Bayesian approach for evaluation of lactation curve in cross bred cattle based on monthly and bimonthly test day milk yield.

In field progeny testing program milk recording at monthly or bimonthly intervals and prediction of first lactation 305-day milk yield (FL305DMY) from these test day yields have been adapted as an alternative to daily milk recording. Wood's incomplete gamma function is the one of the commonly used nonlinear lactation curve model. In recent years Bayesian approach of fitting nonlinear biological models is gaining attention among researchers. In this study Wood's incomplete gamma function was fitted using Bayesian approach using monthly (MTDY) and bimonthly test day (BTDY) yields. The lactation curve parameters thus obtained were used for prediction of FL305DMY. Efficiency of prediction based on monthly and bimonthly test day milk yield were compared using error of prediction. It was found to be 5.78% and 7.59% as root mean square error (RMSE) based on MTDY and BTDY respectively.The Breeding values of 97 Karan Fries sires were estimated using BLUP-AM based on actual and predicted FL305DMY thus obtained. The RMSE was calculated as the difference between estimated breeding values based on actual and predicted yield. It was found that RMSE calculated based on MTDY showed only a marginal superiority of 0.79% over BTDY and showed high degree of correlation with actual yield. Therefore, recording at bimonthly intervals could be an economical alternative without compromising the efficiency.

Boosting predictabilities of agronomic traits in rice using bivariate genomic selection.

The multivariate genomic selection (GS) models have not been adequately studied and their potential remains unclear. In this study, we developed a highly efficient bivariate (2D) GS method and demonstrated its significant advantages over the univariate (1D) rival methods using a rice dataset, where four traditional traits (i.e. yield, 1000-grain weight, grain number and tiller number) as well as 1000 metabolomic traits were analyzed. The novelty of the method is the incorporation of the HAT methodology in the 2D BLUP GS model such that the computational efficiency has been dramatically increased by avoiding the conventional cross-validation. The results indicated that (1) the 2D BLUP-HAT GS analysis generally produces higher predictabilities for two traits than those achieved by the analysis of individual traits using 1D GS model, and (2) selected metabolites may be utilized as ancillary traits in the new 2D BLUP-HAT GS method to further boost the predictability of traditional traits, especially for agronomically important traits with low 1D predictabilities.

Cross-trait prediction accuracy of summary statistics in genome-wide association studies.

In the era of big data, univariate models have widely been used as a workhorse tool for quickly producing marginal estimators; and this is true even when in a high-dimensional dense setting, in which many features are "true," but weak signals. Genome-wide association studies (GWAS) epitomize this type of setting. Although the GWAS marginal estimator is popular, it has long been criticized for ignoring the correlation structure of genetic variants (i.e., the linkage disequilibrium [LD] pattern). In this paper, we study the effects of LD pattern on the GWAS marginal estimator and investigate whether or not additionally accounting for the LD can improve the prediction accuracy of complex traits. We consider a general high-dimensional dense setting for GWAS and study a class of ridge-type estimators, including the popular marginal estimator and the best linear unbiased prediction (BLUP) estimator as two special cases. We show that the performance of GWAS marginal estimator depends on the LD pattern through the first three moments of its eigenvalue distribution. Furthermore, we uncover that the relative performance of GWAS marginal and BLUP estimators highly depends on the ratio of GWAS sample size over the number of genetic variants. Particularly, our finding reveals that the marginal estimator can easily become near-optimal within this class when the sample size is relatively small, even though it ignores the LD pattern. On the other hand, BLUP estimator has substantially better performance than the marginal estimator as the sample size increases toward the number of genetic variants, which is typically in millions. Therefore, adjusting for the LD (such as in the BLUP) is most needed when GWAS sample size is large. We illustrate the importance of our results by using the simulated data and real GWAS.

Validation of single-step genomic BLUP random regression test-day models and SNP effects analysis on milk yield in French Saanen goats.

The shape of the lactation curve is linked to an animal's health, feed requirements, and milk production throughout the year. Random regression models (RRM) are widely used for genetic evaluation of total milk production throughout the lactation and for milk yield persistency. Genomic information used with the single-step genomic BLUP method (ssGBLUP) substantially improves the accuracy of genomic prediction of breeding values in the main dairy cattle breeds. The aim of this study was to implement an RRM using ssGBLUP for milk yield in Saanen dairy goats in France. The data set consisted of 7,904,246 test-day records from 1,308,307 lactations of Saanen goats collected in France between 2000 and 2017. The performance of this type of evaluation was assessed by applying a validation step with data targeting candidate bucks. The model was compared with a nongenomic evaluation and a traditional evaluation that use cumulated performance throughout the lactation model (LM). The incorporation of genomic information increased correlations between daughter yield deviations (DYD) and estimated breeding values (EBV) obtained with a partial data set for candidate bucks. The LM and the RRM had similar correlation between DYD and EBV. However, the RRM reduced overestimation of EBV and improved the slope of the regression of DYD on EBV obtained at birth. This study shows that a genomic evaluation from a ssGBLUP RRM is possible in dairy goats in France and that RRM performance is comparable to a LM but with the additional benefit of a genomic evaluation of persistency. Variance of adjacent SNPs was studied with LM and RRM following the ssGBLUP. Both approaches converged on approximately the same regions explaining more than 1% of total variance. Regions associated with persistency were also found.

SNP- and haplotype-based single-step genomic predictions for body weight, wool, and reproductive traits in North American Rambouillet sheep.

Rambouillet sheep are commonly raised in extensive grazing systems in the US, mainly for wool and meat production. Genomic evaluations in US sheep breeds, including Rambouillet, are still incipient. Therefore, we aimed to evaluate the feasibility of performing genomic prediction of breeding values for various traits in Rambouillet sheep based on single nucleotide polymorphisms (SNP) or haplotypes (fitted as pseudo-SNP) under a single-step GBLUP approach. A total of 28,834 records for birth weight (BWT), 23,306 for postweaning weight (PWT), 5,832 for yearling weight (YWT), 9,880 for yearling fibre diameter (YFD), 11,872 for yearling greasy fleece weight (YGFW), and 15,984 for number of lambs born (NLB) were used in this study. Seven hundred forty-one individuals were genotyped using a moderate (50 K; n = 677) or high (600 K; n = 64) density SNP panel, in which 32 K SNP in common between the two SNP panels (after genotypic quality control) were used for further analyses. Single-step genomic predictions using SNP (H-BLUP) or haplotypes (HAP-BLUP) from blocks with different linkage disequilibrium (LD) thresholds (0.15, 0.35, 0.50, 0.65, and 0.80) were evaluated. We also considered different blending parameters when constructing the genomic relationship matrix used to predict the genomic-enhanced estimated breeding values (GEBV), with alpha equal to 0.95 or 0.50. The GEBV were compared to the estimated breeding values (EBV) obtained from traditional pedigree-based evaluations (A-BLUP). The mean theoretical accuracy ranged from 0.499 (A-BLUP for PWT) to 0.795 (HAP-BLUP using haplotypes from blocks with LD threshold of 0.35 and alpha equal to 0.95 for YFD). The prediction accuracies ranged from 0.143 (A-BLUP for PWT) to 0.330 (A-BLUP for YGFW) while the prediction bias ranged from -0.104 (H-BLUP for PWT) to 0.087 (HAP-BLUP using haplotypes from blocks with LD threshold of 0.15 and alpha equal to 0.95 for YGFW). The GEBV dispersion ranged from 0.428 (A-BLUP for PWT) to 1.035 (A-BLUP for YGFW). Similar results were observed for H-BLUP or HAP-BLUP, independently of the LD threshold to create the haplotypes, alpha value, or trait analysed. Using genomic information (fitting individual SNP or haplotypes) provided similar or higher prediction and theoretical accuracies and reduced the dispersion of the GEBV for body weight, wool, and reproductive traits in Rambouillet sheep. However, there were no clear improvements in the prediction bias when compared to pedigree-based predictions. The next step will be to enlarge the training populations for this breed to increase the benefits of genomic predictions.

Genetic parameters and selection in full-sib families of tall fescue using best linear unbiased prediction (BLUP) analysis.

BACKGROUND: Better understanding of genetic structure of economic traits is crucial for identification and selection of superior genotypes in specific breeding programs. Best linear unbiased prediction (BLUP) is the most efficient method in this regard, which is poorly used in forage plant breeding. The present study aimed to assess genetic variation, estimate genetic parameters, and predict breeding values of five essential traits in full sib families (recognized by EST-SSR markers) of tall fescue using REML/BLUP procedure. METHOD: Forty-two full-sib families of tall fescue (included of 120 individual genotypes), recognized by EST-SSR markers along with twenty-one their corresponding parental genotypes were assessed for biomass production and agro-morphological traits at three harvests (spring, summer, and autumn) in the field during 4 years (2017-2020). RESULTS: Considerable genotypic variability was observed for all traits. Low narrow-sense heritability (h2n) for dry forage yield (DFY) at three harvest indicates that non-additive gene actions may play an important role in the inheritance of this trait. Higher h2n of yield related traits and flowering time and also significant genetic correlation of these traits with forage yield, suggests that selection based on these traits may lead to indirect genetic improvement of DFY. CONCLUSION: Our results showed the adequacy of REML/BLUP procedure for identification and selection of preferable parental genotypes and progenies with higher breeding values for future breeding programs such as variety development in tall fescue. Parental genotypes 21 M, 1 M, and 20 L were identified as superior and stable genotypes and could also produce the best hybrid combinations when they were mostly used as maternal parent.

Single- and multiple-breed genomic evaluations for conformation traits in Canadian Alpine and Saanen dairy goats.

Conformation traits are functional traits known to affect longevity, production efficiency, and profitability of dairy goats. However, genetic progress for these traits is expected to be slower than for milk production traits due to the limited number of herds participating in type classification programs, and often lower heritability estimates. Genomic selection substantially accelerates the rate of genetic progress in many species and industries, especially for lowly heritable, difficult, or expensive to measure traits. Therefore, the main objectives of this study were (1) to evaluate the potential benefits of the implementation of single-step genomic evaluations for conformation traits in Canadian Alpine and Saanen dairy goats, and (2) to investigate the effect of the use of single- and multiple-breed training populations. The phenotypes used in this study were linear conformation scores, on a 1-to-9 scale, for 8 traits (i.e., body capacity, dairy character, fore udder, feet and legs, general appearance, rear udder, medial suspensory ligament, and teats) of 5,158 Alpine and 2,342 Saanen does. Genotypes were available for 833 Alpine and 874 Saanen animals. Averaged across all traits, the use of multiple-breed analyses increased validation accuracy for Saanen, and reduced bias of genomically enhanced breeding values (GEBV) for both Alpine and Saanen compared with single-breed analyses. Little benefit was observed from the use of GEBV relative to pedigree-based EBV in terms of validation accuracy and bias, possibly due to limitations in the validation design, but substantial gains of 0.14 to 0.21 (32-50%) were observed in the theoretical accuracy of validation animals when averaged across traits for single- and multiple-breed analyses. Across the whole genotyped population, average gains in theoretical accuracy for GEBV compared with EBV across all traits ranged from 0.15 to 0.17 (32-37%) for Alpine and 0.17 to 0.19 (40-41%) for Saanen, depending on the model used. The largest gains were observed for does without classification records (0.19-0.22 or 50-55%) and bucks without daughter classification records (0.20-0.27 or 57-82%), which have the least information contributing to their traditional EBV. The use of multiple-breed rather than single-breed models was most beneficial for the Saanen breed, which had fewer phenotypic records available for the analyses. These results suggest that the implementation of genomic selection could increase the accuracy of breeding values for conformation traits in Canadian dairy goats.

Grouping of genomic markers in populations with family structure.

BACKGROUND: Linkage and linkage disequilibrium (LD) between genome regions cause dependencies among genomic markers. Due to family stratification in populations with non-random mating in livestock or crop, the standard measures of population LD such as [Formula: see text] may be biased. Grouping of markers according to their interdependence needs to account for the actual population structure in order to allow proper inference in genome-based evaluations. RESULTS: Given a matrix reflecting the strength of association between markers, groups are built successively using a greedy algorithm; largest groups are built at first. As an option, a representative marker is selected for each group. We provide an implementation of the grouping approach as a new function to the R package hscovar. This package enables the calculation of the theoretical covariance between biallelic markers for half- or full-sib families and the derivation of representative markers. In case studies, we have shown that the number of groups comprising dependent markers was smaller and representative SNPs were spread more uniformly over the investigated chromosome region when the family stratification was respected compared to a population-LD approach. In a simulation study, we observed that sensitivity and specificity of a genome-based association study improved if selection of representative markers took family structure into account. CONCLUSIONS: Chromosome segments which frequently recombine in the underlying population can be identified from the matrix of pairwise dependence between markers. Representative markers can be exploited, for instance, for dimension reduction prior to a genome-based association study or the grouping structure itself can be employed in a grouped penalization approach.

The utility of genomic prediction models in evolutionary genetics.

Variation in complex traits is the result of contributions from many loci of small effect. Based on this principle, genomic prediction methods are used to make predictions of breeding value for an individual using genome-wide molecular markers. In breeding, genomic prediction models have been used in plant and animal breeding for almost two decades to increase rates of genetic improvement and reduce the length of artificial selection experiments. However, evolutionary genomics studies have been slow to incorporate this technique to select individuals for breeding in a conservation context or to learn more about the genetic architecture of traits, the genetic value of missing individuals or microevolution of breeding values. Here, we outline the utility of genomic prediction and provide an overview of the methodology. We highlight opportunities to apply genomic prediction in evolutionary genetics of wild populations and the best practices when using these methods on field-collected phenotypes.

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.

Cross-validation of best linear unbiased predictions of breeding values using an efficient leave-one-out strategy.

Empirical estimates of the accuracy of estimates of breeding values (EBV) can be obtained by cross-validation. Leave-one-out cross-validation (LOOCV) is an extreme case of k-fold cross-validation. Efficient strategies for LOOCV of predictions of phenotypes have been developed for a simple model with an overall mean and random marker or animal genetic effects. The objective here was to develop and evaluate an efficient LOOCV method for prediction of breeding values and other random effects under a general mixed linear model with multiple random effects. Conventional LOOCV of EBV requires inverting an (n-1)×(n-1) covariance matrix for each of n (= number of observations) data sets. Our efficient LOOCV obtains the required inverses from the inverse of the covariance matrix for all n observations. The efficient method can be applied to complex models with multiple fixed and random effects, but requires fixed effects to be treated as random, with large variances. An alternative is to precorrect observations using estimates of fixed effects obtained from the complete data, but this can lead to biases. The efficient LOOCV method was compared to conventional LOOCV of predictions of breeding values in terms of computational demands and accuracy. For a data set with 3,205 observations and a model with multiple random and fixed effects, the efficient LOOCV method was 962 times faster than the conventional LOOCV with precorrection for fixed effects based on each training data set but resulted in identical EBV. A computationally efficient LOOCV for prediction of breeding values for single- and multiple-trait mixed models with multiple fixed and random effects was successfully developed. The method enables cross-validation of predictions of breeding values and of any linear combination of random and/or fixed effects, along with leave-one-out precorrection of validation phenotypes.

Avoiding preselection bias in subsequent single-step genomic BLUP evaluations of genomically preselected animals.

In animal breeding, parents of the next generation are usually selected in multiple stages, and the initial stages of this selection are called preselection. Preselection reduces the information available for subsequent evaluation of preselected animals and this sometimes leads to bias. The objective of this study was to establish the minimum information required to subsequently evaluate genomically preselected animals without bias arising from preselection, with single-step genomic best linear unbiased prediction (ssGBLUP). We simulated a nucleus of a breeding program in which a recent population of 15 generations was produced. In each generation, parents of the next generation were selected in a single-stage selection based on pedigree BLUP. However, in generation 15, 10% of male and 15% of female offspring were preselected on their genomic estimated breeding values (GEBV). These GEBV were estimated using ssGBLUP, including the pedigree of all animals in generations 0-15, genotypes of all animals in generations 13-15 and phenotypes of all animals in generations 11-14. In subsequent ssGBLUP evaluation of these preselected animals, genotypes and phenotypes from various groups of animals were excluded one after another. We found that GEBV of the preselected animals were only estimated without preselection bias when genotypes and phenotypes of all animals in generations 13 and 14 and of the preselected animals were included in the subsequent evaluation. We also found that genotypes of the animals discarded at preselection only helped in reducing preselection bias in GEBV of their preselected sibs when genotypes of their parents were absent or excluded from the subsequent evaluation. We concluded that to prevent preselection bias in subsequent ssGBLUP evaluation of genomically preselected animals, information representative of the reference data used in the evaluation at preselection and genotypes and phenotypes of the preselected animals are needed in the subsequent evaluation.

Achievements and Challenges of Genomics-Assisted Breeding in Forest Trees: From Marker-Assisted Selection to Genome Editing.

Forest tree breeding efforts have focused mainly on improving traits of economic importance, selecting trees suited to new environments or generating trees that are more resilient to biotic and abiotic stressors. This review describes various methods of forest tree selection assisted by genomics and the main technological challenges and achievements in research at the genomic level. Due to the long rotation time of a forest plantation and the resulting long generation times necessary to complete a breeding cycle, the use of advanced techniques with traditional breeding have been necessary, allowing the use of more precise methods for determining the genetic architecture of traits of interest, such as genome-wide association studies (GWASs) and genomic selection (GS). In this sense, main factors that determine the accuracy of genomic prediction models are also addressed. In turn, the introduction of genome editing opens the door to new possibilities in forest trees and especially clustered regularly interspaced short palindromic repeats and CRISPR-associated protein 9 (CRISPR/Cas9). It is a highly efficient and effective genome editing technique that has been used to effectively implement targetable changes at specific places in the genome of a forest tree. In this sense, forest trees still lack a transformation method and an inefficient number of genotypes for CRISPR/Cas9. This challenge could be addressed with the use of the newly developing technique GRF-GIF with speed breeding.

Genetic parameters of gestation length trait in dromedary camels (Camelus dromedarius).

Gestation length (GL) data of dromedary camels were analysed for the period from 2007 to 2018. The database of the largest dairy camel herds (Dubai, United Arab Emirates) was used in this study. The data of 4,084 camels included in the assessment were classified into six ecotypes (Emirati, Emirati cross, Black, Pakistani, Saudi-Sudanese and Saudi cross). The aim of the study was to describe the heritability of GL of camels and the breeding value (BV) of sires for this trait. The genetic parameters of GL were estimated by the General Linear Model method and two Best Linear Unbiased Prediction (BLUP) animal models as well. The mean (±SE) of GL of camels was 384.3 ± 0.2 days. The direct heritability of GL (0.26 ± 0.06-0.36 ± 0.08) was higher than the maternal heritability (0.00 ± 0.05-0.13 ± 0.06) obtained. The maternal permanent environmental effect (0.15 ± 0.05) was similar to the results estimated previously in dromedary camel, but higher than the data reported by relevant sources in other species. Based on the results of this study it can be concluded that the GL of dromedary camels is a species-specific value similar to that in cattle, which is less affected by the maternal influence. Considerable differences (16 days) exist among male dromedaries in their BV for the GL trait.

Design of experiments for fine-mapping quantitative trait loci in livestock populations.

BACKGROUND: Single nucleotide polymorphisms (SNPs) which capture a significant impact on a trait can be identified with genome-wide association studies. High linkage disequilibrium (LD) among SNPs makes it difficult to identify causative variants correctly. Thus, often target regions instead of single SNPs are reported. Sample size has not only a crucial impact on the precision of parameter estimates, it also ensures that a desired level of statistical power can be reached. We study the design of experiments for fine-mapping of signals of a quantitative trait locus in such a target region. METHODS: A multi-locus model allows to identify causative variants simultaneously, to state their positions more precisely and to account for existing dependencies. Based on the commonly applied SNP-BLUP approach, we determine the z-score statistic for locally testing non-zero SNP effects and investigate its distribution under the alternative hypothesis. This quantity employs the theoretical instead of observed dependence between SNPs; it can be set up as a function of paternal and maternal LD for any given population structure. RESULTS: We simulated multiple paternal half-sib families and considered a target region of 1 Mbp. A bimodal distribution of estimated sample size was observed, particularly if more than two causative variants were assumed. The median of estimates constituted the final proposal of optimal sample size; it was consistently less than sample size estimated from single-SNP investigation which was used as a baseline approach. The second mode pointed to inflated sample sizes and could be explained by blocks of varying linkage phases leading to negative correlations between SNPs. Optimal sample size increased almost linearly with number of signals to be identified but depended much stronger on the assumption on heritability. For instance, three times as many samples were required if heritability was 0.1 compared to 0.3. An R package is provided that comprises all required tools. CONCLUSIONS: Our approach incorporates information about the population structure into the design of experiments. Compared to a conventional method, this leads to a reduced estimate of sample size enabling the resource-saving design of future experiments for fine-mapping of candidate variants.

Behavior of the Linear Regression method to estimate bias and accuracies with correct and incorrect genetic evaluation models.

Bias in genetic evaluations has been a constant concern in animal genetics. The interest in this topic has increased in the last years, since many studies have detected overestimation (bias) in estimated breeding values (EBV). Detecting the existence of bias, and the realized accuracy of predictions, is therefore of importance, yet this is difficult when studying small data sets or breeds. In this study, we tested by simulation the recently presented method Linear Regression (LR) for estimation of bias, slope, and accuracy of pedigree EBV. The LR method computes statistics by comparing EBV from a data set containing old, partial information with EBV from a data set containing all information (old and new, a whole data set) for the same individuals. The method proposes an estimator for bias (Δpˆ), an estimator of slope (bpˆ), and 3 estimators related to accuracies: the ratio between accuracies [Formula: see text] the reliability of the partial data set (accp2ˆ), and the ratio of reliabilities (ρp,w2ˆ). We simulated a dairy scheme for low (0.10) and moderate (0.30) heritabilities. In both cases, we checked the behavior of the estimators for 3 scenarios: (1) when the evaluation model is the same as the model used to simulate the data; (2) when the evaluation model uses an incorrect heritability; and (3) when the data includes an environmental trend. For scenarios in which the evaluation model was correct, the LR method was capable of correctly estimating bias, slope, and accuracies, with better performance for higher heritability [i.e., corr(bp,bpˆ) was 0.45 for h2 = 0.10 and 0.59 for h2 = 0.30]. In cases of the use of incorrect heritabilities in the evaluation model, the bias was correctly estimated in direction but not in magnitude. In the same way, the magnitudes of bias and of slope were underestimated in scenarios with environmental trends in data, except for cases in which contemporary groups were random and greatly shrunken. In general, accuracies were well estimated in all scenarios. The LR method is capable of checking bias and accuracy in all cases, if the evaluation model is reasonably correct or robust, and its estimations are more precise with more information (e.g., high heritability). If the model uses an incorrect heritability or a hidden trend exists in the data, it is still possible to estimate the direction and existence of bias and slope but not always their magnitudes.

Symposium review: Single-step genomic evaluations in dairy cattle.

During the last decade, genomic selection has revolutionized dairy cattle breeding. For example, Nordic dairy cows (Denmark, Finland, and Sweden) born in 2018 were >90% sired by young genomically tested bulls. Thus, the average age of sires for Red Dairy Cattle cows born in 2018 was only 3.1 yr, whereas in 2011 it was 5.7 yr. Earlier the key driver of genetic progress was the selection of progeny-tested sires, but now it is the genomic preselection of young sires. This leads to a biased estimation of genetic progress by the traditional genetic evaluations. When these are used as input for multi-step genomic evaluations also they became distorted. The only long-term solution to maintain unbiasedness is to include the genomic information in evaluations. Although means for single-step evaluation models were introduced in 2010, they have not yet been implemented in large-scale national dairy evaluations. At first, single-step evaluations were hindered by computational cost. This has been largely solved, either by sparse presentations of the inverses of the genomic relationship (G) and pedigree relationship (A22) matrices of genotyped animals needed in the single-step evaluation models based on G (ssGBLUP), or by using the single-step marker models. Approaches for G-1 are the APY-G, where the relationships among "young" animals are completely determined by their relationship to the "core" animals, and single-step evaluations where the G-1 is replaced by a computational formula based on the structure of G (ssGTBLUP). The single-step marker models include the marker effects either directly, as effects in the statistical model, or indirectly, to generate genomic relationships among genotyped animals. Concurrently with development of the algorithm, computing resources have evolved in both availability of computer memory and speed. The problems actively studied now are the same for both of the single-step approaches (GBLUP and marker models). Convergence in iterative solving seems to get worse with an increasing number of genotypes. These problems are more pronounced with low-heritability traits and in multi-trait models with high genetic correlations among traits. Problems are also related to the unbalancedness of pedigrees and diverse genetic groups. In many cases, the problem can be solved by properly accounting for contributions of the genotyped animals to genetic groups. The standard solving approach is preconditioned conjugate gradient iteration, in which the convergence has been improved by better preconditioning matrices. Another difficulty to be considered is inflation in genomic evaluations of candidate animals; genomic models seem to overvalue the genomic information. The problem is usually smaller in single-step evaluations than in multi-step evaluations but is more difficult to mitigate by ad hoc adjustments.

Application of multivariate single-step SNP best linear unbiased predictor model and revised SNP list for genomic evaluation of dairy cattle in Australia.

The objectives of this study were (1) to evaluate the computational feasibility of the multitrait test-day single-step SNP-BLUP (ssSNP-BLUP) model using phenotypic records of genotyped and nongenotyped animals, and (2) to compare accuracies (coefficient of determination; R2) and bias of genomic estimated breeding values (GEBV) and de-regressed proofs as response variables in 3 Australian dairy cattle breeds (i.e., Holstein, Jersey, and Red breeds). Additive genomic random regression coefficients for milk, fat, protein yield and somatic cell score were predicted in the first, second, and third lactation. The predicted coefficients were used to derive 305-d GEBV and were compared with the traditional parent averages obtained from a BLUP model without genomic information. Cow fertility traits were evaluated from the 5-trait repeatability model (i.e., calving interval, days from calving to first service, pregnancy diagnosis, first service nonreturn rate, and lactation length). The de-regressed proofs were only for calving interval. Our results showed that ssSNP-BLUP using multitrait test-day model increased reliability and reduced bias of breeding values of young animals when compared with parent average from traditional BLUP in Australian Holsten, Jersey, and Red breeds. The use of a custom selection of approximately 46,000 SNP (custom XT SNP list) increased the reliability of GEBV compared with the results obtained using the commercial Illumina 50K chip (Illumina, San Diego, CA). The use of the second preconditioner substantially improved the convergence rate of the preconditioned conjugate gradient method, but further work is needed to improve the efficiency of the computation of the Kronecker matrix product by vector. Application of ssSNP-BLUP to multitrait random regression models is computationally feasible.

Metafounder approach for single-step genomic evaluations of Red Dairy cattle.

Single-step genomic BLUP (ssGBLUP) is a powerful approach for breeding value prediction in populations with a limited number of genotyped animals. However, conflicting genomic (G) and pedigree (A22) relationship matrices complicate the implementation of ssGBLUP into practice. The metafounder (MF) approach is a recently proposed solution for this problem and has been successfully used on simulated and real multi-breed pig data. Advantages of the method are easily seen across breed evaluations, where pedigrees are traced to several pure breeds, which are thereafter used as MF. Application of the MF method to ruminants is complicated due to multi-breed pedigree structures and the inability to transmit existing unknown parent groups (UPG) to MF. In this study, we apply the MF approach for ssGBLUP evaluation of Finnish Red Dairy cattle treated as a single breed. Relationships among MF were accounted for by a (co)variance matrix (Γ) computed using estimated base population allele frequencies. The attained Γ was used to calculate a relationship matrix A22Γ for the genotyped animals. We tested the influence of SNP selection on the Γ matrix by applying a minor allele frequency (MAF) threshold (ΓMAF) where accepted markers had an MAF ≥0.05. Elements in the ΓMAF matrix were slightly lower than in the Γ matrix. Correlation between diagonal elements of the genomic and pedigree relationship matrices increased from 0.53 (A22) to 0.76 ( A22Γ and [Formula: see text] ). Average diagonal elements of A22Γ and [Formula: see text] matrices increased to the same level as in the G matrix. The ssGBLUP breeding values (GEBV) were solved using either the original 236 or redefined 8 UPG, or 8 MF computed with or without the MAF threshold. For bulls, the GEBV validation test results for the 8 UPG and 8 MF gave the same validation reliability (R2; 0.31) and over-dispersion (0.73, measured by regression coefficient b1). No significant R2 increase was observed in cows. Thus, the MF greatly influenced the pedigree relationship matrices but not the GEBV. Selection of SNP according to MAF had a notable effect on the Γ matrix and made the A22 and G matrices more similar.

Genomic analyses for predicted milk fatty acid composition throughout lactation in North American Holstein cattle.

Milk fat composition has important implications in the nutritional and processing properties of milk. Additionally, milk fat composition is associated with cow physiological and health status. The main objectives of this study were (1) to estimate genetic parameters for 5 milk fatty acid (FA) groups (i.e., short-chain, medium-chain, long-chain, saturated, and unsaturated) predicted from milk infrared spectra using a large data set; (2) to predict genomic breeding values using a longitudinal single-step genomic BLUP approach; and (3) to conduct a single-step GWAS aiming to identify genomic regions, candidate genes, and metabolic pathways associated with milk FA, and consequently, to understand the underlying biology of these traits. We used 629,769 test-day records of 201,465 first-parity Holstein cows from 6,105 herds. A total of 8,865 genotyped (Illumina BovineSNP50K BeadChip, Illumina, San Diego, CA) animals were considered for the genomic analyses. The average daily heritability ranged from 0.24 (unsaturated FA) to 0.47 (medium-chain and saturated FA). The reliability of the genomic breeding values ranged from 0.56 (long-chain fatty acid) to 0.74 (medium-chain fatty acid) when using the default τ and ω scaling parameters, whereas it ranged from 0.58 (long-chain fatty acid) to 0.73 (short-chain fatty acid) when using the optimal τ and ω values (i.e., τ = 1.5 and ω = 0.6), as defined in a previous study in the same population. Relevant chromosomal regions were identified in Bos taurus autosomes 5 and 14. The proportion of the variance explained by 20 adjacent single nucleotide polymorphisms ranged from 0.71% (saturated FA) to 15.12% (long-chain FA). Important candidate genes and pathways were also identified. In summary, our results contribute to a better understanding of the genetic architecture of predicted milk FA in dairy cattle and reinforce the relevance of using genomic information for genetic analyses of these traits.