Improving selection decisions with mating information by accounting for Mendelian sampling variances looking two generations ahead.

BACKGROUND: Breeding programs are judged by the genetic level of animals that are used to disseminate genetic progress. These animals are typically the best ones of the population. To maximise the genetic level of very good animals in the next generation, parents that are more likely to produce top performing offspring need to be selected. The ability of individuals to produce high-performing progeny differs because of differences in their breeding values and gametic variances. Differences in gametic variances among individuals are caused by differences in heterozygosity and linkage. The use of the gametic Mendelian sampling variance has been proposed before, for use in the usefulness criterion or Index5, and in this work, we extend existing approaches by not only considering the gametic Mendelian sampling variance of individuals, but also of their potential offspring. Thus, the criteria developed in this study plan one additional generation ahead. For simplicity, we assumed that the true quantitative trait loci (QTL) effects, genetic map and the haplotypes of all animals are known. RESULTS: In this study, we propose a new selection criterion, ExpBVSelGrOff, which describes the genetic level of selected grand-offspring that are produced by selected offspring of a particular mating. We compare our criterion with other published criteria in a stochastic simulation of an ongoing breeding program for 21 generations for proof of concept. ExpBVSelGrOff performed better than all other tested criteria, like the usefulness criterion or Index5 which have been proposed in the literature, without compromising short-term gains. After only five generations, when selection is strong (1%), selection based on ExpBVSelGrOff achieved 5.8% more commercial genetic gain and retained 25% more genetic variance without compromising inbreeding rate compared to selection based only on breeding values. CONCLUSIONS: Our proposed selection criterion offers a new tool to accelerate genetic progress for contemporary genomic breeding programs. It retains more genetic variance than previously published criteria that plan less far ahead. Considering future gametic Mendelian sampling variances in the selection process also seems promising for maintaining more genetic variance.

Integration of beef cattle international pedigree and genomic estimated breeding values into national evaluations, with an application to the Italian Limousin population.

BACKGROUND: International evaluations combine data from different countries allowing breeders to have access to larger panels of elite bulls and to increase the accuracy of estimated breeding values (EBV). However, international and national evaluations can use different sources of information to compute EBV (EBVINT and EBVNAT, respectively), leading to differences between them. Choosing one of these EBV results in losing the information that is contained only in the discarded EBV. Our objectives were to define and validate a procedure to integrate publishable sires' EBVINT and their associated reliabilities computed from pedigree-based or single-step international beef cattle evaluations into national evaluations to obtain "blended" EBV. The Italian (ITA) pedigree-based national evaluation was used as a case study to validate the integration procedure. METHODS: Publishable sires' international information, i.e. EBVINT and their associated reliabilities, was included in the national evaluation as pseudo-records. Data were available for 444,199 individual age-adjusted weaning weights of Limousin cattle from eight countries and 17,607 genotypes from four countries (ITA excluded). To mimic differences between international and national evaluations, international evaluations included phenotypes (and genotypes) of animals born prior to January 2019, while national evaluations included ITA phenotypes of animals born until April 2019. International evaluations using all available information were considered as reference scenarios. Publishable sires were divided into three groups: sires with ≥ 15, < 15 and no recorded offspring in ITA. RESULTS: Overall, for these three groups, integrating either pedigree-based or single-step international information into national pedigree-based evaluations improved the similarity of the blended EBV with the reference EBV compared to national evaluations without integration. For instance, the correlation with the reference EBV for direct (maternal) EBV went from 0.61 (0.79) for a national evaluation without integration to 0.97 (0.88) when integrating single-step international information, on average across all groups of publishable sires. CONCLUSIONS: Our proposed one-animal-at-a-time integration procedure yields blended EBV that are in close agreement with full international EBV for all groups of animals analysed. The procedure can be directly applied by countries since it does not rely on specific software and is computationally inexpensive, allowing straightforward integration of publishable sires' EBVINT from pedigree-based or single-step based international beef cattle evaluations into national evaluations.

Efficient large-scale single-step evaluations and indirect genomic prediction of genotyped selection candidates.

BACKGROUND: Single-step genomic best linear unbiased prediction (ssGBLUP) models allow the combination of genomic, pedigree, and phenotypic data into a single model, which is computationally challenging for large genotyped populations. In practice, genotypes of animals without their own phenotype and progeny, so-called genotyped selection candidates, can become available after genomic breeding values have been estimated by ssGBLUP. In some breeding programmes, genomic estimated breeding values (GEBV) for these animals should be known shortly after obtaining genotype information but recomputing GEBV using the full ssGBLUP takes too much time. In this study, first we compare two equivalent formulations of ssGBLUP models, i.e. one that is based on the Woodbury matrix identity applied to the inverse of the genomic relationship matrix, and one that is based on marker equations. Second, we present computationally-fast approaches to indirectly compute GEBV for genotyped selection candidates, without the need to do the full ssGBLUP evaluation. RESULTS: The indirect approaches use information from the latest ssGBLUP evaluation and rely on the decomposition of GEBV into its components. The two equivalent ssGBLUP models and indirect approaches were tested on a six-trait calving difficulty model using Irish dairy and beef cattle data that include 2.6 million genotyped animals of which about 500,000 were considered as genotyped selection candidates. When using the same computational approaches, the solving phase of the two equivalent ssGBLUP models showed similar requirements for memory and time per iteration. The computational differences between them were due to the preprocessing phase of the genomic information. Regarding the indirect approaches, compared to GEBV obtained from single-step evaluations including all genotypes, indirect GEBV had correlations higher than 0.99 for all traits while showing little dispersion and level bias. CONCLUSIONS: In conclusion, ssGBLUP predictions for the genotyped selection candidates were accurately approximated using the presented indirect approaches, which are more memory efficient and computationally fast, compared to solving a full ssGBLUP evaluation. Thus, indirect approaches can be used even on a weekly basis to estimate GEBV for newly genotyped animals, while the full single-step evaluation is done only a few times within a year.

Impact of genomic preselection on subsequent ssGBLUP evaluation of preselected animals for scarcely recorded feed intake in pigs.

We have previously shown that single-step genomic best linear unbiased prediction (ssGBLUP) estimates breeding values of genomically preselected animals without preselection bias for widely recorded traits, that is traits recorded for the majority of animals in the breeding population. This study investigated the impact of genomic preselection (GPS) on accuracy and bias in ssGBLUP evaluation of genomically preselected animals for a scarcely recorded trait, that is a trait recorded for only a small proportion of the animals, which generally has a lower prediction accuracy than widely recorded traits, mainly due to having a much smaller number of phenotypes available. We used data from a commercial pig breeding program, considering feed intake as a scarcely recorded target trait, being available for ~30% of the animals with phenotypes for any trait, and average daily gain, backfat thickness and loin depth as widely recorded predictor traits, being available for >95% of the animals with phenotypes for any trait. The data contained the routine GPS implemented by commercial animal breeding programs, and we retrospectively implemented two scenarios with additional layers of GPS by discarding pedigree, genotypes and phenotypes of animals without progeny. The ssGBLUP evaluation following GPS used records only from the target trait, only from the predictor traits, or both. Accuracy for feed intake did not differ statistically across GPS scenarios, although it tended to decrease with more intense GPS. The accuracy had average values of 0.37, 0.44, and 0.45 across all GPS scenarios when, respectively, records from only the target trait, only the predictor traits, or both were used in the ssGBLUP evaluation. Considerable deflation of the genomic breeding values for feed intake was observed in the most stringent GPS scenario, due to the variance components being underestimated as a result of the limited amount of strongly preselected data. As long as (co)variance components were unbiased, no or only marginal bias was observed. These results for accuracy and bias were observed whether records of the scarcely recorded target trait, of the predictor traits, or both were used in the ssGBLUP evaluation. Our results show that for the scarcely recorded feed intake in pigs, ssGBLUP is able to estimate breeding values of preselected animals without preselection bias, similarly as previously observed for widely recorded traits.

Impact of genomic preselection on subsequent genetic evaluations with ssGBLUP using real data from pigs.

BACKGROUND: Empirically assessing the impact of preselection on genetic evaluation of preselected animals requires comparing scenarios that take different approaches into account, including scenarios without preselection. However, preselection is almost always performed in animal breeding programs, so it is difficult to have a dataset without preselection. Hence, most studies on preselection have used simulated datasets, and have concluded that genomic estimated breeding values (GEBV) from subsequent single-step genomic best linear unbiased prediction (ssGBLUP) evaluations are unbiased. The aim of this study was to investigate the impact of genomic preselection (GPS) on accuracy and bias in subsequent ssGBLUP evaluations, using data from a commercial pig breeding program. METHODS: We used data on average daily gain during performance testing, average daily gain throughout life, backfat thickness, and loin depth from one sire line and one dam line of pigs. As these traits have different weights in the breeding goals of the two lines, we analyzed the lines separately. For each line, we implemented a reference GPS scenario that kept all available data, against which the next two scenarios were compared. We then implemented two other scenarios with additional layers of GPS by removing all animals without progeny either (i) only in the validation generation, or (ii) in all generations. We conducted subsequent ssGBLUP evaluations for each GPS scenario, using all the data remaining after implementing the GPS scenario. Accuracy and bias were computed by comparing GEBV against progeny yield deviations of validation animals. RESULTS: Results for all traits and in both lines showed a marginal loss in accuracy due to the additional layers of GPS. Average accuracies across all GPS scenarios in the two lines were 0.39, 0.47, 0.56, and 0.60, for average daily gain during performance testing and throughout life, backfat thickness, and loin depth, respectively. Biases were largely absent, and when present, did not differ greatly between the GPS scenarios. CONCLUSIONS: We conclude that the impact of preselection on accuracy and bias in subsequent ssGBLUP evaluations of selection candidates in pigs is generally minimal. We expect this conclusion to apply for other animal breeding programs as well, since preselection of any type or intensity generally has the same effect in animal breeding programs.

International single-step SNPBLUP beef cattle evaluations for Limousin weaning weight.

BACKGROUND: Compared to national evaluations, international collaboration projects further improve accuracies of estimated breeding values (EBV) by building larger reference populations or performing a joint evaluation using data (or proxy of them) from different countries. Genomic selection is increasingly adopted in beef cattle, but, to date, the benefits of including genomic information in international evaluations have not been explored. Our objective was to develop an international beef cattle single-step genomic evaluation and investigate its impact on the accuracy and bias of genomic evaluations compared to current pedigree-based evaluations. METHODS: Weaning weight records were available for 331,593 animals from seven European countries. The pedigree included 519,740 animals. After imputation and quality control, 17,607 genotypes at a density of 57,899 single nucleotide polymorphisms (SNPs) from four countries were available. We implemented two international scenarios where countries were modelled as different correlated traits: an international genomic single-step SNP best linear unbiased prediction (SNPBLUP) evaluation (ssSNPBLUPINT) and an international pedigree-based BLUP evaluation (PBLUPINT). Two national scenarios were implemented for pedigree and genomic evaluations using only nationally submitted phenotypes and genotypes. Accuracies, level and dispersion bias of EBV of animals born from 2014 onwards, and increases in population accuracies were estimated using the linear regression method. RESULTS: On average across countries, 39 and 17% of sires and maternal-grand-sires with recorded (grand-)offspring across two countries were genotyped. ssSNPBLUPINT showed the highest accuracies of EBV and, compared to PBLUPINT, led to increases in population accuracy of 13.7% for direct EBV, and 25.8% for maternal EBV, on average across countries. Increases in population accuracies when moving from national scenarios to ssSNPBLUPINT were observed for all countries. Overall, ssSNPBLUPINT level and dispersion bias remained similar or slightly reduced compared to PBLUPINT and national scenarios. CONCLUSIONS: International single-step SNPBLUP evaluations are feasible and lead to higher population accuracies for both large and small countries compared to current international pedigree-based evaluations and national evaluations. These results are likely related to the larger multi-country reference population and the inclusion of phenotypes from relatives recorded in other countries via single-step international evaluations. The proposed international single-step approach can be applied to other traits and breeds.

Avoiding preselection bias in subsequent single-step genomic BLUP evaluations of genomically preselected animals.

In animal breeding, parents of the next generation are usually selected in multiple stages, and the initial stages of this selection are called preselection. Preselection reduces the information available for subsequent evaluation of preselected animals and this sometimes leads to bias. The objective of this study was to establish the minimum information required to subsequently evaluate genomically preselected animals without bias arising from preselection, with single-step genomic best linear unbiased prediction (ssGBLUP). We simulated a nucleus of a breeding program in which a recent population of 15 generations was produced. In each generation, parents of the next generation were selected in a single-stage selection based on pedigree BLUP. However, in generation 15, 10% of male and 15% of female offspring were preselected on their genomic estimated breeding values (GEBV). These GEBV were estimated using ssGBLUP, including the pedigree of all animals in generations 0-15, genotypes of all animals in generations 13-15 and phenotypes of all animals in generations 11-14. In subsequent ssGBLUP evaluation of these preselected animals, genotypes and phenotypes from various groups of animals were excluded one after another. We found that GEBV of the preselected animals were only estimated without preselection bias when genotypes and phenotypes of all animals in generations 13 and 14 and of the preselected animals were included in the subsequent evaluation. We also found that genotypes of the animals discarded at preselection only helped in reducing preselection bias in GEBV of their preselected sibs when genotypes of their parents were absent or excluded from the subsequent evaluation. We concluded that to prevent preselection bias in subsequent ssGBLUP evaluation of genomically preselected animals, information representative of the reference data used in the evaluation at preselection and genotypes and phenotypes of the preselected animals are needed in the subsequent evaluation.

Investigating the impact of preselection on subsequent single-step genomic BLUP evaluation of preselected animals.

BACKGROUND: Preselection of candidates, hereafter referred to as preselection, is a common practice in breeding programs. Preselection can cause bias and accuracy loss in subsequent pedigree-based best linear unbiased prediction (PBLUP). However, the impact of preselection on subsequent single-step genomic BLUP (ssGBLUP) is not completely clear yet. Therefore, in this study, we investigated, across different heritabilities, the impact of intensity and type of preselection on subsequent ssGBLUP evaluation of preselected animals. METHODS: We simulated a nucleus of a breeding programme, in which a recent population of 15 generations was produced with PBLUP-based selection. In generation 15 of this recent population, the parents of the next generation were preselected using several preselection scenarios. These scenarios were combinations of three intensities of preselection (no, high or very high preselection) and three types of preselection (genomic, parental average or random), across three heritabilities (0.5, 0.3 or 0.1). Following each preselection scenario, a subsequent evaluation was performed using ssGBLUP by excluding all the information from the preculled animals, and these genetic evaluations were compared in terms of accuracy and bias for the preselected animals, and in terms of realized genetic gain. RESULTS: Type of preselection affected selection accuracy at both preselection and subsequent evaluation stages. While preselection accuracy decreased, accuracy in the subsequent ssGBLUP evaluation increased, from genomic to parent average to random preselection scenarios. Bias was always negligible. Genetic gain decreased from genomic to parent average to random preselection scenarios. Genetic gain also decreased with increasing intensity of preselection, but only by a maximum of 0.1 additive genetic standard deviation from no to very high genomic preselection scenarios. CONCLUSIONS: Using ssGBLUP in subsequent evaluations prevents preselection bias, irrespective of intensity and type of preselection, and heritability. With GPS, in addition to reducing the phenotyping effort considerably, the use of ssGBLUP in subsequent evaluations realizes only a slightly lower genetic gain than that realized without preselection. This is especially the case for traits that are expensive to measure (e.g. feed intake of individual broiler chickens), and traits for which phenotypes can only be measured at advanced stages of life (e.g. litter size in pigs).

Effects of alleles in crossbred pigs estimated for genomic prediction depend on their breed-of-origin.

BACKGROUND: This study investigated if the allele effect of a given single nucleotide polymorphism (SNP) for crossbred performance in pigs estimated in a genomic prediction model differs depending on its breed-of-origin, and how these are related to estimated effects for purebred performance. RESULTS: SNP-allele substitution effects were estimated for a commonly used SNP panel using a genomic best linear unbiased prediction model with breed-specific partial relationship matrices. Estimated breeding values for purebred and crossbred performance were converted to SNP-allele effects by breed-of-origin. Differences between purebred and crossbred, and between breeds-of-origin were evaluated by comparing percentage of variance explained by genomic regions for back fat thickness (BF), average daily gain (ADG), and residual feed intake (RFI). From ten regions explaining most additive genetic variance for crossbred performance, 1 to 5 regions also appeared in the top ten for purebred performance. The proportion of genetic variance explained by a genomic region and the estimated effect of a haplotype in such a region were different depending upon the breed-of-origin. To illustrate underlying mechanisms, we evaluated the estimated effects across breeds-of-origin for haplotypes associated to the melanocortin 4 receptor (MC4R) gene, and for the MC4Rsnp itself which is a missense mutation with a known effect on BF and ADG. Although estimated allele substitution effects of the MC4Rsnp mutation were very similar across breeds, explained genetic variance of haplotypes associated to the MC4R gene using a SNP panel that does not include the mutation, was considerably lower in one of the breeds where the allele frequency of the mutation was the lowest. CONCLUSIONS: Similar regions explaining similar additive genetic variance were observed across purebred and crossbred performance. Moreover, there was some overlap across breeds-of-origin between regions that explained relatively large proportions of genetic variance for crossbred performance; albeit that the actual proportion of variance deviated across breeds-of-origin. Results based on a missense mutation in MC4R confirmed that even if a causal locus has similar effects across breeds-of-origin, estimated effects and explained variance in its region using a commonly used SNP panel can strongly depend on the allele frequency of the underlying causal mutation.

Genomic prediction based on data from three layer lines: a comparison between linear methods.

BACKGROUND: The prediction accuracy of several linear genomic prediction models, which have previously been used for within-line genomic prediction, was evaluated for multi-line genomic prediction. METHODS: Compared to a conventional BLUP (best linear unbiased prediction) model using pedigree data, we evaluated the following genomic prediction models: genome-enabled BLUP (GBLUP), ridge regression BLUP (RRBLUP), principal component analysis followed by ridge regression (RRPCA), BayesC and Bayesian stochastic search variable selection. Prediction accuracy was measured as the correlation between predicted breeding values and observed phenotypes divided by the square root of the heritability. The data used concerned laying hens with phenotypes for number of eggs in the first production period and known genotypes. The hens were from two closely-related brown layer lines (B1 and B2), and a third distantly-related white layer line (W1). Lines had 1004 to 1023 training animals and 238 to 240 validation animals. Training datasets consisted of animals of either single lines, or a combination of two or all three lines, and had 30 508 to 45 974 segregating single nucleotide polymorphisms. RESULTS: Genomic prediction models yielded 0.13 to 0.16 higher accuracies than pedigree-based BLUP. When excluding the line itself from the training dataset, genomic predictions were generally inaccurate. Use of multiple lines marginally improved prediction accuracy for B2 but did not affect or slightly decreased prediction accuracy for B1 and W1. Differences between models were generally small except for RRPCA which gave considerably higher accuracies for B2. Correlations between genomic predictions from different methods were higher than 0.96 for W1 and higher than 0.88 for B1 and B2. The greater differences between methods for B1 and B2 were probably due to the lower accuracy of predictions for B1 (~0.45) and B2 (~0.40) compared to W1 (~0.76). CONCLUSIONS: Multi-line genomic prediction did not affect or slightly improved prediction accuracy for closely-related lines. For distantly-related lines, multi-line genomic prediction yielded similar or slightly lower accuracies than single-line genomic prediction. Bayesian variable selection and GBLUP generally gave similar accuracies. Overall, RRPCA yielded the greatest accuracies for two lines, suggesting that using PCA helps to alleviate the "n ≪ p" problem in genomic prediction.

Differences across herds with different dairy breeds in daily milk yield based proxies for resilience.

Global sustainability issues such as climate change, biodiversity loss and food security require food systems to become more resource efficient and better embedded in the local environment. This needs a transition towards more diverse, circular and low-input dairy farming systems with animals best suited to the specific environmental conditions. When varying environmental challenges are posed to animals, cows need to become resilient to disturbances they face. This resilience of dairy cows for disturbances can be quantified using sensor features and resilience indicators derived from daily milk yield records. The aim of this study was to explore milk yield based sensor features and resilience indicators for different cattle groups according to their breeds and herds. To this end, we calculated 40 different features to describe the dynamics and variability in milk production of first parity dairy cows. After correction for milk production level, we found that various aspects of the milk yield dynamics, milk yield variability and perturbation characteristics indeed differed across herds and breeds. On farms with a lower breed proportion of Holstein Friesian across cows, there was more variability in the milk yield, but perturbations were less severe upon critical disturbances. Non-Holstein Friesian breeds had a more stable milk production with less (severe) perturbations. These differences can be attributed to differences in genetics, environments, or both. This study demonstrates the potential to use milk yield sensor features and resilience indicators as a tool to quantify how cows cope with more dynamic production conditions and select animals for features that best suit a farms' breeding goal and specific environment.

Accelerated matrix-vector multiplications for matrices involving genotype covariates with applications in genomic prediction.

In the last decade, a number of methods have been suggested to deal with large amounts of genetic data in genomic predictions. Yet, steadily growing population sizes and the suboptimal use of computational resources are pushing the practical application of these approaches to their limits. As an extension to the C/CUDA library miraculix, we have developed tailored solutions for the computation of genotype matrix multiplications which is a critical bottleneck in the empirical evaluation of many statistical models. We demonstrate the benefits of our solutions at the example of single-step models which make repeated use of this kind of multiplication. Targeting modern Nvidia® GPUs as well as a broad range of CPU architectures, our implementation significantly reduces the time required for the estimation of breeding values in large population sizes. miraculix is released under the Apache 2.0 license and is freely available at https://github.com/alexfreudenberg/miraculix.

The impact of direct-maternal genetic correlations on international beef cattle evaluations for Limousin weaning weight.

In beef cattle maternally influenced traits, estimates of direct-maternal genetic correlations (rdm) are usually reported to be negative. In international evaluations, rdm can differ both within countries (rdm_WC) and between countries (rdm_BC). The rdm_BC are difficult to estimate and are assumed to be zero in the current model for international beef cattle evaluations (Interbeef). Our objective was to investigate re-ranking of international estimated breeding values (IEBVs) in international beef cattle evaluations between models that either used estimated values for rdm or assumed them to be 0. Age-adjusted weaning weights and pedigree data were available for Limousin beef cattle from ten European countries. International EBVs were obtained using a multi-trait animal model with countries modeled as different traits. We compared IEBVs from a model that uses estimated rdm_BC (ranging between -0.14 and +0.14) and rdm_WC (between -0.33 and +0.40) with IEBVs obtained either from the current model that assumes rdm_BC to be 0, or from an alternative model that assumes both rdm_BC and rdm_WC to be 0. Direct and maternal IEBVs were compared across those three scenarios for different groups of animals. The ratio of population accuracies from the linear regression method was used to further investigate the impact of rdm on international evaluations, for both the whole set of animals in the evaluation and the domestic ones. Ignoring rdm_BC, i.e., replacing estimated values with 0, resulted in no (rank correlations > 0.99) or limited (between 0.98 and 0.99) re-ranking for direct and maternal IEBVs, respectively. Both rdm_BC and rdm_WC had less impact on direct IEBVs than on maternal IEBVs. Re-ranking of maternal IEBVs decreased with increasing reliability. Ignoring rdm_BC resulted in no re-ranking for sires with IEBVs that might be exchanged across countries and limited re-ranking for the top 100 sires. Using estimated rdm_BC values instead of considering them to be 0 resulted in null to limited increases in population accuracy. Ignoring both rdm_BC and rdm_WC resulted in considerable re-ranking of animals' IEBVs in all groups of animals evaluated. This study showed the limited impact of the current practice of ignoring rdm_BC in international evaluations for Limousin weaning weight, most likely because the estimated rdm_BC was close to 0. We expect that these conclusions can be extended to other traits that have reported rdm values in the range of rdm_WC values for weaning weight in Limousin.

Sparse single-step genomic BLUP in crossbreeding schemes.

The algorithm for proven and young animals (APY) efficiently computes an approximated inverse of the genomic relationship matrix, by dividing genotyped animals in the so-called core and noncore animals. The APY leads to computationally feasible single-step genomic Best Linear Unbiased Prediction (ssGBLUP) with a large number of genotyped animals and was successfully applied to real single-breed or line datasets. This study aimed to assess the quality of genomic estimated breeding values (GEBV) when using the APY (GEBVAPY), in comparison to GEBV when using the directly inverted genomic relationship matrix (GEBVDIRECT), for situations based on crossbreeding schemes, including F1 and F2 crosses, such as the ones for pigs and chickens. Based on simulations of a 3-way crossbreeding program, we compared different approximated inverses of a genomic relationship matrix, by varying the size and the composition of the core group. We showed that GEBVAPY were accurate approximations of GEBVDIRECT for multivariate ssGBLUP involving different breeds and their crosses. GEBVAPY as accurate as GEBVDIRECT were obtained when the core groups included animals from different breed compositions and when the core groups had a size between the numbers of the largest eigenvalues explaining 98% and 99% of the variation in the raw genomic relationship matrix.