Crossbreed evaluations in single-step genomic best linear unbiased predictor using adjusted realized relationship matrices

Improving Genomic Predictions in Multi-Breed Cattle Populations: A Comparative Analysis of BayesR and GBLUP Models

Numerous studies have shown that combining populations from similar or closely related genetic breeds improves the accuracy of genomic predictions (GP). Extensive experimentation with diverse Bayesian and genomic best linear unbiased prediction (GBLUP) models have been developed to explore multi-breed genomic selection (GS) in livestock, ultimately establishing them as successful approaches for predicting genomic estimated breeding value (GEBV). This study aimed to assess the effectiveness of using BayesR and GBLUP models with linkage disequilibrium (LD)-weighted genomic relationship matrices (GRMs) for genomic prediction in three different beef cattle breeds to identify the best approach for enhancing the accuracy of multi-breed genomic selection in beef cattle. Additionally, a comparison was conducted to evaluate the predictive precision of different marker densities and genetic correlations among the three breeds of beef cattle. The GRM between Yunling cattle (YL) and other breeds demonstrated modest affinity and highlighted a notable genetic concordance of 0.87 between Chinese Wagyu (WG) and Huaxi (HX) cattle. In the within-breed GS, BayesR demonstrated an advantage over GBLUP. The prediction accuracies for HX cattle using the BayesR model were 0.52 with BovineHD BeadChip data (HD) and 0.46 with whole-genome sequencing data (WGS). In comparison to the GBLUP model, the accuracy increased by 26.8% for HD data and 9.5% for WGS data. For WG and YL, BayesR doubled the within-breed prediction accuracy to 14.3% from 7.1%, outperforming GBLUP across both HD and WGS datasets. Moreover, analyzing multiple breeds using genomic selection showed that BayesR consistently outperformed GBLUP in terms of predictive accuracy, especially when using WGS. For instance, in a mixed reference population of HX and WG, BayesR achieved a significant accuracy of 0.53 using WGS for HX, which was a substantial enhancement over the accuracies obtained with GBLUP models. The research further highlights the benefit of including various breeds in the reference group, leading to enhanced accuracy in predictions and emphasizing the importance of comprehensive genomic selection methods. Our research findings indicate that BayesR exhibits superior performance compared to GBLUP in multi-breed genomic prediction accuracy, achieving a maximum improvement of 33.3%, especially in genetically diverse breeds. The improvement can be attributed to the effective utilization of higher single nucleotide polymorphism (SNP) marker density by BayesR, resulting in enhanced prediction accuracy. This evidence conclusively demonstrates the significant impact of BayesR on enhancing genomic predictions in diverse cattle populations, underscoring the crucial role of genetic relatedness in selection methodologies. In parallel, subsequent studies should focus on refining GRM and exploring alternative models for GP.

Validation with single-step SNPBLUP shows that evaluations can continue using a single mean of genotyped individuals, even with multiple breeds

BACKGROUND

In genomic prediction, it is common to centre the genotypes of single nucleotide polymorphisms based on the allele frequencies in the current population, rather than those in the base generation. The mean breeding value of non-genotyped animals is conditional on the mean performance of genotyped relatives, but can be corrected by fitting the mean performance of genotyped individuals as a fixed regression. The associated covariate vector has been referred to as a 'J-factor', which if fitted as a fixed effect can improve the accuracy and dispersion bias of sire genomic estimated breeding values (GEBV). To date, this has only been performed on populations with a single breed. Here, we investigated whether there was any benefit in fitting a separate J-factor for each breed in a three-way crossbred population, and in using pedigree-based expected or genome-based estimated breed fractions to define the J-factors.

RESULTS

For body weight at 7 days, dispersion bias decreased when fitting multiple J-factors, but only with a low proportion of genotyped individuals with selective genotyping. On average, the mean regression coefficients of validation records on those of GEBV increased with one J-factor compared to none, and further increased with multiple J-factors. However, for body weight at 35 days this was not observed. The accuracy of GEBV remained unchanged regardless of the J-factor method used. Differences between the J-factor methods were limited with correlations approaching 1 for the estimated covariate vector, the estimated coefficients of the regression on the J-factors, and the GEBV.

CONCLUSIONS

Based on our results and in the particular design analysed here, i.e. all the animals with phenotype are of the same type of crossbreds, fitting a single J-factor should be sufficient, to reduce dispersion bias. Fitting multiple J-factors may reduce dispersion bias further but this depends on the trait and genotyping rate. For the crossbred population analysed, fitting multiple J-factors has no adverse consequences and if this is done, it does not matter if the breed fractions used are based on the pedigree-expectation or the genomic estimates. Finally, when GEBV are estimated from crossbred data, any observed bias can potentially be reduced by including a straightforward regression on actual breed proportions.

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.

Leveraging low-density crossbred genotypes to offset crossbred phenotypes and their impact on purebred predictions

The objectives of this study were to 1) investigate the predictability and bias of genomic breeding values (GEBV) of purebred (PB) sires for CB performance when CB genotypes imputed from a low-density panel are available, 2) assess if the availability of those CB genotypes can be used to partially offset CB phenotypic recording, and 3) investigate the impact of including imputed CB genotypes in genomic analyses when using the algorithm for proven and young (APY). Two pig populations with up to 207,375 PB and 32,893 CB phenotypic records per trait and 138,026 PB and 32,893 CB genotypes were evaluated. PB sires were genotyped for a 50K panel, whereas CB animals were genotyped for a low-density panel of 600 SNP and imputed to 50K. The predictability and bias of GEBV of PB sires for backfat thickness (BFX) and average daily gain recorded (ADGX) recorded on CB animals were assessed when CB genotypes were available or not in the analyses. In the first set of analyses, direct inverses of the genomic relationship matrix (G) were used with phenotypic datasets truncated at different time points. In the next step, we evaluated the APY algorithm with core compositions differing in the CB genotype contributions. After that, the performance of core compositions was compared with an analysis using a random PB core from a purely PB genomic set. The number of rounds to convergence was recorded for all APY analyses. With the direct inverse of G in the first set of analyses, adding CB genotypes imputed from a low-density panel (600 SNP) did not improve predictability or reduce the bias of PB sires' GEBV for CB performance, even for sires with fewer CB progeny phenotypes in the analysis. That indicates that the inclusion of CB genotypes primarily used for inferring pedigree in commercial farms is of no benefit to offset CB phenotyping. When CB genotypes were incorporated into APY, a random core composition or a core with no CB genotypes reduced bias and the number of rounds to convergence but did not affect predictability. Still, a PB random core composition from a genomic set with only PB genotypes resulted in the highest predictability and the smallest number of rounds to convergence, although bias increased. Genotyping CB individuals for low-density panels is a valuable identification tool for linking CB phenotypes to pedigree; however, the inclusion of those CB genotypes imputed from a low-density panel (600 SNP) might not benefit genomic predictions for PB individuals or offset CB phenotyping for the evaluated CB performance traits. Further studies will help understand the usefulness of those imputed CB genotypes for traits with lower PB-CB genetic correlations and traits not recorded in the PB environment, such as mortality and disease traits.

Genotyping and phenotyping strategies for genetic improvement of meat quality and carcass composition in swine

Background

Meat quality and composition traits have become valuable in modern pork production; however, genetic improvement has been slow due to high phenotyping costs. Combining genomic information with multi-trait indirect selection based on cheaper indicator traits is an alternative for continued cost-effective genetic improvement.

Methods

Data from an ongoing breeding program were used in this study. Phenotypic and genomic information was collected on three-way crossbred and purebred Duroc animals belonging to 28 half-sib families. We applied different methods to assess the value of using purebred and crossbred information (both genomic and phenotypic) to predict expensive-to-record traits measured on crossbred individuals. Estimation of multi-trait variance components set the basis for comparing the different scenarios, together with a fourfold cross-validation approach to validate the phenotyping schemes under four genotyping strategies.

Results

The benefit of including genomic information for multi-trait prediction depended on the breeding goal trait, the indicator traits included, and the source of genomic information. While some traits benefitted significantly from genotyping crossbreds (e.g., loin intramuscular fat content, backfat depth, and belly weight), multi-trait prediction was advantageous for some traits even in the absence of genomic information (e.g., loin muscle weight, subjective color, and subjective firmness).

Conclusions

Our results show the value of using different sources of phenotypic and genomic information. For most of the traits studied, including crossbred genomic information was more beneficial than performing multi-trait prediction. Thus, we recommend including crossbred individuals in the reference population when these are phenotyped for the breeding objective.

Genomic evaluation with multibreed and crossbred data

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We found low accuracy of genomic evaluation of crossbreds based on purebred data.

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We found higher accuracy for crossbreds based on crossbred data.

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Use of putative sequence variants had a small impact on genomic accuracy.

Several types of multibreed genomic evaluation are in use. These include evaluation of crossbreds based on purebred SNP effects, joint evaluation of all purebreds and crossbreds with a single additive effect, and treating each purebred and crossbred group as a separate trait. Additionally, putative quantitative trait nucleotides can be exploited to increase the accuracy of prediction. Existing studies indicate that the prediction of crossbreds based on purebred data has low accuracy, that a joint evaluation can potentially provide accurate evaluations for crossbreds but could lower accuracy for purebreds compared with single-breed evaluations, and that the use of putative quantitative trait nucleotides only marginally increases the accuracy. One hypothesis is that genomic selection is based on estimation of clusters of independent chromosome segments. Subsequently, predicting a particular group type would require a reference population of the same type, and crosses with same breed percentage but different type (F₁ vs. F₂) would, at best, use separate reference populations. The genomic selection of multibreed population is still an active research topic.

Genomic prediction in Nordic Red dairy cattle considering breed origin of alleles

This study investigated the reliability of genomic prediction (GP) using breed origin of alleles (BOA) approach in the Nordic Red (RDC) population, which has an admixed population structure. The RDC population consists of animals with varying degrees of genetic materials from the Danish Red (RDM), Swedish Red (SRB), Finnish Ayrshire (FAY), and Holstein (HOL) because bulls have been used across the breeds. The BOA approach was tested using 39,550 RDC animals in the reference population and 11,786 in the validation population. Deregressed proofs (DRP) of milk, fat and protein were used as response variable for GP. Direct genomic breeding values (DGV) for animals in the validation population were calculated with (BOA model) or without (joint model) considering breed origin of alleles. The joint model assumed homogeneous marker effects and a single set of marker effects were estimated, whereas BOA model assumed heterogeneous marker effects, and different sets of marker effects were estimated across the breeds. For the BOA approach, we tested scenarios assuming both correlated (BOA_cor) and uncorrelated (BOA_uncor) marker effects between the breeds. Additionally, we investigated GP using a standard Illumina 50K chip and including SNP selected from imputed whole-genome sequencing (50K+WGS). We also studied the effect of estimating (co)variances for genome regions of different sizes to exploit the information of the genome regions contributing to the (co)variance between the breeds. Region sizes were set as 1 SNP, a group of 30 or 100 adjacent SNP, or the whole genome. Reliability of DGV was measured as squared correlations between DGV and DRP divided by the reliability of DRP. Across the 3 traits, in general, RS30 and RS100 SNP yielded the highest reliabilities. Including WGS SNP improved reliabilities in almost all scenarios (0.297 on average for 50K and 0.307 on average for 50K+WGS). The BOA_uncor (0.233 on average) was inferior to the joint model (0.339 on average), but the reliabilities obtained using BOA_cor (0.334 on average) in most cases were not significantly different from those obtained using the joint model. The results indicate that both including additional whole-genome sequencing SNP and dividing the genome into fixed regions improve GP in the RDC. The BOA models have the potential to increase the reliability of GP, but the benefit is limited in populations with a high exchange of genetic material for a long time, as is the case for RDC.

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.

Metafounders May Reduce Bias in Composite Cattle Genomic Predictions

Metafounders are pseudo-individuals that act as proxies for animals in base populations. When metafounders are used, individuals from different breeds can be related through pedigree, improving the compatibility between genomic and pedigree relationships. The aim of this study was to investigate the use of metafounders and unknown parent groups (UPGs) for the genomic evaluation of a composite beef cattle population. Phenotypes were available for scrotal circumference at 14 months of age (SC14), post weaning gain (PWG), weaning weight (WW), and birth weight (BW). The pedigree included 680,551 animals, of which 1,899 were genotyped for or imputed to around 30,000 single-nucleotide polymorphisms (SNPs). Evaluations were performed based on pedigree (BLUP), pedigree with UPGs (BLUP_UPG), pedigree with metafounders (BLUP_MF), single-step genomic BLUP (ssGBLUP), ssGBLUP with UPGs for genomic and pedigree relationship matrices (ssGBLUP_UPG) or only for the pedigree relationship matrix (ssGBLUP_UPGA), and ssGBLUP with metafounders (ssGBLUP_MF). Each evaluation considered either four or 10 groups that were assigned based on breed of founders and intermediate crosses. To evaluate model performance, we used a validation method based on linear regression statistics to obtain accuracy, stability, dispersion, and bias of (genomic) estimated breeding value [(G)EBV]. Overall, relationships within and among metafounders were stronger in the scenario with 10 metafounders. Accuracy was greater for models with genomic information than for BLUP. Also, the stability of (G)EBVs was greater when genomic information was taken into account. Overall, pedigree-based methods showed lower inflation/deflation (regression coefficients close to 1.0) for SC14, WWM, and BWD traits. The level of inflation/deflation for genomic models was small and trait-dependent. Compared with regular ssGBLUP, ssGBLUP_MF4 displayed regression coefficient closer to one SC14, PWG, WWM, and BWD. Genomic models with metafounders seemed to be slightly more stable than models with UPGs based on higher similarity of results with different numbers of groups. Further, metafounders can help to reduce bias in genomic evaluations of composite beef cattle populations without reducing the stability of GEBVs.

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.

Indirect genomic predictions for milk yield in crossbred Holstein-Jersey dairy cattle

The objective of this study was to predict genomic breeding values for milk yield of crossbred dairy cattle under different scenarios using single-step genomic BLUP (ssGBLUP). The data set included 13,880,217 milk yield measurements on 6,830,415 cows. Genotypes of 89,558 Holstein, 40,769 Jersey, and 22,373 Holstein-Jersey crossbred animals were used, of which all Holstein, 9,313 Jersey, and 1,667 crossbred animals had phenotypic records. Genotypes were imputed to 45K SNP markers. The SNP effects were estimated from single-breed evaluations for Jersey (JE), Holstein (HO) and crossbreds (CROSS), and multibreed evaluations including all Jersey and Holstein (JE_HO) or approximately equal proportions of Jersey, Holstein, and crossbred animals (MIX). Indirect predictions (IP) of the validation animals (358 crossbred animals with phenotypes excluded from evaluations) were calculated using the resulting SNP effects. Additionally, breed proportions (BP) of crossbred animals were applied as a weight when IP were estimated based on each pure breed. The predictive ability of IP was calculated as the Pearson correlation between IP and phenotypes of the validation animals adjusted for fixed effects in the model. Regression of adjusted phenotypes on IP was used to assess the inflation of IP. The predictive ability of IP for CROSS, JE, HO, JE_HO, and MIX scenario was 0.50, 0.50, 0.47, 0.50, and 0.46, respectively. Using BP was the least successful, with a predictive ability of 0.32. The inflation of the IP for crossbred animals using CROSS, JE, HO, JE_HO, MIX, and BP scenarios were 1.17, 0.65, 0.55, 0.78, 1.00, and 0.85, respectively. The IP of crossbred animals can be predicted using single-step GBLUP under a scenario that includes purebred genotypes.

Selective genotyping and phenotypic data inclusion strategies of crossbred progeny for combined crossbred and purebred selection in swine breeding

Inclusion of crossbred (CB) data into traditionally purebred (PB) genetic evaluations has been shown to increase the response in CB performance. Currently, it is unrealistic to collect data on all CB animals in swine production systems, thus, a subset of CB animals must be selected to contribute genomic/phenotypic information. The aim of this study was to evaluate selective genotyping strategies in a simulated 3-way swine crossbreeding scheme. The swine crossbreeding scheme was simulated and produced 3-way CB animals for 6 generations with 3 distinct PB breeds each with 25 and 175 mating males and females, respectively. F1 crosses (400 mating females) produced 4,000 terminal CB progeny which were subjected to selective genotyping. The genome consisted of 18 chromosomes with 1,800 QTL and 72k SNP markers. Selection was performed using estimated breeding values (EBV) for CB performance. It was assumed that both PB and CB performance was moderately heritable (h2=0.4). Several scenarios altering the genetic correlation between PB and CB performance (rpc=0.1, 0.3, 0.5, 0.7,or 0.9) were considered. CB animals were chosen based on phenotypes to select 200, 400, or 800 CB animals to genotype per generation. Selection strategies included: (1) Random: random selection, (2) Top: highest phenotype, (3) Bottom: lowest phenotype, (4) Extreme: half highest and half lowest phenotypes, and (5) Middle: average phenotype. Each selective genotyping strategy, except for Random, was considered by selecting animals in half-sib (HS) or full-sib (FS) families. The number of PB animals with genotypes and phenotypes each generation was fixed at 1,680. Each unique genotyping strategy and rpc scenario was replicated 10 times. Selection of CB animals based on the Extreme strategy resulted in the highest (P < 0.05) rates of genetic gain in CB performance (ΔG) when rpc<0.9. For highly correlated traits (rpc=0.9) selective genotyping did not impact (P > 0.05) ΔG. No differences (P > 0.05) were observed in ΔG between top, bottom, or middle when rpc>0.1. Higher correlations between true breeding values (TBV) and EBV were observed using Extreme when rpc<0.9. In general, family sampling method did not impact ΔG or the correlation between TBV and EBV. Overall, the Extreme genotyping strategy produced the greatest genetic gain and the highest correlations between TBV and EBV, suggesting that 2-tailed sampling of CB animals is the most informative when CB performance is the selection goal.

Breed-adjusted genomic relationship matrices as a method to account for population stratification in multibreed populations of tropically adapted beef heifers

Context Beef cattle breeds in Australia can broadly be broken up into two subspecies, namely, Bos indicus and Bos taurus. Due to the time since divergence between the subspecies, it is likely that mutations affecting quantitative traits have developed independently in each. Aims We hypothesise that this will affect the prediction accuracy of genomic selection of admixed and composite populations that include both ancestral subspecies. Our study investigates methods to quantify population stratification in a multibreed population of tropically adapted heifers, with the aim of improving prediction accuracy of genomic selection for reproductive maturity score. Methods We used genotypes and reproductive maturity phenotypes from 3695 tropically adapted heifers from three purebred populations, namely, Brahman, Santa Gertrudis and Droughtmaster. Two of these breeds, Santa Gertrudis and Droughtmaster, are stabilised composites of varying B. indicus × B. taurus ancestry, and the third breed, Brahman, has predominately B. indicus ancestry. Genotypes were imputed to three marker-panel densities and population stratification was accounted for in genomic relationship matrices by using breed-specific allele frequencies when calculating the genomic relationships among animals. Prediction accuracy and bias were determined using a five-fold cross validation of randomly selected multibreed cohorts. Key Results Our results showed that the use of breed-adjusted genomic relationship matrices did not improve either prediction accuracy or bias for a lowly heritable trait such as reproductive maturity score. However, using breed-adjusted genomic relationship matrices allowed the capture of a higher proportion of additive genetic effects when estimating variance components. Conclusions These findings suggest that, despite seeing no improvement in prediction accuracy, it may still be beneficial to use breed-adjusted genomic relationship matrices in multibreed populations to improve the estimation of variance components. Implications As such, genomic evaluations using breed-adjusted genomic relationship matrices may be beneficial in multibreed populations.

Impact of inclusion rates of crossbred phenotypes and genotypes in nucleus selection programs

Numerous methods have been suggested to incorporate crossbred (CB) phenotypes and genotypes into swine selection programs, yet little research has focused on the implicit trade-off decisions between generating data at the nucleus or commercial level. The aim of this study was to investigate the impact of altering the proportion of purebred (PB) and CB phenotypes and genotypes in genetic evaluations on the response to selection of CB performance. Assuming CB and PB performance with moderate heritabilities (h2=0.4), a three-breed swine crossbreeding scheme was simulated and selection was practiced for six generations, where the goal was to increase CB performance. Phenotypes, genotypes, and pedigrees for three PB breeds (25 and 175 mating males and females for each breed, respectively), F1 crosses (400 mating females), and terminal cross progeny (2,500) were simulated. The genome consisted of 18 chromosomes with 1,800 quantitative trait loci and 72k single nucleotide polymorphism (SNP) markers. Selection was performed in PB breeds using estimated breeding value for each phenotyping/genotyping strategy. Strategies investigated were: 1) increasing the proportion of CB with genotypes, phenotypes, and sire pedigree relationships, 2) decreasing the proportion of PB phenotypes and genotypes, and 3) altering the genetic correlation between PB and CB performance (rpc). Each unique rpc scenario and data collection strategy was replicated 10 times. Results showed that including CB data improved the CB performance regardless of  rpc or data collection strategy compared with when no CB data were included. Compared with using only PB information, including 10% of CB progeny per generation with sire pedigrees and phenotypes increased the response in CB phenotype by 134%, 55%, 33%, 23%, and 21% when rpc was 0.1, 0.3, 0.5, 0.7, and 0.9, respectively. When the same 10% of CB progeny were also genotyped, CB performance increased by 243%, 54%, 38%, 23%, and 20% when the rpc was 0.1, 0.3, 0.5, 0.7, and 0.9, respectively, compared with when no CB data were utilized. Minimal change was observed in the average CB phenotype when PB phenotypes were included or proportionally removed when CB were genotyped. Removal of both PB phenotypes and genotypes when CB were genotyped greatly reduced the response in CB performance. In practice, the optimal inclusion rate of CB and PB data depends upon the genetic correlation between CB and PB animals and the expense of additional CB data collection compared with the economic benefit associated with increased CB performance.

Optimizing genomic reference populations to improve crossbred performance

Background

In pig and poultry breeding, the objective is to improve the performance of crossbred production animals, while selection takes place in the purebred parent lines. One way to achieve this is to use genomic prediction with a crossbred reference population. A crossbred reference population benefits from expressing the breeding goal trait but suffers from a lower genetic relatedness with the purebred selection candidates than a purebred reference population. Our aim was to investigate the benefit of using a crossbred reference population for genomic prediction of crossbred performance for: (1) different levels of relatedness between the crossbred reference population and purebred selection candidates, (2) different levels of the purebred-crossbred correlation, and (3) different reference population sizes. We simulated a crossbred breeding program with 0, 1 or 2 multiplication steps to generate the crossbreds, and compared the accuracy of genomic prediction of crossbred performance in one generation using either a purebred or a crossbred reference population. For each scenario, we investigated the empirical accuracy based on simulation and the predicted accuracy based on the estimated effective number of independent chromosome segments between the reference animals and selection candidates.

Results

When the purebred-crossbred correlation was 0.75, the accuracy was highest for a two-way crossbred reference population but similar for purebred and four-way crossbred reference populations, for all reference population sizes. When the purebred-crossbred correlation was 0.5, a purebred reference population always resulted in the lowest accuracy. Among the different crossbred reference populations, the accuracy was slightly lower when more multiplication steps were used to create the crossbreds. In general, the benefit of crossbred reference populations increased when the size of the reference population increased. All predicted accuracies overestimated their corresponding empirical accuracies, but the different scenarios were ranked accurately when the reference population was large.

Conclusions

The benefit of a crossbred reference population becomes larger when the crossbred population is more related to the purebred selection candidates, when the purebred-crossbred correlation is lower, and when the reference population is larger. The purebred-crossbred correlation and reference population size interact with each other with respect to their impact on the accuracy of genomic estimated breeding values.

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.

Assessment of sire contribution and breed-of-origin of alleles in a three-way crossbred broiler dataset

Broiler breeding programs rely on crossbreeding. With genomic selection, widespread use of crossbred performance in breeding programs comes within reach. Commercial crossbreds, however, may have unknown pedigrees and their genomes may include DNA from 2 to 4 different breeds. Our aim was, for a broiler dataset with a limited number of sires having both purebred and crossbred offspring generated using natural mating, to rapidly derive parentage, assess the distribution of the sire contribution to the offspring generation, and to assess breed-of-origin of alleles in crossbreds. The dataset contained genotypes for 56,075 SNPs for 5,882 purebred and 10,943 3-way crossbred offspring generated by natural mating of 164 purebred sires to 1,016 purebred and 1,386 F1 crossbred hens. Using our algorithm FindParents, joint parentage derivation for the offspring and parent generations required only 1 m 29 s to retrieve parentage for 20,253 animals considering 4,504 possible parents. FindParents was similarly accurate as a maximum likelihood based method, apart from situations where settings of FindParents did not match the genotyping error rate in the data. Numbers of offspring per sire had a very skewed distribution, ranging from 1 to 270 crossbreds and 1 to 154 purebreds. Derivation of breed-of-origin of alleles relied on phasing all genotypes, including 8,205, 372, and 720 animals from the 3 pure lines involved, and allocating haplotypes in the crossbreds to purebred lines based on observed frequencies in the purebred lines. Breed-of-origin could be derived for 96.94% of the alleles of the 1,386 F1 crossbred hens and for 91.88% of the alleles of the 10,943 3-way crossbred offspring, of which 49.49% to the sire line. The achieved percentage of assignment to the sire line was sufficient to proceed with subsequent analyses requiring only the breed-of-origin of the paternal alleles to be known. Although required number of animals may be population dependent, to increase the total percentage of assigned alleles, it seems advisable to use at least approx. 1,000 genotyped purebred animals for each of the lines involved.

Comparing Alternative Single-Step GBLUP Approaches and Training Population Designs for Genomic Evaluation of Crossbred Animals

As crossbreeding is extensively used in some livestock species, we aimed to evaluate the performance of single-step GBLUP (ssGBLUP) and weighted ssGBLUP (WssGBLUP) methods to predict Genomic Estimated Breeding Values (GEBVs) of crossbred animals. Different training population scenarios were evaluated: (SC1) ssGBLUP based on a single-trait model considering purebred and crossbred animals in a joint training population; (SC2) ssGBLUP based on a multiple-trait model to enable considering phenotypes recorded in purebred and crossbred training animals as different traits; (SC3) WssGBLUP based on a single-trait model considering purebred and crossbred animals jointly in the training population (both populations were used for SNP weights' estimation); (SC4) WssGBLUP based on a single-trait model considering only purebred animals in the training population (crossbred population only used for SNP weights' estimation); (SC5) WssGBLUP based on a single-trait model and the training population characterized by purebred animals (purebred population used for SNP weights' estimation). A complex trait was simulated assuming alternative genetic architectures. Different scaling factors to blend the inverse of the genomic (G -1) and pedigree (A 22 - 1 ) relationship matrices were also tested. The predictive performance of each scenario was evaluated based on the validation accuracy and regression coefficient. The genetic correlations across simulated populations in the different scenarios ranged from moderate to high (0.71-0.99). The scenario mimicking a completely polygenic trait (h Q T L 2 = 0) yielded the lowest validation accuracy (0.12; for SC3 and SC4). The simulated scenarios assuming 4,500 QTLs affecting the trait andh Q T L 2 = h 2 resulted in the greatest GEBV accuracies (0.47; for SC1 and SC2). The regression coefficients ranged from 0.28 (for SC3 assuming polygenic effect) to 1.27 (for SC2 considering 4,500 QTLs). In general, SC3 and SC5 resulted in inflated GEBVs, whereas other scenarios yielded deflated GEBVs. The scaling factors used to combine G -1 andA 22 - 1 had a small influence on the validation accuracies, but a greater effect on the regression coefficients. Due to the complexity of multiple-trait models and WssGBLUP analyses, and a similar predictive performance across the methods evaluated, SC1 is recommended for genomic evaluation in crossbred populations with similar genetic structures [moderate-to-high (0.71-0.99) genetic correlations between purebred and crossbred populations].

Current status of genomic evaluation

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

Genomic predictions in purebreds with a multibreed genomic relationship matrix1

Combining breeds in a multibreed evaluation can have a negative impact on prediction accuracy, especially if single nucleotide polymorphism (SNP) effects differ among breeds. The aim of this study was to evaluate the use of a multibreed genomic relationship matrix (G), where SNP effects are considered to be unique to each breed, that is, nonshared. This multibreed G was created by treating SNP of different breeds as if they were on nonoverlapping positions on the chromosome, although, in reality, they were not. This simple setup may avoid spurious Identity by state (IBS) relationships between breeds and automatically considers breed-specific allele frequencies. This scenario was contrasted to a regular multibreed evaluation where all SNPs were shared, that is, the same position, and to single-breed evaluations. Different SNP densities (9k and 45k) and different effective population sizes (Ne) were tested. Five breeds mimicking recent beef cattle populations that diverged from the same historical population were simulated using different selection criteria. It was assumed that quantitative trait locus (QTL) effects were the same over all breeds. For the recent population, generations 1-9 had approximately half of the animals genotyped, whereas all animals in generation 10 were genotyped. Generation 10 animals were set for validation; therefore, each breed had a validation group. Analyses were performed using single-step genomic best linear unbiased prediction. Prediction accuracy was calculated as the correlation between true (T) and genomic estimated breeding values (GEBV). Accuracies of GEBV were lower for the larger Ne and low SNP density. All three evaluation scenarios using 45k resulted in similar accuracies, suggesting that the marker density is high enough to account for relationships and linkage disequilibrium with QTL. A shared multibreed evaluation using 9k resulted in a decrease of accuracy of 0.08 for a smaller Ne and 0.12 for a larger Ne. This loss was mostly avoided when markers were treated as nonshared within the same G matrix. A G matrix with nonshared SNP enables multibreed evaluations without considerably changing accuracy, especially with limited information per breed.

Genomic predictions for crossbred dairy cattle

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

Validation of genomic predictions for body weight in broilers using crossbred information and considering breed-of-origin of alleles

Background

Pig and poultry breeding programs aim at improving crossbred (CB) performance. Selection response may be suboptimal if only purebred (PB) performance is used to compute genomic estimated breeding values (GEBV) because the genetic correlation between PB and CB performance (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{pc}$$\end{document}rpc) is often lower than 1. Thus, it may be beneficial to use information on both PB and CB performance. In addition, the accuracy of GEBV of PB animals for CB performance may improve when the breed-of-origin of alleles (BOA) is considered in the genomic relationship matrix (GRM). Thus, our aim was to compare scenarios where GEBV are computed and validated by using (1) either CB offspring averages or individual CB records for validation, (2) either a PB or CB reference population, and (3) a GRM that either accounts for or ignores BOA in the CB individuals. For this purpose, we used data on body weight measured at around 7 (BW7) or 35 (BW35) days in PB and CB broiler chickens and evaluated the accuracy of GEBV based on the correlation GEBV with phenotypes in the validation population (validation correlation).

Results

With validation on CB offspring averages, the validation correlation of GEBV of PB animals for CB performance was lower with a CB reference population than with a PB reference population for BW35 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{pc}$$\end{document}rpc = 0.96), and about equal for BW7 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{pc}$$\end{document}rpc = 0.80) when BOA was ignored. However, with validation on individual CB records, the validation correlation was higher with a CB reference population for both traits. The use of a GRM that took BOA into account increased the validation correlation for BW7 but reduced it for BW35.

Conclusions

We argue that the benefit of using a CB reference population for genomic prediction of PB animals for CB performance should be assessed either by validation on CB offspring averages, or by validation on individual CB records while using a GRM that accounts for BOA in the CB individuals. With this recommendation in mind, our results show that the accuracy of GEBV of PB animals for CB performance was equal to or higher with a CB reference population than with a PB reference population for a trait with an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{pc}$$\end{document}rpc of 0.8, but lower for a trait with an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{pc}$$\end{document}rpc of 0.96. In addition, taking BOA into account was beneficial for a trait with an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{pc}$$\end{document}rpc of 0.8 but not for a trait with an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{pc}$$\end{document}rpc of 0.96.

Electronic supplementary material

The online version of this article (10.1186/s12711-019-0481-7) contains supplementary material, which is available to authorized users.

Crossbred evaluations using single-step genomic BLUP and algorithm for proven and young with different sources of data1

Genomic selection (GS) is routinely applied to many purebreds and lines of farm species. However, this method can be extended to predictions across purebreds as well as for crossbreds. This is useful for swine and poultry, for which selection in nucleus herds is typically performed on purebred animals, whereas the commercial product is the crossbred animal. Single-step genomic BLUP (ssGBLUP) is a widely applied method that can explore the recently developed algorithm for proven and young (APY). The APY allows for greater efficiency in computing BLUP solutions by exploiting the theory of limited dimensionality of genomic information and chromosome segments (Me). This study investigates the predictivity as a proxy for accuracy across and within 2 purebred pig lines and their crosses, under the application of APY in ssGBLUP setup, and different levels of Me overlapping across populations. The data consisted of approximately 210k phenotypic records for 2 traits (T1 and T2) with moderate heritability. Genotypes for 43k SNP markers were available for approximately 46k animals, from which 26k and 16k belong to 2 pure lines (L1 and L2), and approximately 4k are crossbreds. The complete pedigree had more than 720k animals. Different multivariate ssGBLUP models were applied, either with the regular or APY inverse of the genomic relationship matrix (G). The models included a standard bivariate animal model with 3 lines evaluated as 1 joint line, and for each trait individually, a 3-trait animal model with each line treated as a separate trait. Both models provided the same predictivity across and within the lines. Using either of the pure lines data as a training set resulted in a similar predictivity for the crossbreed animals (0.18 to 0.21). Across-line predictive ability was limited to less than half of the maximum predictivity for each line (L1T1 0.33, L1T2 0.25, L2T1 0.35, L2T2 0.36). For crossbred predictions, APY performed equivalently to regular G inverse when the number of core animals was equal to the number of eigenvalues explaining between 98% and 99% of the variance of G (4k to 8k) including all lines. Predictivity across the lines is achievable because of the shared Me between them. The number of those shared segments can be obtained via eigenvalue decomposition of genomic information available for each line.

Genomic prediction for crossbred performance using metafounders

Future genomic evaluation models to be used routinely in breeding programs for pigs and poultry need to be able to optimally use information of crossbred (CB) animals to predict breeding values for CB performance of purebred (PB) selection candidates. Important challenges in the commonly used single-step genomic best linear unbiased prediction (ssGBLUP) model are the definition of relationships between the different line compositions and the definition of the base generation per line. The use of metafounders (MFs) in ssGBLUP has been proposed to overcome these issues. When relationships between lines are known to be different from 0, the use of MFs generalizes the concept of genetic groups relying on the genotype data. Our objective was to investigate the effect of using MFs in genomic prediction for CB performance on estimated variance components, and accuracy and bias of GEBV. This was studied using stochastic simulation to generate data representing a three-way crossbreeding scheme in pigs, with the parental lines being either closely related or unrelated. Results show that using MFs, the variance components should be scaled appropriately, especially when basing them on estimates obtained with, for example a pedigree-based model. The accuracies of GEBV that were obtained using MFs were similar to accuracies without using MFs, regardless whether the lines involved in the CB were closely related or unrelated. The use of MFs resulted in a model that had similar or somewhat better convergence properties compared to other models. We recommend the use of MFs in ssGBLUP for genomic evaluations in crossbreeding schemes.

Genomic data reveals large similarities among Canadian and French maternal pig lines

Combining reference populations from different countries and breeds could be an affordable way to enlarge the size of the reference populations for genomic prediction of breeding values. Therefore, the main objectives of this study were to assess the genetic diversity within and between two Canadian and French pig breeds (Landrace and Yorkshire) and the genomic relatedness among populations to evaluate the feasibility of an across-country reference population for pig genomic selection. A total of 14 756 pigs were genotyped on two single nucleotide polymorphism (SNP) chip panels (∼65K SNPs). A principal component analysis clearly discriminated Landrace and Yorkshire breeds, and also, but to a lesser extent, the Canadian and French purebred pigs of each breed. Linkage disequilibrium (LD) between adjacent SNPs was similar within Yorkshire populations. However, levels of LD were slightly different for Landrace populations. The consistency of gametic phase was very high between Yorkshire populations (0.96 at 0.05 Mb) and high for Landrace (0.88 at 0.05 Mb). Based on consistency of gametic phase, Canadian and French pig maternal lines are genetically close to each other. These results are promising, as they indicate that the accuracy of estimated genomic breeding values may increase by combining reference populations from the two countries.

Sparse single-step genomic BLUP in crossbreeding schemes

The algorithm for proven and young animals (APY) efficiently computes an approximated inverse of the genomic relationship matrix, by dividing genotyped animals in the so-called core and noncore animals. The APY leads to computationally feasible single-step genomic Best Linear Unbiased Prediction (ssGBLUP) with a large number of genotyped animals and was successfully applied to real single-breed or line datasets. This study aimed to assess the quality of genomic estimated breeding values (GEBV) when using the APY (GEBVAPY), in comparison to GEBV when using the directly inverted genomic relationship matrix (GEBVDIRECT), for situations based on crossbreeding schemes, including F1 and F2 crosses, such as the ones for pigs and chickens. Based on simulations of a 3-way crossbreeding program, we compared different approximated inverses of a genomic relationship matrix, by varying the size and the composition of the core group. We showed that GEBVAPY were accurate approximations of GEBVDIRECT for multivariate ssGBLUP involving different breeds and their crosses. GEBVAPY as accurate as GEBVDIRECT were obtained when the core groups included animals from different breed compositions and when the core groups had a size between the numbers of the largest eigenvalues explaining 98% and 99% of the variation in the raw genomic relationship matrix.

Including crossbred pigs in the genomic relationship matrix through utilization of both linkage disequilibrium and linkage analysis

In pig breeding, the final product is a crossbred (CB) animal, while selection is performed at the purebred (PB) level using mainly PB data. However, incorporating CB data in genetic evaluations is expected to result in greater genetic progress at the CB level. Currently, there is no optimal way to include CB genotypes into the genomic relationship matrix. This is because, in single-step genomic BLUP, which is the most commonly used method, genomic and pedigree relationships must refer to the same base. This may not be the case when several breeds and CB are included. An alternative to overcome this issue may be to use a genomic relationship matrix (G matrix) that accounts for both linkage disequilibrium (LD) and linkage analysis (LA), called G. The objectives of this study were to further develop the G matrix approach to utilize both PB and CB genotypes simultaneously, to investigate its performance, and the general added value of including CB genotypes in genomic evaluations. Data were available on Dutch Landrace, Large White, and the F1 cross of those breeds. In total, 7 different G matrix compositions (PB alone, PB together, each PB with the CB, all genotypes across breeds, and G) were tested on 3 maternal traits: total number born (TNB), live born (LB), and gestation length (GL). Results show that G gave the greatest prediction accuracy of all the relationship matrices tested for PB prediction, but not for CB prediction. Including CB genotypes in general increased prediction accuracy for all breeds. However, in some cases, these increases in prediction accuracy were not significant (at < 0.05). To conclude, CB genotypes increased prediction accuracy for some of the traits and breeds, but not for all. The G matrix had significantly greater prediction accuracy in PB than the other G matrix with both PB and CB genotypes, except in one case. While for CB, the G matrix with genotypes across all breeds gave the greatest accuracy, though this was not significantly different from G. Computation time was high for G, and research will be needed to reduce its computational costs to make it feasible for use in routine evaluations. The main conclusion is that inclusion of CB genotypes is beneficial for both PB and CB animals.

Genomic evaluation for a three-way crossbreeding system considering breed-of-origin of alleles

BACKGROUND

Genomic prediction of purebred animals for crossbred performance can be based on a model that estimates effects of single nucleotide polymorphisms (SNPs) in purebreds on crossbred performance. For crossbred performance, SNP effects might be breed-specific due to differences between breeds in allele frequencies and linkage disequilibrium patterns between SNPs and quantitative trait loci. Accurately tracing the breed-of-origin of alleles (BOA) in three-way crosses is possible with a recently developed procedure called BOA. A model that accounts for breed-specific SNP effects (BOA model), has never been tested empirically on a three-way crossbreeding scheme. Therefore, the objectives of this study were to evaluate the estimates of variance components and the predictive accuracy of the BOA model compared to models in which SNP effects for crossbred performance were assumed to be the same across breeds, using either breed-specific allele frequencies ([Formula: see text] model) or allele frequencies averaged across breeds ([Formula: see text] model). In this study, we used data from purebred and three-way crossbred pigs on average daily gain (ADG), back fat thickness (BF), and loin depth (LD).

RESULTS

Estimates of variance components for crossbred performance from the BOA model were mostly similar to estimates from models [Formula: see text] and [Formula: see text]. Heritabilities for crossbred performance ranged from 0.24 to 0.46 between traits. Genetic correlations between purebred and crossbred performance ([Formula: see text]) across breeds ranged from 0.30 to 0.62 for ADG and from 0.53 to 0.74 for BF and LD. For ADG, prediction accuracies of the BOA model were higher than those of the [Formula: see text] and [Formula: see text] models, with significantly higher accuracies only for one maternal breed. For BF and LD, prediction accuracies of models [Formula: see text] and [Formula: see text] were higher than those of the BOA model, with no significant differences. Across all traits, models [Formula: see text] and [Formula: see text] yielded similar predictions.

CONCLUSIONS

The BOA model yielded a higher prediction accuracy for ADG in one maternal breed, which had the lowest [Formula: see text] (0.30). Using the BOA model was especially relevant for traits with a low [Formula: see text]. In all other cases, the use of crossbred information in models [Formula: see text] and [Formula: see text], does not jeopardize predictions and these models are more easily implemented than the BOA model.

Multi-population Genomic Relationships for Estimating Current Genetic Variances Within and Genetic Correlations Between Populations

Different methods are available to calculate multi-population genomic relationship matrices. Since those matrices differ in base population, it is anticipated that the method used to calculate genomic relationships affects the estimate of genetic variances, covariances, and correlations. The aim of this article is to define the multi-population genomic relationship matrix to estimate current genetic variances within and genetic correlations between populations. The genomic relationship matrix containing two populations consists of four blocks, one block for population 1, one block for population 2, and two blocks for relationships between the populations. It is known, based on literature, that by using current allele frequencies to calculate genomic relationships within a population, current genetic variances are estimated. In this article, we theoretically derived the properties of the genomic relationship matrix to estimate genetic correlations between populations and validated it using simulations. When the scaling factor of across-population genomic relationships is equal to the product of the square roots of the scaling factors for within-population genomic relationships, the genetic correlation is estimated unbiasedly even though estimated genetic variances do not necessarily refer to the current population. When this property is not met, the correlation based on estimated variances should be multiplied by a correction factor based on the scaling factors. In this study, we present a genomic relationship matrix which directly estimates current genetic variances as well as genetic correlations between populations.

Genomic selection for crossbred performance accounting for breed-specific effects

Background

Breed-specific effects are observed when the same allele of a given genetic marker has a different effect depending on its breed origin, which results in different allele substitution effects across breeds. In such a case, single-breed breeding values may not be the most accurate predictors of crossbred performance. Our aim was to estimate the contribution of alleles from each parental breed to the genetic variance of traits that are measured in crossbred offspring, and to compare the prediction accuracies of estimated direct genomic values (DGV) from a traditional genomic selection model (GS) that are trained on purebred or crossbred data, with accuracies of DGV from a model that accounts for breed-specific effects (BS), trained on purebred or crossbred data. The final dataset was composed of 924 Large White, 924 Landrace and 924 two-way cross (F1) genotyped and phenotyped animals. The traits evaluated were litter size (LS) and gestation length (GL) in pigs.

Results

The genetic correlation between purebred and crossbred performance was higher than 0.88 for both LS and GL. For both traits, the additive genetic variance was larger for alleles inherited from the Large White breed compared to alleles inherited from the Landrace breed (0.74 and 0.56 for LS, and 0.42 and 0.40 for GL, respectively). The highest prediction accuracies of crossbred performance were obtained when training was done on crossbred data. For LS, prediction accuracies were the same for GS and BS DGV (0.23), while for GL, prediction accuracy for BS DGV was similar to the accuracy of GS DGV (0.53 and 0.52, respectively).

Conclusions

In this study, training on crossbred data resulted in higher prediction accuracy than training on purebred data and evidence of breed-specific effects for LS and GL was demonstrated. However, when training was done on crossbred data, both GS and BS models resulted in similar prediction accuracies. In future studies, traits with a lower genetic correlation between purebred and crossbred performance should be included to further assess the value of the BS model in genomic predictions.

Prediction of the reliability of genomic breeding values for crossbred performance

Background

In crossbreeding programs, various genomic prediction models have been proposed for using phenotypic records of crossbred animals to increase the selection response for crossbred performance in purebred animals. A possible model is a model that assumes identical single nucleotide polymorphism (SNP) effects for the crossbred performance trait across breeds (ASGM). Another model is a genomic model that assumes breed-specific effects of SNP alleles (BSAM) for crossbred performance. The aim of this study was to derive and validate equations for predicting the reliability of estimated genomic breeding values for crossbred performance in both these models. Prediction equations were derived for situations when all (phenotyping and) genotyping data have already been collected, i.e. based on the genetic evaluation model, and for situations when all genotyping data are not yet available, i.e. when designing breeding programs.

Results

When all genotyping data are available, prediction equations are based on selection index theory. Without availability of all genotyping data, prediction equations are based on population parameters (e.g., heritability of the traits involved, genetic correlation between purebred and crossbred performance, effective number of chromosome segments). Validation of the equations for predicting the reliability of genomic breeding values without all genotyping data was performed based on simulated data of a two-way crossbreeding program, using either two closely-related breeds, or two unrelated breeds, to produce crossbred animals. The proposed equations can be used for an easy comparison of the reliability of genomic estimated breeding values across many scenarios, especially if all genotyping data are available. We show that BSAM outperforms ASGM for a specific breed, if the effective number of chromosome segments that originate from this breed and are shared by selection candidates of this breed and crossbred reference animals is less than half the effective number of all chromosome segments that are independently segregating in the same animals.

Conclusions

The derived equations can be used to predict the reliability of genomic estimated breeding values for crossbred performance using ASGM or BSAM in many scenarios, and are thus useful to optimize the design of breeding programs. Scenarios can vary in terms of the genetic correlation between purebred and crossbred performances, heritabilities, number of reference animals, or distance between breeds.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-017-0318-1) contains supplementary material, which is available to authorized users.

Metafounders are related to F st fixation indices and reduce bias in single-step genomic evaluations

Background

Metafounders are pseudo-individuals that encapsulate genetic heterozygosity and relationships within and across base pedigree populations, i.e. ancestral populations. This work addresses the estimation and usefulness of metafounder relationships in single-step genomic best linear unbiased prediction (ssGBLUP).

Results

We show that ancestral relationship parameters are proportional to standardized covariances of base allelic frequencies across populations, such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{\text{st}}$$\end{document}Fst fixation indexes. These covariances of base allelic frequencies can be estimated from marker genotypes of related recent individuals and pedigree. Simple methods for their estimation include naïve computation of allele frequencies from marker genotypes or a method of moments that equates average pedigree-based and marker-based relationships. Complex methods include generalized least squares (best linear unbiased estimator (BLUE)) or maximum likelihood based on pedigree relationships. To our knowledge, methods to infer \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{\text{st}}$$\end{document}Fst coefficients from marker data have not been developed for related individuals. We derived a genomic relationship matrix, compatible with pedigree relationships, that is constructed as a cross-product of {−1,0,1} codes and that is equivalent (apart from scale factors) to an identity-by-state relationship matrix at genome-wide markers. Using a simulation with a single population under selection in which only males and youngest animals are genotyped, we observed that generalized least squares or maximum likelihood gave accurate and unbiased estimates of the ancestral relationship parameter (true value: 0.40) whereas the naïve method and the method of moments were biased (average estimates of 0.43 and 0.35). We also observed that genomic evaluation by ssGBLUP using metafounders was less biased in terms of estimates of genetic trend (bias of 0.01 instead of 0.12), resulted in less overdispersed (0.94 instead of 0.99) and as accurate (0.74) estimates of breeding values than ssGBLUP without metafounders and provided consistent estimates of heritability.

Conclusions

Estimation of metafounder relationships can be achieved using BLUP-like methods with pedigree and markers. Inclusion of metafounder relationships reduces bias of genomic predictions with no loss in accuracy.

Dimensionality of genomic information and performance of the Algorithm for Proven and Young for different livestock species

Background

A genomic relationship matrix (GRM) can be inverted efficiently with the Algorithm for Proven and Young (APY) through recursion on a small number of core animals. The number of core animals is theoretically linked to effective population size (N_e). In a simulation study, the optimal number of core animals was equal to the number of largest eigenvalues of GRM that explained 98% of its variation. The purpose of this study was to find the optimal number of core animals and estimate N_e for different species.

Methods

Datasets included phenotypes, pedigrees, and genotypes for populations of Holstein, Jersey, and Angus cattle, pigs, and broiler chickens. The number of genotyped animals varied from 15,000 for broiler chickens to 77,000 for Holsteins, and the number of single-nucleotide polymorphisms used for genomic prediction varied from 37,000 to 61,000. Eigenvalue decomposition of the GRM for each population determined numbers of largest eigenvalues corresponding to 90, 95, 98, and 99% of variation.

Results

The number of eigenvalues corresponding to 90% (98%) of variation was 4527 (14,026) for Holstein, 3325 (11,500) for Jersey, 3654 (10,605) for Angus, 1239 (4103) for pig, and 1655 (4171) for broiler chicken. Each trait in each species was analyzed using the APY inverse of the GRM with randomly selected core animals, and their number was equal to the number of largest eigenvalues. Realized accuracies peaked with the number of core animals corresponding to 98% of variation for Holstein and Jersey and closer to 99% for other breed/species. N_e was estimated based on comparisons of eigenvalue decomposition in a simulation study. Assuming a genome length of 30 Morgan, N_e was equal to 149 for Holsteins, 101 for Jerseys, 113 for Angus, 32 for pigs, and 44 for broilers.

Conclusions

Eigenvalue profiles of GRM for common species are similar to those in simulation studies although they are affected by number of genotyped animals and genotyping quality. For all investigated species, the APY required less than 15,000 core animals. Realized accuracies were equal or greater with the APY inverse than with regular inversion. Eigenvalue analysis of GRM can provide a realistic estimate of N_e.