Phenotypic and genomic modeling of lactation curves: A longitudinal perspective

Lactation curves, which describe the production pattern of milk-related traits over time, provide insightful information about individual cow health, resilience, and milk production efficiency. Key functional traits can be derived through lactation curve modeling, such as lactation peak and persistency. Furthermore, novel traits such as resilience indicators can be derived based on the variability of the deviations of observed milk yield from the expected lactation curve fitted for each animal. Lactation curve parameters are heritable, indicating that one can modify the average lactation curve of a population through selective breeding. Various statistical methods can be used for modeling longitudinal traits. Among them, the use of random regression models enables a more flexible and robust modeling of lactation curves compared with traditional models used to evaluate accumulated milk 305-d yield, as they enable the estimation of both genetic and environmental effects affecting milk production traits over time. In this symposium review, we discuss the importance of evaluating lactation curves from a longitudinal perspective and various statistical and mathematical models used to analyze longitudinal data. We also highlighted the key factors that influence milk production over time, and the potential applications of longitudinal analyses of lactation curves in improving animal health, resilience, and milk production efficiency. Overall, analyzing the longitudinal nature of milk yield will continue to play a crucial role in improving the production efficiency and sustainability of the dairy industry, and the methods and models developed can be easily translated to other longitudinal traits.

Combined single-step evaluation of functional longevity of dairy cows including correlated traits

BACKGROUND

For years, multiple trait genetic evaluations have been used to increase the accuracy of estimated breeding values (EBV) using information from correlated traits. In France, accurate approximations of multiple trait evaluations were implemented for traits that are described by different models by combining the results of univariate best linear unbiased prediction (BLUP) evaluations. Functional longevity (FL) is the trait that has most benefited from this approach. Currently, with many single-step (SS) evaluations, only univariate FL evaluations can be run. The aim of this study was to implement a "combined" SS (CSS) evaluation that extends the "combined" BLUP evaluation to obtain more accurate genomic (G) EBV for FL when information from five correlated traits (somatic cell score, clinical mastitis, conception rate for heifers and cows, and udder depth) is added.

RESULTS

GEBV obtained from univariate SS (USS) evaluations and from a CSS evaluation were compared. The correlations between these GEBV showed the benefits of including information from correlated traits. Indeed, a CSS evaluation run without any performances on FL showed that the indirect information from correlated traits to evaluate FL was substantial. USS and CSS evaluations that mimic SS evaluations with data available in 2016 were compared. For each evaluation separately, the GEBV were sorted and then split into 10 consecutive groups (deciles). Survival curves were calculated for each group, based on the observed productive life of these cows as known in 2021. Regardless of their genotyping status, the worst group of heifers based on their GEBV in 2016 was well identified in the CSS evaluation and they had a substantially shorter herd life, while those in the best heifer group had a longer herd life. The gaps between groups were more important for the genotyped than the ungenotyped heifers, which indicates better prediction of future survival.

CONCLUSIONS

A CSS evaluation is an efficient tool to improve FL. It allows a proper combination of information on functional traits that influence culling. In contrast, because of the strong selection intensity on young bulls for functional traits, the benefit of such a "combined" evaluation of functional traits is more modest for these males.

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.

Accelerated matrix-vector multiplications for matrices involving genotype covariates with applications in genomic prediction

In the last decade, a number of methods have been suggested to deal with large amounts of genetic data in genomic predictions. Yet, steadily growing population sizes and the suboptimal use of computational resources are pushing the practical application of these approaches to their limits. As an extension to the C/CUDA library miraculix, we have developed tailored solutions for the computation of genotype matrix multiplications which is a critical bottleneck in the empirical evaluation of many statistical models. We demonstrate the benefits of our solutions at the example of single-step models which make repeated use of this kind of multiplication. Targeting modern Nvidia® GPUs as well as a broad range of CPU architectures, our implementation significantly reduces the time required for the estimation of breeding values in large population sizes. miraculix is released under the Apache 2.0 license and is freely available at https://github.com/alexfreudenberg/miraculix.

An effective hyper-parameter can increase the prediction accuracy in a single-step genetic evaluation

The H-matrix best linear unbiased prediction (HBLUP) method has been widely used in livestock breeding programs. It can integrate all information, including pedigree, genotypes, and phenotypes on both genotyped and non-genotyped individuals into one single evaluation that can provide reliable predictions of breeding values. The existing HBLUP method requires hyper-parameters that should be adequately optimised as otherwise the genomic prediction accuracy may decrease. In this study, we assess the performance of HBLUP using various hyper-parameters such as blending, tuning, and scale factor in simulated and real data on Hanwoo cattle. In both simulated and cattle data, we show that blending is not necessary, indicating that the prediction accuracy decreases when using a blending hyper-parameter <1. The tuning process (adjusting genomic relationships accounting for base allele frequencies) improves prediction accuracy in the simulated data, confirming previous studies, although the improvement is not statistically significant in the Hanwoo cattle data. We also demonstrate that a scale factor, α, which determines the relationship between allele frequency and per-allele effect size, can improve the HBLUP accuracy in both simulated and real data. Our findings suggest that an optimal scale factor should be considered to increase prediction accuracy, in addition to blending and tuning processes, when using HBLUP.

Efficient large-scale single-step evaluations and indirect genomic prediction of genotyped selection candidates

BACKGROUND

Single-step genomic best linear unbiased prediction (ssGBLUP) models allow the combination of genomic, pedigree, and phenotypic data into a single model, which is computationally challenging for large genotyped populations. In practice, genotypes of animals without their own phenotype and progeny, so-called genotyped selection candidates, can become available after genomic breeding values have been estimated by ssGBLUP. In some breeding programmes, genomic estimated breeding values (GEBV) for these animals should be known shortly after obtaining genotype information but recomputing GEBV using the full ssGBLUP takes too much time. In this study, first we compare two equivalent formulations of ssGBLUP models, i.e. one that is based on the Woodbury matrix identity applied to the inverse of the genomic relationship matrix, and one that is based on marker equations. Second, we present computationally-fast approaches to indirectly compute GEBV for genotyped selection candidates, without the need to do the full ssGBLUP evaluation.

RESULTS

The indirect approaches use information from the latest ssGBLUP evaluation and rely on the decomposition of GEBV into its components. The two equivalent ssGBLUP models and indirect approaches were tested on a six-trait calving difficulty model using Irish dairy and beef cattle data that include 2.6 million genotyped animals of which about 500,000 were considered as genotyped selection candidates. When using the same computational approaches, the solving phase of the two equivalent ssGBLUP models showed similar requirements for memory and time per iteration. The computational differences between them were due to the preprocessing phase of the genomic information. Regarding the indirect approaches, compared to GEBV obtained from single-step evaluations including all genotypes, indirect GEBV had correlations higher than 0.99 for all traits while showing little dispersion and level bias.

CONCLUSIONS

In conclusion, ssGBLUP predictions for the genotyped selection candidates were accurately approximated using the presented indirect approaches, which are more memory efficient and computationally fast, compared to solving a full ssGBLUP evaluation. Thus, indirect approaches can be used even on a weekly basis to estimate GEBV for newly genotyped animals, while the full single-step evaluation is done only a few times within a year.

Multibreed genomic prediction using summary statistics and a breed-origin-of-alleles approach

Because of an increasing interest in crossbreeding between dairy breeds in dairy cattle herds, farmers are requesting breeding values for crossbred animals. However, genomically enhanced breeding values are difficult to predict in crossbred populations because the genetic make-up of crossbred individuals is unlikely to follow the same pattern as for purebreds. Furthermore, sharing genotype and phenotype information between breed populations are not always possible, which means that genetic merit (GM) for crossbred animals may be predicted without the information needed from some pure breeds, resulting in low prediction accuracy. This simulation study investigated the consequences of using summary statistics from single-breed genomic predictions for some or all pure breeds in two- and three-breed rotational crosses, rather than their raw data. A genomic prediction model taking into account the breed-origin of alleles (BOA) was considered. Because of a high genomic correlation between the breeds simulated (0.62-0.87), the prediction accuracies using the BOA approach were similar to a joint model, assuming homogeneous SNP effects for these breeds. Having a reference population with summary statistics available from all pure breeds and full phenotype and genotype information from crossbreds yielded almost as high prediction accuracies (0.720-0.768) as having a reference population with full information from all pure breeds and crossbreds (0.753-0.789). Lacking information from the pure breeds yielded much lower prediction accuracies (0.590-0.676). Furthermore, including crossbred animals in a combined reference population also benefitted prediction accuracies in the purebred animals, especially for the smallest breed population.

Genomic evaluation for two-way crossbred performance in cattle

BACKGROUND

Dairy cattle production systems are mostly based on purebreds, but recently the use of crossbreeding has received increased interest. For genetic evaluations including crossbreds, several methods based on single-step genomic best linear unbiased prediction (ssGBLUP) have been proposed, including metafounder ssGBLUP (MF-ssGBLUP) and breed-specific ssGBLUP (BS-ssGBLUP). Ideally, models that account for breed effects should perform better than simple models, but knowledge on the performance of these methods is lacking for two-way crossbred cattle. In addition, the differences in the estimates of genetic parameters (such as the genetic variance component and heritability) between these methods have rarely been investigated. Therefore, the aims of this study were to (1) compare the estimates of genetic parameters for average daily gain (ADG) and feed conversion ratio (FCR) between these methods; and (2) evaluate the impact of these methods on the predictive ability for crossbred performance.

METHODS

Bivariate models using standard ssGBLUP, MF-ssGBLUP and BS-ssGBLUP for the genetic evaluation of ADG and FCR were investigated. To measure the predictive ability of these three methods, we estimated four estimators, bias, dispersion, population accuracy and ratio of population accuracies, using the linear regression (LR) method.

RESULTS

The results show that, for both ADG and FCR, the heritabilities were low with the three methods. For FCR, the differences in the estimated genetic parameters were small between the three methods, while for ADG, those estimated with BS-ssGBLUP deviated largely from those estimated with the other two methods. Bias and dispersion were similar across the three methods. Population accuracies for both ADG and FCR were always higher with MF-ssGBLUP than with ssGBLUP, while with BS-ssGBLUP the population accuracy was highest for FCR and lowest for ADG.

CONCLUSIONS

Our results indicate that in the genetic evaluation for crossbred performance in a two-way crossbred cattle production system, the predictive ability of MF-ssGBLUP and BS-ssGBLUP is greater than that of ssGBLUP, when the estimated variance components are consistent across the three methods. Compared with BS-ssGBLUP, MF-ssGBLUP is more robust in its superiority over ssGBLUP.

Invited review: Reliability computation from the animal model era to the single-step genomic model era

The calculation of exact reliabilities involving the inversion of mixed model equations poses a heavy computational challenge when the system of equations is large. This has prompted the development of different approximation methods. We give an overview of the various methods and computational approaches in calculating reliability from the era before the animal model to the era of single-step genomic models. The different methods are discussed in terms of modeling, development, and applicability in large dairy cattle populations. The paper also describes the problems faced in reliability computation. Many details dispersed throughout the literature are presented in this paper. It is clear that a universal solution applicable to every model and input data may not be possible, but we point out several efficient and accurate algorithms developed recently for a variety of very large genomic evaluations.

A computationally efficient method for approximating reliabilities in large-scale single-step genomic prediction

BACKGROUND

In this study, computationally efficient methods to approximate the reliabilities of genomic estimated breeding values (GEBV) in a single-step genomic prediction model including a residual polygenic (RPG) effect are described. In order to calculate the reliabilities of the genotyped animals, a single nucleotide polymorphism best linear unbiased prediction (SNPBLUP) or a genomic BLUP (GBLUP), was used, where two alternatives to account for the RPG effect were tested. In the direct approach, the genomic model included the RPG effect, while in the blended method, it did not but an index was used to weight the genomic and pedigree-based BLUP (PBLUP) reliabilities. In order to calculate the single-step GBLUP reliabilities for the breeding values for the non-genotyped animals, a simplified weighted-PBLUP model that included a general mean and additive genetic effects with weights accounting for the non-genomic and genomic information was used. We compared five schemes for the weights. Two datasets, i.e., a small (Data 1) one and a large (Data 2) one were used.

RESULTS

For the genotyped animals in Data 1, correlations between approximate reliabilities using the blended method and exact reliabilities ranged from 0.993 to 0.996 across three lactations. The slopes observed by regressing the reliabilities of GEBV from the exact method on those from the blended method were 1.0 for all three lactations. For Data 2, the correlations and slopes ranged, respectively, from 0.980 to 0.986 and from 0.91 to 0.96, and for the non-genotyped animals in Data 1, they ranged, respectively, from 0.987 to 0.994 and from 0.987 to 1, which indicate that the approximations were in line with the exact results. The best approach achieved correlations of 0.992 to 0.994 across lactations.

CONCLUSIONS

Our results demonstrate that the approximated reliabilities calculated using our proposed approach are in good agreement with the exact reliabilities. The blended method for the genotyped animals is computationally more feasible than the direct method when RPG effects are included, particularly for large-scale datasets. The approach can serve as an effective strategy to estimate the reliabilities of GEBV in large-scale single-step genomic predictions.

Animal board invited review: Genomic-based improvement of cattle in response to climate change

Climate change brings challenges to cattle production, such as the need to adapt to new climates and pressure to reduce greenhouse emissions (GHG). In general, the improvement of traits in current breeding goals is favourably correlated with the reduction of GHG. Current breeding goals and tools for increasing cattle production efficiency have reduced GHG. The same amount of production can be achieved by a much smaller number of animals. Genomic selection (GS) may offer a cost-effective way of using an efficient breeding approach, even in low- and middle-income countries. As climate change increases the intensity of heatwaves, adaptation to heat stress leads to lower efficiency of production and, thus, is unfavourable to the goal of reducing GHG. Furthermore, there is evidence that heat stress during cow pregnancy can have many generation-long lowering effects on milk production. Both adaptation and reduction of GHG are among the difficult-to-measure traits for which GS is more efficient and suitable than the traditional non-genomic breeding evaluation approach. Nevertheless, the commonly used within-breed selection may be insufficient to meet the new challenges; thus, cross-breeding based on selecting highly efficient and highly adaptive breeds may be needed. Genomic introgression offers an efficient approach for cross-breeding that is expected to provide high genetic progress with a low rate of inbreeding. However, well-adapted breeds may have a small number of animals, which is a source of concern from a genetic biodiversity point of view. Furthermore, low animal numbers also limit the efficiency of genomic introgression. Sustainable cattle production in countries that have already intensified production is likely to emphasise better health, reproduction, feed efficiency, heat stress and other adaptation traits instead of higher production. This may require the application of innovative technologies for phenotyping and further use of new big data techniques to extract information for breeding.

Single-step genomic BLUP with many metafounders

Single-step genomic BLUP (ssGBLUP) model for routine genomic prediction of breeding values is developed intensively for many dairy cattle populations. Compatibility between the genomic (G) and the pedigree (A) relationship matrices remains an important challenge required in ssGBLUP. The compatibility relates to the amount of missing pedigree information. There are two prevailing approaches to account for the incomplete pedigree information: unknown parent groups (UPG) and metafounders (MF). unknown parent groups have been used routinely in pedigree-based evaluations to account for the differences in genetic level between groups of animals with missing parents. The MF approach is an extension of the UPG approach. The MF approach defines MF which are related pseudo-individuals. The MF approach needs a Γ matrix of the size number of MF to describe relationships between MF. The UPG and MF can be the same. However, the challenge in the MF approach is the estimation of Γ having many MF, typically needed in dairy cattle. In our study, we present an approach to fit the same amount of MF as UPG in ssGBLUP with Woodbury matrix identity (ssGTBLUP). We used 305-day milk, protein, and fat yield data from the DFS (Denmark, Finland, Sweden) Red Dairy cattle population. The pedigree had more than 6 million animals of which 207,475 were genotyped. We constructed the preliminary gamma matrix (Γpre) with 29 MF which was expanded to 148 MF by a covariance function (Γ148). The quality of the extrapolation of the Γpre matrix was studied by comparing average off-diagonal elements between breed groups. On average relationships among MF in Γ148 were 1.8% higher than in Γpre. The use of Γ148 increased the correlation between the G and A matrices by 0.13 and 0.11 for the diagonal and off-diagonal elements, respectively. [G]EBV were predicted using the ssGTBLUP and Pedigree-BLUP models with the MF and UPG. The prediction reliabilities were slightly higher for the ssGTBLUP model using MF than UPG. The ssGBLUP MF model showed less overprediction compared to other models.

Single-step genomic BLUP with genetic groups and automatic adjustment for allele coding

Background

Genomic estimated breeding values (GEBV) by single-step genomic BLUP (ssGBLUP) are affected by the centering of marker information used. The use of a fixed effect called J factor will lead to GEBV that are unaffected by the centering used. We extended the use of a single J factor to a group of J factors.

Results

J factor(s) are usually included in mixed model equations (MME) as regression effects but a transformation similar to that regularly used for genetic groups can be applied to obtain a simpler MME, which is sparser than the original MME and does not need computation of the J factors. When the J factor is based on the same structure as the genetic groups, then MME can be transformed such that coefficients for the genetic groups no longer include information from the genomic relationship matrix. We illustrate the use of J factors in the analysis of a Red dairy cattle data set for fertility.

Conclusions

The GEBV from these analyses confirmed the theoretical derivations that show that the resulting GEBV are allele coding independent when a J factor is used. Transformed MME led to faster computing time than the original regression-based MME.

A review of inbreeding depression in dairy cattle: current status, emerging control strategies, and future prospects

Dairy cattle breeding has historically focused on relatively small numbers of elite bulls as sires of sons. In recent years, even if generation intervals were reduced and more diverse sires of sons could have been selected, genomic selection has not fundamentally changed the fact that a large number of individuals are being analyzed. However, a relatively small number of elite bulls are still siring those animals. Therefore inbreeding-derived negative consequences in the gene pool have brought concern. The detrimental effects of non-additive genetic changes such as inbreeding depression and dominance have been widely disseminated while seriously affecting bioeconomically important parameters because of an antagonistic relationship between dairy production and reproductive traits. Therefore, the estimation of benefits and limitations of inbreeding and variance of the selection response deserves to be evaluated and discussed to preserve genetic variability, a significant concern in the selection of individuals for reproduction and production. Short-term strategies for genetic merit improvement through modern breeding programs have severely lowered high-producing dairy cattle fertility potential. Since the current selection programs potentially increase long-term costs, genetic diversity has decreased globally as a consequence. Therefore, a greater understanding of the potential that selection programs have for supporting long-term genetic sustainability and genetic diversity among dairy cattle populations should be prioritized in managing farm profitability. The present review provides a broad approach to current inbreeding-derived problems, identifying critical points to be solved and possible alternative strategies to control selection against homozygous haplotypes while maintaining sustained selection pressure. Moreover, this manuscript explores future perspectives, emphasizing theoretical applications and critical points, and strategies to avoid the adverse effects of inbreeding in dairy cattle. Finally, this review provides an overview of challenges that will soon require multidisciplinary approaches to managing dairy cattle populations, intending to combine increases in productive trait phenotypes with improvements in reproductive, health, welfare, linear conformation, and adaptability traits into the foreseeable future.

Single-step genomic evaluation of Russian dairy cattle using internal and external information

Genomic data are widely used in predicting the breeding values of dairy cattle. The accuracy of genomic prediction depends on the size of the reference population and how related the candidate animals are to it. For populations with limited numbers of progeny‐tested bulls, the reference populations must include cows and data from external populations. The aim of this study was to implement state‐of‐the‐art single‐step genomic evaluations for milk and fat yield in Holstein and Russian Black & White cattle in the Leningrad region (LR, Russia), using only a limited number of genotyped animals. We complemented internal information with external pseudo‐phenotypic and genotypic data of bulls from the neighbouring Danish, Finnish and Swedish Holstein (DFS) population. Three data scenarios were used to perform single‐step GBLUP predictions in the LR dairy cattle population. The first scenario was based on the original LR reference population, which constituted 1,080 genotyped cows and 427 genotyped bulls. In the second scenario, the genotypes of 414 bulls related to the LR from the DFS population were added to the reference population. In the third scenario, LR data were further augmented with pseudo‐phenotypic data from the DFS population. The inclusion of foreign information increased the validation reliability of the milk yield by up to 30%. Suboptimal data recording practices hindered the improvement of fat yield. We confirmed that the single‐step model is suitable for populations with a low number of genotyped animals, especially when external information is integrated into the evaluations. Genomic prediction in populations with a low number of progeny‐tested bulls can be based on data from genotyped cows and on the inclusion of genotypes and pseudo‐phenotypes from the external population. This approach increased the validation reliability of the implemented single‐step model in the milk yield, but shortcomings in the LR data recording scheme prevented improvements in fat yield.

Invited review: Unknown-parent groups and metafounders in single-step genomic BLUP

Single-step genomic BLUP (ssGBLUP) is a method for genomic prediction that integrates matrices of pedigree (A) and genomic (G) relationships into a single unified additive relationship matrix whose inverse is incorporated into a set of mixed model equations (MME) to compute genomic predictions. Pedigree information in dairy cattle is often incomplete. Missing pedigree potentially causes biases and inflation in genomic estimated breeding values (GEBV) obtained with ssGBLUP. Three major issues are associated with missing pedigree in ssGBLUP, namely biased predictions by selection, missing inbreeding in pedigree relationships, and incompatibility between G and A in level and scale. These issues can be solved using a proper model for unknown-parent groups (UPG). The theory behind the use of UPG is well established for pedigree BLUP, but not for ssGBLUP. This study reviews the development of the UPG model in pedigree BLUP, the properties of UPG models in ssGBLUP, and the effect of UPG on genetic trends and genomic predictions. Similarities and differences between UPG and metafounder (MF) models, a generalized UPG model, are also reviewed. A UPG model (QP) derived using a transformation of the MME has a good convergence behavior. However, with insufficient data, the QP model may yield biased genetic trends and may underestimate UPG. The QP model can be altered by removing the genomic relationships linking GEBV and UPG effects from MME. This altered QP model exhibits less bias in genetic trends and less inflation in genomic predictions than the QP model, especially with large data sets. Recently, a new model, which encapsulates the UPG equations into the pedigree relationships for genotyped animals, was proposed in simulated purebred populations. The MF model is a comprehensive solution to the missing pedigree issue. This model can be a choice for multibreed or crossbred evaluations if the data set allows the estimation of a reasonable relationship matrix for MF. Missing pedigree influences genetic trends, but its effect on the predictability of genetic merit for genotyped animals should be negligible when many proven bulls are genotyped. The SNP effects can be back-solved using GEBV from older genotyped animals, and these predicted SNP effects can be used to calculate GEBV for young-genotyped animals with missing parents.

Genomic prediction of milk-production traits and somatic cell score using single-step genomic best linear unbiased predictor with random regression test-day model in Thai dairy cattle

Cow genotypes are expected to improve the accuracy of genomic estimated breeding values (GEBV) for young bulls in relatively small populations such as Thai Holstein-Friesian crossbred dairy cattle in Thailand. The objective of this study was to investigate the effect of cow genotypes on the predictive ability and individual accuracies of GEBV for young dairy bulls in Thailand. Test-day data included milk yield (n = 170,666), milk component traits (fat yield, protein yield, total solids yield, fat percentage, protein percentage, and total solids percentage; n = 160,526), and somatic cell score (n = 82,378) from 23,201, 82,378, and 13,737 (for milk yield, milk component traits, and SCS, respectively) cows calving between 1993 and 2017, respectively. Pedigree information included 51,128; 48,834; and 32,743 animals for milk yield, milk component traits, and somatic cell score, respectively. Additionally, 876, 868, and 632 pedigreed animals (for milk yield, milk component traits, and SCS, respectively) were genotyped (152 bulls and 724 cows), respectively, using Illumina Bovine SNP50 BeadChip. We cut off the data in the last 6 yr, and the validation animals were defined as genotyped bulls with no daughters in the truncated set. We calculated GEBV using a single-step random regression test-day model (SS-RR-TDM), in comparison with estimated breed value (EBV) based on the pedigree-based model used as the official method in Thailand (RR-TDM). Individual accuracies of GEBV were obtained by inverting the coefficient matrix of the mixed model equations, whereas validation accuracies were measured by the Pearson correlation between deregressed EBV from the full data set and (G)EBV predicted with the reduced data set. When only bull genotypes were used, on average, SS-RR-TDM increased individual accuracies by 0.22 and validation accuracies by 0.07, compared with RR-TDM. With cow genotypes, the additional increase was 0.02 for individual accuracies and 0.06 for validation accuracies. The inflation of GEBV tended to be reduced using cow genotypes. Genomic evaluation by SS-RR-TDM is feasible to select young bulls for the longitudinal traits in Thai dairy cattle, and the accuracy of selection is expected to be increased with more genotypes. Genomic selection using the SS-RR-TDM should be implemented in the routine genetic evaluation of the Thai dairy cattle population. The genetic evaluation should consider including genotypes of both sires and cows.

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.

Estimation of individual animal SNP-BLUP reliability using full Monte Carlo sampling

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Computing time for the full Monte Carlo (MC)-SNP-BLUP was less than for the exact genomic BLUP.

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The full MC-SNP-BLUP better approximated estimated breeding value reliability than an incomplete MCbased SNP-BLUP approach when the residual polygenic effect was high.

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The higher the exact reliability, the smaller the inflation.

Calculation of individual animal reliability of estimated genomic breeding value by SNP-BLUP requires inversion of the mixed model equations (MME). When the SNP-BLUP model includes a residual polygenic (RPG) effect, the size of the MME will be at least the number of genotyped animals (n) plus the number of SNP markers (m). Inversion of the MME in SNP-BLUP involves computations proportional to the cube of the MME size; that is, (n + m)³, which can present a considerable computational burden. We introduce a full Monte Carlo (MC) sampling-based method for approximating reliability in the SNP-BLUP model and compare its performance to the genomic BLUP (GBLUP) model. The performance of the full MC approach was evaluated using 2 data sets, including 19,757 and 222,619 genotyped animals selected from populations with 231,186 and 13.35 million pedigree animals, respectively. Genotypes were available in the data sets for 11,729 and 50,240 SNP markers. An advantage of the full MC approximation method was its low computational demand. A drawback was its tendency to overestimate reliability for animals with low reliability, especially when the weight of the RPG effect was high. The overestimation can be lessened by increasing the number of MC samples.

Genomic predictions for yield traits in US Holsteins with unknown parent groups

The objective of this study was to assess the reliability and bias of estimated breeding values (EBV) from traditional BLUP with unknown parent groups (UPG), genomic EBV (GEBV) from single-step genomic BLUP (ssGBLUP) with UPG for the pedigree relationship matrix (A) only (SS_UPG), and GEBV from ssGBLUP with UPG for both A and the relationship matrix among genotyped animals (A₂₂; SS_UPG2) using 6 large phenotype-pedigree truncated Holstein data sets. The complete data included 80 million records for milk, fat, and protein yields from 31 million cows recorded since 1980. Phenotype-pedigree truncation scenarios included truncation of phenotypes for cows recorded before 1990 and 2000 combined with truncation of pedigree information after 2 or 3 ancestral generations. A total of 861,525 genotyped bulls with progeny and cows with phenotypic records were used in the analyses. Reliability and bias (inflation/deflation) of GEBV were obtained for 2,710 bulls based on deregressed proofs, and on 381,779 cows born after 2014 based on predictivity (adjusted cow phenotypes). The BLUP reliabilities for young bulls varied from 0.29 to 0.30 across traits and were unaffected by data truncation and number of generations in the pedigree. Reliabilities ranged from 0.54 to 0.69 for SS_UPG and were slightly affected by phenotype-pedigree truncation. Reliabilities ranged from 0.69 to 0.73 for SS_UPG2 and were unaffected by phenotype-pedigree truncation. The regression coefficient of bull deregressed proofs on (G)EBV (i.e., GEBV and EBV) ranged from 0.86 to 0.90 for BLUP, from 0.77 to 0.94 for SS_UPG, and was 1.00 ± 0.03 for SS_UPG2. Cow predictivity ranged from 0.22 to 0.28 for BLUP, 0.48 to 0.51 for SS_UPG, and 0.51 to 0.54 for SS_UPG2. The highest cow predictivities for BLUP were obtained with the most extreme truncation, whereas for SS_UPG2, cow predictivities were also unaffected by phenotype-pedigree truncations. The regression coefficient of cow predictivities on (G)EBV was 1.02 ± 0.02 for SS_UPG2 with the most extreme truncation, which indicated the least biased predictions. Computations with the complete data set took 17 h with BLUP, 58 h with SS_UPG, and 23 h with SS_UPG2. The same computations with the most extreme phenotype-pedigree truncation took 7, 36, and 15 h, respectively. The SS_UPG2 converged in fewer rounds than BLUP, whereas SS_UPG took up to twice as many rounds. Thus, the ssGBLUP with UPG assigned to both A and A₂₂ provided accurate and unbiased evaluations, regardless of phenotype-pedigree truncation scenario. Old phenotypes (before 2000 in this data set) did not affect the reliability of predictions for young selection candidates, especially in SS_UPG2.

Genomic Analysis, Progress and Future Perspectives in Dairy Cattle Selection: A Review

Genomics comprises a set of current and valuable technologies implemented as selection tools in dairy cattle commercial breeding programs. The intensive progeny testing for production and reproductive traits based on genomic breeding values (GEBVs) has been crucial to increasing dairy cattle productivity. The knowledge of key genes and haplotypes, including their regulation mechanisms, as markers for productivity traits, may improve the strategies on the present and future for dairy cattle selection. Genome-wide association studies (GWAS) such as quantitative trait loci (QTL), single nucleotide polymorphisms (SNPs), or single-step genomic best linear unbiased prediction (ssGBLUP) methods have already been included in global dairy programs for the estimation of marker-assisted selection-derived effects. The increase in genetic progress based on genomic predicting accuracy has also contributed to the understanding of genetic effects in dairy cattle offspring. However, the crossing within inbred-lines critically increased homozygosis with accumulated negative effects of inbreeding like a decline in reproductive performance. Thus, inaccurate-biased estimations based on empirical-conventional models of dairy production systems face an increased risk of providing suboptimal results derived from errors in the selection of candidates of high genetic merit-based just on low-heritability phenotypic traits. This extends the generation intervals and increases costs due to the significant reduction of genetic gains. The remarkable progress of genomic prediction increases the accurate selection of superior candidates. The scope of the present review is to summarize and discuss the advances and challenges of genomic tools for dairy cattle selection for optimizing breeding programs and controlling negative inbreeding depression effects on productivity and consequently, achieving economic-effective advances in food production efficiency. Particular attention is given to the potential genomic selection-derived results to facilitate precision management on modern dairy farms, including an overview of novel genome editing methodologies as perspectives toward the future.

Genomic information allows for more accurate breeding values for milkability in dual-purpose Italian Simmental cattle

Milkability is a trait related to the milking efficiency of an animal, and it is a component of the herd profitability. Due to its economic importance, milkability is currently included in the selection index of the Italian Simmental cattle breed with a weight of 7.5%. This lowly heritable trait is measured on a subjective scale from 1 to 3 (1 = slow, 3 = fast), and genetic evaluations are performed by pedigree-based BLUP. Genomic information is now available for some animals in the Italian Simmental population, and its inclusion in the genetic evaluation system could increase accuracy of breeding values and genetic progress for milkability. The aim of this study was to test the feasibility and advantages of having a genomic evaluation for this trait in the Italian Simmental population. Phenotypes were available for 131,308 cows. A total of 9,526 animals had genotypes for 42,152 loci; among the genotyped animals, 2,455 were cows with phenotypes, and the other were their relatives. The youngest cows with both phenotypes and genotypes (n = 900) were identified as selection candidates. Variance components and heritability were estimated using pedigree information, whereas genetic and genomic evaluations were carried out using BLUP and single-step genomic BLUP (ssGBLUP), respectively. In addition, a weighted ssGBLUP was assessed using genomic regions from a genome-wide association study. Evaluation models were validated using theoretical and realized accuracies. The estimated heritability for milkability was 0.12 ± 0.01. The mean theoretical accuracies for selection candidates were 0.43 ± 0.08 (BLUP) and 0.53 ± 0.06 (ssGBLUP). The mean realized accuracies based on linear regression statistics were 0.29 (BLUP) and 0.40 (ssGBLUP). No genomic regions were significantly associated with milkability, thus no improvements in accuracy were observed when using weighted ssGBLUP. Results indicated that genomic information could improve the accuracy of breeding values and increase genetic progress for milkability in Italian Simmental.

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.