Performance of using opposing homozygotes for paternity testing in Japanese Black cattle

Genome-wide single nucleotide polymorphism (SNP) markers in Japanese Black cattle enable genomic prediction and verifying parent–offspring relationships. We assessed the performance of opposing homozygotes (OH) for paternity testing in Japanese Black cattle, using SNP genotype information of 50 sires and 3,420 fattened animals, 1,945 of which were fathered by the 50 genotyped sires. The number of OH was counted for each sire–progeny pair in 28,764 SNPs with minor allele frequencies of ≥0.05 in this population. Across all pairs of animals, the number of OH tended to increase as the pedigree-based coefficient of relationship decreased. With a threshold of 288 (1% of SNPs) for paternity testing, most sire–progeny pairs were detected as true relationships. The frequency of Mendelian inconsistencies was 2.4%, reflecting the high accuracy of pedigree information in Japanese Black cattle population. The results indicate the utility of OH for paternity testing in Japanese Black cattle.     

Implementation of Optimum Contributions Selection in endangered local breeds: the case of the Menorca Horse population

Limiting the inbreeding rate (?F) while maximizing genetic gain for any trait of economic interest is especially important in small populations of local breeds, like the Menorca Horse. In this breed, dressage performance is important for the profitability of the breed and should be accounted in the selection criterion. The aim of this study was to assess if a breeding programme aiming at improved dressage performance is feasible in such a small breed. To perform the analysis, animals that were currently available for breeding (between 3 and 20 years) were used. Selection was based on the estimated breeding values for dressage obtained by BLUP. The pedigree and molecular coancestry between potential breeding horses was used (separately or in combination) to account for the restriction on ?F. Results show that it is possible to avoid large increases in inbreeding while obtaining acceptable levels of genetic gain (i.e. a ?F of 1% would imply a maximum loss in genetic gain of 2%). Thus, the Menorca Horse population is suitable for a management procedure which jointly optimizes the response to selection and the levels of variability and inbreeding (Optimal Contribution selection). Regarding the source of information used to calculate the relationships, molecular information would provide a greater range of solutions to increase genetic gain than using pedigree coancestry (gain was 1–4% higher for the same levels of restriction on the increase in inbreeding).     

Analysis of genetic diversity and the determination of relationships among western Mediterranean horse breeds using microsatellite markers

The distribution of genetic diversity and the genetic relationships among western Mediterranean horse breeds were investigated using microsatellite markers. The examined sample included seven Spanish and three Italian local horse breeds and populations, plus a Spanish Thoroughbred outgroup. The total number of animals examined was 682 (on average 62 animals per breed; range 20–122). The microsatellite marker set analysed provided 128 alleles (10.7 alleles per locus). Within‐breed genetic diversity was always high (>0.70), with breeds contributing about 8% of the total genetic variability. The mean molecular coancestry of the entire population examined was 0.205, Losino being the breed that contributed most. In addition to Nei's standard and Reynolds’ genetic distances, pair‐wise kinship distance and molecular coancestry were estimated. Remarkably similar breed rankings were obtained with all methods. Clustering analysis provided an accurate representation of the current genetic relationships among the breeds. Determining coancestry is useful for analysing genetic diversity distribution between and within breeds and provides a good framework for jointly analysing molecular markers and pedigree information. An integrated analysis was undertaken to obtain information on the population dynamics in western Mediterranean native horse populations, and to better determine conservation priorities.     

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

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

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

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

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.     

Considering dominance in reduced single‐step genomic evaluations

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

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.     

Effect of selection and selective genotyping for creation of reference on bias and accuracy of genomic prediction

Reference populations for genomic selection usually involve selected individuals, which may result in biased prediction of estimated genomic breeding values (GEBV). In a simulation study, bias and accuracy of GEBV were explored for various genetic models with individuals selectively genotyped in a typical nucleus breeding program. We compared the performance of three existing methods, that is, Best Linear Unbiased Prediction of breeding values using pedigree‐based relationships (PBLUP), genomic relationships for genotyped animals only (GBLUP) and a Single‐Step approach (SSGBLUP) using both. For a scenario with no‐selection and random mating (RR), prediction was unbiased. However, lower accuracy and bias were observed for scenarios with selection and random mating (SR) or selection and positive assortative mating (SA). As expected, bias disappeared when all individuals were genotyped and used in GBLUP. SSGBLUP showed higher accuracy compared to GBLUP, and bias of prediction was negligible with SR. However, PBLUP and SSGBLUP still showed bias in SA due to high inbreeding. SSGBLUP and PBLUP were unbiased provided that inbreeding was accounted for in the relationship matrices. Selective genotyping based on extreme phenotypic contrasts increased the prediction accuracy, but prediction was biased when using GBLUP. SSGBLUP could correct the biasedness while gaining higher accuracy than GBLUP. In a typical animal breeding program, where it is too expensive to genotype all animals, it would be appropriate to genotype phenotypically contrasting selection candidates and use a Single‐Step approach to obtain accurate and unbiased prediction of GEBV.     

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

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

Genotypes and allele frequencies of buried SNPs in a bovine single‐nucleotide polymorphism array in Japanese Black cattle

Single nucleotide polymorphism (SNP) arrays are widely used for genetic and genomic analyses in cattle breeding; thus, data derived from SNP arrays have accumulated on a large scale nationwide. Commercial SNP arrays contain a considerable number of unassigned SNPs on the chromosome/position on the genome; these SNPs are excluded in subsequent analyses. Notably, the position‐unassigned SNPs, or “buried SNPs” include some of the markers associated with genetic disease. In this study, we identified the position of buried SNPs using the Basic Local Alignment Search Tool against the surrounding sequences and characterized the relationship between SNPs and genetic diseases in Online Mendelian Inheritance in Animals based on the genomic position. We determined the position of 285 buried SNPs on the genome and surveyed the genotype and allele frequencies of these SNPs in 5,955 individual Japanese Black cattle. Eleven SNPs associated with genetic disease, which contained five buried SNPs, were found in the population with the risk allele frequency ranging from 0.00008396 to 0.46. These results indicate that buried SNPs in the bovine SNP array can be utilized to identify associations with genetic disorders from large scale accumulated SNP genotype data in Japanese Black cattle.     

Prediction of accuracy of estimated Mendelian sampling terms

This study describes a general framework for predicting the accuracy of Mendelian sampling terms when truncation selection is applied on best linear unbiased prediction (BLUP) estimated breeding values. A selection index approach is followed. The pseudo‐BLUP index is extended to include terms related to the Mendelian sampling term. Predicted accuracies are compared with those obtained through stochastic computer simulation. Good predictions for the accuracy of the Mendelian sampling term were obtained both at selection time and at convergence of long‐term contributions of selected candidates for a range of heritabilities and population structures. The prediction approach developed provides a key tool for obtaining predictions of genetic response from quadratic optimization that maximizes the rate of genetic progress while restricting the rate of inbreeding.     

A robust method for simultaneous estimation of single gene and polygenic effects in dairy cows using externally estimated breeding values as prior information

The aim of this study was to develop a robust method to estimate single gene and random polygenic animal effects simultaneously in a small field dataset with limited pedigree information. The new method was based on a Bayesian approach using additional prior information on the distribution of externally estimated breeding values. The field dataset consisted of 40 269 test‐day records for milk performance traits for 1455 genotyped dairy cows for the 11 bp‐deletion in the coding sequence of the myostatin gene. For all traits, estimated additive effects of the favoured wild‐type allele (‘+’ allele) were smaller when applying the new method in comparison with the application of a conventional mixed inheritance test‐day model. Dominance effects of the myostatin gene showed the same behaviour but were generally lower than additive effects. Robustness of methods was tested using a data‐splitting technique, based on the correlation of estimated breeding values from two samples, with one‐half of the data eliminated randomly from the first sample and the remaining data eliminated from the second sample. Results for 100 replicates showed that the correlation between split datasets when prior information included was higher than the conventional method. The new method led to more robust estimations for genetic effects and therefore has potential for use when only a small number of genotyped animals with field data and limited pedigree information are available.     

Partial-genome evaluation of postweaning feed intake and efficiency of crossbred beef cattle

The effects of individual SNP and the variation explained by sets of SNP associated with DMI, metabolic midtest BW, BW gain, and feed efficiency, expressed as phenotypic and genetic residual feed intake, were estimated from BW and the individual feed intake of 1,159 steers on dry lot offered a 3.0 Mcal/kg ration for at least 119 d before slaughter. Parents of these F(1) × F(1) (F(1)(2)) steers were AI-sired F(1) progeny of Angus, Charolais, Gelbvieh, Hereford, Limousin, Red Angus, and Simmental bulls mated to US Meat Animal Research Center Angus, Hereford, and MARC III composite females. Steers were genotyped with the BovineSNP50 BeadChip assay (Illumina Inc., San Diego, CA). Effects of 44,163 SNP having minor allele frequencies >0.05 in the F(1)(2) generation were estimated with a mixed model that included genotype, breed composition, heterosis, age of dam, and slaughter date contemporary groups as fixed effects, and a random additive genetic effect with recorded pedigree relationships among animals. Variance in this population attributable to sets of SNP was estimated with models that partitioned the additive genetic effect into a polygenic component attributable to pedigree relationships and a genotypic component attributable to genotypic relationships. The sets of SNP evaluated were the full set of 44,163 SNP and subsets containing 6 to 40,000 SNP selected according to association with phenotype. Ninety SNP were strongly associated (P < 0.0001) with at least 1 efficiency or component trait; these 90 accounted for 28 to 46% of the total additive genetic variance of each trait. Trait-specific sets containing 96 SNP having the strongest associations with each trait explained 50 to 87% of additive variance for that trait. Expected accuracy of steer breeding values predicted with pedigree and genotypic relationships exceeded the accuracy of their sires predicted without genotypic information, although gains in accuracy were not sufficient to encourage that performance testing be replaced by genotyping and genomic evaluations.     

Segment-based coancestry,additive relationship and genetic variance within and between the Norwegian and the Swedish Fjord horse populations

ABSTRACT

The Fjord horse originates from Norway but forms a global population due to several small populations in foreign countries. There exists no information about the additive relationship and the genetic variance between these subpopulations. By collecting blood samples from Norwegian and Swedish Fjord horses, a sample of 311 Norwegian and 102 Swedish horses gave 485,918 SNPs available for analysis. Their inbreeding coefficients were calculated and compared to the pairwise coancestry and the shared genomic segments. The effective population size was almost similar with the two methods in the Norwegian Fjord horse population (63 and 71), but very different in the Swedish population (269 and 1136) and unprecise due to a much smaller number of observations. The study showed that coancestry from shared genomic segments can be used to estimate additive genetic relationship and genetic variation within and between the global populations of the Fjord horse.     

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

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

Strategy for applying genome-wide selection in dairy cattle

Animals can be genotyped for thousands of single nucleotide polymorphisms (SNPs) at one time, where the SNPs are located at roughly 1‐cM intervals throughout the genome. For each contiguous pair of SNPs there are four possible haplotypes that could be inherited from the sire. The effects of each interval on a trait can be estimated for all intervals simultaneously in a model where interval effects are random factors. Given the estimated effects of each haplotype for every interval in the genome, and given an animal's genotype, a ‘genomic’ estimated breeding value is obtained by summing the estimated effects for that genotype. The accuracy of that estimator of breeding values is around 80%. Because the genomic estimated breeding values can be calculated at birth, and because it has a high accuracy, a strategy that utilizes these advantages was compared with a traditional progeny testing strategy under a typical Canadian‐like dairy cattle situation. Costs of proving bulls were reduced by 92% and genetic change was increased by a factor of 2. Genome‐wide selection may become a popular tool for genetic improvement in livestock.     

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.     

Genomic predictions across Nordic Holstein and Nordic Red using the genomic best linear unbiased prediction model with different genomic relationship matrices

This study investigated genomic predictions across Nordic Holstein and Nordic Red using various genomic relationship matrices. Different sources of information, such as consistencies of linkage disequilibrium (LD) phase and marker effects, were used to construct the genomic relationship matrices (G‐matrices) across these two breeds. Single‐trait genomic best linear unbiased prediction (GBLUP) model and two‐trait GBLUP model were used for single‐breed and two‐breed genomic predictions. The data included 5215 Nordic Holstein bulls and 4361 Nordic Red bulls, which was composed of three populations: Danish Red, Swedish Red and Finnish Ayrshire. The bulls were genotyped with 50 000 SNP chip. Using the two‐breed predictions with a joint Nordic Holstein and Nordic Red reference population, accuracies increased slightly for all traits in Nordic Red, but only for some traits in Nordic Holstein. Among the three subpopulations of Nordic Red, accuracies increased more for Danish Red than for Swedish Red and Finnish Ayrshire. This is because closer genetic relationships exist between Danish Red and Nordic Holstein. Among Danish Red, individuals with higher genomic relationship coefficients with Nordic Holstein showed more increased accuracies in the two‐breed predictions. Weighting the two‐breed G‐matrices by LD phase consistencies, marker effects or both did not further improve accuracies of the two‐breed predictions.     

Efficient computation of the genomic relationship matrix and other matrices used in single-step evaluation

Genomic evaluations can be calculated using a unified procedure that combines phenotypic, pedigree and genomic information. Implementation of such a procedure requires the inverse of the relationship matrix based on pedigree and genomic relationships. The objective of this study was to investigate efficient computing options to create relationship matrices based on genomic markers and pedigree information as well as their inverses. SNP maker information was simulated for a panel of 40 K SNPs, with the number of genotyped animals up to 30 000. Matrix multiplication in the computation of the genomic relationship was by a simple 'do' loop, by two optimized versions of the loop, and by a specific matrix multiplication subroutine. Inversion was by a generalized inverse algorithm and by a LAPACK subroutine. With the most efficient choices and parallel processing, creation of matrices for 30 000 animals would take a few hours. Matrices required to implement a unified approach can be computed efficiently. Optimizations can be either by modifications of existing code or by the use of efficient automatic optimizations provided by open source or third-party libraries.