D. A. L. Lourenco

Genetic evaluation using single-step genomic best linear unbiased predictor in American Angus1

Predictive ability of genomic EBV when using single-step genomic BLUP (ssGBLUP) in Angus cattle was investigated. Over 6 million records were available on birth weight (BiW) and weaning weight (WW), almost 3.4 million on postweaning gain (PWG), and over 1.3 million on calving ease (CE). Genomic information was available on, at most, 51,883 animals, which included high and low EBV accuracy animals. Traditional EBV was computed by BLUP and genomic EBV by ssGBLUP and indirect prediction based on SNP effects was derived from ssGBLUP; SNP effects were calculated based on the following reference populations: ref_2k (contains top bulls and top cows that had an EBV accuracy for BiW ≥0.85), ref_8k (contains all parents that were genotyped), and ref_33k (contains all genotyped animals born up to 2012). Indirect prediction was obtained as direct genomic value (DGV) or as an index of DGV and parent average (PA). Additionally, runs with ssGBLUP used the inverse of the genomic relationship matrix calculated by an algorithm for proven and young animals (APY) that uses recursions on a small subset of reference animals. An extra reference subset included 3,872 genotyped parents of genotyped animals (ref_4k). Cross-validation was used to assess predictive ability on a validation population of 18,721 animals born in 2013. Computations for growth traits used multiple-trait linear model and, for CE, a bivariate CE-BiW threshold-linear model. With BLUP, predictivities were 0.29, 0.34, 0.23, and 0.12 for BiW, WW, PWG, and CE, respectively. With ssGBLUP and ref_2k, predictivities were 0.34, 0.35, 0.27, and 0.13 for BiW, WW, PWG, and CE, respectively, and with ssGBLUP and ref_33k, predictivities were 0.39, 0.38, 0.29, and 0.13 for BiW, WW, PWG, and CE, respectively. Low predictivity for CE was due to low incidence rate of difficult calving. Indirect predictions with ref_33k were as accurate as with full ssGBLUP. Using the APY and recursions on ref_4k gave 88% gains of full ssGBLUP and using the APY and recursions on ref_8k gave 97% gains of full ssGBLUP. Genomic evaluation in beef cattle with ssGBLUP is feasible while keeping the models (maternal, multiple trait, and threshold) already used in regular BLUP. Gains in predictivity are dependent on the composition of the reference population. Indirect predictions via SNP effects derived from ssGBLUP allow for accurate genomic predictions on young animals, with no advantage of including PA in the index if the reference population is large. With the APY conditioning on about 10,000 reference animals, ssGBLUP is potentially applicable to a large number of genotyped animals without compromising predictive ability.

Are evaluations on young genotyped animals benefiting from the past generations

Data sets of US Holsteins, Israeli Holsteins, and pigs from PIC (a Genus company, Hendersonville, TN) were used to evaluate the effect of different numbers of generations on ability to predict genomic breeding values of young genotyped animals. The influence of including only 2 generations of ancestors (A2) or all ancestors (Af) was also investigated. A total of 34,506 US Holsteins, 1,305 Israeli Holsteins, and 5,236 pigs were genotyped. The evaluations were computed by traditional BLUP and single-step genomic BLUP, and computing performance was assessed for the latter method. For the 2 Holstein data sets, coefficients of determination (R(2)) and regression (δ) of deregressed evaluations from a full data set with records up to 2011 on estimated breeding values and genomic estimated breeding values from the truncated data sets were computed. The thresholds for data deletion were set by intervals of 5 yr, based on the average generation interval in dairy cattle. For the PIC data set, correlations between corrected phenotypes and estimated or genomic estimated breeding values were used to evaluate predictive ability on young animals born in 2010 and 2011. The reduced data set contained data up to 2009, and the thresholds were set based on an average generation interval of 3 yr. The number of generations that could be deleted without a reduction in accuracy depended on data structure and trait. For US Holsteins, removing 3 and 4 generations of data did not reduce accuracy of evaluations for final score in Af and A2 scenarios, respectively. For Israeli Holsteins, the accuracies for milk, fat, and protein yields were the highest when only phenotypes recorded in 2000 and later were included and full pedigrees were applied. Of the 135 Israeli bulls with genotypes (validation set) and daughter records only in the complete data set, 38 and 97 were sons of Israeli and foreign bulls, respectively. Although more phenotypic data increased the prediction accuracy for sons of Israeli bulls, the reverse was true for sons of foreign bulls. Also, more phenotypic data caused large inflation of genomic estimated breeding values for sons of foreign bulls, whereas the opposite was true with the deletion of all but the most recent phenotypic data. Results for protein and fat percentage were different from those for milk, fat, and protein yields; however, relatively, the changes in coefficients of determination and regression were smaller for percentage traits. For PIC data set, removing data from up to 5 generations did not erode predictive ability for genotyped animals for the 2 reproductive traits used in validation. Given the data used in this study, truncating old data reduces computation requirements but does not decrease the accuracy. For small populations that include local and imported animals, truncation may be beneficial for one group of animals and detrimental to another group.

Implementation of genomic recursions in single-step genomic best linear unbiased predictor for US Holsteins with a large number of genotyped animals.

The objectives of this study were to develop and evaluate an efficient implementation in the computation of the inverse of genomic relationship matrix with the recursion algorithm, called the algorithm for proven and young (APY), in single-step genomic BLUP. We validated genomic predictions for young bulls with more than 500,000 genotyped animals in final score for US Holsteins. Phenotypic data included 11,626,576 final scores on 7,093,380 US Holstein cows, and genotypes were available for 569,404 animals. Daughter deviations for young bulls with no classified daughters in 2009, but at least 30 classified daughters in 2014 were computed using all the phenotypic data. Genomic predictions for the same bulls were calculated with single-step genomic BLUP using phenotypes up to 2009. We calculated the inverse of the genomic relationship matrix GAPY(-1) based on a direct inversion of genomic relationship matrix on a small subset of genotyped animals (core animals) and extended that information to noncore animals by recursion. We tested several sets of core animals including 9,406 bulls with at least 1 classified daughter, 9,406 bulls and 1,052 classified dams of bulls, 9,406 bulls and 7,422 classified cows, and random samples of 5,000 to 30,000 animals. Validation reliability was assessed by the coefficient of determination from regression of daughter deviation on genomic predictions for the predicted young bulls. The reliabilities were 0.39 with 5,000 randomly chosen core animals, 0.45 with the 9,406 bulls, and 7,422 cows as core animals, and 0.44 with the remaining sets. With phenotypes truncated in 2009 and the preconditioned conjugate gradient to solve mixed model equations, the number of rounds to convergence for core animals defined by bulls was 1,343; defined by bulls and cows, 2,066; and defined by 10,000 random animals, at most 1,629. With complete phenotype data, the number of rounds decreased to 858, 1,299, and at most 1,092, respectively. Setting up GAPY(-1) for 569,404 genotyped animals with 10,000 core animals took 1.3h and 57 GB of memory. The validation reliability with APY reaches a plateau when the number of core animals is at least 10,000. Predictions with APY have little differences in reliability among definitions of core animals. Single-step genomic BLUP with APY is applicable to millions of genotyped animals.

Accuracy of estimated breeding values with genomic information on males, females, or both: an example on broiler chicken

BackgroundAs more and more genotypes become available, accuracy of genomic evaluations can potentially increase. However, the impact of genotype data on accuracy depends on the structure of the genotyped cohort. For populations such as dairy cattle, the greatest benefit has come from genotyping sires with high accuracy, whereas the benefit due to adding genotypes from cows was smaller. In broiler chicken breeding programs, males have less progeny than dairy bulls, females have more progeny than dairy cows, and most production traits are recorded for both sexes. Consequently, genotyping both sexes in broiler chickens may be more advantageous than in dairy cattle.MethodsWe studied the contribution of genotypes from males and females using a real dataset with genotypes on 15 723 broiler chickens. Genomic evaluations used three training sets that included only males (4648), only females (8100), and both sexes (12 748). Realized accuracies of genomic estimated breeding values (GEBV) were used to evaluate the benefit of including genotypes for different training populations on genomic predictions of young genotyped chickens.ResultsUsing genotypes on males, the average increase in accuracy of GEBV over pedigree-based EBV for males and females was 12 and 1 percentage points, respectively. Using female genotypes, this increase was 1 and 18 percentage points, respectively. Using genotypes of both sexes increased accuracies by 19 points for males and 20 points for females. For two traits with similar heritabilities and amounts of information, realized accuracies from cross-validation were lower for the trait that was under strong selection.ConclusionsOverall, genotyping males and females improves predictions of all young genotyped chickens, regardless of sex. Therefore, when males and females both contribute to genetic progress of the population, genotyping both sexes may be the best option.

Methods for genomic evaluation of a relatively small genotyped dairy population and effect of genotyped cow information in multiparity analyses

Methods for genomic prediction were evaluated for an Israeli Holstein dairy population of 713,686 cows and 1,305 progeny-tested bulls with genotypes. Inclusion of genotypes of 343 elite cows in an evaluation method that considers pedigree, phenotypes, and genotypes simultaneously was also evaluated. Two data sets were available: a complete data set with production records from 1985 through 2011, and a reduced data set with records after 2006 deleted. For each production trait, a multitrait animal model was used to compute traditional genetic evaluations for parities 1 through 3 as separate traits. Evaluations were calculated for the reduced and complete data sets. The evaluations from the reduced data set were used to calculate parent average for validation bulls, which was the benchmark for comparing gain in predictive ability from genomics. Genomic predictions for bulls in 2006 were calculated using a Bayesian regression method (BayesC), genomic BLUP (GBLUP), single-step GBLUP (ssGBLUP), and weighted ssGBLUP (WssGBLUP). Predictions using BayesC and GBLUP were calculated either with or without an index that included parent average. Genomic predictions that included elite cow genotypes were calculated using ssGBLUP and WssGBLUP. Predictive ability was assessed by coefficients of determination (R(2)) and regressions of predictions of 135 validation bulls with no daughters in 2006 on deregressed evaluations of those bulls in 2011. A reduction in R(2) and regression coefficients was observed from parities 1 through 3. Fat and protein yields had the lowest R(2) for all the methods. On average, R(2) was lowest for parent averages, followed by GBLUP, BayesC, ssGBLUP, and WssGBLUP. For some traits, R(2) for direct genomic values from BayesC and GBLUP were lower than those for parent averages. Genomic estimated breeding values using ssGBLUP were the least biased, and this method appears to be a suitable tool for genomic evaluation of a small genotyped population, as it automatically accounts for parental index, allows for inclusion of female genomic information without preadjustments in evaluations, and uses the same model as in traditional evaluations. Weighted ssGBLUP has the potential for higher evaluation accuracy.

The Dimensionality of Genomic Information and Its Effect on Genomic Prediction.

The genomic relationship matrix (GRM) can be inverted by the algorithm for proven and young (APY) based on recursion on a random subset of animals. While a regular inverse has a cubic cost, the cost of the APY inverse can be close to linear. Theory for the APY assumes that the optimal size of the subset (maximizing accuracy of genomic predictions) is due to a limited dimensionality of the GRM, which is a function of the effective population size (Ne). The objective of this study was to evaluate these assumptions by simulation. Six populations were simulated with approximate effective population size (Ne) from 20 to 200. Each population consisted of 10 nonoverlapping generations, with 25,000 animals per generation and phenotypes available for generations 1–9. The last 3 generations were fully genotyped assuming genome length L = 30. The GRM was constructed for each population and analyzed for distribution of eigenvalues. Genomic estimated breeding values (GEBV) were computed by single-step GBLUP, using either a direct or an APY inverse of GRM. The sizes of the subset in APY were set to the number of the largest eigenvalues explaining x% of variation (EIGx, x = 90, 95, 98, 99) in GRM. Accuracies of GEBV for the last generation with the APY inverse peaked at EIG98 and were slightly lower with EIG95, EIG99, or the direct inverse. Most information in the GRM is contained in ∼NeL largest eigenvalues, with no information beyond 4NeL. Genomic predictions with the APY inverse of the GRM are more accurate than by the regular inverse.

Changes in variance explained by top SNP windows over generations for three traits in broiler chicken.

The purpose of this study was to determine if the set of genomic regions inferred as accounting for the majority of genetic variation in quantitative traits remain stable over multiple generations of selection. The data set contained phenotypes for five generations of broiler chicken for body weight, breast meat, and leg score. The population consisted of 294,632 animals over five generations and also included genotypes of 41,036 single nucleotide polymorphism (SNP) for 4,866 animals, after quality control. The SNP effects were calculated by a GWAS type analysis using single step genomic BLUP approach for generations 1–3, 2–4, 3–5, and 1–5. Variances were calculated for windows of 20 SNP. The top ten windows for each trait that explained the largest fraction of the genetic variance across generations were examined. Across generations, the top 10 windows explained more than 0.5% but less than 1% of the total variance. Also, the pattern of the windows was not consistent across generations. The windows that explained the greatest variance changed greatly among the combinations of generations, with a few exceptions. In many cases, a window identified as top for one combination, explained less than 0.1% for the other combinations. We conclude that identification of top SNP windows for a population may have little predictive power for genetic selection in the following generations for the traits here evaluated.

Accuracies of genomic prediction of feed efficiency traits using different prediction and validation methods in an experimental Nelore cattle population1

Animal feeding is the most important economic component of beef production systems. Selection for feed efficiency has not been effective mainly due to difficult and high costs to obtain the phenotypes. The application of genomic selection using SNP can decrease the cost of animal evaluation as well as the generation interval. The objective of this study was to compare methods for genomic evaluation of feed efficiency traits using different cross-validation layouts in an experimental beef cattle population genotyped for a high-density SNP panel (BovineHD BeadChip assay 700k, Illumina Inc., San Diego, CA). After quality control, a total of 437,197 SNP genotypes were available for 761 Nelore animals from the Institute of Animal Science, Sertãozinho, São Paulo, Brazil. The studied traits were residual feed intake, feed conversion ratio, ADG, and DMI. Methods of analysis were traditional BLUP, single-step genomic BLUP (ssGBLUP), genomic BLUP (GBLUP), and a Bayesian regression method (BayesCπ). Direct genomic values (DGV) from the last 2 methods were compared directly or in an index that combines DGV with parent average. Three cross-validation approaches were used to validate the models: 1) YOUNG, in which the partition into training and testing sets was based on year of birth and testing animals were born after 2010; 2) UNREL, in which the data set was split into 3 less related subsets and the validation was done in each subset a time; and 3) RANDOM, in which the data set was randomly divided into 4 subsets (considering the contemporary groups) and the validation was done in each subset at a time. On average, the RANDOM design provided the most accurate predictions. Average accuracies ranged from 0.10 to 0.58 using BLUP, from 0.09 to 0.48 using GBLUP, from 0.06 to 0.49 using BayesCπ, and from 0.22 to 0.49 using ssGBLUP. The most accurate and consistent predictions were obtained using ssGBLUP for all analyzed traits. The ssGBLUP seems to be more suitable to obtain genomic predictions for feed efficiency traits on an experimental population of genotyped animals.

Weighting Strategies for Single-Step Genomic BLUP: An Iterative Approach for Accurate Calculation of GEBV and GWAS

Genomic Best Linear Unbiased Predictor (GBLUP) assumes equal variance for all single nucleotide polymorphisms (SNP). When traits are influenced by major SNP, Bayesian methods have the advantage of SNP selection. To overcome the limitation of GBLUP, unequal variance or weights for all SNP are applied in a method called weighted GBLUP (WGBLUP). If only a fraction of animals is genotyped, single-step WGBLUP (WssGBLUP) can be used. Default weights in WGBLUP or WssGBLUP are obtained iteratively based on single SNP effect squared (u2) and/or heterozygosity. When the weights are optimal, prediction accuracy, and ability to detect major SNP are maximized. The objective was to develop optimal weights for WGBLUP-based methods. We evaluated 5 new procedures that accounted for locus-specific or windows-specific variance to maximize accuracy of predicting genomic estimated breeding value (GEBV) and SNP effect. Simulated datasets consisted of phenotypes for 13,000 animals, including 1540 animals genotyped for 45,000 SNP. Scenarios with 5, 100, and 500 simulated quantitative trait loci (QTL) were considered. The 5 new procedures for SNP weighting were: (1) u2 plus a constant equal to the weight of the top SNP; (2) from a heavy-tailed distribution (similar to BayesA); (3) for every 20 SNP in a window along the whole genome, the largest effect (u2) among them; (4) the mean effect of every 20 SNP; and (5) the summation of every 20 SNP. Those methods were compared to the default WssGBLUP, GBLUP, BayesB, and BayesC. WssGBLUP methods were evaluated over 10 iterations. The accuracy of predicting GEBV was the correlation between true and estimated genomic breeding values for 300 genotyped animals from the last generation. The ability to detect the simulated QTL was also investigated. For most of the QTL scenarios, the accuracies obtained with all WssGBLUP procedures were higher compared to those from BayesB and BayesC, partly due to automatic inclusion of parent average in the former. Manhattan plots had higher resolution with 5 and 100 QTL. Using a common weight for a window of 20 SNP that sums or averages the SNP variance enhances accuracy of predicting GEBV and provides accurate estimation of marker effects.

Crossbreed evaluations in single-step genomic best linear unbiased predictor using adjusted realized relationship matrices1

Combining purebreed and crossbreed information is beneficial for genetic evaluation of some livestock species. Genetic evaluations can use relationships based on genomic information, relying on allele frequencies that are breed specific. Single-step genomic BLUP (ssGBLUP) does not account for different allele frequencies, which could limit the genetic gain in crossbreed evaluations. In this study, we tested the performance of different breed-specific genomic relationship matrices () in ssGBLUP for crossbreed evaluations; we also tested the importance of genotyping crossbred animals. Genotypes were available for purebreeds (AA and BB) and crossbreeds (F) in simulated and real pig populations. The number of genotyped animals was, on average, 4,315 for the simulated population and 15,798 for the real population. Cross-validation was performed on 1,200 and 3,117 F animals in the simulated and real populations, respectively. Simulated scenarios were under no artificial selection, mass selection, or BLUP selection. Two genomic relationship matrices were constructed based on breed-specific allele frequencies: 1) , a genomic relationship matrix centered by breed-specific allele frequencies, and 2) , a genomic relationship matrix centered and scaled by breed-specific allele frequencies. All (the across-breed genomic relationship matrix), , and were also tuned to account for selective genotyping. Using breed-specific allele frequencies reduced the number of negative relationships between 2 purebreeds, pulling the average closer to 0, as in the pedigree-based relationship matrix. For simulated populations that included mass selection, genomic EBV (GEBV) in F, when using and , were, on average, 10% more accurate than ; however, after tuning to account for selective genotyping, provided the same accuracy as for breed-specific genomic relationship matrices. For the real population, accuracies for litter size in F were 0.62 for , , and , and tuning had no impact on accuracy, except for , which was 1 percentage point less accurate. Accuracy of GEBV for number of stillborns in F1 was 0.5 for all tested genomic relationship matrices with no changes after tuning. We observed that genotyping F increased accuracies of GEBV for the same animals by up to 39% compared with having genotypes for only AA and BB. In crossbreed evaluations, accounting for breed-specific allele frequencies promoted changes in G that were not influential enough to improve accuracy of GEBV. Therefore, the best performance of ssGBLUP for crossbreed evaluations requires genotypes for pure- and crossbreeds and no breed-specific adjustments in the realized relationship matrix.