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.

Genetic parameters, reciprocal cross differences, and age-related heterosis of egg-laying performance in chickens.

BACKGROUND: Egg-laying performance is economically important in poultry breeding programs. Crossbreeding between indigenous and elite commercial lines to exploit heterosis has been an upward trend in traditional layer breeding for niche markets. The objective of this study was to analyse the genetic background and to estimate the heterosis of longitudinal egg-laying traits in reciprocal crosses between an indigenous Beijing-You and an elite commercial White Leghorn layer line. Egg weights were measured for the first three eggs, monthly from 28 to 76 weeks of age, and at 86 and 100 weeks of age. Egg quality traits were measured at 32, 54, 72, 86, and 100 weeks of age. Egg production traits were measured from the start of lay until 43, 72, and 100 weeks of age. Heritabilities and phenotypic and genetic correlations were estimated. Heterosis was estimated as the percentage difference of performance of a crossbred from that of the parental average. Reciprocal cross differences were estimated as the difference between the reciprocal crossbreds as a percentage of the parental average. RESULTS: Estimates of heritability of egg weights ranged from 0.29 to 0.75. Estimates of genetic correlations between egg weights at different ages ranged from 0.72 to 1.00. Estimates of heritability for cumulative egg numbers until 43, 72, and 100 weeks of age were around 0.15. Estimates of heterosis for egg weight and cumulative egg number increased with age, ranging from 1.0 to 9.0% and from 1.4 to 11.6%, respectively. From 72 to 100 weeks of age, crossbreds produced more eggs per week than the superior parent White Leghorn (3.5 eggs for White Leghorn, 3.8 and 3.9 eggs for crossbreds). Heterosis for eggshell thickness ranged from 2.7 to 6.6% when using Beijing-You as the sire breed. No significant difference between reciprocal crosses was observed for the investigated traits, except for eggshell strength at 54 weeks of age. CONCLUSIONS: The heterosis was substantial for egg weight and cumulative egg number, and increased with age, suggesting that non-additive genetic effects are important in crossbreds between the indigenous and elite breeds. Generally, the crossbreds performed similar to or even outperformed the commercial White Leghorns for egg production persistency.

Predicting the impact of genotype-by-genotype interaction on the purebred-crossbred genetic correlation from phenotype and genotype marker data of parental lines.

BACKGROUND: The genetic correlation between purebred (PB) and crossbred (CB) performances ([Formula: see text]) partially determines the response in CB when selection is on PB performance in the parental lines. An earlier study has derived expressions for an upper and lower bound of [Formula: see text], using the variance components of the parental purebred lines, including e.g. the additive genetic variance in the sire line for the trait expressed in one of the dam lines. How to estimate these variance components is not obvious, because animals from one parental line do not have phenotypes for the trait expressed in the other line. Thus, the aim of this study was to propose and compare three methods for approximating the required variance components. The first two methods are based on (co)variances of genomic estimated breeding values (GEBV) in the line of interest, either accounting for shrinkage (VCGEBV-S) or not (VCGEBV). The third method uses restricted maximum likelihood (REML) estimates directly from univariate and bivariate analyses (VCREML) by ignoring that the variance components should refer to the line of interest, rather than to the line in which the trait is expressed. We validated these methods by comparing the resulting predicted bounds of [Formula: see text] with the [Formula: see text] estimated from PB and CB data for five traits in a three-way cross in pigs. RESULTS: With both VCGEBV and VCREML, the estimated [Formula: see text] (plus or minus one standard error) was between the upper and lower bounds in 14 out of 15 cases. However, the range between the bounds was much smaller with VCREML (0.15-0.22) than with VCGEBV (0.44-0.57). With VCGEBV-S, the estimated [Formula: see text] was between the upper and lower bounds in only six out of 15 cases, with the bounds ranging from 0.21 to 0.44. CONCLUSIONS: We conclude that using REML estimates of variance components within and between parental lines to predict the bounds of [Formula: see text] resulted in better predictions than methods based on GEBV. Thus, we recommend that the studies that estimate [Formula: see text] with genotype data also report estimated genetic variance components within and between the parental lines.

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.

Estimation of dam line composition of 3-way crossbred animals using genomic information.

BACKGROUND: In genomic prediction including data of 3- or 4-way crossbred animals, line composition is usually fitted as a regression on expected line proportions, which are 0.5, 0.25 and 0.25, respectively, for 3-way crossbred animals. However, actual line proportions for the dam lines can vary between ~ 0.1 and 0.4, and ignoring this variation may affect the genomic estimated breeding values of purebred selection candidates. Our aim was to validate a proposed gold standard to evaluate different approaches for estimating line proportions using simulated data, and to subsequently use this in actual 3-way crossbred broiler data to evaluate several other methods. RESULTS: Analysis of simulated data confirmed that line proportions computed from assigned breed-origin-of-alleles (BOA) provide a very accurate gold standard, even if the parental lines are closely related. Alternative investigated methods were linear regression of genotypes on line-specific allele frequencies, maximum likelihood estimation using the program ADMIXTURE, and the genomic relationship of crossbred animals with their maternal grandparents. The results from the simulated data showed that the genomic relationship with the maternal grandparent was most accurate, and least affected by closer relationships between the dam lines. Linear regression and ADMIXTURE performed similarly for unrelated lines, but their accuracy dropped considerably when the dam lines were more closely related. In almost all cases, estimates improved after adjusting them to ensure that the sum of dam line contributions within animals was equal to 0.5, and within dam line and across animals the average was equal to 0.25. Results from the broiler data were much more similar between methods. In both cases, stringent linkage disequilibrium pruning of genotype data led to a relatively low accuracy of predicted line proportions, due to the loss of too many single nucleotide polymorphisms. CONCLUSIONS: With relatively unrelated parental lines as typical in crosses in pigs and poultry, linear regression of crossbred genotypes on line-specific allele frequencies and ADMIXTURE are very competitive methods. Thus, linear regression may be the method of choice, as it does not require genotypes of grandparents, is computationally very efficient, and easily implemented and adapted for considering the specific nature of the crossbred animals analysed.

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.

The long-term effects of genomic selection: 1. Response to selection, additive genetic variance, and genetic architecture.

BACKGROUND: Genomic selection has revolutionized genetic improvement in animals and plants, but little is known about its long-term effects. Here, we investigated the long-term effects of genomic selection on response to selection, genetic variance, and the genetic architecture of traits using stochastic simulations. We defined the genetic architecture as the set of causal loci underlying each trait, their allele frequencies, and their statistical additive effects. We simulated a livestock population under 50 generations of phenotypic, pedigree, or genomic selection for a single trait, controlled by either only additive, additive and dominance, or additive, dominance, and epistatic effects. The simulated epistasis was based on yeast data. RESULTS: Short-term response was always greatest with genomic selection, while response after 50 generations was greater with phenotypic selection than with genomic selection when epistasis was present, and was always greater than with pedigree selection. This was mainly because loss of genetic variance and of segregating loci was much greater with genomic and pedigree selection than with phenotypic selection. Compared to pedigree selection, selection response was always greater with genomic selection. Pedigree and genomic selection lost a similar amount of genetic variance after 50 generations of selection, but genomic selection maintained more segregating loci, which on average had lower minor allele frequencies than with pedigree selection. Based on this result, genomic selection is expected to better maintain genetic gain after 50 generations than pedigree selection. The amount of change in the genetic architecture of traits was considerable across generations and was similar for genomic and pedigree selection, but slightly less for phenotypic selection. Presence of epistasis resulted in smaller changes in allele frequencies and less fixation of causal loci, but resulted in substantial changes in statistical additive effects across generations. CONCLUSIONS: Our results show that genomic selection outperforms pedigree selection in terms of long-term genetic gain, but results in a similar reduction of genetic variance. The genetic architecture of traits changed considerably across generations, especially under selection and when non-additive effects were present. In conclusion, non-additive effects had a substantial impact on the accuracy of selection and long-term response to selection, especially when selection was accurate.

Comparison of linkage disequilibrium estimated from genotypes versus haplotypes for crossbred populations.

BACKGROUND: Linkage disequilibrium (LD) is commonly measured based on the squared coefficient of correlation [Formula: see text] between the alleles at two loci that are carried by haplotypes. LD can also be estimated as the [Formula: see text] between unphased genotype dosage at two loci when the allele frequencies and inbreeding coefficients at both loci are identical for the parental lines. Here, we investigated whether [Formula: see text] for a crossbred population (F1) can be estimated using genotype data. The parental lines of the crossbred (F1) can be purebred or crossbred. METHODS: We approached this by first showing that inbreeding coefficients for an F1 crossbred population are negative, and typically differ in size between loci. Then, we proved that the expected [Formula: see text] computed from unphased genotype data is expected to be identical to the [Formula: see text] computed from haplotype data for an F1 crossbred population, regardless of the inbreeding coefficients at the two loci. Finally, we investigated the bias and precision of the [Formula: see text] estimated using unphased genotype versus haplotype data in stochastic simulation. RESULTS: Our findings show that estimates of [Formula: see text] based on haplotype and unphased genotype data are both unbiased for different combinations of allele frequencies, sample sizes (900, 1800, and 2700), and levels of LD. In general, for any allele frequency combination and [Formula: see text] value scenarios considered, and for both methods to estimate [Formula: see text], the precision of the estimates increased, and the bias of the estimates decreased as sample size increased, indicating that both estimators are consistent. For a given scenario, the [Formula: see text] estimates using haplotype data were more precise and less biased using haplotype data than using unphased genotype data. As sample size increased, the difference in precision and biasedness between the [Formula: see text] estimates using haplotype data and unphased genotype data decreased. CONCLUSIONS: Our theoretical derivations showed that estimates of LD between loci based on unphased genotypes and haplotypes in F1 crossbreds have identical expectations. Based on our simulation results, we conclude that the LD for an F1 crossbred population can be accurately estimated from unphased genotype data. The results also apply for other crosses (F2, F3, Fn, BC1, BC2, and BCn), as long as (selected) individuals from the two parental lines mate randomly.

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.

Predicting the purebred-crossbred genetic correlation from the genetic variance components in the parental lines.

BACKGROUND: The genetic correlation between purebred and crossbred performance ([Formula: see text]) is an important parameter in pig and poultry breeding, because response to selection in crossbred performance depends on the value of [Formula: see text] when selection is based on purebred (PB) performance. The value of [Formula: see text] can be substantially lower than 1, which is partly due to differences in allele frequencies between parental lines when non-additive genetic effects are present. This relationship between [Formula: see text] and parental allele frequencies suggests that [Formula: see text] can be expressed as a function of genetic parameters for the trait in the parental lines. In this study, we derived expressions for [Formula: see text] based on genetic variances within, and the genetic covariance between parental lines. It is important to note that the variance components used in our expressions are not the components that are typically estimated in empirical data. The expressions were derived for a genetic model with additive and dominance effects (D), and additive and epistatic additive-by-additive effects (EAA). We validated our expressions using simulations of purebred parental lines and their crosses, where the parental lines were either selected or not. Finally, using these simulations, we investigated the value of [Formula: see text] for genetic models with both dominance and epistasis or with other types of epistasis, for which expressions could not be derived. RESULTS: Our simulations show that when non-additive effects are present, [Formula: see text] decreases with increasing differences in allele frequencies between the parental lines. Genetic models that involve dominance result in lower values of [Formula: see text] than genetic models that involve epistasis only. Using information of parental lines only, our expressions provide exact estimates of [Formula: see text] for models D and EAA, and accurate upper and lower bounds of [Formula: see text] for two other genetic models. CONCLUSION: This work lays the foundation to enable estimation of [Formula: see text] from information collected in PB parental lines only.

Convergence behavior of single-step GBLUP and SNPBLUP for different termination criteria.

BACKGROUND: The preconditioned conjugate gradient (PCG) method is the current method of choice for iterative solving of genetic evaluations. The relative difference between two successive iterates and the relative residual of the system of equations are usually chosen as a termination criterion for the PCG method in animal breeding. However, our initial analyses showed that these two commonly used termination criteria may report that a PCG method applied to a single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) is not converged yet, whereas the solutions are accurate enough for practical use. Therefore, the aim of this study was to propose two termination criteria that have been (partly) developed in other fields, but are new in animal breeding, and to compare their behavior to that of the two termination criteria widely used in animal breeding for the PCG method applied to ssSNPBLUP. The convergence patterns of ssSNPBLUP were also compared to the convergence patterns of single-step genomic BLUP (ssGBLUP). RESULTS: Building upon previous work, we propose two termination criteria that take the properties of the system of equations into account. These two termination criteria are directly related to the relative error of the iterates with respect to the true solutions. Based on pig and dairy cattle datasets, we show that the preconditioned coefficient matrices of ssSNPBLUP and ssGBLUP have similar properties when using a second-level preconditioner for ssSNPBLUP. Therefore, the PCG method applied to ssSNPBLUP and ssGBLUP converged similarly based on the relative error of the iterates with respect to the true solutions. This similar convergence behavior between ssSNPBLUP and ssGBLUP was observed for both proposed termination criteria. This was, however, not the case for the termination criterion defined as the relative residual when applied to the dairy cattle evaluations. CONCLUSION: Our results showed that the PCG method can converge similarly when applied to ssSNPBLUP and to ssGBLUP. The two proposed termination criteria always depicted these similar convergence behaviors, and we recommend them for comparing convergence properties of different models and for routine evaluations.

Technical note: Genetic groups in single-step single nucleotide polymorphism best linear unbiased predictor.

Genetic groups, also called unknown or phantom parents groups, are often used in dairy cattle genetic evaluations to account for selection that cannot be accounted for by known genetic relationships. With the advent of genomic evaluations, the theory of genetic groups was extended to the so-called single-step genomic BLUP (ssGBLUP). In short, genetic groups can be fitted in ssGBLUP through regression effects, or by including them in the pedigree and computing the adequate combined pedigree and genomic relationship matrix. In this study, we applied the so-called Quaas and Pollak transformation to a system of equations for single-step SNP BLUP (ssSNPBLUP), such that genetic groups can thereafter be included in the pedigree. The example in this study showed that including the genetic groups in the pedigree for ssSNPBLUP allowed reduced memory burden and computational costs in comparison to genetic groups fitted as covariates.

Factors affecting accuracy of estimated effective number of chromosome segments for numerically small breeds.

For numerically small breeds, obtaining a sufficiently large breed-specific reference population for genomic prediction is challenging or simply not possible, but may be overcome by adding individuals from another breed. To prioritize among available breeds, the effective number of chromosome segments (Me ) can be used as an indicator of relatedness between individuals from different breeds. The Me is also an important parameter in determining the accuracy of genomic prediction. The Me can be estimated both within a population and between two populations or breeds, as the reciprocal of the variance of genomic relationships. However, the threshold for number of individuals needed to accurately estimate within or between populations Me is currently unknown. It is also unknown if a discrepancy in number of genotyped individuals in two breeds affects the estimates of Me between populations. In this study, we conducted a simulation that mimics current domestic cattle populations in order to investigate how estimated Me is affected by number of genotyped individuals, single-nucleotide polymorphism (SNP) density and pedigree availability. Our results show that a small sample of 10 genotyped individuals may result in substantial over or underestimation of Me . While estimates of within population Me were hardly affected by SNP density, between population Me values were highly dependent on the number of available SNPs, with higher SNP densities being able to detect more independent chromosome segments. When subtracting pedigree from genomic relationships before computing Me , estimates of within population Me were three to four times higher than estimates with genotypes only; however, between Me estimates remained the same. For accurate estimation of within and between population Me , at least 50 individuals should be genotyped per population. Estimates of within Me were highly affected by whether pedigree was used or not. For within Me , even the smallest SNP density (~11k) resulted in accurate representation of family relationships in the population; however, for between Me , many more markers are needed to capture all independent segments.

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.

Optimizing genomic reference populations to improve crossbred performance.

BACKGROUND: In pig and poultry breeding, the objective is to improve the performance of crossbred production animals, while selection takes place in the purebred parent lines. One way to achieve this is to use genomic prediction with a crossbred reference population. A crossbred reference population benefits from expressing the breeding goal trait but suffers from a lower genetic relatedness with the purebred selection candidates than a purebred reference population. Our aim was to investigate the benefit of using a crossbred reference population for genomic prediction of crossbred performance for: (1) different levels of relatedness between the crossbred reference population and purebred selection candidates, (2) different levels of the purebred-crossbred correlation, and (3) different reference population sizes. We simulated a crossbred breeding program with 0, 1 or 2 multiplication steps to generate the crossbreds, and compared the accuracy of genomic prediction of crossbred performance in one generation using either a purebred or a crossbred reference population. For each scenario, we investigated the empirical accuracy based on simulation and the predicted accuracy based on the estimated effective number of independent chromosome segments between the reference animals and selection candidates. RESULTS: When the purebred-crossbred correlation was 0.75, the accuracy was highest for a two-way crossbred reference population but similar for purebred and four-way crossbred reference populations, for all reference population sizes. When the purebred-crossbred correlation was 0.5, a purebred reference population always resulted in the lowest accuracy. Among the different crossbred reference populations, the accuracy was slightly lower when more multiplication steps were used to create the crossbreds. In general, the benefit of crossbred reference populations increased when the size of the reference population increased. All predicted accuracies overestimated their corresponding empirical accuracies, but the different scenarios were ranked accurately when the reference population was large. CONCLUSIONS: The benefit of a crossbred reference population becomes larger when the crossbred population is more related to the purebred selection candidates, when the purebred-crossbred correlation is lower, and when the reference population is larger. The purebred-crossbred correlation and reference population size interact with each other with respect to their impact on the accuracy of genomic estimated breeding values.

Computational strategies for the preconditioned conjugate gradient method applied to ssSNPBLUP, with an application to a multivariate maternal model.

BACKGROUND: The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) is one of the single-step evaluations that enable a simultaneous analysis of phenotypic and pedigree information of genotyped and non-genotyped animals with a large number of genotypes. The aim of this study was to develop and illustrate several computational strategies to efficiently solve different ssSNPBLUP systems with a large number of genotypes on current computers. RESULTS: The different developed strategies were based on simplified computations of some terms of the preconditioner, and on splitting the coefficient matrix of the different ssSNPBLUP systems into multiple parts to perform its multiplication by a vector more efficiently. Some matrices were computed explicitly and stored in memory (e.g. the inverse of the pedigree relationship matrix), or were stored using a compressed form (e.g. the Plink 1 binary form for the genotype matrix), to permit the use of efficient parallel procedures while limiting the required amount of memory. The developed strategies were tested on a bivariate genetic evaluation for livability of calves for the Netherlands and the Flemish region in Belgium. There were 29,885,286 animals in the pedigree, 25,184,654 calf records, and 131,189 genotyped animals. The ssSNPBLUP system required around 18 GB Random Access Memory and 12 h to be solved with the most performing implementation. CONCLUSIONS: Based on our proposed approaches and results, we showed that ssSNPBLUP provides a feasible approach in terms of memory and time requirements to estimate genomic breeding values using current computers.

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).

Impact of sub-setting the data of the main Limousin beef cattle population on the estimates of across-country genetic correlations.

BACKGROUND: Cattle international genetic evaluations allow the comparison of estimated breeding values (EBV) across different environments, i.e. countries. For international evaluations, across-country genetic correlations (rg) need to be estimated. However, lack of convergence of the estimated parameters and high standard errors of the rg are often experienced for beef cattle populations due to limited across-country genetic connections. Furthermore, using all available genetic connections to estimate rg is prohibitive due to computational constraints, thus sub-setting the data is necessary. Our objective was to investigate and compare the impact of strategies of data sub-setting on estimated across-country rg and their computational requirements. METHODS: Phenotype and pedigree information for age-adjusted weaning weight was available for ten European countries and 3,128,338 Limousin beef cattle males and females. Using a Monte Carlo based expectation-maximization restricted maximum likelihood (MC EM REML) methodology, we estimated across-country rg by using a multi-trait animal model where countries are modelled as different correlated traits. Values of rg were estimated using the full data and four different sub-setting strategies that aimed at selecting the most connected herds from the largest population. RESULTS: Using all available data, direct and maternal rg (standard errors in parentheses) were on average equal to 0.79 (0.14) and 0.71 (0.19), respectively. Direct-maternal within-country and between-country rg were on average equal to - 0.12 (0.09) and 0.00 (0.14), respectively. Data sub-setting scenarios gave similar results: on average, estimated rg were smaller compared to using all data for direct (0.02) and maternal (0.05) genetic effects. The largest differences were obtained for the direct-maternal within-country and between-country rg, which were, on average 0.13 and 0.12 smaller compared to values obtained by using all data. Standard errors always increased when reducing the data, by 0.02 to 0.06, on average. The proposed sub-setting strategies reduced the required computing time up to 22% compared to using all data. CONCLUSIONS: Estimating all 120 across-country rg that are required for beef cattle international evaluations, using a multi-trait MC EM REML approach, is feasible but involves long computing time. We propose four strategies to reduce computational requirements while keeping a multi-trait estimation approach. In all scenarios with data sub-setting, the estimated rg were consistently smaller (mainly for direct-maternal rg) and had larger standard errors.