validate the single-step model, phenotype data in the last 2 years were removed in a forward validation study. For the conventional and single-step approaches, the genomic estimated breeding values of validation animals and other animals were compared between the truncated and the full evaluations. The correlation of the GEBVs between the full and truncated evaluations in the validation animals was slightly higher in the single-step evaluation. The regression of the full GEBVs on truncated GEBVs was close to the optimal value of 1 for both the pedigree-based and the single-step evaluations. The SNP effect estimates from the truncated evaluation were highly correlated with those from the full evaluation, with values ranging from 0.79 to 0.94. The correlation of the SNP effect was influenced by the number of genotyped animals shared between the full and truncated evaluations. The regression coefficients of the SNP effect of the full evaluation on the truncated evaluation were all close to the expected value of 1, indicating unbiased estimates of the SNP markers for the production traits. The Manhattan plot of the SNP effect estimates identified chromosomal regions harbouring major genes for muscling and body weight in breeds of French origin. Based on the regression intercept and slope of the GEBVs of validation animals, the single-step evaluation was neither inflated nor deflated across the six breeds. Overall, the single-step model resulted in a more accurate and stable evaluation. However, due to the small number of genotyped individuals, the single-step method only provided slightly better results when compared to the pedigree-based method.

Genomic evaluation of carcass traits of Korean beef cattle Hanwoo using a single-step marker effect model

Hanwoo beef cattle are well known for the flavor and tenderness of their meat. Genetic improvement programs have been extremely successful over the last 40 years. Recently, genomic selection was initiated in Hanwoo to enhance genetic progress. Routine genomic evaluation based on the single-step breeding value model was implemented in 2020 for all economically important traits. In this study, we tested a single-step marker effect model for the genomic evaluation of four carcass traits, namely, carcass weight, eye muscle area, backfat thickness, and marbling score. In total, 8,023,666 animals with carcass records were jointly evaluated, including 29,965 genotyped animals. To assess the prediction stability of the single-step model, carcass data from the last four years were removed in a forward validation study. The estimated genomic breeding values (GEBV) of the validation animals and other animals were compared between the truncated and full evaluations. A parallel conventional best linear unbiased prediction (BLUP) evaluation with either the full or the truncated dataset was also conducted for comparison with the single-step model. The estimates of the marker effect from the truncated evaluation were highly correlated with those from the full evaluation, ranging from 0.88-0.92. The regression coefficients of the estimates of the marker effect for the full and truncated evaluations were close to their expected value of 1, indicating unbiased estimates for all carcass traits. Estimates of the marker effect revealed three chromosomal regions (chromosomes 4, 6, and 14) harboring the major genes for carcass weight in Hanwoo. For validation of cows or steers, the single-step model had a much higher R2 value for the linear regression model than the conventional BLUP model. Based on the regression intercept and slope of the validation, the single-step evaluation was neither inflated nor deflated. For genotyped animals, the estimated GEBV from the full and truncated evaluations were more correlated than the estimated breeding values from the two conventional BLUP evaluations. The single-step model provided a more accurate and stable evaluation over time.

Comparing BeadChip and WGS Genotyping: Non-Technical Failed Calling Is Attributable to Additional Variation within the Probe Target Sequence

Microarray-based genomic selection is a central tool to increase the genetic gain of economically significant traits in dairy cattle. Yet, the effectivity of this tool is slightly limited, as estimates based on genotype data only partially explain the observed heritability. In the analysis of the genomes of 17 Israeli Holstein bulls, we compared genotyping accuracy between whole-genome sequencing (WGS) and microarray-based techniques. Using the standard GATK pipeline, the short-variant discovery within sequence reads mapped to the reference genome (ARS-UCD1.2) was compared to the genotypes from Illumina BovineSNP50 BeadChip and to an alternative method, which computationally mimics the hybridization procedure by mapping reads to 50 bp spanning the BeadChip source sequences. The number of mismatches between the BeadChip and WGS genotypes was low (0.2%). However, 17,197 (40% of the informative SNPs) had extra variation within 50 bp of the targeted SNP site, which might interfere with hybridization-based genotyping. Consequently, with respect to genotyping errors, BeadChip varied significantly and systematically from WGS genotyping, introducing null allele-like effects and Mendelian errors (<0.5%), whereas the GATK algorithm of local de novo assembly of haplotypes successfully resolved the genotypes in the extra-variable regions. These findings suggest that the microarray design should avoid polymorphic genomic regions that are prone to extra variation and that WGS data may be used to resolve erroneous genotyping, which may partially explain missing heritability.

Efficient approximation of reliabilities for single-step genomic BLUP models with the Algorithm for Proven and Young

The objectives of this study were to develop an efficient algorithm for calculating prediction error variances (PEV) for GBLUP models using the Algorithm for Proven and Young (APY), extend it to single-step GBLUP (ssGBLUP), and to apply this algorithm for approximating the theoretical reliabilities for single and multiple trait models in ssGBLUP. The PEV with APY was calculated by block-sparse inversion, efficiently exploiting the sparse structure of the inverse of the genomic relationship matrix with APY. Single-step GBLUP reliabilities were approximated by combining reliabilities with and without genomic information in terms of effective record contributions. Multi-trait reliabilities relied on single-trait results adjusted using the genetic and residual covariance matrices among traits. Tests involved two datasets provided by the American Angus Association. A small dataset (Data1) was used for comparing the approximated reliabilities with the reliabilities obtained by the inversion of the left-hand side of the mixed model equations. The large dataset (Data2) was used for evaluating the computational performance of the algorithm. Analyses with both datasets used single-trait and three-trait models. The number of animals in the pedigree ranged from 167,951 in Data1 to 10,213,401 in Data2, with 50,000 and 20,000 genotyped animals for single-trait and multiple trait-analysis, respectively, in Data1 and 335,325 in Data2. Correlations between estimated and exact reliabilities obtained by inversion ranged from 0.97 to 0.99, whereas the intercept and slope of the regression of the exact on the approximated reliabilities ranged from 0.00 to 0.04 and from 0.93 to 1.05, respectively. For the three-trait model with the largest dataset (Data2), the elapsed time for the reliability estimation was eleven minutes. The computational complexity of the proposed algorithm increased linearly with the number of genotyped animals and with the number of traits in the model. This algorithm can efficiently approximate the theoretical reliability of genomic estimated breeding values in ssGBLUP with APY for large numbers of genotyped animals at a low cost.

Practical implementation of genetic groups in single-step genomic evaluations with Woodbury matrix identity-based genomic relationship inverse

The growing amount of genomic information in dairy cattle has increased computational and modeling challenges in the single-step evaluations. The computational challenges are due to the dense inverses of genomic (G) and pedigree (A₂₂) relationship matrices of genotyped animals in the single-step mixed model equations. An equivalent mixed model equation is given by single-step genomic BLUP that are based on the T matrix (ssGTBLUP), where these inverses are avoided by expressing G^-1 through a product of 2 rectangular matrices, and (A₂₂)^-1 through sparse matrix blocks of the inverse of full relationship matrix A^-1. A proper way to account genetic groups through unknown parent groups (UPG) after the Quaas-Pollak transformation (QP) is one key factor in a single-step model. When the UPG effects are incompletely accounted, the iterative solving method may have convergence problems. In this study, we investigated computational and predictive performance of ssGTBLUP with residual polygenic (RPG) effect and UPG. The QP transformation used A^-1 and, in the complete form, T and (A₂₂)^-1 matrices as well. The models were tested with official Nordic Holstein milk production test-day data and model. The results show that UPG can be easily implemented in ssGTBLUP having RPG. The complete QP transformation was computationally feasible when preconditioned conjugate gradient iteration and iteration on data without explicitly setting up G or A₂₂ matrices were used. Furthermore, for good convergence of the preconditioned conjugate gradient method, a complete QP transformation was necessary.

Emerging issues in genomic selection

Genomic selection (GS) is now practiced successfully across many species. However, many questions remain, such as long-term effects, estimations of genomic parameters, robustness of genome-wide association study (GWAS) with small and large datasets, and stability of genomic predictions. This study summarizes presentations from the authors at the 2020 American Society of Animal Science (ASAS) symposium. The focus of many studies until now is on linkage disequilibrium between two loci. Ignoring higher-level equilibrium may lead to phantom dominance and epistasis. The Bulmer effect leads to a reduction of the additive variance; however, the selection for increased recombination rate can release anew genetic variance. With genomic information, estimates of genetic parameters may be biased by genomic preselection, but costs of estimation can increase drastically due to the dense form of the genomic information. To make the computation of estimates feasible, genotypes could be retained only for the most important animals, and methods of estimation should use algorithms that can recognize dense blocks in sparse matrices. GWASs using small genomic datasets frequently find many marker-trait associations, whereas studies using much bigger datasets find only a few. Most of the current tools use very simple models for GWAS, possibly causing artifacts. These models are adequate for large datasets where pseudo-phenotypes such as deregressed proofs indirectly account for important effects for traits of interest. Artifacts arising in GWAS with small datasets can be minimized by using data from all animals (whether genotyped or not), realistic models, and methods that account for population structure. Recent developments permit the computation of P-values from genomic best linear unbiased prediction (GBLUP), where models can be arbitrarily complex but restricted to genotyped animals only, and single-step GBLUP that also uses phenotypes from ungenotyped animals. Stability was an important part of nongenomic evaluations, where genetic predictions were stable in the absence of new data even with low prediction accuracies. Unfortunately, genomic evaluations for such animals change because all animals with genotypes are connected. A top-ranked animal can easily drop in the next evaluation, causing a crisis of confidence in genomic evaluations. While correlations between consecutive genomic evaluations are high, outliers can have differences as high as 1 SD. A solution to fluctuating genomic evaluations is to base selection decisions on groups of animals. Although many issues in GS have been solved, many new issues that require additional research continue to surface.

Application of Genomic Data for Reliability Improvement of Pig Breeding Value Estimates

Replacement pigs' genomic prediction for reproduction (total number and born alive piglets in the first parity), meat, fatness and growth traits (muscle depth, days to 100 kg and backfat thickness over 6-7 rib) was tested using single-step genomic best linear unbiased prediction ssGBLUP methodology. These traits were selected as the most economically significant and different in terms of heritability. The heritability for meat, fatness and growth traits varied from 0.17 to 0.39 and for reproduction traits from 0.12 to 0.14. We confirm from our data that ssGBLUP is the most appropriate method of genomic evaluation. The validation of genomic predictions was performed by calculating the correlation between preliminary GEBV (based on pedigree and genomic data only) with high reliable conventional estimates (EBV) (based on pedigree, own phenotype and offspring records) of validating animals. Validation datasets include 151 and 110 individuals for reproduction, meat and fattening traits, respectively. The level of correlation (r) between EBV and GEBV scores varied from +0.44 to +0.55 for meat and fatness traits, and from +0.75 to +0.77 for reproduction traits. Average breeding value (EBV) of group selected on genomic evaluation basis exceeded the group selected on parental average estimates by 22, 24 and 66% for muscle depth, days to 100 kg and backfat thickness over 6-7 rib, respectively. Prediction based on SNP markers data and parental estimates showed a significant increase in the reliability of low heritable reproduction traits (about 40%), which is equivalent to including information about 10 additional descendants for sows and 20 additional descendants for boars in the evaluation dataset.

Favorable Conditions for Genomic Evaluation to Outperform Classical Pedigree Evaluation Highlighted by a Proof-of-Concept Study in Poplar

Forest trees like poplar are particular in many ways compared to other domesticated species. They have long juvenile phases, ongoing crop-wild gene flow, extensive outcrossing, and slow growth. All these particularities tend to make the conduction of breeding programs and evaluation stages costly both in time and resources. Perennials like trees are therefore good candidates for the implementation of genomic selection (GS) which is a good way to accelerate the breeding process, by unchaining selection from phenotypic evaluation without affecting precision. In this study, we tried to compare GS to pedigree-based traditional evaluation, and evaluated under which conditions genomic evaluation outperforms classical pedigree evaluation. Several conditions were evaluated as the constitution of the training population by cross-validation, the implementation of multi-trait, single trait, additive and non-additive models with different estimation methods (G-BLUP or weighted G-BLUP). Finally, the impact of the marker densification was tested through four marker density sets. The population under study corresponds to a pedigree of 24 parents and 1,011 offspring, structured into 35 full-sib families. Four evaluation batches were planted in the same location and seven traits were evaluated on 1 and 2 years old trees. The quality of prediction was reported by the accuracy, the Spearman rank correlation and prediction bias and tested with a cross-validation and an independent individual test set. Our results show that genomic evaluation performance could be comparable to the already well-optimized pedigree-based evaluation under certain conditions. Genomic evaluation appeared to be advantageous when using an independent test set and a set of less precise phenotypes. Genome-based methods showed advantages over pedigree counterparts when ranking candidates at the within-family levels, for most of the families. Our study also showed that looking at ranking criteria as Spearman rank correlation can reveal benefits to genomic selection hidden by biased predictions.

Effect of genotyped bulls with different numbers of phenotyped progenies on quantitative trait loci detection and genomic evaluation in a simulated cattle population

The objective of this study was to assess the effect of genotyped bulls with different numbers of phenotyped progenies on quantitative trait loci (QTL) detection and genomic evaluation using a simulated cattle population. Twelve generations (G1–G12) were simulated from the base generation (G0). The recent population had different effective population sizes, heritability, and number of QTL. G0–G4 were used for pedigree information. A total of 300 genotyped bulls from G5–G10 were randomly selected. Their progenies were generated in G6–G11 with different numbers of progeny per bull. Scenarios were considered according to the number of progenies and whether the genotypes were possessed by the bulls or the progenies. A genome‐wide association study and genomic evaluation were performed with a single‐step genomic best linear unbiased prediction method to calculate the power of QTL detection and the genomic estimated breeding value (GEBV). We found that genotyped bulls could be available for QTL detection depending on conditions. Additionally, using a reference population, including genotyped bulls, which had more progeny phenotypes, enabled a more accurate prediction of GEBV. However, it is desirable to have more than 4,500 individuals consisting of both genotypes and phenotypes for practical genomic evaluation.

Symposium review: Development, implementation, and perspectives of health evaluations in the United States

The rate at which new traits are being developed is increasing, leading to an expanding number of evaluations provided to dairy producers, especially for functional traits. This review will discuss the development and implementation of genetic evaluations for direct health traits in the United States, as well as potential future developments. Beginning in April 2018, routine official genomic evaluations for 6 direct health traits in Holsteins were made available to US producers from the Council on Dairy Cattle Breeding (Bowie, MD). Traits include resistance to milk fever, displaced abomasum, ketosis, clinical mastitis, metritis, and retained placenta. These health traits were included in net merit indices beginning in August 2018, with a total weight of approximately 2%. Previously, improvement of cow health was primarily made through changes to management practices or genetic selection on indicator traits, such as somatic cell score, productive life, or livability. Widespread genomic testing now allows for accelerated improvement of traits with low heritabilities such as health; however, phenotypes remain essential to the success of genomic evaluations. Establishment and maintenance of data pipelines is a critical component of health trait evaluations, as well as appropriate data quality control standards. Data standardization is a necessary process when multiple data sources are involved. Model refinement continues, including implementation of variance adjustments beginning with the April 2019 evaluation. Mastitis evaluations are submitted to Interbull along with somatic cell score for international validation and evaluation of udder health. Additional areas of research include evaluation of other breeds for direct health traits, use of multiple-trait models, and evaluations for additional functional traits such as calf health and feed efficiency. Future developments will require new and continued cooperation among numerous industry stakeholders. There is more information available than ever before with which to make better selection decisions; however, this also makes it increasingly important to provide accurate and unbiased information.

Symposium review: Exploiting homozygosity in the era of genomics-Selection, inbreeding, and mating programs

The advent of genomic selection paved the way for an unprecedented acceleration in genetic progress. The increased ability to select superior individuals has been coupled with a drastic reduction in the generation interval for most dairy populations, representing both an opportunity and a challenge. Homozygosity is now rapidly accumulating in dairy populations. Currently, inbreeding depression is managed mostly by culling at the farm level and by controlling the overall accumulation of homozygosity at the population level. A better understanding of how homozygosity and recessive load are related will guarantee continued genetic improvement while curtailing the accumulation of harmful recessives and maintaining enough genetic variability to ensure the possibility of selection in the face of changing environmental conditions. In this review, we present a snapshot of the current dairy selection structure as it relates to response to selection and accumulation of homozygosity, briefly outline the main approaches currently used to manage inbreeding and overall variability, and present some approaches that can be used in the short term to control accumulation of harmful recessives while maintaining sustained selection pressure.

Using Monte Carlo method to include polygenic effects in calculation of SNP-BLUP model reliability

An SNP-BLUP model is computationally scalable even for large numbers of genotyped animals. When genetic variation cannot be completely captured by SNP markers, a more accurate model is obtained by fitting a residual polygenic effect (RPG) as well. However, inclusion of the RPG effect increases the size of the SNP-BLUP mixed model equations (MME) by the number of genotyped animals. Consequently, the calculation of model reliabilities requiring elements of the inverted MME coefficient matrix becomes more computationally challenging with increasing numbers of genotyped animals. We present a Monte Carlo (MC)-based sampling method to estimate the reliability of the SNP-BLUP model including the RPG effect, where the MME size depends on the number of markers and MC samples. We compared reliabilities calculated using different RPG proportions and different MC sample sizes in analyzing 2 data sets. Data set 1 (data set 2) contained 19,757 (222,619) genotyped animals, with 11,729 (50,240) SNP markers, and 231,186 (13.35 million) pedigree animals. Correlations between the correct and the MC-calculated reliabilities were above 98% even with 5,000 MC samples and an 80% RPG proportion in both data sets. However, more MC samples were needed to achieve a small maximum absolute difference and mean squared error, particularly when the RPG proportion exceeded 20%. The computing time for MC SNP-BLUP was shorter than for GBLUP. In conclusion, the MC-based approach can be an effective strategy for calculating SNP-BLUP model reliability with an RPG effect included.

Current status of genomic evaluation

Early application of genomic selection relied on SNP estimation with phenotypes or de-regressed proofs (DRP). Chips of 50k SNP seemed sufficient for an accurate estimation of SNP effects. Genomic estimated breeding values (GEBV) were composed of an index with parent average, direct genomic value, and deduction of a parental index to eliminate double counting. Use of SNP selection or weighting increased accuracy with small data sets but had minimal to no impact with large data sets. Efforts to include potentially causative SNP derived from sequence data or high-density chips showed limited or no gain in accuracy. After the implementation of genomic selection, EBV by BLUP became biased because of genomic preselection and DRP computed based on EBV required adjustments, and the creation of DRP for females is hard and subject to double counting. Genomic selection was greatly simplified by single-step genomic BLUP (ssGBLUP). This method based on combining genomic and pedigree relationships automatically creates an index with all sources of information, can use any combination of male and female genotypes, and accounts for preselection. To avoid biases, especially under strong selection, ssGBLUP requires that pedigree and genomic relationships are compatible. Because the inversion of the genomic relationship matrix (G) becomes costly with more than 100k genotyped animals, large data computations in ssGBLUP were solved by exploiting limited dimensionality of genomic data due to limited effective population size. With such dimensionality ranging from 4k in chickens to about 15k in cattle, the inverse of G can be created directly (e.g., by the algorithm for proven and young) at a linear cost. Due to its simplicity and accuracy, ssGBLUP is routinely used for genomic selection by the major chicken, pig, and beef industries. Single step can be used to derive SNP effects for indirect prediction and for genome-wide association studies, including computations of the P-values. Alternative single-step formulations exist that use SNP effects for genotyped or for all animals. Although genomics is the new standard in breeding and genetics, there are still some problems that need to be solved. This involves new validation procedures that are unaffected by selection, parameter estimation that accounts for all the genomic data used in selection, and strategies to address reduction in genetic variances after genomic selection was implemented.

Genomic predictions for crossbred dairy cattle

Genomic evaluations are useful for crossbred as well as purebred populations when selection is applied to commercial herds. Dairy farmers had already spent more than $1 million to genotype over 32,000 crossbred animals before US genomic evaluations became available for those animals. Thus, new tools were needed to provide accurate genomic predictions for crossbreds. Genotypes for crossbreds are imputed more accurately when the imputation reference population includes purebreds. Therefore, genotypes of 6,296 crossbred animals were imputed from lower-density chips by including either 3,119 ancestors or 834,367 genotyped animals in the reference population. Crossbreds in the imputation study included 733 Jersey × Holstein F₁ animals, 55 Brown Swiss × Holstein F₁ animals, 2,300 Holstein backcrosses, 2,026 Jersey backcrosses, 27 Brown Swiss backcrosses, and 502 other crossbreds of various breed combinations. Another 653 animals appeared to be purebreds that owners had miscoded as a different breed. Genomic breed composition was estimated from 60,671 markers using the known breed identities for purebred, progeny-tested Holstein, Jersey, Brown Swiss, Ayrshire, and Guernsey bulls as the 5 traits (breed fractions) to be predicted. Estimates of breed composition were adjusted so that no percentages were negative or exceeded 100%, and breed percentages summed to 100%. Another adjustment set percentages above 93.5% equal to 100%, and the resulting value was termed breed base representation (BBR). Larger percentages of missing alleles were imputed by using a crossbred reference population rather than only the closest purebred reference population. Crossbred predictions were averages of genomic predictions computed using marker effects for each pure breed, which were weighted by the animal's BBR. Marker and polygenic effects were estimated separately for each breed on the all-breed scale instead of within-breed scales. For crossbreds, genomic predictions weighted by BBR were more accurate than the average of parents' breeding values and slightly more accurate than predictions using only the predominant breed. For purebreds, single-trait predictions using only within-breed data were as accurate as multi-trait predictions with allele effects in different breeds treated as correlated effects. Crossbred genomic predicted transmitting abilities were implemented by the Council on Dairy Cattle Breeding in April 2019 and will aid producers in managing their breeding programs and selecting replacement heifers.

A study of Genomic Prediction across Generations of Two Korean Pig Populations

Simple Summary

Commercial genotyping has become accessible at a relatively low cost and nowadays it is widely used by breeders to predict production and economic traits. Many studies explored the benefits of using DNA information in breeding programs, and many methods have been established to optimize the use of such information. To date, however, very few studies have explored how prediction accuracies change across generations. Here we present a short evaluation across five generations in two pig breeds and evaluate the accuracy of the prediction of relevant production traits using different generational groups.

Abstract

Genomic models that incorporate dense marker information have been widely used for predicting genomic breeding values since they were first introduced, and it is known that the relationship between individuals in the reference population and selection candidates affects the prediction accuracy. When genomic evaluation is performed over generations of the same population, prediction accuracy is expected to decay if the reference population is not updated. Therefore, the reference population must be updated in each generation, but little is known about the optimal way to do it. This study presents an empirical assessment of the prediction accuracy of genomic breeding values of production traits, across five generations in two Korean pig breeds. We verified the decay in prediction accuracy over time when the reference population was not updated. Additionally we compared the prediction accuracy using only the previous generation as the reference population, as opposed to using all previous generations as the reference population. Overall, the results suggested that, although there is a clear need to continuously update the reference population, it may not be necessary to keep all ancestral genotypes. Finally, comprehending how the accuracy of genomic prediction evolves over generations within a population adds relevant information to improve the performance of genomic selection.

Short communication: Phenotypic and genetic effects of the polled haplotype on yield, longevity, and fertility in US Brown Swiss, Holstein, and Jersey cattle

Phenotypes from the December 2018 US national genetic evaluations were used to compute effects of the polled haplotype in US Brown Swiss (BS), Holstein (HO), and Jersey (JE) cattle on milk, fat, and protein yields, somatic cell score, single-trait productive life, daughter pregnancy rate, heifer conception rate, and cow conception rate. Lactation records pre-adjusted for nongenetic factors and direct genomic values were used to estimate phenotypic and genetic effects of the polled haplotype, respectively. No phenotypic or direct genomic values effects were different from zero for any trait in any breed. Genomic PTA (gPTA) for the lifetime net merit (NM$) selection index of bulls born since January 1, 2012, that received a marketing code from the National Association of Animal Breeders (Madison, WI), and cows born on or after January 1, 2015, were compared to determine whether there was a systematic benefit to polled or horned genetics. Horned bulls had the highest average gPTA for NM$ in all 3 breeds, but that difference was significant only in HO and JE (HO: 615.4 ± 1.9, JE: 402.3 ± 3.4). Homozygous polled BS cows had significantly higher average gPTA for NM$ than their heterozygous polled or horned contemporaries (PP = 261.4 ± 43.5, Pp = 166.1 ± 13.7, pp = 174.1 ± 1.8), but the sample size was very small (n = 9). In HO and JE, horned cows had higher gPTA for NM$ (HO = 378.3 ± 0.2, JE = 283.3 ± 0.3). Selection for polled cattle should not have a detrimental effect on yield, fertility, or longevity, but these differences show that, in the short term, selection for polled over horned cattle will result in lower rates of genetic gain.

Genomic analysis of claw lesions in Holstein cows: Opportunities for genomic selection, quantitative trait locus detection, and gene identification

Claw lesions are the third most important health issue in dairy cattle, after mastitis and reproductive disorders, and genomic selection is a key component for long-term improvement of claw health. The objectives of this study were to assess the feasibility of a genomic evaluation for claw health in French Holstein cows, explore possibilities to increase evaluation accuracy, and gain a better understanding of the genetic determinism of claw health traits. The data set consisted of 48,685 trimmed Holstein cows, including 9,646 that were genotyped; 478 genotyped sires were also used. Seven claw lesion traits were evaluated using BLUP, genomic BLUP, BayesC, and single-step genomic BLUP, and the accuracies obtained using these approaches were measured through a validation study. The BayesC approach was used to detect quantitative trait locus (QTL) regions associated with the 7 individual traits (digital dermatitis, heel horn erosion, interdigital hyperplasia, sole hemorrhage circumscribed, sole hemorrhage diffused, sole ulcer, and white line fissure) based on their Bayes factor. Annotated genes on these regions were reported. Genomic evaluation approaches generally did not allow for greater accuracies than BLUP, except for single-step genomic BLUP. Accuracies were moderate, but best and worst validation animals were correctly discriminated and showed significant differences in lesion frequencies. A total of 192 QTL regions were identified, including 13 with major evidence or involved for 2 of the traits. A high number of genes were present on these regions, and several had functions associated with the immune system. In particular, the EPYC gene is located close to a major evidence QTL for resistance to digital dermatitis that is also a QTL for interdigital hyperplasia (on chromosome 5, around 20.9 MB) and has been associated with Ehlers-Danlos syndrome in cattle. Genomic selection can be used to improve resistance to individual claw lesions, and several possibilities exist to improve accuracies of genomic evaluations.

Accuracy of genomic evaluation with weighted single-step genomic best linear unbiased prediction for milk production traits, udder type traits, and somatic cell scores in French dairy goats

Genomic evaluation of French dairy goats is routinely conducted using the single-step genomic BLUP (ssGBLUP) method. This method has the advantage of simultaneously using all phenotypes, pedigrees, and genotypes. However, ssGBLUP assumes that all SNP explain the same amount of genetic variance, which is unlikely in the case of traits whose major genes or QTL are segregating. In this study, we investigated the effect of weighted ssGBLUP and its alternatives, which give more weight to SNP associated with the trait, on the accuracy of genomic evaluation of milk production, udder type traits, and somatic cell scores. The data set included 2,955 genotyped animals and 2,543,680 pedigree animals. The number of phenotypes varied with the trait. The accuracy of genomic evaluation was assessed on 205 genotyped Alpine and 146 genotyped Saanen goats born between 2009 and 2012. For traits with unknown QTL, weighted ssGBLUP was less accurate than, or as accurate as, ssGBLUP. For traits with identified QTL (i.e., QTL only present in the Saanen breed), weighted ssGBLUP outperformed ssGBLUP by between 2 and 14%.

Impact of genotyping strategy on the accuracy of genomic prediction in simulated populations of purebred swine

Single-step genomic BLUP (ssGBLUP) has been widely used in genomic evaluation due to relatively higher prediction accuracy and simplicity of use. The prediction accuracy from ssGBLUP depends on the amount of information available concerning both genotype and phenotype. This study investigated how information on genotype and phenotype that had been acquired from previous generations influences the prediction accuracy of ssGBLUP, and thus we sought an optimal balance about genotypic and phenotypic information to achieve a cost-effective and computationally efficient genomic evaluation. We generated two genetically correlated traits (h2 = 0.35 for trait A, h2 = 0.10 for trait B and genetic correlation 0.20) as well as two distinct populations mimicking purebred swine. Phenotypic and genotypic information in different numbers of previous generations and different genotyping rates for each litter were set to generate different datasets. Prediction accuracy was evaluated by correlating genomic estimated breeding values with true breeding values for genotyped animals in the last generation. The results revealed a negligible impact of previous generations that lacked genotyped animals on the prediction accuracy. Phenotypic and genotypic data, including the most recent three to four generations with a genotyping rate of 40% or 50% for each litter, could lead to asymptotic maximum prediction accuracy for genotyped animals in the last generation. Single-step genomic best linear unbiased prediction yielded an optimal balance about genotypic and phenotypic information to ensure a cost-effective and computationally efficient genomic evaluation of populations of polytocous animals such as purebred pigs.

Efficient single-step genomic evaluation for a multibreed beef cattle population having many genotyped animals

An equivalent computational approach called ssGTBLUP was formulated for the original single-step GBLUP (ssGBLUP). In ssGTBLUP, the genomic relationship matrix has the form = ' + , where the (centered and scaled) marker matrix has size x (numbers of genotypes and markers), and the matrix can be easily inverted. The inverse can be written as = - ' where is an by matrix. When the preconditioned conjugate gradient (PCG) method is used to solve the mixed model equations, a matrix vector product needs to be computed. In ssGBLUP, this requires multiplications, but in ssGTBLUP, the product ' has 2 multiplications and has multiplications with the constant independent of or . In an approximate approach called ssGTBLUP(p), the eigendecomposition of ' is used to reduce the number of rows in the matrix. Here, p is the percentage of total variance explained by the accepted eigenvalues. The objective of this study was to compare the performance of ssGBLUP, ssGTBLUP, ssGTBLUP(p), and the APY (algorithm for proven and young) method. In APY, the core had 50,000 (APY50K), 30,000 (APY30K), or 10,000 (APY10K) animals. The approaches were tested on the Irish beef carcass conformation genetic evaluation which has a heterogeneous multibreed population. The pedigree had 13.3 million animals. There were = 54,620 markers available from = 163,277 genotyped animals. For genotyped animals, the correlations of breeding values between ssGBLUP and ssGTBLUP(p) for the 11 traits in the model ranged from 0.999-1.000 for p = 99, 0.998-1.000 for p = 98, and 0.992-0.998 for p = 95 but were 0.994-1.000 for APY50K, 0.969-0.997 for APY30K, and 0.899-0.967 for APY10K. Computing times per iteration were 4.43, 3.30, 2.69, 2.29, 1.55, 1.76, 1.27, and 0.55 min for ssGBLUP, ssGTBLUP, ssGTBLUP(99), ssGTBLUP(98), ssGTBLUP(95), APY50K, APY30K, and APY10K, respectively. The ssGTBLUP(p) approach allowed a well-defined approximation to ssGBLUP and fast computations.

Genomic and single-step evaluations of carcass traits of young bulls in dual-purpose cattle

Genetic evaluations for carcass traits of young bulls in Normande and Montbeliarde breeds are currently being developed in France. In order to determine a suitable genomic evaluation for three carcass traits of young bulls, genomic breeding values were estimated for young candidates to selection using different approaches. Records of 111,789 Normande and 118,183 Montbeliarde were used. Average progeny pre-adjusted performances (DYD) were calculated for sires. Evaluation approaches were compared based on an assessment of their accuracy (correlation between DYD and estimated breeding values [EBVs]) and bias (regression coefficient of DYD on EBVs) on the 20% youngest AI sires. All genomic approaches were generally more accurate than BLUP (+.045 to +.116 correlation points), except for age at slaughter where single-step GBLUP (SSGBLUP) was the only genomic method leading to a greater accuracy (+.038 to +.126 points). The best setting of the SSGBLUP relationship matrix was characterized by a weight of 30% for pedigree information in the genomic relationship matrix. SSGBLUP was the most valuable evaluation approach for the evaluation of carcass traits of Normande and Montbeliarde young bulls.

Genomic evaluation, breed identification, and population structure of Guernsey cattle in North America, Great Britain, and the Isle of Guernsey

As of December 2015, 2,376 Guernsey bulls and cows had genotypes from collaboration between the United States, Canada, the United Kingdom, and the Isle of Guernsey. Of those, 439 bulls and 504 cows had traditional US evaluations, which provided sufficient data to justify investigation of the possible benefits of genomic evaluation for the Guernsey breed. Evaluation accuracy was assessed using a traditional 4-yr cutoff study. Twenty-two traits were analyzed (5 yield traits, 3 functional traits, and 14 conformation traits). Mean reliability gain over that for parent average was 16.8 percentage points across traits, which compares with 8.2, 18.5, 20.0, and 32.6 percentage points reported for Ayrshires, Brown Swiss, Jerseys, and Holsteins, respectively. Highest Guernsey reliability gains were for rump width (44.5 percentage points) and dairy form (40.5 percentage points); lowest gains were for teat length (1.9 percentage points) and rear legs (side view) (2.3 percentage points). Slight reliability losses (1.5 to 4.5 percentage points) were found for udder cleft, final score, and udder depth as well as a larger loss (13.6 percentage points) for fore udder attachment. Twenty-one single nucleotide polymorphisms were identified for Guernsey breed determination and can be used in routine genotype quality control to confirm breed and identify crossbreds. No haplotypes that affect fertility were identified from the current data set. Principal component analysis showed some divergence of US and Isle of Guernsey subpopulations. However, the overlap of US, Canadian, UK, and Isle of Guernsey subpopulations indicated the presence of gene flow, and the similarities in the subpopulations supports a common genomic evaluation system across the regions.

Increasing the number of single nucleotide polymorphisms used in genomic evaluation of dairy cattle

GeneSeek (Neogen Corp., Lexington, KY) designed a new version of the GeneSeek Genomic Profiler HD BeadChip for Dairy Cattle, which originally had >77,000 single nucleotide polymorphisms (SNP). A set of >140,000 SNP was selected that included all SNP on the existing GeneSeek chip, all SNP used in US national genomic evaluations, SNP that were possible functional mutations, and other informative SNP. Because SNP with a lower minor allele frequency might track causative variants better, 30,000 more SNP were selected from the Illumina BovineHD Genotyping BeadChip (Illumina Inc., San Diego, CA) by choosing SNP to maximize differences in minor allele frequency between a SNP being considered for the new chip and the 2 SNP that flanked it. Single-gene tests were included if their location was known and bioinformatics indicated relevance for dairy cattle. To determine which SNP from the new chip should be included in genomic evaluations, genotypes available from chips already in use were used to impute and evaluate the SNP set. Effects for 134,511 usable SNP were estimated for all breed-trait combinations; SNP with the largest absolute values for effects were selected (5,000 for Holsteins, 1,000 for Jerseys, and 500 each for Brown Swiss and Ayrshires for each trait). To increase overlap with the 60,671 SNP currently used for genomic evaluation, 12,094 more SNP with the largest effects were added. After removing SNP with many parent-progeny conflicts, 84,937 SNP remained. Three cutoff studies were conducted with 3 SNP sets to determine reliability gain over that for parent average when evaluations based on August 2011 data were used to predict December 2014 performance. Across all traits, mean Holstein reliability gains were 32.5, 33.4, and 32.0 percentage points for 60,671, 84,937, and 134,511 SNP, respectively. After genotypes from the new chip became available, the proposed set was reduced from 84,937 to 77,321 SNP to remove SNP that were not included during manufacture, reduce computing time, and improve imputation performance. The set of 77,321 SNP was evaluated using August 2011 data to predict April 2015 performance. Reliability gain over 60,671 SNP was 1.4 percentage points across traits for Holsteins. Improvement over 84,937 SNP was partially the result of 4mo of additional data and genotypes from the new chip. Revision of the SNP set used for genomic evaluation is expected to be an ongoing process to increase evaluation accuracy.

Implementation of genomic recursions in single-step genomic best linear unbiased predictor for US Holsteins with a large number of genotyped animals

The objectives of this study were to develop and evaluate an efficient implementation in the computation of the inverse of genomic relationship matrix with the recursion algorithm, called the algorithm for proven and young (APY), in single-step genomic BLUP. We validated genomic predictions for young bulls with more than 500,000 genotyped animals in final score for US Holsteins. Phenotypic data included 11,626,576 final scores on 7,093,380 US Holstein cows, and genotypes were available for 569,404 animals. Daughter deviations for young bulls with no classified daughters in 2009, but at least 30 classified daughters in 2014 were computed using all the phenotypic data. Genomic predictions for the same bulls were calculated with single-step genomic BLUP using phenotypes up to 2009. We calculated the inverse of the genomic relationship matrix GAPY(-1) based on a direct inversion of genomic relationship matrix on a small subset of genotyped animals (core animals) and extended that information to noncore animals by recursion. We tested several sets of core animals including 9,406 bulls with at least 1 classified daughter, 9,406 bulls and 1,052 classified dams of bulls, 9,406 bulls and 7,422 classified cows, and random samples of 5,000 to 30,000 animals. Validation reliability was assessed by the coefficient of determination from regression of daughter deviation on genomic predictions for the predicted young bulls. The reliabilities were 0.39 with 5,000 randomly chosen core animals, 0.45 with the 9,406 bulls, and 7,422 cows as core animals, and 0.44 with the remaining sets. With phenotypes truncated in 2009 and the preconditioned conjugate gradient to solve mixed model equations, the number of rounds to convergence for core animals defined by bulls was 1,343; defined by bulls and cows, 2,066; and defined by 10,000 random animals, at most 1,629. With complete phenotype data, the number of rounds decreased to 858, 1,299, and at most 1,092, respectively. Setting up GAPY(-1) for 569,404 genotyped animals with 10,000 core animals took 1.3h and 57 GB of memory. The validation reliability with APY reaches a plateau when the number of core animals is at least 10,000. Predictions with APY have little differences in reliability among definitions of core animals. Single-step genomic BLUP with APY is applicable to millions of genotyped animals.

Considering genetic characteristics in German Holstein breeding programs

Recently, several research groups have demonstrated that several haplotypes may cause embryonic loss in the homozygous state. Up to now, carriers of genetic disorders were often excluded from mating, resulting in a decrease of genetic gain and a reduced number of sires available for the breeding program. Ongoing research is very likely to identify additional genetic defects causing embryonic loss and calf mortality by genotyping a large proportion of the female cattle population and sequencing key ancestors. Hence, a clear demand is present to develop a method combining selection against recessive defects (e.g., Holstein haplotypes HH1-HH5) with selection for economically beneficial traits (e.g., polled) for mating decisions. Our proposed method is a genetic index that accounts for the allele frequencies in the population and the economic value of the genetic characteristic without excluding carriers from breeding schemes. Fertility phenotypes from routine genetic evaluations were used to determine the economic value per embryo lost. Previous research has shown that embryo loss caused by HH1 and HH2 occurs later than the loss for HH3, HH4, and HH5. Therefore, an economic value of € 97 was used against HH1 and HH2 and € 70 against HH3, HH4, and HH5. For polled, € 7 per polled calf was considered. Minor allele frequencies of the defects ranged between 0.8 and 3.3%. The polled allele has a frequency of 4.1% in the German Holstein population. A genomic breeding program was simulated to study the effect of changing the selection criteria from assortative mating based on breeding values to selecting the females using the genetic index. Selection for a genetic index on the female path is a useful method to control the allele frequencies by reducing undesirable alleles and simultaneously increasing economical beneficial characteristics maintaining most of the genetic gain in production and functional traits. Additionally, we applied the genetic index to real data and found a decrease of the genetic trend for the birth years 1990 to 2006. Since 2010 the genetic index has increased due to a strong increase in the polled frequency. However, further investigation is needed to better understand the biology to determine the correct time of embryo loss and the economic value of fertility disorders.

Single-step genomic evaluation using multitrait random regression model and test-day data

The objectives of this study were to evaluate the feasibility of use of the test-day (TD) single-step genomic BLUP (ssGBLUP) using phenotypic records of Nordic Red Dairy cows. The critical point in ssGBLUP is how genomically derived relationships (G) are integrated with population-based pedigree relationships (A) into a combined relationship matrix (H). Therefore, we also tested how different weights for genomic and pedigree relationships affect ssGBLUP, validation reliability, and validation regression coefficients. Deregressed proofs for 305-d milk, protein, and fat yields were used for a posteriori validation. The results showed that the use of phenotypic TD records in ssGBLUP is feasible. Moreover, the TD ssGBLUP model gave considerably higher validation reliabilities and validation regression coefficients than the TD model without genomic information. No significant differences were found in validation reliability between the different TD ssGBLUP models according to bootstrap confidence intervals. However, the degree of inflation in genomic enhanced breeding values is affected by the method used in construction of the H matrix. The results showed that ssGBLUP provides a good alternative to the currently used multi-step approach but there is a great need to find the best option to combine pedigree and genomic information in the genomic matrix.

Short communication: Analysis of genomic predictor population for Holstein dairy cattle in the United States--Effects of sex and age

Increased computing time for the ever-growing predictor population and linkage decay between the ancestral population and current animals have become concerns for genomic evaluation systems. The effects on reliability of US genomic evaluations from including cows and bulls in the Holstein predictor population and also from excluding older bulls from the predictor population were examined. Holstein data collected for December 2013 US genomic evaluations were used in cutoff studies to determine reliability gains, regression coefficients, and bias for 5 yield, 3 fitness, 2 fertility, and 18 conformation traits. Three predictor populations were examined based on animal sex: 30,852 cows with traditional evaluations as of August 2012, 21,883 bulls with traditional evaluations as of August 2012, and a combined group of all bulls and cows. Three subsets of the bull predictor population were examined to determine effect of age: bulls born before 1996 excluded (25% of bulls excluded), bulls born before 2001 excluded (50%), and bulls born before 2005 excluded (75%). The validation set for all predictor populations was either bulls or cows first receiving a traditional evaluation between August 2012 and December 2013. Across all traits, the addition of cows to the bull predictor population increased reliability gains by 0.4 percentage points for validation bulls and 4.4 points for validation cows. Across all traits, excluding bulls born before 1996 from the bull-only predictor population decreased gains in genomic reliability by 1.8 percentage points. For 19 of 28 traits, excluding bulls born before 2005 from the predictor population resulted in lower bias in genomic evaluations of validation bulls. Although the contribution of cows and older bulls to improved accuracy of US genomic evaluations is small, a plateau of achievable gain has not yet been reached.

Short communication: Genotyping of cows to speed up availability of genomic estimated breeding values for direct health traits in Austrian Fleckvieh (Simmental) cattle--genetic and economic aspects

The aim of this study was to quantify the impact of genotyping cows with reliable phenotypes for direct health traits on annual monetary genetic gain (AMGG) and discounted profit. The calculations were based on a deterministic approach using ZPLAN software (University of Hohenheim, Stuttgart, Germany). It was assumed that increases in reliability of the total merit index (TMI) of 5, 15, and 25 percentage points were achieved through genotyping 5,000, 25,000, and 50,000 cows, respectively. Costs for phenotyping, genotyping, and genomic estimated breeding values vary between €150 and €20 per cow. The gain in genotyping cows for traits with medium to high heritability is more than for direct health traits with low heritability. The AMGG is increased by 1.5% if the reliability of TMI is 5 percentage points higher (i.e., 5,000 cows genotyped) and 6.53% higher AMGG can be expected when the reliability of TMI is increased by 25 percentage points (i.e., 50,000 cows genotyped). The discounted profit depends not only on the costs of genotyping but also on the population size. This study indicates that genotyping cows with reliable phenotypes is feasible to speed up the availability of genomic estimated breeding values for direct health traits. But, because of the huge amount of valid phenotypes and genotypes needed to establish an efficient genomic evaluation, it is likely that financial constraints will be the main limiting factor for implementation into breeding program such as Fleckvieh Austria.

On the limited increase in validation reliability using high-density genotypes in genomic best linear unbiased prediction: observations from Fleckvieh cattle

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.

On the additive and dominant variance and covariance of individuals within the genomic selection scope

Genomic evaluation models can fit additive and dominant SNP effects. Under quantitative genetics theory, additive or "breeding" values of individuals are generated by substitution effects, which involve both "biological" additive and dominant effects of the markers. Dominance deviations include only a portion of the biological dominant effects of the markers. Additive variance includes variation due to the additive and dominant effects of the markers. We describe a matrix of dominant genomic relationships across individuals, D, which is similar to the G matrix used in genomic best linear unbiased prediction. This matrix can be used in a mixed-model context for genomic evaluations or to estimate dominant and additive variances in the population. From the "genotypic" value of individuals, an alternative parameterization defines additive and dominance as the parts attributable to the additive and dominant effect of the markers. This approach underestimates the additive genetic variance and overestimates the dominance variance. Transforming the variances from one model into the other is trivial if the distribution of allelic frequencies is known. We illustrate these results with mouse data (four traits, 1884 mice, and 10,946 markers) and simulated data (2100 individuals and 10,000 markers). Variance components were estimated correctly in the model, considering breeding values and dominance deviations. For the model considering genotypic values, the inclusion of dominant effects biased the estimate of additive variance. Genomic models were more accurate for the estimation of variance components than their pedigree-based counterparts.