Comparison of different validation methods for single-step genomic evaluations based on a simulated cattle population

The validation of estimated breeding values from single-step genomic BLUP (ssGBLUP) is an important topic, as more and more countries and animal populations are currently changing their genomic prediction to single-step. The objective of this work was to compare different methods to validate single-step genomic breeding values (GEBV). The investigations were carried out using a simulation study based on the German-Austrian-Czech Fleckvieh population. To test the validation methods under different conditions, several biased and unbiased scenarios were simulated. The application of the widely used Interbull GEBV test to the single-step method is only possible to a limited extent, partly because of genomic preselection, which biases conventional estimated breeding values. Alternative validation methods considered in the study are the linear regression method proposed by Legarra and Reverter, the improved genomic validation including additional regressions as suggested by VanRaden and an adaptation of the Interbull GEBV test using daughter yield deviations (DYD) from ssGBLUP instead of pedigree BLUP. The comparison of the different methods for the different scenarios showed that for males the methods based on GEBV estimate the dispersion more accurate and less biased compared with the GEBV test using DYD from ssGBLUP, whereas the standard Interbull GEBV test is highly affected by genomic preselection for males. For females, the GEBV test using yield deviations from ssGBLUP results in better estimations for the true dispersion.

Application of single-step single nucleotide polymorphism best linear unbiased predictor model with unknown-parent groups for type traits in Japanese Holsteins

The objectives of this study were to investigate the computational performance and the predictive ability and bias of a single-step SNP BLUP model (ssSNPBLUP) in genotyped young animals with unknown-parent groups (UPG) for type traits, using national genetic evaluation data from the Japanese Holstein population. The phenotype, genotype, and pedigree data were the same as those used in a national genetic evaluation of linear type traits classified between April 1984 and December 2020. In the current study, 2 data sets were prepared: the full data set containing all entries up to December 2020 and a truncated data set ending with December 2016. Genotyped animals were classified into 3 types: sires with classified daughters (S), cows with records (C), and young animals (Y). The computing performance and prediction accuracy of ssSNPBLUP were compared for the following 3 groups of genotyped animals: sires with classified daughters and young animals (SY); cows with records and young animals (CY); and sires with classified daughters, cows with records, and young animals (SCY). In addition, we tested 3 parameters of residual polygenic variance in ssSNPBLUP (0.1, 0.2, or 0.3). Daughter yield deviations (DYD) for the validation bulls and phenotypes adjusted for all fixed effects and random effects other than animal and residual (Y_adj) for the validation cows were obtained using the full data set from the pedigree-based BLUP model. The regression coefficients of DYD for bulls (or Y_adj for cows) on the genomic estimated breeding value (GEBV) using the truncated data set were used to measure the inflation of the predictions of young animals. The coefficient of determination of DYD on GEBV was used to measure the predictive ability of the predictions for the validation bulls. The reliability of the predictions for the validation cows was calculated as the square of the correlation between Y_adj and GEBV divided by heritability. The predictive ability was highest in the SCY group and lowest in the CY group. However, minimal difference was found in predictive abilities with or without UPG models using different parameters of residual polygenic variance. The regression coefficients approached 1.0 as the parameter of residual polygenic variance increased, but regression coefficients were mostly similar regardless of the use of UPG across the groups of genotyped animals. The ssSNPBLUP model, including UPG, was demonstrated as feasible for implementation in the national evaluation of type traits in Japanese Holsteins.

Selective genotyping to implement genomic selection in beef cattle breeding

Genomic selection (GS) plays an essential role in livestock genetic improvement programs. In dairy cattle, the method is already a recognized tool to estimate the breeding values of young animals and reduce generation intervals. Due to the different breeding structures of beef cattle, the implementation of GS is still a challenge and has been adopted to a much lesser extent than dairy cattle. This study aimed to evaluate genotyping strategies in terms of prediction accuracy as the first step in the implementation of GS in beef while some restrictions were assumed for the availability of phenotypic and genomic information. For this purpose, a multi-breed population of beef cattle was simulated by imitating the practical system of beef cattle genetic evaluation. Four genotyping scenarios were compared to traditional pedigree-based evaluation. Results showed an improvement in prediction accuracy, albeit a limited number of animals being genotyped (i.e., 3% of total animals in genetic evaluation). The comparison of genotyping scenarios revealed that selective genotyping should be on animals from both ancestral and younger generations. In addition, as genetic evaluation in practice covers traits that are expressed in either sex, it is recommended that genotyping covers animals from both sexes.

Changes in genetic trends in US dairy cattle since the implementation of genomic selection

Genomic selection increases accuracy and decreases generation interval, accelerating genetic changes in populations. Assumptions of genetic improvement must be addressed to quantify the magnitude and direction of change. Genetic trends of US dairy cattle breeds were examined to determine the genetic gain since the implementation of genomic evaluations in 2009. Inbreeding levels and generation intervals were also investigated. Breeds included Ayrshire, Brown Swiss, Guernsey, Holstein (HO), and Jersey (JE), which were characterized by the evaluation breed the animal received. Mean genomic predicted breeding values (PBV¯) were analyzed per year to calculate genetic trends for bulls and cows. The data set contained 154,008 bulls and 33,022,242 cows born since 1975. Breakpoints were estimated using linear regression, and nonlinear regression was used to fit the piecewise model for the small sample number in some years. Generation intervals and inbreeding levels were also investigated since 1975. Milk, fat, and protein yields, somatic cell score, productive life, daughter pregnancy rate, and livability PBV¯ were documented. In 2017, 100% of bulls in this data set were genotyped. The percentage of genotyped cows has increased 23 percentage points since 2010. Overall, production traits have increased steadily over time, as expected. The HO and JE breeds have benefited most from genomics, with up to 192% increase in genetic gain since 2009. Due to the low number of observations, trends for Ayrshire, Brown Swiss, and Guernsey are difficult to infer from. Trends in fertility are most substantial; particularly, most breeds are trending downwards and daughter pregnancy rate for JE has been decreasing steadily since 1975 for bulls and cows. Levels of genomic inbreeding are increasing in HO bulls and cows. In 2017, genomic inbreeding levels were 12.7% for bulls and 7.9% for cows. A suggestion to control this is to include the genomic inbreeding coefficient with a negative weight to the selection index of bulls with high future genomic inbreeding levels. For sires of bulls, the current generation intervals are 2.2 yr in HO, 3.2 in JE, 4.4 in Brown Swiss, 5.1 in Ayrshire, and 4.3 in Guernsey. The number of colored breed bulls in the United States is currently at an extremely low level, and this number will only increase with a market incentive or additional breed association involvement. Increased education and extension could be beneficial to increase knowledge about inbreeding levels, use of genomics and genetic improvement, and genetic diversity in the genomic selection era.

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.

Impact of genomic preselection on subsequent genetic evaluations with ssGBLUP using real data from pigs

Background

Empirically assessing the impact of preselection on genetic evaluation of preselected animals requires comparing scenarios that take different approaches into account, including scenarios without preselection. However, preselection is almost always performed in animal breeding programs, so it is difficult to have a dataset without preselection. Hence, most studies on preselection have used simulated datasets, and have concluded that genomic estimated breeding values (GEBV) from subsequent single-step genomic best linear unbiased prediction (ssGBLUP) evaluations are unbiased. The aim of this study was to investigate the impact of genomic preselection (GPS) on accuracy and bias in subsequent ssGBLUP evaluations, using data from a commercial pig breeding program.

Methods

We used data on average daily gain during performance testing, average daily gain throughout life, backfat thickness, and loin depth from one sire line and one dam line of pigs. As these traits have different weights in the breeding goals of the two lines, we analyzed the lines separately. For each line, we implemented a reference GPS scenario that kept all available data, against which the next two scenarios were compared. We then implemented two other scenarios with additional layers of GPS by removing all animals without progeny either (i) only in the validation generation, or (ii) in all generations. We conducted subsequent ssGBLUP evaluations for each GPS scenario, using all the data remaining after implementing the GPS scenario. Accuracy and bias were computed by comparing GEBV against progeny yield deviations of validation animals.

Results

Results for all traits and in both lines showed a marginal loss in accuracy due to the additional layers of GPS. Average accuracies across all GPS scenarios in the two lines were 0.39, 0.47, 0.56, and 0.60, for average daily gain during performance testing and throughout life, backfat thickness, and loin depth, respectively. Biases were largely absent, and when present, did not differ greatly between the GPS scenarios.

Conclusions

We conclude that the impact of preselection on accuracy and bias in subsequent ssGBLUP evaluations of selection candidates in pigs is generally minimal. We expect this conclusion to apply for other animal breeding programs as well, since preselection of any type or intensity generally has the same effect in animal breeding programs.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12711-022-00727-5.

Improvement of Genomic Predictions in Small Breeds by Construction of Genomic Relationship Matrix Through Variable Selection

Genomic selection has been increasingly implemented in the animal breeding industry, and it is becoming a routine method in many livestock breeding contexts. However, its use is still limited in several small-population local breeds, which are, nonetheless, an important source of genetic variability of great economic value. A major roadblock for their genomic selection is accuracy when population size is limited: to improve breeding value accuracy, variable selection models that assume heterogenous variance have been proposed over the last few years. However, while these models might outperform traditional and genomic predictions in terms of accuracy, they also carry a proportional increase of breeding value bias and dispersion. These mutual increases are especially striking when genomic selection is performed with a low number of phenotypes and high shrinkage value—which is precisely the situation that happens with small local breeds. In our study, we tested several alternative methods to improve the accuracy of genomic selection in a small population. First, we investigated the impact of using only a subset of informative markers regarding prediction accuracy, bias, and dispersion. We used different algorithms to select them, such as recursive feature eliminations, penalized regression, and XGBoost. We compared our results with the predictions of pedigree-based BLUP, single-step genomic BLUP, and weighted single-step genomic BLUP in different simulated populations obtained by combining various parameters in terms of number of QTLs and effective population size. We also investigated these approaches on a real data set belonging to the small local Rendena breed. Our results show that the accuracy of GBLUP in small-sized populations increased when performed with SNPs selected via variable selection methods both in simulated and real data sets. In addition, the use of variable selection models—especially those using XGBoost—in our real data set did not impact bias and the dispersion of estimated breeding values. We have discussed possible explanations for our results and how our study can help estimate breeding values for future genomic selection in small breeds.

Dissecting genetic trends to understand breeding practices in livestock: a maternal pig line example

Background

Understanding whether genomic selection has been effective in livestock and when the results of genomic selection became visible are essential questions which we have addressed in this paper. Three criteria were used to identify practices of breeding programs over time: (1) the point of divergence of estimated genetic trends based on pedigree-based best linear unbiased prediction (BLUP) versus single-step genomic BLUP (ssGBLUP), (2) the point of divergence of realized Mendelian sampling (RMS) trends based on BLUP and ssGBLUP, and (3) the partition of genetic trends into that contributed by genotyped and non-genotyped individuals and by males and females.

Methods

We used data on 282,035 animals from a commercial maternal line of pigs, of which 32,856 were genotyped for 36,612 single nucleotide polymorphisms (SNPs) after quality control. Phenotypic data included 228,427, 101,225, and 11,444 records for birth weight, average daily gain in the nursery, and feed intake, respectively. Breeding values were predicted in a multiple-trait framework using BLUP and ssGBLUP.

Results

The points of divergence of the genetic and RMS trends estimated by BLUP and ssGBLUP indicated that genomic selection effectively started in 2019. Partitioning the overall genetic trends into that for genotyped and non-genotyped individuals revealed that the contribution of genotyped animals to the overall genetic trend increased rapidly from ~ 74% in 2016 to 90% in 2019. The contribution of the female pathway to the genetic trend also increased since genomic selection was implemented in this pig population, which reflects the changes in the genotyping strategy in recent years.

Conclusions

Our results show that an assessment of breeding program practices can be done based on the point of divergence of genetic and RMS trends between BLUP and ssGBLUP and based on the partitioning of the genetic trend into contributions from different selection pathways. However, it should be noted that genetic trends can diverge before the onset of genomic selection if superior animals are genotyped retroactively. For the pig population example, the results showed that genomic selection was effective in this population.

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.

Invited review: A quarter of a century-International genetic evaluation of dairy sires using MACE methodology

For the past few decades, the international exchange of genetic materials has accelerated. This acceleration has been more substantial for dairy cattle compared with other species. The industry faced the need to put international genetic evaluation (IGE) systems in place. The Interbull Centre has been conducting IGE for various dairy cattle breeds and traits. This study reviews the past and the current status of IGE for dairy cattle, emphasizing the most prominent and well-established method of IGE, namely multiple across-country evaluation (MACE), and the challenges that should be addressed in the future of IGE. The first IGE methods were simple conversion equations. Only a limited number of common bulls between pairs of countries were considered. These bulls were a biased sample of highly selected animals, with their daughters under preferential treatment in the importing countries. Genetic relationships among animals were not considered either. The MACE method was the first IGE method based on mixed-model theory that could handle genotype by environment interaction (G × E) between countries. The G × E between countries is handled by treating the same trait in different countries as different traits, with genetic correlations less than unity between the traits. The G × E between countries is not solely due to different genetic expressions in different environments (countries), but is also attributable to different units or ways of measuring the trait, data editing, and statistical approaches and models used in different countries. The MACE method also considers different genetic means, genetic groups for unknown parents, heterogeneous genetic and residual variances among countries, and heterogeneous residual variances (precision weights for observations) within countries. Other IGE methods that came after MACE are rooted in MACE. The genomic revolution of the industry created new needs and opportunities. However, an unwanted aspect of it was genomic preselection bias. Genomic preselection causes directional information loss from pre-culled animals (bias) in statistical models for genetic and genomic evaluations, and preselected progeny of a mating are no longer a random sample of possible progeny from that mating. National genetic evaluations without genotypes are input to MACE, and biases in national evaluations are propagated internationally through MACE. Genomic preselection for the Holstein breed is a source of concern for introducing bias to MACE, especially when genomic preselection is practiced intensively in the population. However, MACE continues to be useful for other breeds, among other species, or for non-IGE purposes. Future methods will need to make optimum use of genomic information and be free of genomic preselection bias.

Detecting effective starting point of genomic selection by divergent trends from best linear unbiased prediction and single-step genomic best linear unbiased prediction in pigs, beef cattle, and broilers

Genomic selection has been adopted nationally and internationally in different livestock and plant species. However, understanding whether genomic selection has been effective or not is an essential question for both industry and academia. Once genomic evaluation started being used, estimation of breeding values with pedigree best linear unbiased prediction (BLUP) became biased because this method does not consider selection using genomic information. Hence, the effective starting point of genomic selection can be detected in two possible ways including the divergence of genetic trends and Realized Mendelian sampling (RMS) trends obtained with BLUP and single-step genomic BLUP (ssGBLUP). This study aimed to find the start date of genomic selection for a set of economically important traits in three livestock species by comparing trends obtained using BLUP and ssGBLUP. Three datasets were used for this purpose: 1) a pig dataset with 117k genotypes and 1.3M animals in pedigree, 2) an Angus cattle dataset consisted of ~842k genotypes and 11.5M animals in pedigree, and 3) a purebred broiler chicken dataset included ~154k genotypes and 1.3M birds in pedigree were used. The genetic trends for pigs diverged for the genotyped animals born in 2014 for average daily gain (ADG) and backfat (BF). In beef cattle, the trends started diverging in 2009 for weaning weight (WW) and in 2016 for postweaning gain (PWG), with little divergence for birth weight (BTW). In broiler chickens, the genetic trends estimated by ssGBLUP and BLUP diverged at breeding cycle 6 for two out of the three production traits. The RMS trends for the genotyped pigs diverged for animals born in 2014, more for ADG than for BF. In beef cattle, the RMS trends started diverging in 2009 for WW and in 2016 for PWG, with a trivial trend for BTW. In broiler chickens, the RMS trends from ssGBLUP and BLUP diverged strongly for two production traits at breeding cycle 6, with a slight divergence for another trait. Divergence of the genetic trends from ssGBLUP and BLUP indicates the onset of the genomic selection. The presence of trends for RMS indicates selective genotyping, with or without the genomic selection. The onset of genomic selection and genotyping strategies agrees with industry practices across the three species. In summary, the effective start of genomic selection can be detected by the divergence between genetic and RMS trends from BLUP and ssGBLUP.

Across-country genomic predictions in Norwegian and New Zealand Composite sheep populations with similar development history

The goal of this study was to assess the feasibility of across-country genomic predictions in Norwegian White Sheep (NWS) and New Zealand Composite (NZC) sheep populations with similar development history. Different training populations were evaluated (i.e., including only NWS or NZC, or combining both populations). Predictions were performed using the actual phenotypes (normalized) and the single-step GBLUP via Bayesian inference. Genotyped NWS animals born in 2016 (N = 267) were used to assess the accuracy and bias of genomic estimated breeding values (GEBVs) predicted for birth weight (BW), weaning weight (WW), carcass weight (CW), EUROP carcass classification (EUC), and EUROP fat grading (EUF). The accuracy and bias of GEBVs differed across traits and training population used. For instance, the GEBV accuracies ranged from 0.13 (BW) to 0.44 (EUC) for GEBVs predicted including only NWS, from 0.06 (BW) to 0.15 (CW) when including only NZC, and from 0.10 (BW) to 0.41 (EUC) when including both NWS and NZC animals in the training population. The regression coefficients used to assess the spread of GEBVs (bias) ranged from 0.26 (BW) to 0.64 (EUF) for only NWS, 0.10 (EUC) to 0.52 (CW) for only NZC, and from 0.42 (WW) to 2.23 (EUC) for both NWS and NZC in the training population. Our findings suggest that across-country genomic predictions based on ssGBLUP might be possible for NWS and NZC, especially for novel traits.

Genomic Prediction in Local Breeds: The Rendena Cattle as a Case Study

Simple Summary

Although genomic selection is being used in many livestock species, it has not yet been considered in local breeds due to the lower population size and the potential less effective impact on the genetic evaluation of these breeds. The current research aims to investigate how genomic data can impact the accuracy of genetic predictions for beef traits in Rendena, a small local cattle breed of the North-East of Italy selected for a dual purpose. Classical animal models using only phenotypic information were compared with two models that integrated genomic data with pedigree information. The genomic models presented better accuracy in estimated breeding values of the animals than the ‘classical’ animal model, especially the ‘simpler’ one assuming homogeneous variances of single nucleotide polymorphisms. Our results show that the inclusion of genomic information can be successfully applied to breeding selection scenarios even in small local cattle breeds such as Rendena.

Abstract

The maintenance of local cattle breeds is key to selecting for efficient food production, landscape protection, and conservation of biodiversity and local cultural heritage. Rendena is an indigenous cattle breed from the alpine North-East of Italy, selected for dual purpose, but with lesser emphasis given to beef traits. In this situation, increasing accuracy for beef traits could prevent detrimental effects due to the antagonism with milk production. Our study assessed the impact of genomic information on estimated breeding values (EBVs) in Rendena performance-tested bulls. Traits considered were average daily gain, in vivo EUROP score, and in vivo estimate of dressing percentage. The final dataset contained 1691 individuals with phenotypes and 8372 animals in pedigree, 1743 of which were genotyped. Using the cross-validation method, three models were compared: (i) Pedigree-BLUP (PBLUP); (ii) single-step GBLUP (ssGBLUP), and (iii) weighted single-step GBLUP (WssGBLUP). Models including genomic information presented higher accuracy, especially WssGBLUP. However, the model with the best overall properties was the ssGBLUP, showing higher accuracy than PBLUP and optimal values of bias and dispersion parameters. Our study demonstrated that integrating phenotypes for beef traits with genomic data can be helpful to estimate EBVs, even in a small local breed.

Emerging issues in genomic selection

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

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.

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.

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.

Bias in genomic predictions by mating practices for linear type traits in a large-scale genomic evaluation

The objective of this study was to clarify how bias in genomic predictions is created by investigating a relationship among selection intensity, a change in heritability (Δh²), and assortative mating (ASM). A change in heritability, resulting from selection, reflects the impact that the Bulmer effect has on the reduction in between-family variation, whereas assortative mating impacts the within-family variance or Mendelian sampling variation. A partial data set up to 2014, including 841K genotyped animals, was used to calculate genomic predictions with a single-step genomic model for 18 linear type traits in US Holsteins. A full data set up to 2018, including 2.3 million genotyped animals, was used to calculate benchmark genomic predictions. Inbreeding and unknown parent groups for missing parents of animals were included in the model. Genomic evaluation was performed using 2 different genetic parameters: those estimated 14 yr ago, which have been used in the national genetic evaluation for linear type traits in the United States, and those newly estimated with recent records from 2015 to 2018 and those corresponding pedigrees. Genetic trends for 18 type traits were estimated for bulls with daughters and cows with phenotypes in 2018. Based on selection intensity and mating decisions, these traits can be categorized into 3 groups: (a) high directional selection, (b) moderate selection, and (c) intermediate optimum selection. The first 2 categories can be explained by positive assortative mating, and the last can be explained by negative assortative or disassortative mating. Genetic progress was defined by genetic gain per year based on average standardized genomic predictions for cows from 2000 to 2014. Traits with more genetic progress tended to have more "inflated" genomic predictions (i.e., "inflation" means here that genomic predictions are larger in absolute values than expected, whereas "deflation" means smaller than expected). Heritability estimates for 14 out of 18 traits declined in the last 16 yr, and Δh² ranged from -0.09 to 0.04. Traits with a greater decline in heritability tended to have more deflated genomic predictions. Biases (inflation or deflation) in genomic predictions were not improved by using the latest genetic parameters, implying that bias in genomic predictions due to preselection was not substantial for a large-scale genomic evaluation. Moreover, the strong selection intensity was not fully responsible for bias in genomic predictions. The directional selection can decrease heritability; however, positive assortative mating, which was strongly associated with large genetic gains, could minimize the decline in heritability for a trait under strong selection and could affect bias in genomic predictions.

Investigating the impact of preselection on subsequent single-step genomic BLUP evaluation of preselected animals

Background

Preselection of candidates, hereafter referred to as preselection, is a common practice in breeding programs. Preselection can cause bias and accuracy loss in subsequent pedigree-based best linear unbiased prediction (PBLUP). However, the impact of preselection on subsequent single-step genomic BLUP (ssGBLUP) is not completely clear yet. Therefore, in this study, we investigated, across different heritabilities, the impact of intensity and type of preselection on subsequent ssGBLUP evaluation of preselected animals.

Methods

We simulated a nucleus of a breeding programme, in which a recent population of 15 generations was produced with PBLUP-based selection. In generation 15 of this recent population, the parents of the next generation were preselected using several preselection scenarios. These scenarios were combinations of three intensities of preselection (no, high or very high preselection) and three types of preselection (genomic, parental average or random), across three heritabilities (0.5, 0.3 or 0.1). Following each preselection scenario, a subsequent evaluation was performed using ssGBLUP by excluding all the information from the preculled animals, and these genetic evaluations were compared in terms of accuracy and bias for the preselected animals, and in terms of realized genetic gain.

Results

Type of preselection affected selection accuracy at both preselection and subsequent evaluation stages. While preselection accuracy decreased, accuracy in the subsequent ssGBLUP evaluation increased, from genomic to parent average to random preselection scenarios. Bias was always negligible. Genetic gain decreased from genomic to parent average to random preselection scenarios. Genetic gain also decreased with increasing intensity of preselection, but only by a maximum of 0.1 additive genetic standard deviation from no to very high genomic preselection scenarios.

Conclusions

Using ssGBLUP in subsequent evaluations prevents preselection bias, irrespective of intensity and type of preselection, and heritability. With GPS, in addition to reducing the phenotyping effort considerably, the use of ssGBLUP in subsequent evaluations realizes only a slightly lower genetic gain than that realized without preselection. This is especially the case for traits that are expensive to measure (e.g. feed intake of individual broiler chickens), and traits for which phenotypes can only be measured at advanced stages of life (e.g. litter size in pigs).

Single-Step Genomic Evaluations from Theory to Practice: Using SNP Chips and Sequence Data in BLUPF90

Single-step genomic evaluation became a standard procedure in livestock breeding, and the main reason is the ability to combine all pedigree, phenotypes, and genotypes available into one single evaluation, without the need of post-analysis processing. Therefore, the incorporation of data on genotyped and non-genotyped animals in this method is straightforward. Since 2009, two main implementations of single-step were proposed. One is called single-step genomic best linear unbiased prediction (ssGBLUP) and uses single nucleotide polymorphism (SNP) to construct the genomic relationship matrix; the other is the single-step Bayesian regression (ssBR), which is a marker effect model. Under the same assumptions, both models are equivalent. In this review, we focus solely on ssGBLUP. The implementation of ssGBLUP into the BLUPF90 software suite was done in 2009, and since then, several changes were made to make ssGBLUP flexible to any model, number of traits, number of phenotypes, and number of genotyped animals. Single-step GBLUP from the BLUPF90 software suite has been used for genomic evaluations worldwide. In this review, we will show theoretical developments and numerical examples of ssGBLUP using SNP data from regular chips to sequence data.

Variance estimates are similar using pedigree or genomic relationships with or without the use of metafounders or the algorithm for proven and young animals1

With an increase in the number of animals genotyped there has been a shift from using pedigree relationship matrices (A) to genomic ones. As the use of genomic relationship matrices (G) has increased, new methods to build or approximate G have developed. We investigated whether the way variance components are estimated should reflect these changes. We estimated variance components for maternal sow traits by solving with restricted maximum likelihood, with four methods of calculating the inverse of the relationship matrix. These methods included using just the inverse of A (A−1), combining A−1 and the direct inverse of G (HDIRECT−1), including metafounders (HMETA−1), or combining A−1 with an approximated inverse of G using the algorithm for proven and young animals (HAPY−1). There was a tendency for higher additive genetic variances and lower permanent environmental variances estimated with A−1 compared with the three H−1 methods, which supports that G−1 is better than A−1 at separating genetic and permanent environmental components, due to a better definition of the actual relationships between animals. There were limited or no differences in variance estimates between HDIRECT−1, HMETA−1, and HAPY−1. Importantly, there was limited differences in variance components, repeatability or heritability estimates between methods. Heritabilities ranged between <0.01 to 0.04 for stayability after second cycle, and farrowing rate, between 0.08 and 0.15 for litter weight variation, maximum cycle number, total number born, total number still born, and prolonged interval between weaning and first insemination, and between 0.39 and 0.44 for litter birth weight and gestation length. The limited differences in heritabilities suggest that there would be very limited changes to estimated breeding values or ranking of animals across models using the different sets of variance components. It is suggested that variance estimates continue to be made using A−1, however including G−1 is possibly more appropriate if refining the model, for traits that fit a permanent environmental effect.

Changes in genetic parameters for fitness and growth traits in pigs under genomic selection

Genomic selection increases accuracy and decreases generation interval, speeding up genetic changes in the populations. However, intensive changes caused by selection can reduce the genetic variation and can strengthen undesirable genetic correlations. The purpose of this study was to investigate changes in genetic parameters for fitness traits related with prolificacy (FT1) and litter survival (FT2 and FT3), and for growth (GT1 and GT2) traits in pigs over time. The data set contained 21,269 (FT1), 23,246 (FT2), 23,246 (FT3), 150,492 (GT1), and 150,493 (GT2) phenotypic records obtained from 2009 to 2018. The pedigree file included 369,776 animals born between 2001 and 2018, of which 39,103 were genotyped. Genetic parameters were estimated with bivariate models (FT1-GT1, FT1-GT2, FT2-GT1, FT2-GT2, FT3-GT1, and FT3-GT2) using 3-yr sliding subsets. With a Bayesian implementation using the GIBBS3F90 program computations were performed as genomic analysis (GEN) or pedigree-based analysis (PED), that is, with or without genotypes, respectively. For GEN (PED), the changes in heritability from the first to the last year interval, that is, from 2009–2011 to 2015–2018 were 8.6 to 5.6 (7.9 to 8.8) for FT1, 7.8 to 7.2 (7.7 to 10.8) for FT2, 11.4 to 7.6 (10.1 to 7.5) for FT3, 35.1 to 16.5 (32.5 to 23.7) for GT1, and 35.9 to 16.5 (32.6 to 24.1) for GT2. Differences were also observed for genetic correlations as they changed from −0.31 to −0.58 (−0.28 to −0.73) for FT1-GT1, −0.32 to −0.50 (−0.29 to −0.74) for FT1-GT2, −0.27 to −0.45 (−0.30 to −0.65) for FT2-GT1, −0.28 to −0.45 (−0.32 to −0.66) for FT2-GT2, 0.14 to 0.17 (0.11 to 0.04) for FT3-GT1, and 0.14 to 0.18 (0.11 to 0.05) for FT3-GT2. Strong selection in pigs reduced heritabilities and emphasized the antagonistic genetic relationships between fitness and growth traits. With genotypes considered, heritability estimates were smaller and genetic correlations were greater than estimates with only pedigree and phenotypes. When selection is based on genomic information, genetic parameters estimated without this information can be biased because preselection is not accounted for by the model.

Current status of genomic evaluation

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

Controlling bias in genomic breeding values for young genotyped bulls

The objectives of this study were to investigate bias in genomic predictions for dairy cattle and to find a practical approach to reduce the bias. The simulated data included phenotypes, pedigrees, and genotypes, mimicking a dairy cattle population (i.e., cows with phenotypes and bulls with no phenotypes) and assuming selection by breeding values or no selection. With the simulated data, genomic estimated breeding values (GEBV) were calculated with a single-step genomic BLUP and compared with true breeding values. Phenotypes and genotypes were simulated in 10 generations and in the last 4 generations, respectively. Phenotypes in the last generation were removed to predict breeding values for those individuals using only genomic and pedigree information. Complete pedigrees and incomplete pedigrees with 50% missing dams were created to construct the pedigree-based relationship matrix with and without inbreeding. With missing dams, unknown parent groups (UPG) were assigned in relationship matrices. Regression coefficients (b₁) and coefficients of determination (R²) of true breeding values on (G)EBV were calculated to investigate inflation and accuracy in GEBV for genotyped animals, respectively. In addition to the simulation study, 18 linear type traits of US Holsteins were examined. For the 18 type traits, b₁ and R² of GEBV with full data sets on GEBV with partial data sets for young genotyped bulls were calculated. The results from the simulation study indicated inflation in GEBV for genotyped males that were evaluated with only pedigree and genomic information under BLUP selection. However, when UPG for only pedigree-based relationships were included, the inflation was reduced, accuracy was highest, and genetic trends had no bias. For the linear type traits, when UPG for only pedigree-based relationships were included, the results were generally in agreement with those from the simulation study, implying less bias in genetic trends. However, when including no UPG, UPG in pedigree-based relationships, or UPG in genomic relationships, inflation and accuracy in GEBV were similar. The results from the simulation and type traits suggest that UPG must be defined accurately to be estimable and inbreeding should be included in pedigree-based relationships. In dairy cattle, known pedigree information with inbreeding and estimable UPG plays an important role in improving compatibility between pedigree-based and genomic relationship matrices, resulting in more reliable genomic predictions.

Invited review: Advances and applications of random regression models: From quantitative genetics to genomics

An important goal in animal breeding is to improve longitudinal traits; that is, traits recorded multiple times during an individual's lifetime or physiological cycle. Longitudinal traits were first genetically evaluated based on accumulated phenotypic expression, phenotypic expression at specific time points, or repeatability models. Until now, the genetic evaluation of longitudinal traits has mainly focused on using random regression models (RRM). Random regression models enable fitting random genetic and environmental effects over time, which results in higher accuracy of estimated breeding values compared with other statistical approaches. In addition, RRM provide insights about temporal variation of biological processes and the physiological implications underlying the studied traits. Despite the fact that genomic information has substantially contributed to increase the rates of genetic progress for a variety of economically important traits in several livestock species, less attention has been given to longitudinal traits in recent years. However, including genomic information to evaluate longitudinal traits using RRM is a feasible alternative to yield more accurate selection and culling decisions, because selection of young animals may be based on the complete pattern of the production curve with higher accuracy compared with the use of traditional parent average (i.e., without genomic information). Moreover, RRM can be used to estimate SNP effects over time in genome-wide association studies. Thus, by analyzing marker associations over time, regions with higher effects at specific points in time are more likely to be identified. Despite the advances in applications of RRM in genetic evaluations, more research is needed to successfully combine RRM and genomic information. Future research should provide a better understanding of the temporal variation of biological processes and their physiological implications underlying the longitudinal traits.

The impact of selective genotyping on the response to selection using single-step genomic best linear unbiased prediction

Across the majority livestock species, routinely collected genomic and pedigree information has been incorporated into evaluations using single-step methods. As a result, strategies that reduce genotyping costs without reducing the response to selection are important as they could have substantial economic impacts on breeding programs. Therefore, the objective of the current study was to investigate the impact of selectively genotyping selection candidates on the selection response using simulation. Populations were simulated to mimic the genome and population structure of a swine and cattle population undergoing selection on an index comprised of the estimated breeding values (EBV) for 2 genetically correlated quantitative traits. Ten generations were generated and genotyping began generation 7. Two phenotyping scenarios were simulated that assumed the first trait was recorded early in life on all individuals and the second trait was recorded on all versus a random subset of the individuals. The EBV were generated from a bivariate animal model. Multiple genotyping scenarios were generated that ranged from not genotyping any selection candidates, a proportion of the selection candidates based on either their index value or chosen at random, and genotyping all selection candidates. An interim index value was utilized to decide who to genotype for the selective genotype strategy. The interim value assumed only the first trait was observed and the only genotypic information available was on animals in previous generations. Within each genotyping scenario 25 replicates were generated. Within each genotyping scenario the mean response per generation and the degree to which EBV were inflated/deflated was calculated. Across both species and phenotyping strategies, the plateau of diminishing returns was observed when 60% of the selection candidates with the largest index values were genotyped. When randomly genotyping selection candidates, either 80 or 100% of the selection candidates needed to be genotyped for there not to be a reduction in the index response. Across both populations, no differences in the degree that EBV were inflated/deflated for either trait 1 or 2 were observed between nongenotyped and genotyped animals. The current study has shown that animals can be selectively genotyped in order to optimize the response to selection as a function of the cost to conduct a breeding program using single-step genomic best linear unbiased prediction.

International bull evaluations by genomic BLUP with a prediction population

The purpose of this study was to determine whether multi-country genomic evaluation can be accomplished by multiple-trait genomic best linear unbiased predictor (GBLUP) without sharing genotypes of important animals. Phenotypes and genotypes with 40k SNP were simulated for 25,000 animals, each with 4 traits assuming the same genetic variance and 0.8 genetic correlations. The population was split into 4 subpopulations corresponding to 4 countries, one for each trait. Additionally, a prediction population was created from genotyped animals that were not present in the individual countries but were related to each country's population. Genomic estimated breeding values were computed for each country and subsequently converted to SNP effects. Phenotypes were reconstructed for the prediction population based on the SNP effects of a country and the prediction animals' genotypes. The prediction population was used as the basis for the international evaluation, enabling bull comparisons without sharing genotypes and only sharing SNP effects. The computations were such that SNP effects computed within-country or in the prediction population were the same. Genomic estimated breeding values were calculated by single-trait GBLUP for within-country and multiple-trait GBLUP for multi-country predictions. The true accuracy for the prediction population with reconstructed phenotypes was at most 0.02 less than the accuracy with the original data. The differences increased when countries were assumed unequally sized. However, accuracies by multiple-trait GBLUP with the prediction population were always greater than accuracies from any single within-country prediction. Multi-country genomic evaluations by multiple-trait GBLUP are possible without using original genotypes at a cost of lower accuracy compared with explicitly combining countries' data.