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

Joint Nordic (Denmark, Finland, Sweden) genetic evaluation of female fertility is currently based on the multiple trait multilactation animal model (BLUP). Here, single step genomic model (ssGBLUP) was applied for the Nordic Red dairy cattle fertility evaluation. The 11 traits comprised of nonreturn rate and days from first to last insemination in heifers and first three parities, and days from calving to first insemination in the first three parities. Traits had low heritabilities (0.015–0.04), but moderately high genetic correlations between the parities (0.60–0.88). Phenotypic data included 4,226,715 animals with records and pedigree 5,445,392 animals. Unknown parents were assigned into 332 phantom parent groups (PPG). In mixed model equations animals were associated with PPG effects through the pedigree or both the pedigree and genomic information. Genotype information of 46,914 SNPs was available for 33,969 animals in the pedigree. When PPG used pedigree information only, BLUP converged after 2,420 iterations whereas the ssGBLUP evaluation needed over ten thousand iterations. When the PPG effects were solved accounting both the pedigree and the genomic information, the ssGBLUP model converged after 2,406 iterations. Also, with the latter model breeding values by ssGBLUP and BLUP became more consistent and genetic trends followed each other well. Models were validated using forward prediction of the young bulls. Reliabilities and variance inflation of predicted genomic breeding values (values for parent averages in brackets) for the 11 traits ranged 0.22–0.31 (0.10–0.27) and 0.81–0.95 (0.83–1.06), respectively. The ssGBLUP model gave always higher validation reliabilities than BLUP, but largest increases were for the cow fertility traits.     

Validation of single‐step GBLUP genomic predictions from threshold models using the linear regression method: An application in chicken mortality

The objective of this study was to determine whether the linear regression (LR) method could be used to validate genomic threshold models. Statistics for the LR method were computed from estimated breeding values (EBVs) using the whole and truncated data sets with variances from the reference and validation populations. The method was tested using simulated and real chicken data sets. The simulated data set included 10 generations of 4,500 birds each; genotypes were available for the last three generations. Each animal was assigned a continuous trait, which was converted to a binary score assuming an incidence of failure of 7%. The real data set included the survival status of 186,596 broilers (mortality rate equal to 7.2%) and genotypes of 18,047 birds. Both data sets were analysed using best linear unbiased predictor (BLUP) or single‐step GBLUP (ssGBLUP). The whole data set included all phenotypes available, whereas in the partial data set, phenotypes of the most recent generation were removed. In the simulated data set, the accuracies based on the LR formulas were 0.45 for BLUP and 0.76 for ssGBLUP, whereas the correlations between true breeding values and EBVs (i.e. true accuracies) were 0.37 and 0.65, respectively. The gain in accuracy by adding genomic information was overestimated by 0.09 when using the LR method compared to the true increase in accuracy. However, when the estimated ratio between the additive variance computed based on pedigree only and on pedigree and genomic information was considered, the difference between true and estimated gain was <0.02. Accuracies of BLUP and ssGBLUP with the real data set were 0.41 and 0.47, respectively. This small improvement in accuracy when using ssGBLUP with the real data set was due to population structure and lower heritability. The LR method is a useful tool for estimating improvements in accuracy of EBVs due to the inclusion of genomic information when traditional validation methods as k‐fold validation and predictive ability are not applicable.     

Selection of core animals in the Algorithm for Proven and Young using a simulation model

The Algorithm for Proven and Young (APY) enables the implementation of single‐step genomic BLUP (ssGBLUP) in large, genotyped populations by separating genotyped animals into core and non‐core subsets and creating a computationally efficient inverse for the genomic relationship matrix ( G ). As APY became the choice for large‐scale genomic evaluations in BLUP‐based methods, a common question is how to choose the animals in the core subset. We compared several core definitions to answer this question. Simulations comprised a moderately heritable trait for 95,010 animals and 50,000 genotypes for animals across five generations. Genotypes consisted of 25,500 SNP distributed across 15 chromosomes. Genotyping errors and missing pedigree were also mimicked. Core animals were defined based on individual generations, equal representation across generations, and at random. For a sufficiently large core size, core definitions had the same accuracies and biases, even if the core animals had imperfect genotypes. When genotyped animals had unknown parents, accuracy and bias were significantly better (p ≤ .05) for random and across generation core definitions.     

Accurate genomic predictions for BCWD resistance in rainbow trout are achieved using low‐density SNP panels: Evidence that long‐range LD is a major contributing factor

Previously accurate genomic predictions for Bacterial cold water disease (BCWD) resistance in rainbow trout were obtained using a medium‐density single nucleotide polymorphism (SNP) array. Here, the impact of lower‐density SNP panels on the accuracy of genomic predictions was investigated in a commercial rainbow trout breeding population. Using progeny performance data, the accuracy of genomic breeding values (GEBV) using 35K, 10K, 3K, 1K, 500, 300 and 200 SNP panels as well as a panel with 70 quantitative trait loci (QTL)‐flanking SNP was compared. The GEBVs were estimated using the Bayesian method BayesB, single‐step GBLUP (ssGBLUP) and weighted ssGBLUP (wssGBLUP). The accuracy of GEBVs remained high despite the sharp reductions in SNP density, and even with 500 SNP accuracy was higher than the pedigree‐based prediction (0.50–0.56 versus 0.36). Furthermore, the prediction accuracy with the 70 QTL‐flanking SNP (0.65–0.72) was similar to the panel with 35K SNP (0.65–0.71). Genomewide linkage disequilibrium (LD) analysis revealed strong LD (r² ≥ 0.25) spanning on average over 1 Mb across the rainbow trout genome. This long‐range LD likely contributed to the accurate genomic predictions with the low‐density SNP panels. Population structure analysis supported the hypothesis that long‐range LD in this population may be caused by admixture. Results suggest that lower‐cost, low‐density SNP panels can be used for implementing genomic selection for BCWD resistance in rainbow trout breeding programs.     

Efficient approximation of reliabilities for single-step genomic best linear unbiased predictor models with the Algorithm for Proven and Young

The objectives of this study were to develop an efficient algorithm for calculating prediction error variances (PEVs) for genomic best linear unbiased prediction (GBLUP) models using the Algorithm for Proven and Young (APY), extend it to single-step GBLUP (ssGBLUP), and apply this algorithm for approximating the theoretical reliabilities for single- and multiple-trait models in ssGBLUP. The PEV with APY was calculated by block sparse inversion, efficiently exploiting the sparse structure of the inverse of the genomic relationship matrix with APY. Single-step GBLUP reliabilities were approximated by combining reliabilities with and without genomic information in terms of effective record contributions. Multi-trait reliabilities relied on single-trait results adjusted using the genetic and residual covariance matrices among traits. Tests involved two datasets provided by the American Angus Association. A small dataset (Data1) was used for comparing the approximated reliabilities with the reliabilities obtained by the inversion of the left-hand side of the mixed model equations. A large dataset (Data2) was used for evaluating the computational performance of the algorithm. Analyses with both datasets used single-trait and three-trait models. The number of animals in the pedigree ranged from 167,951 in Data1 to 10,213,401 in Data2, with 50,000 and 20,000 genotyped animals for single-trait and multiple-trait analysis, respectively, in Data1 and 335,325 in Data2. Correlations between estimated and exact reliabilities obtained by inversion ranged from 0.97 to 0.99, whereas the intercept and slope of the regression of the exact on the approximated reliabilities ranged from 0.00 to 0.04 and from 0.93 to 1.05, respectively. For the three-trait model with the largest dataset (Data2), the elapsed time for the reliability estimation was 11 min. The computational complexity of the proposed algorithm increased linearly with the number of genotyped animals and with the number of traits in the model. This algorithm can efficiently approximate the theoretical reliability of genomic estimated breeding values in ssGBLUP with APY for large numbers of genotyped animals at a low cost.     

Implications of SNP weighting on single‐step genomic predictions for different reference population sizes

We investigated the importance of SNP weighting in populations with 2,000 to 25,000 genotyped animals. Populations were simulated with two effective sizes (20 or 100) and three numbers of QTL (10, 50 or 500). Pedigree information was available for six generations; phenotypes were recorded for the four middle generations. Animals from the last three generations were genotyped for 45,000 SNP. Single‐step genomic BLUP (ssGBLUP) and weighted ssGBLUP (WssGBLUP) were used to estimate genomic EBV using a genomic relationship matrix ( G ). The WssGBLUP performed better in small genotyped populations; however, any advantage for WssGBLUP was reduced or eliminated when more animals were genotyped. WssGBLUP had greater resolution for genome‐wide association (GWA) as did increasing the number of genotyped animals. For few QTL, accuracy was greater for WssGBLUP than ssGBLUP; however, for many QTL, accuracy was the same for both methods. The largest genotyped set was used to assess the dimensionality of genomic information (number of effective SNP). The number of effective SNP was considerably less in weighted G than in unweighted G . Once the number of independent SNP is well represented in the genotyped population, the impact of SNP weighting becomes less important.     

Estimation of total genetic effects for survival time in crossbred laying hens showing cannibalism,using pedigree or genomic information

Mortality of laying hens due to cannibalism is a major problem in the egg‐laying industry. Survival depends on two genetic effects: the direct genetic effect of the individual itself (DGE) and the indirect genetic effects of its group mates (IGE). For hens housed in sire‐family groups, DGE and IGE cannot be estimated using pedigree information, but the combined effect of DGE and IGE is estimated in the total breeding value (TBV). Genomic information provides information on actual genetic relationships between individuals and might be a tool to improve TBV accuracy. We investigated whether genomic information of the sire increased TBV accuracy compared with pedigree information, and we estimated genetic parameters for survival time. A sire model with pedigree information (BLUP) and a sire model with genomic information (ssGBLUP) were used. We used survival time records of 7290 crossbred offspring with intact beaks from four crosses. Cross‐validation was used to compare the models. Using ssGBLUP did not improve TBV accuracy compared with BLUP which is probably due to the limited number of sires available per cross (~50). Genetic parameter estimates were similar for BLUP and ssGBLUP. For both BLUP and ssGBLUP, total heritable variance (T²), expressed as a proportion of phenotypic variance, ranged from 0.03 ± 0.04 to 0.25 ± 0.09. Further research is needed on breeding value estimation for socially affected traits measured on individuals kept in single‐family groups.     

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.     

Modeling genetic differences of combined broiler chicken populations in single-step GBLUP

The introduction of animals from a different environment or population is a common practice in commercial livestock populations. In this study, we modeled the inclusion of a group of external birds into a local broiler chicken population for the purpose of genomic evaluations. The pedigree was composed of 242,413 birds and genotypes were available for 107,216 birds. A five-trait model that included one growth, two yield, and two efficiency traits was used for the analyses. The strategies to model the introduction of external birds were to include a fixed effect representing the origin of parents and to use unknown parent groups (UPG) or metafounders (MF). Genomic estimated breeding values (GEBV) were obtained with single-step GBLUP using the Algorithm for Proven and Young. Bias, dispersion, and accuracy of GEBV for the validation birds, that is, from the most recent generation, were computed. The bias and dispersion were estimated with the linear regression (LR) method,whereas accuracy was estimated by the LR method and predictive ability. When fixed UPG were fit without estimated inbreeding, the model did not converge. In contrast, models with fixed UPG and estimated inbreeding or random UPG converged and resulted in similar GEBV. The inclusion of an extra fixed effect in the model made the GEBV unbiased and reduced the inflation. Genomic predictions with MF were slightly biased and inflated due to the unbalanced number of observations assigned to each metafounder. When combining local and external populations, the greatest accuracy can be obtained by adding an extra fixed effect to account for the origin of parents plus UPG with estimated inbreeding or random UPG. To estimate the accuracy, the LR method is more consistent among scenarios, whereas the predictive ability greatly depends on the model specification.     

The use of coancestry based on shared segments for maintaining genetic diversity

We have evaluated the use of genomic coancestry coefficients based on shared segments for the maintenance of genetic diversity through optimal contributions methodology for populations of three different Austrian cattle breeds. This coancestry measure has been compared with the genomic coancestry coefficient calculated on a SNP‐by‐SNP basis and with pedigree‐based coancestry. The regressions of the shared segments coancestry on the other two coefficients suggest that the former mainly reflect Identity By Descent but with the advantage over pedigree‐based coancestry of providing the realized Identity By Descent rather than an expectation. The effective population size estimated from the rate of coancestry based on shared segments was very similar to those obtained with the other coefficients and of small magnitude (from 26.24 to 111.90). This result highlights the importance of implementing active management strategies to control the increase of inbreeding and the loss of genetic diversity in livestock breeds, even when the population size is reasonably large. One problem for the implementation of coancestry based on shared segments is the need of estimating the gametic phases of the SNPs which, given the techniques used to obtain the genotypes, are a priori unknown. This study shows, through computer simulations, that using estimates of gametic phases for computing coancestry based on shared segments does not lead to a significant loss in the diversity maintained. This has been shown to be true even when the size of the population is very small as it is usually the case in populations subjected to conservation programmes.     

Reducing bias in the dairy cattle single‐step genomic evaluation by ignoring bulls without progeny

The number of genotyped animals has increased rapidly creating computational challenges for genomic evaluation. In animal model BLUP, candidate animals without progeny and phenotype do not contribute information to the evaluation and can be discarded. In theory, genotyped candidate animal without progeny can bring information into single‐step BLUP (ssGBLUP) and affect the estimation of other breeding values. We studied the effect of including or excluding genomic information of culled bull calves on genomic breeding values (GEBV) from ssGBLUP. In particular, GEBVs of genotyped bulls with daughters and GEBVs of young bulls selected into AI to be progeny tested (test bulls) were studied. The ssGBLUP evaluation was computed using Nordic test day (TD) model and TD data for the Nordic Red Dairy Cattle. The results indicate that genomic information of culled bull calves does not affect the GEBVs of progeny tested reference animals, but if genotypes of the culled bulls are used in the TD ssGBLUP, the genetic trend in the test bulls is considerably higher compared to the situation when genomic information of the culled bull calves is excluded. It seems that by discarding genomic information of culled bull calves without progeny, upward bias of GEBVs of test bulls is reduced.     

Effect of different genomic relationship matrices on accuracy and scale

Phenotypic data on BW and breast meat area were available on up to 287,614 broilers. A total of 4,113 birds were genotyped for 57,636 SNP. Data were analyzed by a single-step genomic BLUP (ssGBLUP), which accounts for all phenotypic, pedigree, and genomic information. The genomic relationship matrix (G) in ssGBLUP was constructed using either equal (0.5; GEq) or current (GC) allele frequencies, and with all SNP or with SNP with minor allele frequencies (MAF) below multiple thresholds (0.1, 0.2, 0.3, and 0.4) ignored. Additionally, a pedigree-based relationship matrix for genotyped birds (A(22)) was available. The matrices and their inverses were compared with regard to average diagonal (AvgD) and off-diagonal (AvgOff) elements. In A(22), AvgD was 1.004 and AvgOff was 0.014. In GEq, both averages decreased with the increasing thresholds for MAF, with AvgD decreasing from 1.373 to 1.020 and AvgOff decreasing from 0.722 to 0.025. In GC, AvgD was approximately 1.01 and AvgOff was 0 for all MAF. For inverses of the relationship matrices, all AvgOff were close to 0; AvgD was 2.375 in A(22), varied from 11.563 to 12.943 for GEq, and increased from 8.675 to 12.859 for GC as the threshold for MAF increased. Predictive ability with all GEq and GC was similar except that at MAF = 0.4, they declined by 0.01 for BW and improved by 0.01 for breast meat area. Compared with BLUP, EBV in the ssGBLUP were, on average, increased by up to 1 additive SD greater with GEq and decreased by 2 additive SD less with GC. Genotyped animals were biased upward with GEq and downward with GC. The biases and differences in EBV could be controlled by adding a constant to GC; they were eliminated with a constant of 0.014, which corresponds to AvgOff in A(22). Unbiased evaluation in the ssGBLUP may be obtained with GC scaled to be compatible with A(22). The reduction of SNP with small MAF has a small effect on the real accuracy, but it may falsely increase the estimated accuracies by inversion.     

Application of single‐step genomic best linear unbiased prediction with a multiple‐lactation random regression test‐day model for Japanese Holsteins

This study aimed to evaluate a validation reliability of single‐step genomic best linear unbiased prediction (ssGBLUP) with a multiple‐lactation random regression test‐day model and investigate an effect of adding genotyped cows on the reliability. Two data sets for test‐day records from the first three lactations were used: full data from February 1975 to December 2015 (60 850 534 records from 2 853 810 cows) and reduced data cut off in 2011 (53 091 066 records from 2 502 307 cows). We used marker genotypes of 4480 bulls and 608 cows. Genomic enhanced breeding values (GEBV) of 305‐day milk yield in all the lactations were estimated for at least 535 young bulls using two marker data sets: bull genotypes only and both bulls and cows genotypes. The realized reliability (R²) from linear regression analysis was used as an indicator of validation reliability. Using only genotyped bulls, R² was ranged from 0.41 to 0.46 and it was always higher than parent averages. The very similar R² were observed when genotyped cows were added. An application of ssGBLUP to a multiple‐lactation random regression model is feasible and adding a limited number of genotyped cows has no significant effect on reliability of GEBV for genotyped bulls.     

Use of genomic recursions and algorithm for proven and young animals for single‐step genomic BLUP analyses – a simulation study

The purpose of this study was to examine accuracy of genomic selection via single‐step genomic BLUP (ssGBLUP) when the direct inverse of the genomic relationship matrix ( G ) is replaced by an approximation of G ^?1 based on recursions for young genotyped animals conditioned on a subset of proven animals, termed algorithm for proven and young animals (APY). With the efficient implementation, this algorithm has a cubic cost with proven animals and linear with young animals. Ten duplicate data sets mimicking a dairy cattle population were simulated. In a first scenario, genomic information for 20k genotyped bulls, divided in 7k proven and 13k young bulls, was generated for each replicate. In a second scenario, 5k genotyped cows with phenotypes were included in the analysis as young animals. Accuracies (average for the 10 replicates) in regular EBV were 0.72 and 0.34 for proven and young animals, respectively. When genomic information was included, they increased to 0.75 and 0.50. No differences between genomic EBV (GEBV) obtained with the regular G ^?1 and the approximated G ^?1 via the recursive method were observed. In the second scenario, accuracies in GEBV (0.76, 0.51 and 0.59 for proven bulls, young males and young females, respectively) were also higher than those in EBV (0.72, 0.35 and 0.49). Again, no differences between GEBV with regular G ^?1 and with recursions were observed. With the recursive algorithm, the number of iterations to achieve convergence was reduced from 227 to 206 in the first scenario and from 232 to 209 in the second scenario. Cows can be treated as young animals in APY without reducing the accuracy. The proposed algorithm can be implemented to reduce computing costs and to overcome current limitations on the number of genotyped animals in the ssGBLUP method.     

Differences between genomic‐based and pedigree‐based relationships in a chicken population,as a function of quality control and pedigree links among individuals

This work studied differences between expected (calculated from pedigree) and realized (genomic, from markers) relationships in a real population, the influence of quality control on these differences, and their fit to current theory. Data included 4940 pure line chickens across five generations genotyped for 57 636 SNP. Pedigrees (5762 animals) were available for the five generations, pedigree starting on the first one. Three levels of quality control were used. With no quality control, mean difference between realized and expected relationships for different type of relationships was ≤ 0.04 with standard deviation ≤ 0.10. With strong quality control (call rate ≥ 0.9, parent‐progeny conflicts, minor allele frequency and use of only autosomal chromosomes), these numbers reduced to ≤ 0.02 and ≤ 0.04, respectively. While the maximum difference was 1.02 with the complete data, it was only 0.18 with the latest three generations of genotypes (but including all pedigrees). Variation of expected minus realized relationships agreed with theoretical developments and suggests an effective number of loci of 70 for this population. When the pedigree is complete and as deep as the genotypes, the standard deviation of difference between the expected and realized relationships is around 0.04, all categories confounded. Standard deviation of differences larger than 0.10 suggests bad quality control, mistakes in pedigree recording or genotype labelling, or insufficient depth of pedigree.     

Comparison of heritabilities of dairy traits in Australian Holstein‐Friesian cattle from genomic and pedigree data and implications for genomic evaluations

The reliability of genomic evaluations depends on the proportion of genetic variation explained by the DNA markers. In this study, we have estimated the proportion of variance in daughter trait deviations (DTDs) of dairy bulls explained by 45 993 genome wide single‐nucleotide poly‐ morphism (SNP) markers for 29 traits in Australian Holstein‐Friesian dairy cattle. We compare these proportions to the proportion of variance in DTDs explained by the additive relationship matrix derived from the pedigree, as well as the sum of variance explained by both pedigree and marker information when these were fitted simultaneously. The propor‐ tion of genetic variance in DTDs relative to the total genetic variance (the total genetic variance explained by the genomic relationships and pedigree relationships when both were fitted simultaneously) varied from 32% for fertility to approximately 80% for milk yield traits. When fitting genomic and pedigree relationships simultaneously, the variance unexplained (i.e. the residual variance) in DTDs of the total variance for most traits was reduced compared to fitting either individually, suggesting that there is not complete overlap between the effects. The proportion of genetic variance accounted by the genomic relationships can be used to modify the blending equations used to calculate genomic estimated breeding value (GEBV) from direct genomic breeding value (DGV) and parent average. Our results, from a validation population of young dairy bulls with DTD, suggest that this modification can improve the reliability of GEBV by up to 5%.     

Genome‐wide association study and genomic evaluation of feed efficiency traits in Japanese Black cattle using single‐step genomic best linear unbiased prediction method

The objectives of this study were to better understand the genetic architecture and the possibility of genomic evaluation for feed efficiency traits by (i) performing genome‐wide association studies (GWAS), and (ii) assessing the accuracy of genomic evaluation for feed efficiency traits, using single‐step genomic best linear unbiased prediction (ssGBLUP)‐based methods. The analyses were performed in residual feed intake (RFI), residual body weight gain (RG), and residual intake and body weight gain (RIG) during three different fattening periods. The phenotypes from 4,578 Japanese Black steers, which were progenies of 362 progeny‐tested bulls and the genotypes from the bulls were used in this study. The results of GWAS showed that a total of 16, 8, and 12 gene ontology terms were related to RFI, RG, and RIG, respectively, and the candidate genes identified in RFI and RG were involved in olfactory transduction and the phosphatidylinositol signaling system, respectively. The realized reliabilities of genomic estimated breeding values were low to moderate in the feed efficiency traits. In conclusion, ssGBLUP‐based method can lead to understand some biological functions related to feed efficiency traits, even with small population with genotypes, however, an alternative strategy will be needed to enhance the reliability of genomic evaluation.     

Estimates of genetic variance and variance of predicted genetic merits using pedigree or genomic relationship matrices in six Brown Swiss cattle populations for different traits

The amount of variance captured in genetic estimations may depend on whether a pedigree‐based or genomic relationship matrix is used. The purpose of this study was to investigate the genetic variance as well as the variance of predicted genetic merits (PGM) using pedigree‐based or genomic relationship matrices in Brown Swiss cattle. We examined a range of traits in six populations amounting to 173 population‐trait combinations. A main aim was to determine how using different relationship matrices affect variance estimation. We calculated ratios between different types of estimates and analysed the impact of trait heritability and population size. The genetic variances estimated by REML using a genomic relationship matrix were always smaller than the variances that were similarly estimated using a pedigree‐based relationship matrix. The variances from the genomic relationship matrix became closer to estimates from a pedigree relationship matrix as heritability and population size increased. In contrast, variances of predicted genetic merits obtained using a genomic relationship matrix were mostly larger than variances of genetic merit predicted using pedigree‐based relationship matrix. The ratio of the genomic to pedigree‐based PGM variances decreased as heritability and population size rose. The increased variance among predicted genetic merits is important for animal breeding because this is one of the factors influencing genetic progress.     

Core-dependent changes in genomic predictions using the Algorithm for Proven and Young in single-step genomic best linear unbiased prediction

Single-step genomic best linear unbiased prediction with the Algorithm for Proven and Young (APY) is a popular method for large-scale genomic evaluations. With the APY algorithm, animals are designated as core or noncore, and the computing resources to create the inverse of the genomic relationship matrix (GRM) are reduced by inverting only a portion of that matrix for core animals. However, using different core sets of the same size causes fluctuations in genomic estimated breeding values (GEBVs) up to one additive standard deviation without affecting prediction accuracy. About 2% of the variation in the GRM is noise. In the recursion formula for APY, the error term modeling the noise is different for every set of core animals, creating changes in breeding values. While average changes are small, and correlations between breeding values estimated with different core animals are close to 1.0, based on the normal distribution theory, outliers can be several times bigger than the average. Tests included commercial datasets from beef and dairy cattle and from pigs. Beyond a certain number of core animals, the prediction accuracy did not improve, but fluctuations decreased with more animals. Fluctuations were much smaller than the possible changes based on prediction error variance. GEBVs change over time even for animals with no new data as genomic relationships ties all the genotyped animals, causing reranking of top animals. In contrast, changes in nongenomic models without new data are small. Also, GEBV can change due to details in the model, such as redefinition of contemporary groups or unknown parent groups. In particular, increasing the fraction of blending of the GRM with a pedigree relationship matrix from 5% to 20% caused changes in GEBV up to 0.45 SD, with a correlation of GEBV > 0.99. Fluctuations in genomic predictions are part of genomic evaluation models and are also present without the APY algorithm when genomic evaluations are computed with updated data. The best approach to reduce the impact of fluctuations in genomic evaluations is to make selection decisions not on individual animals with limited individual accuracy but on groups of animals with high average accuracy.     

Considering dominance in reduced single‐step genomic evaluations

Single‐step models including dominance can be an enormous computational task and can even be prohibitive for practical application. In this study, we try to answer the question whether a reduced single‐step model is able to estimate breeding values of bulls and breeding values, dominance deviations and total genetic values of cows with acceptable quality. Genetic values and phenotypes were simulated (500 repetitions) for a small Fleckvieh pedigree consisting of 371 bulls (180 thereof genotyped) and 553 cows (40 thereof genotyped). This pedigree was virtually extended for 2,407 non‐genotyped daughters. Genetic values were estimated with the single‐step model and with different reduced single‐step models. Including more relatives of genotyped cows in the reduced single‐step model resulted in a better agreement of results with the single‐step model. Accuracies of genetic values were largest with single‐step and smallest with reduced single‐step when only the cows genotyped were modelled. The results indicate that a reduced single‐step model is suitable to estimate breeding values of bulls and breeding values, dominance deviations and total genetic values of cows with acceptable quality.