Single step genomic evaluation for female fertility in Nordic Red dairy cattle

Genetic evaluations and genome-wide association studies for specific digital dermatitis diagnoses in dairy cows considering genotype × housing system interactions

The present study aimed to use detailed phenotyping for the claw disorder digital dermatitis (DD) considering specific DD stages in 2 housing systems (conventional cubicle barns [CON] and compost-bedded pack barns [CBPB]) to infer possible genotype × housing system interactions. The DD stages included 2,980 observations for the 3 traits DD-sick, DD-acute, and DD-chronic from 1,311 Holstein-Friesian and 399 Fleckvieh-Simmental cows. Selection of the 5 CBPB and 5 CON herds was based on a specific protocol to achieve a high level of herd similarity with regard to climate, feeding, milking system, and location, but with pronounced housing-system differences. Five other farms had a "mixed system" with 2 subherds, one representing CBPB and the other one CON. The CBPB system was represented by 899 cows (1,530 observations), and 811 cows (1,450 observations) represented the CON system. The average disease prevalence was 20.47% for DD-sick, 13.88% for DD-acute, and 5.34% for DD-chronic, with a higher prevalence in CON than in CBPB. After quality control of 50K genotypes, 38,495 SNPs from 926 cows remained for the ongoing genomic analyses. Genetic parameters for DD-sick, DD-acute, and DD-chronic were estimated by applying single-step approaches for single-trait repeatability animal models considering the whole dataset, and separately for the CON and CBPB subsets. Genetic correlations between same DD traits from different housing systems, and between DD-sick, DD-chronic, and DD-acute, were estimated via bivariate animal models. Heritabilities based on the whole dataset were 0.16 for DD-sick, 0.14 for DD-acute, and 0.11 for DD-chronic. A slight increase of heritabilities and genetic variances was observed in CON compared with the "well-being" CBPB system, indicating a stronger genetic differentiation of diseases in a more challenging environment. Genetic correlations between same DD traits recorded in CON or CBPB were close to 0.80, disproving obvious genotype × housing system interactions. Genetic correlations among DD-sick, DD-acute and DD-chronic ranged from 0.58 to 0.81. SNP main effects and SNP × housing system interaction effects were estimated simultaneously via GWAS, considering only the phenotypes from genotyped cows. Ongoing annotations of potential candidate genes focused on chromosomal segments 100 kb upstream and downstream from the significantly associated candidate SNP. GWAS for main effects indicated heterogeneous Manhattan plots especially for DD-acute and DD-chronic, indicating particularities in disease pathogenesis. Nevertheless, a few shared annotated potential candidate genes, that is, METTL25, AFF3, PRKG1, and TENM4 for DD-sick and DD-acute, were identified. These genes have direct or indirect effects on disease resistance or immunology. For the SNP × housing system interaction, the annotated genes ASXL1 and NOL4L on BTA 13 were relevant for DD-sick and DD-acute. Overall, the very similar genetic parameters for the same traits in different environments and negligible genotype × housing system interactions indicate only minor effects on genetic evaluations for DD due to housing-system particularities.

Unknown parent groups and truncated pedigree in single-step genomic evaluations of Murrah buffaloes

Missing pedigree may produce bias in genomic evaluations. Thus, strategies to deal with this problem have been proposed as using unknown parent groups (UPG) or truncated pedigrees. The aim of this study was to investigate the impact of modeling missing pedigree under ssGBLUP evaluations for productive and reproductive traits in dairy buffalos using different approaches: 1) traditional BLUP without UPG (BLUP), 2) traditional BLUP including UPG (BLUP/UPG), 3) ssGBLUP without UPG (ssGBLUP), 4) ssGBLUP including UPG in the A and A22 matrices (ssGBLUP/A_UPG), 5) ssGBLUP including UPG in all elements of the H matrix (ssGBLUP/H_UPG), 6) BLUP with pedigree truncation for the last 3 generations (BLUP/truncated), and 7) ssGBLUP with pedigree truncation for the last 3 generations (ssGBLUP/ truncated). UPGs were not used in the scenarios with truncated pedigree. A total of 3,717, 4,126 and 3,823 records of the first lactation for accumulated 305 d milk yield (MY), age at first calving (AFC) and lactation length (LL), respectively were used. Accuracies ranged from 0.27 for LL (BLUP) to 0.46 for MY (BLUP), bias ranged from -0.62 for MY (ssGBLUP) to 0.0002 for AFC (BLUP/truncated), and dispersion ranged from 0.88 for MY (BLUP/ A_UPG) to 1.13 for LL (BLUP). Genetic trend showed genetic gains for all traits across 20 years of selection and the impact of including either genomic information, UPG or pedigree truncation under GEBV accuracies ranged among the evaluated traits. Overall, methods using UPGs, truncation pedigree and genomic information exhibited potential to improve GEBV accuracies, bias and dispersion for all traits compared with other methods. Truncated scenarios promoted high genetic gains. In small populations with few genotyped animals, combining truncated pedigree or UPG with genomic information is a feasible approach to deal with missing pedigrees.

Genomic prediction in Brazilian Guzerá cattle: application of a single-step approach to productive and reproductive traits

This study aimed to investigate the feasibility of genomic prediction for productive and reproductive traits in Guzerá cattle using single-step genomic best linear unbiased prediction (ssGBLUP). Evaluations included the 305-day cumulative yields (first lactation, in kg) of milk, lactose, protein, fat, and total solids; adjusted body weight (kg) at the ages of 450, 365, and 210 days; and age at first calving (in days), from a database containing 197,283 measurements from Guzerá males and females born between 1954 and 2018. The pedigree included 433,823 animals spanning up to 14 overlapping generations. A total of 1618 animals were genotyped. The analyses were performed using ssGBLUP and traditional BLUP methods. Predictive ability and bias were accessed using cross-validation: predictive ability was similar between the methods and ranged from 0.27 to 0.47 for the genomic-based model and from 0.30 to 0.45 for the pedigree-based model; the bias was also similar between the methods, ranging from 0.88 to 1.35 in the genomic-based model and from 0.96 to 1.41 in the pedigree-based model. The individual accuracies of breeding values were evidently increased in the genomic evaluation, with values ranging from 0.41 to 0.56 in the genomic-based model and from 0.26 to 0.54 in the pedigree-based model. Even based on a small number of genotyped animals and a small database for some traits, the results suggest that ssGBLUP is feasible and may be applied to national genetic evaluation of the breed to increase the accuracy of breeding values without greatly impacting predictive ability and bias.

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.

Genomic Estimated Breeding Value of Milk Performance and Fertility Traits in the Russian Black-and-White Cattle Population

A breakthrough in cattle breeding was achieved with the incorporation of animal genomic data into breeding programs. The introduction of genomic selection has a major impact on traditional genetic assessment systems and animal genetic improvement programs. Since 2010, genomic selection has been officially introduced in the evaluation of the breeding and genetic potential of cattle in Europe, the U.S., Canada, and many other developed countries. The purpose of this study is to develop a system for a genomic evaluation of the breeding value of the domestic livestock of Black-and-White and Russian Holstein cattle based on 3 milk performance traits: daily milk yield (kg), daily milk fat (%), and daily milk protein content (%) and 6 fertility traits: age at first calving (AFC), calving interval (CI), calving to first insemination interval (CFI), interval between first and last insemination (IFL), days open (DO), and number of services (NS). We built a unified database of breeding animals from 523 breeding farms in the Russian Federation. The database included pedigree information on 2,551,529 cows and 69,131 bulls of the Russian Holstein and Black-and-White cattle breeds, as well as information on the milk performance of 1,597,426 cows with 4,771,366 completed lactations. The date of birth of the animals included in the database was between 1975 and 2017. Genotyping was performed in 672 animals using a BovineSNP50 v3 DNA Analysis BeadChip microarray (Illumina, USA). The genomic estimated breeding value (GEBV) was evaluated only for 644 animals (427 bulls and 217 cows) using the single-step genomic best linear unbiased prediction – animal model (ssGBLUP-AM). The mean genetic potential was +0.88 and +1.03 kg for the daily milk yield, -0.002% for the milk fat content, and –0.003 and 0.001% for the milk protein content in the cows and bulls, respectively. There was negative genetic progress in the fertility traits in the studied population between 1975 and 2017. The reliability of the estimated breeding value (EBV) for genotyped bulls ranged from 89 to 93% for the milk performance traits and 85 to 90% for the fertility traits, whereas the reliability of the genomic estimated breeding value (GEBV) varied 54 to 64% for the milk traits and 23 to 60% for the fertility traits. This result shows that it is possible to use the genomic estimated breeding value with rather high reliability to evaluate the domestic livestock of Russian Holstein and Black-and-White cattle breeds for fertility and milk performance traits. This system of genomic evaluation may help bring domestic breeding in line with modern competitive practices and estimate the breeding value of cattle at birth based on information on the animal’s genome.

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.

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.

Comparison of models for missing pedigree in single-step genomic prediction

Pedigree information is often missing for some animals in a breeding program. Unknown-parent groups (UPGs) are assigned to the missing parents to avoid biased genetic evaluations. Although the use of UPGs is well established for the pedigree model, it is unclear how UPGs are integrated into the inverse of the unified relationship matrix (H-inverse) required for single-step genomic best linear unbiased prediction. A generalization of the UPG model is the metafounder (MF) model. The objectives of this study were to derive 3 H-inverses and to compare genetic trends among models with UPG and MF H-inverses using a simulated purebred population. All inverses were derived using the joint density function of the random breeding values and genetic groups. The breeding values of genotyped animals (u2) were assumed to be adjusted for UPG effects (g) using matrix Q2 as u2∗=u2+Q2g before incorporating genomic information. The Quaas-Pollak-transformed (QP) H-inverse was derived using a joint density function of u2∗ and g updated with genomic information and assuming nonzero cov(u2∗,g'). The modified QP (altered) H-inverse also assumes that the genomic information updates u2∗ and g, but cov(u2∗,g')=0. The UPG-encapsulated (EUPG) H-inverse assumed genomic information updates the distribution of u2∗. The EUPG H-inverse had the same structure as the MF H-inverse. Fifty percent of the genotyped females in the simulation had a missing dam, and missing parents were replaced with UPGs by generation. The simulation study indicated that u2∗ and g in models using the QP and altered H-inverses may be inseparable leading to potential biases in genetic trends. Models using the EUPG and MF H-inverses showed no genetic trend biases. These 2 H-inverses yielded the same genomic EBV (GEBV). The predictive ability and inflation of GEBVs from young genotyped animals were nearly identical among models using the QP, altered, EUPG, and MF H-inverses. Although the choice of H-inverse in real applications with enough data may not result in biased genetic trends, the EUPG and MF H-inverses are to be preferred because of theoretical justification and possibility to reduce biases.

Autoregressive single-step model for genomic evaluation of longitudinal reproductive traits in portuguese holstein cattle

We investigated the applicability of ssGBLUP methodology under the autoregressive model (H-AR) for genomic evaluation of longitudinal reproductive traits in Portuguese Holstein cattle. The genotype data of 1,230 bulls and 1,645 cows were considered in our study. The reproductive traits evaluated were interval from calving to first service (ICF), calving interval (CI) and daughter pregnancy rate (DPR) measured during the first four parities. Reliability and rank correlation were used to compare the H-AR with the traditional pedigree-based autoregressive models (A-AR). In addition, a validation study was performed considering different scenarios. Higher genomic estimated breeding values (GEBV) reliabilities were obtained for genotyped bulls when evaluated under the H-AR model, with emphasis on bulls with less than 9 daughters. For this group, the averages of GEBV reliabilities corresponded to 0.62, 0.69 and 0.62 for ICF, CI and DPR, respectively, while the averages obtained by the A-AR model were 0.27, 0.15 and 0.16. The validation study was favourable to H-AR. The best results were observed in the scenario where genotyped cows were combined with contributing bulls (genotyped bulls with daughter or relationship information in the population). Overall, the results suggest that ssGBLUP methodology under the autoregressive model is a feasible and applicable approach to be used in genomic analyses of longitudinal reproductive traits in Portuguese Holstein cattle.

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.

Effects of ignoring inbreeding in model-based accuracy for BLUP and SSGBLUP

Model-based accuracy, defined as the theoretical correlation between true and estimated breeding value, can be obtained for each individual as a function of its prediction error variance (PEV) and inbreeding coefficient F, in BLUP, GBLUP and SSGBLUP genetic evaluations. However, for computational convenience, inbreeding is often ignored in two places. First, in the computation of reliability = 1-PEV/(1 + F). Second, in the set-up, using Henderson's rules, of the inverse of the pedigree-based relationship matrix A. Both approximations have an effect in the computation of model-based accuracy and result in wrong values. In this work, first we present a reminder of the theory and extend it to SSGBLUP. Second, we quantify the error of ignoring inbreeding with real data in three scenarios: BLUP evaluation and SSGBLUP in Uruguayan dairy cattle, and BLUP evaluations in a line of rabbit closed for >40 generations with steady increase of inbreeding up to an average of 0.30. We show that ignoring inbreeding in the set-up of the A-inverse is equivalent to assume that non-inbred animals are actually inbred. This results in an increase of apparent PEV that is negligible for dairy cattle but considerable for rabbit. Ignoring inbreeding in reliability = 1-PEV/(1 + F) leads to underestimation of reliability for BLUP evaluations, and this underestimation is very large for rabbit. For SSGBLUP in dairy cattle, it leads to both underestimation and overestimation of reliability, both for genotyped and non-genotyped animals. We strongly recommend to include inbreeding both in the set-up of A-inverse and in the computation of reliability from PEVs.