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Extreme weather conditions such as cold stress influence the productivity and survivability of beef cattle raised on pasture. The objective of this study was to identify and evaluate the extent of the impact of genotype by environment interaction due to cold stress on birth weight (BW) and weaning weight (WW) in a composite beef cattle population. The effect of cold stress was modelled as the accumulation of total cold load (TCL) calculated using the Comprehensive Climate Index units, considering three TCL classes defined based on temperature: less than -5°C (TCL5), -15°C (TCL15) and -25°C (TCL25). A total of 4221 and 4217 records for BW and WW, respectively, were used from a composite beef cattle population (50% Red Angus, 25% Charolais and 25% Tarentaise) between 2002 and 2015. For both BW and WW, a univariate model (ignoring cold stress) and a reaction norm model were implemented. As cold load increased, the direct heritability slightly increased in both BW and WW for TCL5 class; however, this heritability remained consistent across the cold load of TCL25 class. In contrast, the maternal heritability of BW was constant with cold load increase in all TCL classes, although a slight increase of maternal heritability was observed for TCL5 and TCL15. The direct and maternal genetic correlation for BW and maternal genetic correlation for WW across different cold loads between all TCL classes were high (r > 0.99), whereas the lowest direct genetic correlations observed for WW were 0.88 for TCL5 and 0.85 for TCL15. The Spearman rank correlation between the estimated breeding value of top bulls (n = 79) using univariate and reaction norm models across TCL classes showed some re-ranking in direct and maternal effects for both BW and WW particularly for TCL5 and TCL15. In general, cold stress did not have a big impact on direct and maternal genetic effects of BW and WW.

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Causal variants inferred from sequence data analysis are expected to increase accuracy of genomic selection. In this work we evaluated the gain in reliability of genomic predictions, for stature in US Holsteins, when adding selected sequence variants to a pre-existent SNP chip. Two prediction methods were tested: de-regressed proofs assuming heterogeneous (genomic BLUP; GBLUP) residual variances and by single-step GBLUP (ssGBLUP) using actual phenotypes. Phenotypic data included 3,999,631 records for stature on 3,027,304 Holstein cows. Genotypes on 54,087 SNP markers (54k) were available for 26,877 bulls. Additionally, 16,648 selected sequence variants were combined with the 54k markers, for a total of 70,735 (70k) markers. In all methods, SNP in the genomic relationship matrix (G) were unweighted or weighted iteratively, with weights derived either by SNP effects squared or by a nonlinear method that resembles BayesA (nonlinear A). Reliability of genomic predictions were obtained by cross validation. With unweighted G derived from 54k markers, the reliabilities (× 100) were 72.4 for GBLUP and 75.3 for ssGBLUP. With unweighted G derived from 70k markers, the reliabilities were 73.4 and 76.0, respectively. Weighting by nonlinear A changed reliabilities to 73.3, and 75.9, respectively. Addition of selected sequence variants had a small effect on reliabilities. Weighting by quadratic functions reduced reliabilities. Weighting by nonlinear A increased reliabilities for GBLUP but had only a small effect in ssGBLUP. Reliabilities for direct genomic values extracted from ssGBLUP using unweighted G with 54k were higher than reliabilities by any GBLUP. Thus, ssGBLUP seems to capture more information than GBLUP and there is less room for extra reliability. Improvements in GBLUP may be because the weights in G change the covariance structure, which can explain a proportion of the variance that is accounted for when a heterogeneous residual variance is assumed by considering a different number of daughters per bull.

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

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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.

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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.

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Genetically linked small and large dairy cattle populations were simulated to test the effect of different sources of information from foreign populations on the accuracy of predicting breeding values for young animals in a small population. A large dairy cattle population (PL) with >20 generations was simulated, and a small subpopulation (PS) with 3 generations was formed as a related population, including phenotypes and genomic information. Predicted breeding values for young animals in the small population were calculated using BLUP and single-step genomic BLUP (ssGBLUP) in 4 different scenarios: (S1) 3,166 phenotypes, 22,855 pedigree animals, and 1,000 to 6,000 genotypes for PS; (S2) S1 plus genomic estimated breeding value (GEBV) for 4,475 sires from PL as external information; (S3) S1 plus 221,580 phenotypes, 402,829 pedigree animals, and 53,558 genotypes for PL; and (S4) single nucleotide polymorphism (SNP) effects calculated based on PL data. The ability to predict true breeding value was assessed in the youngest third of the genotyped animals in the small population. When data only from the small population were used and 1,000 animals were genotyped, the accuracy of GEBV was only 1 point greater than the estimated breeding value accuracy (0.32 vs. 0.31). Adding external GEBV for sires from PL did not considerably increase accuracy (0.33 vs. 0.32 in S1). Combining phenotypes, pedigree, and genotypes for PS and PL was beneficial for predicting accuracy of GEBV in the small population, and the prediction accuracy of GEBV in this scenario was 0.38 compared with 0.31 from estimated breeding values. When SNP effects from PL were used to predict GEBV for young genotyped animals from PS, accuracy was greatest (0.56). With 6,000 genotyped animal in PS, accuracy was greatest (0.61) with the combined populations. In a small population with few genotypes, the highest accuracy of evaluation may be obtained by using SNP effects derived from a related large population.

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This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.

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The objective of the study was to investigate the relationships between vaginal temperature during the dry-period and health, milk production, and reproduction in the subsequent lactation of cows during the warm season. A total of 105 nonlactating Holstein cows from 2 dairies were enrolled in the study during summer. At enrollment, cows were between 250 and 260 d of gestation. Vaginal temperature (VT) and corral ambient temperature and humidity were recorded every 5 min for 4 consecutive days starting at enrollment. Cows were categorized as presenting high (HT) or low temperature (LT) based on the median values of average VT and were followed until 300 d in milk (DIM) of the subsequent lactation to evaluate health disorders, culling rate, milk yield, and reproductive efficiency. Cows that became pregnant were followed until subsequent calving. Cows were monitored for uterine diseases (UTD) and mastitis (MAST) by farm personnel. Individual milk yield was recorded monthly until 300 DIM. Cows classified as HT had shorter ( < 0.01) gestation length (273.9 ± 0.9 vs. 278.7 ± 1.0 d) and spent fewer ( < 0.01) days in the close-up pen (14.3 ± 0.8 vs. 19.4 ± 1.0 d) than LT cows. Hazard to UTD or MAST in the first 60 DIM was greater for HT than LT cows (adjusted hazard ratio [AHR] = 5.15, 95% CI = 1.91 to 13.86). Cows classified as HT had greater hazard to MAST in the first 300 DIM compared with LT cows (AHR = 2.39; 1.03 to 5.56). Vaginal temperature was not associated with milk yield. In contrast, the interaction between VT category and month of lactation tended to influence milk yield. This interaction was observed because cows categorized as LT had greater ( < 0.01) milk yield in the first month of lactation compared with HT cows (39.2 ± 1.6 vs. 33.7 ± 1.5 kg), whereas milk yield tended ( = 0.07) and was greater ( = 0.05) for HT cows in the ninth (32.7 ± 1.6 vs. 28.5 ± 1.9 kg) and tenth (29.9 ± 1.7 vs. 25.0 ± 2.0 kg) month of lactation, respectively. Pregnancy per AI at first service, interval from calving to pregnancy, and percentage of cows calving in the subsequent lactation did not differ between HT and LT cows. In conclusion, VT assessed between 20 and 30 d before expected calving is associated with health outcomes and milk production in the subsequent lactation. In addition, cows susceptible to be affected by postpartum disorders after calving may be identified during the summer by evaluating VT temperature at 250 to 260 d of gestation.

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The objectives were to assess the impact of heat stress and to develop a model for genetic evaluation of growth heat tolerance in Angus cattle. The American Angus Association provided weaning weight (WW) and yearling weight (YW) data, and records from the Upper South region were used because of the hot climatic conditions. Heat stress was characterized by a weaning (yearling) heat load function defined as the mean temperature-humidity index (THI) units greater than 75 (70) for 30 (150) d prior to the weigh date. Therefore, a weaning (yearling) heat load of 5 units corresponded to 80 (75) for the corresponding period prior to the weigh date. For all analyses, 82,669 WW and 69,040 YW were used with 3 ancestral generations in the pedigree. Univariate models were a proxy for the Angus growth evaluation, and reaction norms using 2 B-splines for heat load were fit separately for weaning and yearling heat loads. For both models, random effects included direct genetic, maternal genetic, maternal permanent environment (WW only), and residual. Fixed effects included a linear age covariate, age-of-dam class (WW only), and contemporary group for both models and fixed regressions on the B-splines in the reaction norm. Direct genetic correlations for WW were strong for modest heat load differences but decreased to less than 0.50 for large differences. Reranking of proven sires occurred for only WW direct effects for the reaction norms with extreme heat load differences. Conversely, YW results indicated little effect of heat stress on genetic merit. Therefore, weaning heat tolerance was a better candidate for developing selection tools. Maternal heritabilities were consistent across heat loads, and maternal genetic correlations were greater than 0.90 for nearly all heat load combinations. No evidence existed for a genotype × environment interaction for the maternal component of growth. Overall, some evidence exists for phenotypic plasticity for the direct genetic effects of WW, but traditional national cattle evaluations are likely adequately ranking sires for nonextreme environmental conditions.

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This study evaluated the impact of region and season on growth in Angus seed stock. To assess geographic differences, the United States was partitioned into 9 regions based on similar climate and topography related to cow-calf production. Seasonal effects were associated with the month that animals were weighed. The American Angus Association provided growth data, and records were assigned to regions based on the owner's zip code. Most Angus cattle were in the Cornbelt, Lower Plains, Rocky Mountain, Upper Plains, and Upper South regions, with proportionally fewer Angus in Texas compared with the national cow herd. Most calves were born in the spring, especially February and March. Weaning weights (WW; = 49,886) and yearling weights (YW; = 45,168) were modeled with fixed effects of age-of-dam class (WW only), weigh month, region, month-region interaction, and linear covariate of age. Random effects included contemporary group nested within month-region combination and residual. The significant month-region interaction ( < 0.0001) was expected because of the diverse production environments across the country and cyclical fluctuations in forage availability. Additionally, significant seasonal contrasts existed for several regions. Fall-born calves were heavier ( < 0.01) than spring-born calves in the hot and humid Lower South region coinciding with fall being the primary calving season. The North and Upper Plains regions had heavier, spring-born calves ( < 0.01), more than 90% spring calving, and colder climates. Interestingly, no seasonal WW or YW differences existed between spring- and fall-born calves in the upper South region despite challenging environmental conditions. Angus seed stock producers have used calving seasons to adapt to the specific environmental conditions in their regions and to optimize growth in young animals.

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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.

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The purpose of this study was to analyze the impact of seasonal losses due to heat stress in different environments and genetic group combinations. Data were available for 2 different swine populations: purebred Duroc animals raised in nucleus farms in Texas and North Carolina and crosses of Duroc and F females (Landrace × Large White) raised in commercial farms in Missouri and North Carolina; pedigrees provided links between animals from different states. Traits included BW at harvest age for purebred animals and HCW for crossbred animals. Weather data were collected at airports located close to the farms. Heat stress was quantified by a heat load function, defined by the units of temperature-humidity of temperature-humidity index (THI) greater than a certain threshold for 30 to 70 d before phenotype collection. Heat stress responses were quantified by a linear regression of phenotype on heat load. The greatest coefficient of determination occurred with a length of 30 d before phenotype measurements for all states and genetic groups. In the crossbreed data, THI thresholds were 67 in Missouri and 72 in North Carolina. For pure breeds, heat load had the best fit for THI thresholds greater than 70 in North Carolina, although differences in coefficient of determinations were negligible. On the other hand, no optimal THI threshold existed in Texas. In this study, heat stress had a greater impact in commercial farms than in nucleus farms and the effect of heat stress on weight varied by year and state.

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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.

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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.

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The purposes of this study were to analyze the impact of seasonal losses due to heat stress in pigs from different breeds raised in different environments and to evaluate the accuracy improvement from adding genomic information to genetic evaluations. Data were available for 2 different swine populations: purebred Duroc animals raised in Texas and North Carolina and commercial crosses of Duroc and F females (Landrace × Large White) raised in Missouri and North Carolina; pedigrees provided links for animals from different states. Pedigree information was available for 553,442 animals, of which 8,232 pure breeds were genotyped. Traits were BW at 170 d for purebred animals and HCW for crossbred animals. Analyses were done with an animal model as either single- or 2-trait models using phenotypes measured in different states as separate traits. Additionally, reaction norm models were fitted for 1 or 2 traits using heat load index as a covariable. Heat load was calculated as temperature-humidity index greater than 70 and was averaged over 30 d prior to data collection. Variance components were estimated with average information REML, and EBV and genomic EBV (GEBV) with BLUP or single-step genomic BLUP (ssGBLUP). Validation was assessed for 146 genotyped sires with progeny in the last generation. Accuracy was calculated as a correlation between EBV and GEBV using reduced data (all animals, except the last generation) and using complete data. Heritability estimates for purebred animals were similar across states (varying from 0.23 to 0.26), and reaction norm models did not show evidence of a heat stress effect. Genetic correlations between states for heat loads were always strong (>0.91). For crossbred animals, no differences in heritability were found in single- or 2-trait analysis (from 0.17 to 0.18), and genetic correlations between states were moderate (0.43). In the reaction norm for crossbreeds, heritabilities ranged from 0.15 to 0.30 and genetic correlations between heat loads were as weak as 0.36, with heat load ranging from 0 to 12. Accuracies with ssGBLUP were, on average, 25% greater than with BLUP. Accuracies were greater in 2-trait reaction norm models and at extreme heat load values. Impacts of seasonality are evident only for crossbred animals. Genomic information can help producers mitigate heat stress in swine by identifying superior sires that are more resistant to heat stress.

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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.

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The study reported here evaluated genotype × environment interaction in individual performance and progeny tests in beef cattle. Genetic parameters for final weight (FW), ADG, and scrotal circumference (SC) of 33,013 Nellore young bulls tested on pasture or in feedlots were analyzed. The posterior means (and highest posterior density interval with 90% of samples [HPD90]) of heritability for traits measured on pasture-raised and feedlot-raised animals were 0.44 (HPD90 = 0.40 to 0.48) and 0.50 (HPD90 = 0.43 to 0.56) for FW, 0.26 (HPD90 = 0.23 to 0.29) and 0.26 (HPD90 = 0.20 to 0.32) for ADG, and 0.53 (HPD90 = 0.48 to 0.59) and 0.65 (HPD90 = 0.55 to 0.74) for SC, respectively. The posterior means (and HPD90) of genetic correlations for FW, ADG, and SC on pasture and in feedlots were 0.75 (HPD90 = 0.66 to 0.87), 0.49 (HPD90 = 0.31 to 0.66), and 0.89 (HPD90 = 0.83 to 0.97), respectively. When the selection intensity was kept the same for both the environments, the greatest direct responses for FW and ADG were exhibited by the animals reared and selected in feedlots. The correlated responses relative to production on pasture and based on selection in feedlots were similar to the direct responses, whereas the correlated responses for production in feedlots and based on selection on pasture were lower than the direct responses. When the selection intensity on pasture was higher than the selection intensity in feedlots, the responses to direct selection were similar for both the environments and correlated responses obtained in feedlots by selection on pasture were similar to the direct responses in feedlots. Analyses of few or poor indicators of genotype × environment interaction result in incorrect interpretations of its existence and implications. The present work demonstrated that traits with lower heritability are more susceptible to genotype × environment interaction and that selection intensity plays an important role in the study of genotype × environment interaction in beef cattle.

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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.

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The purpose of this study was to evaluate the accuracy of genomic selection in single-step genomic BLUP (ssGBLUP) when the inverse of the genomic relationship matrix (G) is derived by the "algorithm for proven and young animals" (APY). This algorithm implements genomic recursions on a subset of "proven" animals. Only a relationship matrix for animals treated as "proven" needs to be inverted, and the extra costs of adding animals treated as "young" are linear. Analyses involved 10,102,702 final scores on 6,930,618 Holstein cows. Final score, which is a composite of type traits, is popular trait in the United States and was easily available for this study. A total of 100,000 animals with genotypes were used in the analyses and included 23,000 sires (16,000 with >5 progeny), 27,000 cows, and 50,000 young animals. Genomic EBV (GEBV) were calculated with a regular inverse of G, and with the G inverse approximated by APY. Animals in the proven subset included only sires (23,000), sires+cows (50,000), only cows (27,000), or sires with >5 progeny (16,000). The correlations of GEBV with APY and regular GEBV for young genotyped animals were 0.994, 0.995, 0.992, and 0.992, respectively Later, animals in the proven subset were randomly sampled from all genotyped animals in sets of 2,000, 5,000, 10,000, 15,000, and 20,000; each sample was replicated 4 times. Respective correlations were 0.97 (5,000 sample), 0.98 (10,000 sample), and 0.99 (20,000 sample), with minimal difference between samples of the same size. Genomic EBV with APY were accurate when the number of animals used in the subset is between 10,000 and 20,000, with little difference between the ways of creating the subset. Due to the approximately linear cost of APY, ssGBLUP with APY could support any number of genotyped animals without affecting accuracy.

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The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) polynomials. In general, the Legendre and quadratic B-spline models that included more covariance parameters provided a better fit with the data. When comparing models with the same number of parameters, the quadratic B-spline provided a better fit than the Legendre polynomials. The quadratic B-spline with four intervals provided the best fit for the Nellore and MA groups. The fitting of random regression models with different types of polynomials (Legendre polynomials or B-spline) affected neither the genetic parameters estimates nor the ranking of the Nellore young bulls. However, fitting different type of polynomials affected the genetic parameters estimates and the ranking of the MA young bulls. Parsimonious Legendre or quadratic B-spline models could be used for genetic evaluation of body weight of Nellore young bulls in performance tests, whereas these parsimonious models were less efficient for animals of the MA genetic group owing to limited data at the extreme ages.

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