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.     

Genome-wide marker-assisted selection combining all pedigree phenotypic information with genotypic data in one step: An example using broiler chickens

Data of broiler chickens for 2 pure lines across 3 generations were used for genomic evaluation. A complete population (full data set; FDS) consisted of 183,784 and 164,246 broilers for the 2 lines. The genotyped subsets (SUB) consisted of 3,284 and 3,098 broilers with 57,636 SNP. Genotyped animals were preselected based on more than 20 traits with different index applied to each line. Three traits were analyzed: BW at 6 wk (BW6), ultrasound measurement of breast meat (BM), and leg score (LS) coded 1 = no and 2 = yes for leg defect. Some phenotypes were missing for BM. The training population consisted of the first 2 generations including all animals in FDS or only genotyped animals in SUB. The validation data set contained only genotyped animals in the third generation. Genetic evaluations were performed using 3 approaches: 1) phenotypic BLUP, 2) extending BLUP methodologies to utilize pedigree and genomic information in a single step (ssGBLUP), and 3) Bayes A. Whereas BLUP and ssGBLUP utilized all phenotypic data, Bayes A could use only those of the genotyped subset. Heritabilities were 0.17 to 0.20 for BW6, 0.30 to 0.35 for BM, and 0.09 to 0.11 for LS. The average accuracies of the validation population with BLUP for BW6, BM, and LS were 0.46, 0.30, and <0 with SUB and 0.51, 0.34, and 0.28 with FDS. With ssGBLUP, those accuracies were 0.60, 0.34, and 0.06 with SUB and 0.61, 0.40, and 0.37 with FDS, respectively. With Bayes A, the accuracies were 0.60, 0.36, and 0.09 with SUB. With SUB, Bayes A and ssGBLUP had similar accuracies. For traits of high heritability, the accuracy of Bayes A/SUB and ssGBLUP/FDS were similar, and up to 50% better than BLUP/FDS. However, with low heritability, ssGBLUP/FDS was 4 to 6 times more accurate than Bayes A/SUB and 50% better than BLUP/FDS. An optimal genomic evaluation would be multi-trait and involve all traits and records on which selection is based.     

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.     

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.     

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.     

Effect of genotyped bulls with different numbers of phenotyped progenies on quantitative trait loci detection and genomic evaluation in a simulated cattle population

The objective of this study was to assess the effect of genotyped bulls with different numbers of phenotyped progenies on quantitative trait loci (QTL) detection and genomic evaluation using a simulated cattle population. Twelve generations (G1–G12) were simulated from the base generation (G0). The recent population had different effective population sizes, heritability, and number of QTL. G0–G4 were used for pedigree information. A total of 300 genotyped bulls from G5–G10 were randomly selected. Their progenies were generated in G6–G11 with different numbers of progeny per bull. Scenarios were considered according to the number of progenies and whether the genotypes were possessed by the bulls or the progenies. A genome‐wide association study and genomic evaluation were performed with a single‐step genomic best linear unbiased prediction method to calculate the power of QTL detection and the genomic estimated breeding value (GEBV). We found that genotyped bulls could be available for QTL detection depending on conditions. Additionally, using a reference population, including genotyped bulls, which had more progeny phenotypes, enabled a more accurate prediction of GEBV. However, it is desirable to have more than 4,500 individuals consisting of both genotypes and phenotypes for practical genomic evaluation.     

Mixture models detect large effect QTL better than GBLUP and result in more accurate and persistent predictions

Background: Accurate evaluation of SNP effects is important for genome wide association studies and for genomic prediction. The genetic architecture of quantitative traits differs widely, with some traits exhibiting few if any quantitative trait loci(QTL) with large effects, while other traits have one or several easily detectable QTL with large effects.Methods: Body weight in broilers and egg weight in layers are two examples of traits that have QTL of large effect.A commonly used method for genome wide association studies is to fit a mixture model such as Bayes B that assumes some known proportion of SNP effects are zero. In contrast, the most commonly used method for genomic prediction is known as GBLUP, which involves fitting an animal model to phenotypic data with the variance-covariance or genomic relationship matrix among the animals being determined by genome wide SNP genotypes. Genotypes at each SNP are typically weighted equally in determining the genomic relationship matrix for GBLUP. We used the equivalent marker effects model formulation of GBLUP for this study. We compare these two classes of models using egg weight data collected over 8 generations from 2,324 animals genotyped with a42 K SNP panel.Results: Using data from the first 7 generations, both Bayes B and GBLUP found the largest QTL in a similar well-recognized QTL region, but this QTL was estimated to account for 24 % of genetic variation with Bayes B and less than 1 % with GBLUP. When predicting phenotypes in generation 8 Bayes B accounted for 36 % of the phenotypic variation and GBLUP for 25 %. When using only data from any one generation, the same QTL was identified with Bayes B in all but one generation but never with GBLUP. Predictions of phenotypes in generations 2 to 7 based on only 295 animals from generation 1 accounted for 10 % phenotypic variation with Bayes B but only6 % with GBLUP. Predicting phenotype using only the marker effects in the 1 Mb region that accounted for the largest effect on egg weight from generation 1 data alone accounted for almost 8 % variation using Bayes B but had no predictive power with GBLUP.Conclusions: In conclusion, In the presence of large effect QTL, Bayes B did a better job of QTL detection and its genomic predictions were more accurate and persistent than those from GBLUP.     

Determining the stability of accuracy of genomic estimated breeding values in future generations in commercial pig populations

Genomic information has a limited dimensionality (number of independent chromosome segments [M_e]) related to the effective population size. Under the additive model, the persistence of genomic accuracies over generations should be high when the nongenomic information (pedigree and phenotypes) is equivalent to M_e animals with high accuracy. The objective of this study was to evaluate the decay in accuracy over time and to compare the magnitude of decay with varying quantities of data and with traits of low and moderate heritability. The dataset included 161,897 phenotypic records for a growth trait (GT) and 27,669 phenotypic records for a fitness trait (FT) related to prolificacy in a population with dimensionality around 5,000. The pedigree included 404,979 animals from 2008 to 2020, of which 55,118 were genotyped. Two single-trait models were used with all ancestral data and sliding subsets of 3-, 2-, and 1-generation intervals. Single-step genomic best linear unbiased prediction (ssGBLUP) was used to compute genomic estimated breeding values (GEBV). Estimated accuracies were calculated by the linear regression (LR) method. The validation population consisted of single generations succeeding the training population and continued forward for all generations available. The average accuracy for the first generation after training with all ancestral data was 0.69 and 0.46 for GT and FT, respectively. The average decay in accuracy from the first generation after training to generation 9 was −0.13 and −0.19 for GT and FT, respectively. The persistence of accuracy improves with more data. Old data have a limited impact on the predictions for young animals for a trait with a large amount of information but a bigger impact for a trait with less information.     

Evaluation of the utility of diagonal elements of the genomic relationship matrix as a diagnostic tool to detect mislabelled genotyped animals in a broiler chicken population

This study explored distributions of diagonal elements of genomic relationship matrix (G), evaluated the utility of G as a diagnostic tool to detect mislabelled animals in a genomic dataset and evaluated the effect of mislabelled animals on the accuracy of genomic evaluation. Populations of 10 000 animals were simulated with 60 000 SNP varying in allele frequency at each locus between 0.02 and 0.98. Diagonal elements of G were distributed with a single peak (mean = 1.00 ± 0.03) and ranged from 0.84 through 1.36. Mixed populations were also simulated: 7 000 animals with frequencies of second alleles ranging from 0.02 through 0.98 were combined with 1750 or 7000 animals with frequencies of second alleles ranging from 0.0 through 1.0. The resulting distributions of diagonal elements of G were bimodal. Body weight at 6 weeks was provided by Cobb-Vantress for broiler chickens, of which 3285 were genotyped for 57 636 SNP. Analysis used a combined genomic and pedigree relationship matrix; G was scaled using current allele frequencies. The distribution of diagonal elements was multimodal and ranged from 0.54 to 3.23. Animals with diagonal elements >1.5 were identified as coming from another chicken line or as having low call rates. Removal of mislabelled animals increased accuracy by 0.01. For the studied type of population, diagonal elements of G may be a useful tool to help identify mislabelled animals or secondary populations.     

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.     

Detection of single nucleotide polymorphisms associated with ultrasonic backfat depth in a segregating Meishan x White Composite population

Multiple genomic scans have identified QTL for backfat deposition across the porcine genome. The objective of this study was to detect SNP and genomic regions associated with ultrasonic backfat. A total of 74 SNP across 5 chromosomes (SSC 1, 3, 7, 8, and 10) were selected based on their proximity to backfat QTL or to QTL for other traits of interest in the experimental population. Gilts were also genotyped for a SNP thought to influence backfat in the thyroxine-binding globulin gene (TBG) on SSC X. Genotypic data were collected on 298 gilts, divided between the F8 and F10 generations of the US Meat Animal Research Center Meishan resource population (composition, one-quarter Meishan). Backfat depths were recorded by ultrasound from 3 locations along the back at approximately 210 and 235 d of age in the F8 and F10 generations, respectively. Ultrasound measures were averaged for association analyses. Regressors for additive, dominant, and parent-of-origin effects of each SNP were calculated using genotypic probabilities computed by allelic peeling algorithms in GenoProb. The association model included the fixed effects of scan date and TBG genotype, the covariates of weight and SNP regressors, and random additive polygenic effects to account for genetic similarities between animals not explained by known genotypes. Variance components for polygenic effects and error were estimated using MTDFREML. Initially, each SNP was fitted (once with and once without parent-of-origin effects) separately due to potential multi-collinearity between regressions of closely linked markers. To form a final model, all significant SNP across chromosomes were included in a common model and were individually removed in successive iterations based on their significance. Across all analyses, TBG was significant, with an additive effect of approximately 1.2 to 1.6 mm of backfat. Three SNP on SSC3 remained in the final model even though few studies have identified QTL for backfat on this chromosome. Two of these SNP exhibited irregular parent-of-origin effects and may not have been detected in other genome scans. One significant SNP on SSC7 remained in the final, backward-selected model; the estimated effect of this marker was similar in magnitude and direction to previously identified QTL. This SNP can potentially be used to introgress the leaner Meishan allele into commercial swine populations.     

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.     

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.     

Improving accuracy of genomic prediction in Brangus cattle by adding animals with imputed low‐density SNP genotypes

Reliable genomic prediction of breeding values for quantitative traits requires the availability of sufficient number of animals with genotypes and phenotypes in the training set. As of 31 October 2016, there were 3,797 Brangus animals with genotypes and phenotypes. These Brangus animals were genotyped using different commercial SNP chips. Of them, the largest group consisted of 1,535 animals genotyped by the GGP‐LDV4 SNP chip. The remaining 2,262 genotypes were imputed to the SNP content of the GGP‐LDV4 chip, so that the number of animals available for training the genomic prediction models was more than doubled. The present study showed that the pooling of animals with both original or imputed 40K SNP genotypes substantially increased genomic prediction accuracies on the ten traits. By supplementing imputed genotypes, the relative gains in genomic prediction accuracies on estimated breeding values (EBV) were from 12.60% to 31.27%, and the relative gain in genomic prediction accuracies on de‐regressed EBV was slightly small (i.e. 0.87%–18.75%). The present study also compared the performance of five genomic prediction models and two cross‐validation methods. The five genomic models predicted EBV and de‐regressed EBV of the ten traits similarly well. Of the two cross‐validation methods, leave‐one‐out cross‐validation maximized the number of animals at the stage of training for genomic prediction. Genomic prediction accuracy (GPA) on the ten quantitative traits was validated in 1,106 newly genotyped Brangus animals based on the SNP effects estimated in the previous set of 3,797 Brangus animals, and they were slightly lower than GPA in the original data. The present study was the first to leverage currently available genotype and phenotype resources in order to harness genomic prediction in Brangus beef cattle.     

Power of a genome scan to detect and locate quantitative trait loci in cattle using dense single nucleotide polymorphisms

There is increasing use of dense single nucleotide polymorphisms (SNPs) for whole‐genome association studies (WGAS) in livestock to map and identify quantitative trait loci (QTL). These studies rely on linkage disequilibrium (LD) to detect an association between SNP genotypes and phenotypes. The power and precision of these WGAS are unknown, and will depend on the extent of LD in the experimental population. One complication for WGAS in livestock populations is that they typically consist of many paternal half‐sib families, and in some cases full‐sib families; unless this subtle population stratification is accounted for, many spurious associations may be reported. Our aim was to investigate the power, precision and false discovery rates of WGAS for QTL discovery, with a commercial SNP array, given existing patterns of LD in cattle. We also tested the efficiency of selective genotyping animals. A total of 365 cattle were genotyped for 9232 SNPs. We simulated a QTL effect as well as polygenic and environmental effects for all animals. One QTL was simulated on a randomly chosen SNP and accounted for 5%, 10% or 18% of the total variance. The power to detect a moderate‐sized additive QTL (5% of the phenotypic variance) with 365 animals genotyped was 37% (p < 0.001). Most importantly, if pedigree structure was not accounted for, the number of false positives significantly increased above those expected by chance alone. Selective genotyping also resulted in a significant increase in false positives, even when pedigree structure was accounted for.     

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.     

Bias in heritability estimates from genomic restricted maximum likelihood methods under different genotyping strategies

We investigated the effects of different strategies for genotyping populations on variance components and heritabilities estimated with an animal model under restricted maximum likelihood (REML), genomic REML (GREML), and single‐step GREML (ssGREML). A population with 10 generations was simulated. Animals from the last one, two or three generations were genotyped with 45,116 SNP evenly distributed on 27 chromosomes. Animals to be genotyped were chosen randomly or based on EBV. Each scenario was replicated five times. A single trait was simulated with three heritability levels (low, moderate, high). Phenotypes were simulated for only females to mimic dairy sheep and also for both sexes to mimic meat sheep. Variance component estimates from genomic data and phenotypes for one or two generations were more biased than from three generations. Estimates in the scenario without selection were the most accurate across heritability levels and methods. When selection was present in the simulations, the best option was to use genotypes of randomly selected animals. For selective genotyping, heritabilities from GREML were more biased compared to those estimated by ssGREML, because ssGREML was less affected by selective or limited genotyping.     

一种适用于单胎动物多品种选择的基因组关系矩阵

旨在提出一种新型基因组关系矩阵并验证其在多品种联合群体中的模拟应用效果。本研究利用QMsim软件模拟牛的表型数据和基因型数据;利用Gmatrix软件构建常规G阵;利用R语言构建新型G阵,新型G阵在常规G阵的基础上,将多品种联合群体的非哈代-温伯格平衡位点考虑在内;利用DMU软件使用“一步”法模型计算基因组估计育种值（estimated genomic breeding value,GEBV）;比较不同情况下使用两种G阵的GEBV预测准确性。结果表明,在不同遗传力及QTL数下,不对新型G阵使用A₂₂阵加权就能达到常规G阵使用A₂₂阵加权时的GEBV预测准确性。在系谱部分缺失时,新型G阵不加权较常规G阵加权时GEBV预测准确性高。证明,在系谱有部分缺失时,新型G阵对多品种GEBV的预测有一定优势。     

Linkage disequilibrium and effective population size in Gir cattle selected for yearling weight

Linkage disequilibrium (LD) plays an important role in genomic selection and mapping of quantitative trait loci (QTL). This study investigated the pattern of LD and effective population size (N_e) in Gir cattle selected for yearling weight. For this purpose, 173 animals with imputed genotypes (from 18 animals genotyped with the Illumina BovineHD BeadChip and 155 animals genotyped with the Bovine LDv4 panel) were analysed. The LD was evaluated at distances of 25–50 kb, 50–100 kb, 100–500 kb and 0.5–1 Mb. The N_e was estimated based on 5 past generations. The r² values (a measure of LD) were, respectively, .35, .29, .18 and .032 for the distances evaluated. The LD estimates decreased with increasing distance of SNP pairs and LD persisted up to a distance of 100 kb (r² = .29). The N_e was greater in generations 4 and 5 (24 and 30 animals, respectively) and declined drastically after the last generation (12 animals). The results showed high levels of LD and low N_e, which were probably due to the loss of genetic variability as a consequence of the structure of the Gir population studied.     

Development of genomic predictions for Angus cattle in Brazil incorporating genotypes from related American sires

Genomic prediction has become the new standard for genetic improvement programs, and currently, there is a desire to implement this technology for the evaluation of Angus cattle in Brazil. Thus, the main objective of this study was to assess the feasibility of evaluating young Brazilian Angus (BA) bulls and heifers for 12 routinely recorded traits using single-step genomic BLUP (ssGBLUP) with and without genotypes from American Angus (AA) sires. The second objective was to obtain estimates of effective population size (N_e) and linkage disequilibrium (LD) in the Brazilian Angus population. The dataset contained phenotypic information for up to 277,661 animals belonging to the Promebo breeding program, pedigree for 362,900, of which 1,386 were genotyped for 50k, 77k, and 150k single nucleotide polymorphism (SNP) panels. After imputation and quality control, 61,666 SNPs were available for the analyses. In addition, genotypes from 332 American Angus (AA) sires widely used in Brazil were retrieved from the AA Association database to be used for genomic predictions. Bivariate animal models were used to estimate variance components, traditional EBV, and genomic EBV (GEBV). Validation was carried out with the linear regression method (LR) using young-genotyped animals born between 2013 and 2015 without phenotypes in the reduced dataset and with records in the complete dataset. Validation animals were further split into progeny of BA and AA sires to evaluate if their progenies would benefit by including genotypes from AA sires. The N_e was 254 based on pedigree and 197 based on LD, and the average LD (±SD) and distance between adjacent single nucleotide polymorphisms (SNPs) across all chromosomes were 0.27 (±0.27) and 40743.68 bp, respectively. Prediction accuracies with ssGBLUP outperformed BLUP for all traits, improving accuracies by, on average, 16% for BA young bulls and heifers. The GEBV prediction accuracies ranged from 0.37 (total maternal for weaning weight and tick count) to 0.54 (yearling precocity) across all traits, and dispersion (LR coefficients) fluctuated between 0.92 and 1.06. Inclusion of genotyped sires from the AA improved GEBV accuracies by 2%, on average, compared to using only the BA reference population. Our study indicated that genomic information could help us to improve GEBV accuracies and hence genetic progress in the Brazilian Angus population. The inclusion of genotypes from American Angus sires heavily used in Brazil just marginally increased the GEBV accuracies for selection candidates.