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.

The long-term effects of genomic selection: 2. Changes in allele frequencies of causal loci and new mutations.

Genetic selection has been applied for many generations in animal, plant, and experimental populations. Selection changes the allelic architecture of traits to create genetic gain. It remains unknown whether the changes in allelic architecture are different for the recently introduced technique of genomic selection compared to traditional selection methods and whether they depend on the genetic architectures of traits. Here, we investigate the allele frequency changes of old and new causal loci under 50 generations of phenotypic, pedigree, and genomic selection, for a trait controlled by either additive, additive and dominance, or additive, dominance, and epistatic effects. Genomic selection resulted in slightly larger and faster changes in allele frequencies of causal loci than pedigree selection. For each locus, allele frequency change per generation was not only influenced by its statistical additive effect but also to a large extent by the linkage phase with other loci and its allele frequency. Selection fixed a large number of loci, and 5 times more unfavorable alleles became fixed with genomic and pedigree selection than with phenotypic selection. For pedigree selection, this was mainly a result of increased genetic drift, while genetic hitchhiking had a larger effect on genomic selection. When epistasis was present, the average allele frequency change was smaller (∼15% lower), and a lower number of loci became fixed for all selection methods. We conclude that for long-term genetic improvement using genomic selection, it is important to consider hitchhiking and to limit the loss of favorable alleles.

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.

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.

The correlation of substitution effects across populations and generations in the presence of nonadditive functional gene action.

Allele substitution effects at quantitative trait loci (QTL) are part of the basis of quantitative genetics theory and applications such as association analysis and genomic prediction. In the presence of nonadditive functional gene action, substitution effects are not constant across populations. We develop an original approach to model the difference in substitution effects across populations as a first order Taylor series expansion from a "focal" population. This expansion involves the difference in allele frequencies and second-order statistical effects (additive by additive and dominance). The change in allele frequencies is a function of relationships (or genetic distances) across populations. As a result, it is possible to estimate the correlation of substitution effects across two populations using three elements: magnitudes of additive, dominance, and additive by additive variances; relationships (Nei's minimum distances or Fst indexes); and assumed heterozygosities. Similarly, the theory applies as well to distinct generations in a population, in which case the distance across generations is a function of increase of inbreeding. Simulation results confirmed our derivations. Slight biases were observed, depending on the nonadditive mechanism and the reference allele. Our derivations are useful to understand and forecast the possibility of prediction across populations and the similarity of GWAS effects.

Review: optimizing genomic selection for crossbred performance by model improvement and data collection.

Breeding programs aiming to improve the performance of crossbreds may benefit from genomic prediction of crossbred (CB) performance for purebred (PB) selection candidates. In this review, we compared genomic prediction strategies that differed in 1) the genomic prediction model used or 2) the data used in the reference population. We found 27 unique studies, two of which used deterministic simulation, 11 used stochastic simulation, and 14 real data. Differences in accuracy and response to selection between strategies depended on i) the value of the purebred crossbred genetic correlation (rpc), ii) the genetic distance between the parental lines, iii) the size of PB and CB reference populations, and iv) the relatedness of these reference populations to the selection candidates. In studies where a PB reference population was used, the use of a dominance model yielded accuracies that were equal to or higher than those of additive models. When rpc was lower than ~0.8, and was caused mainly by G × E, it was beneficial to create a reference population of PB animals that are tested in a CB environment. In general, the benefit of collecting CB information increased with decreasing rpc. For a given rpc, the benefit of collecting CB information increased with increasing size of the reference populations. Collecting CB information was not beneficial when rpc was higher than ~0.9, especially when the reference populations were small. Collecting only phenotypes of CB animals may slightly improve accuracy and response to selection, but requires that the pedigree is known. It is, therefore, advisable to genotype these CB animals as well. Finally, considering the breed-origin of alleles allows for modeling breed-specific effects in the CB, but this did not always lead to higher accuracies. Our review shows that the differences in accuracy and response to selection between strategies depend on several factors. One of the most important factors is rpc, and we, therefore, recommend to obtain accurate estimates of rpc of all breeding goal traits. Furthermore, knowledge about the importance of components of rpc (i.e., dominance, epistasis, and G × E) can help breeders to decide which model to use, and whether to collect data on animals in a CB environment. Future research should focus on the development of a tool that predicts accuracy and response to selection from scenario specific parameters.

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.

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.

Inbreeding depression across the genome of Dutch Holstein Friesian dairy cattle.

BACKGROUND: Inbreeding depression refers to the decrease in mean performance due to inbreeding. Inbreeding depression is caused by an increase in homozygosity and reduced expression of (on average) favourable dominance effects. Dominance effects and allele frequencies differ across loci, and consequently inbreeding depression is expected to differ along the genome. In this study, we investigated differences in inbreeding depression across the genome of Dutch Holstein Friesian cattle, by estimating dominance effects and effects of regions of homozygosity (ROH). METHODS: Genotype (75 k) and phenotype data of 38,792 cows were used. For nine yield, fertility and udder health traits, GREML models were run to estimate genome-wide inbreeding depression and estimate additive, dominance and ROH variance components. For this purpose, we introduced a ROH-based relationship matrix. Additive, dominance and ROH effects per SNP were obtained through back-solving. In addition, a single SNP GWAS was performed to identify significant additive, dominance or ROH associations. RESULTS: Genome-wide inbreeding depression was observed for all yield, fertility and udder health traits. For example, a 1% increase in genome-wide homozygosity was associated with a decrease in 305-d milk yield of approximately 99 kg. For yield traits only, including dominance and ROH effects in the GREML model resulted in a better fit (P < 0.05) than a model with only additive effects. After correcting for the effect of genome-wide homozygosity, dominance and ROH variance explained less than 1% of the phenotypic variance for all traits. Furthermore, dominance and ROH effects were distributed evenly along the genome. The most notable region with a favourable dominance effect for yield traits was on chromosome 5, but overall few regions with large favourable dominance effects and significant dominance associations were detected. No significant ROH-associations were found. CONCLUSIONS: Inbreeding depression was distributed quite equally along the genome and was well captured by genome-wide homozygosity. These findings suggest that, based on 75 k SNP data, there is little benefit of accounting for region-specific inbreeding depression in selection schemes.

Bayesian neural networks with variable selection for prediction of genotypic values.

BACKGROUND: Estimating the genetic component of a complex phenotype is a complicated problem, mainly because there are many allele effects to estimate from a limited number of phenotypes. In spite of this difficulty, linear methods with variable selection have been able to give good predictions of additive effects of individuals. However, prediction of non-additive genetic effects is challenging with the usual prediction methods. In machine learning, non-additive relations between inputs can be modeled with neural networks. We developed a novel method (NetSparse) that uses Bayesian neural networks with variable selection for the prediction of genotypic values of individuals, including non-additive genetic effects. RESULTS: We simulated several populations with different phenotypic models and compared NetSparse to genomic best linear unbiased prediction (GBLUP), BayesB, their dominance variants, and an additive by additive method. We found that when the number of QTL was relatively small (10 or 100), NetSparse had 2 to 28 percentage points higher accuracy than the reference methods. For scenarios that included dominance or epistatic effects, NetSparse had 0.0 to 3.9 percentage points higher accuracy for predicting phenotypes than the reference methods, except in scenarios with extreme overdominance, for which reference methods that explicitly model dominance had 6 percentage points higher accuracy than NetSparse. CONCLUSIONS: Bayesian neural networks with variable selection are promising for prediction of the genetic component of complex traits in animal breeding, and their performance is robust across different genetic models. However, their large computational costs can hinder their use in practice.

A deterministic equation to predict the accuracy of multi-population genomic prediction with multiple genomic relationship matrices.

BACKGROUND: A multi-population genomic prediction (GP) model in which important pre-selected single nucleotide polymorphisms (SNPs) are differentially weighted (MPMG) has been shown to result in better prediction accuracy than a multi-population, single genomic relationship matrix ([Formula: see text]) GP model (MPSG) in which all SNPs are weighted equally. Our objective was to underpin theoretically the advantages and limits of the MPMG model over the MPSG model, by deriving and validating a deterministic prediction equation for its accuracy. METHODS: Using selection index theory, we derived an equation to predict the accuracy of estimated total genomic values of selection candidates from population [Formula: see text] ([Formula: see text]), when individuals from two populations, [Formula: see text] and [Formula: see text], are combined in the training population and two [Formula: see text], made respectively from pre-selected and remaining SNPs, are fitted simultaneously in MPMG. We used simulations to validate the prediction equation in scenarios that differed in the level of genetic correlation between populations, heritability, and proportion of genetic variance explained by the pre-selected SNPs. Empirical accuracy of the MPMG model in each scenario was calculated and compared to the predicted accuracy from the equation. RESULTS: In general, the derived prediction equation resulted in accurate predictions of [Formula: see text] for the scenarios evaluated. Using the prediction equation, we showed that an important advantage of the MPMG model over the MPSG model is its ability to benefit from the small number of independent chromosome segments ([Formula: see text]) due to the pre-selected SNPs, both within and across populations, whereas for the MPSG model, there is only a single value for [Formula: see text], calculated based on all SNPs, which is very large. However, this advantage is dependent on the pre-selected SNPs that explain some proportion of the total genetic variance for the trait. CONCLUSIONS: We developed an equation that gives insight into why, and under which conditions the MPMG outperforms the MPSG model for GP. The equation can be used as a deterministic tool to assess the potential benefit of combining information from different populations, e.g., different breeds or lines for GP in livestock or plants, or different groups of people based on their ethnic background for prediction of disease risk scores.

Optimizing design to estimate genetic correlations between environments with common environmental effects.

Breeding programs for different species aim to improve performance by testing members of full-sib (FS) and half-sib (HS) families in different environments. When genotypes respond differently to changes in the environment, this is defined as genotype by environment (G × E) interaction. The presence of common environmental effects within families generates covariance between siblings, and these effects should be taken into account when estimating a genetic correlation. Therefore, an optimal design should be established to accurately estimate the genetic correlation between environments in the presence of common environmental effects. We used stochastic simulation to find the optimal population structure using a combination of FS and HS groups with different levels of common environmental effects. Results show that in a population with a constant population size of 2,000 individuals per environment, ignoring common environmental effects when they are present in the population will lead to an upward bias in the estimated genetic correlation of on average 0.3 when the true genetic correlation is 0.5. When no common environmental effects are present in the population, the lowest standard error (SE) of the estimated genetic correlation was observed with a mating ratio of one dam per sire, and 10 offspring per sire per environment. When common environmental effects are present in the population and are included in the model, the lowest SE is obtained with mating ratios of at least 5 dams per sire and with a minimum number of 10 offspring per sire per environment. We recommend that studies that aim to estimate the magnitude of G × E in pigs, chicken, and fish should acknowledge the potential presence of common environmental effects and adjust the mating ratio accordingly.

Breeding Top Genotypes and Accelerating Response to Recurrent Selection by Selecting Parents with Greater Gametic Variance.

Because of variation in linkage phase and heterozygosity among individuals, some individuals produce genetically more variable gametes than others. With the availability of genomic EBVs (GEBVs) or estimates of SNP-effects together with phased genotypes, differences in gametic variability can be quantified by simulating a set of virtual gametes of each selection candidate. Previous results in dairy cattle show that gametic variance can be large. Here, we show that breeders can increase the probability of breeding a top-ranking genotype and response to recurrent selection by selecting parents that produce more variable gametes, using the index [Formula: see text] where [Formula: see text] is the standardized normal truncation point belonging to selected proportion p, and SDgGEBV is the SD of the GEBV of an individual's gametes. Benefits of the index were considerably larger in an ongoing selection program with equilibrium genetic parameters than in an initially unselected population. Superiority of the index over selection on GEBV increased strongly with the magnitude of the [Formula: see text] indicating that benefits of the index may vary considerably among populations. Compared to selection on ordinary GEBV, the probability of breeding a top-ranking individual can be increased by ∼36%, and response to selection by ∼3.6% when selection is strong (P = 0.001) based on values for the Holstein-Friesian dairy cattle population. Two-stage selection, with a preselection on GEBV and a final selection on the index, considerably reduced computational requirements with little loss of benefits. Response to multiple generations of selection and inheritance of the SDgEBV require further study.

The Impact of Non-additive Effects on the Genetic Correlation Between Populations.

Average effects of alleles can show considerable differences between populations. The magnitude of these differences can be measured by the additive genetic correlation between populations ([Formula: see text]). This [Formula: see text] can be lower than one due to the presence of non-additive genetic effects together with differences in allele frequencies between populations. However, the relationship between the nature of non-additive effects, differences in allele frequencies, and the value of [Formula: see text] remains unclear, and was therefore the focus of this study. We simulated genotype data of two populations that have diverged under drift only, or under drift and selection, and we simulated traits where the genetic model and magnitude of non-additive effects were varied. Results showed that larger differences in allele frequencies and larger non-additive effects resulted in lower values of [Formula: see text] In addition, we found that with epistasis, [Formula: see text] decreases with an increase of the number of interactions per locus. For both dominance and epistasis, we found that, when non-additive effects became extremely large, [Formula: see text] had a lower bound that was determined by the type of inter-allelic interaction, and the difference in allele frequencies between populations. Given that dominance variance is usually small, our results show that it is unlikely that true [Formula: see text] values lower than 0.80 are due to dominance effects alone. With realistic levels of epistasis, [Formula: see text] dropped as low as 0.45. These results may contribute to the understanding of differences in genetic expression of complex traits between populations, and may help in explaining the inefficiency of genomic trait prediction across populations.

Correction to: Validation of genomic predictions for body weight in broilers using crossbred information and considering breed-of-origin of alleles.

Following publication of original article [1], we noticed that there was an error: Eq. (3) on page 5 is the genomic relationship matrix that.

Validation of genomic predictions for body weight in broilers using crossbred information and considering breed-of-origin of alleles.

BACKGROUND: Pig and poultry breeding programs aim at improving crossbred (CB) performance. Selection response may be suboptimal if only purebred (PB) performance is used to compute genomic estimated breeding values (GEBV) because the genetic correlation between PB and CB performance ([Formula: see text]) is often lower than 1. Thus, it may be beneficial to use information on both PB and CB performance. In addition, the accuracy of GEBV of PB animals for CB performance may improve when the breed-of-origin of alleles (BOA) is considered in the genomic relationship matrix (GRM). Thus, our aim was to compare scenarios where GEBV are computed and validated by using (1) either CB offspring averages or individual CB records for validation, (2) either a PB or CB reference population, and (3) a GRM that either accounts for or ignores BOA in the CB individuals. For this purpose, we used data on body weight measured at around 7 (BW7) or 35 (BW35) days in PB and CB broiler chickens and evaluated the accuracy of GEBV based on the correlation GEBV with phenotypes in the validation population (validation correlation). RESULTS: With validation on CB offspring averages, the validation correlation of GEBV of PB animals for CB performance was lower with a CB reference population than with a PB reference population for BW35 ([Formula: see text] = 0.96), and about equal for BW7 ([Formula: see text] = 0.80) when BOA was ignored. However, with validation on individual CB records, the validation correlation was higher with a CB reference population for both traits. The use of a GRM that took BOA into account increased the validation correlation for BW7 but reduced it for BW35. CONCLUSIONS: We argue that the benefit of using a CB reference population for genomic prediction of PB animals for CB performance should be assessed either by validation on CB offspring averages, or by validation on individual CB records while using a GRM that accounts for BOA in the CB individuals. With this recommendation in mind, our results show that the accuracy of GEBV of PB animals for CB performance was equal to or higher with a CB reference population than with a PB reference population for a trait with an [Formula: see text] of 0.8, but lower for a trait with an [Formula: see text] of 0.96. In addition, taking BOA into account was beneficial for a trait with an [Formula: see text] of 0.8 but not for a trait with an [Formula: see text] of 0.96.

Estimating the purebred-crossbred genetic correlation of body weight in broiler chickens with pedigree or genomic relationships.

BACKGROUND: In pig and poultry breeding programs, the breeding goal is to improve crossbred (CB) performance, whereas selection in the purebred (PB) lines is often based on PB performance. Thus, response to selection may be suboptimal, because the genetic correlation between PB and CB performance ([Formula: see text]) is generally lower than 1. Accurate estimates of the [Formula: see text] are needed, so that breeders can decide if they should collect data from CB animals. [Formula: see text] can be estimated either from pedigree or genomic relationships, which may produce different results. With genomic relationships, the [Formula: see text] estimate could be improved when relationships between purebred and crossbred animals are based only on the alleles that originate from the PB line of interest. This work presents the first comparison of estimated [Formula: see text] and variance components of body weight in broilers, using pedigree-based or genotype-based models, where the breed-of-origin of alleles was either ignored or considered. We used genotypes and body weight measurements of PB and CB animals that have a common sire line. RESULTS: Our results showed that the [Formula: see text] estimates depended on the relationship matrix used. Estimates were 5 to 25% larger with genotype-based models than with pedigree-based models. Moreover, [Formula: see text] estimates were similar (max. 7% difference) regardless of whether the model considered breed-of-origin of alleles or not. Standard errors of [Formula: see text] estimates were smaller with genotype-based than with pedigree-based methods, and smaller with models that ignored breed-of-origin than with models that considered breed-of-origin. CONCLUSIONS: We conclude that genotype-based models can be useful for estimating [Formula: see text], even when the PB and CB animals that have phenotypes are closely related. Considering breed-of-origin of alleles did not yield different estimates of [Formula: see text], probably because the parental breeds of the CB animals were distantly related.

Required properties for markers used to calculate unbiased estimates of the genetic correlation between populations.

BACKGROUND: Generally, populations differ in terms of environmental and genetic factors, which can create differences in allele substitution effects between populations. Therefore, a single genotype may have different additive genetic values in different populations. The correlation between the two additive genetic values of a single genotype in two populations is known as the additive genetic correlation between populations and thus, can differ from 1. Our objective was to investigate whether differences in linkage disequilibrium (LD) and allele frequencies of markers and causal loci between populations affect the bias of the estimated genetic correlation. We simulated two populations that were separated by 50 generations and differed in LD pattern between markers and causal loci, as measured by the LD-statistic r. We used a high marker density to represent a high consistency of LD between populations, and lower marker densities to represent situations with a lower consistency of LD between populations. Markers and causal loci were selected to have either similar or different allele frequencies in the two populations. RESULTS: Our results show that genetic correlations were underestimated only slightly when the difference in allele frequencies between the two populations was similar for the markers and the causal loci. A lower marker density, representing a lower consistency of LD between populations, had only a minor effect on the underestimation of the genetic correlation. When the difference in allele frequencies between the two populations was not similar for markers and causal loci, genetic correlations were severely underestimated. This bias occurred because the markers did not predict accurately the relationships at causal loci. CONCLUSIONS: For an unbiased estimation of the genetic correlation between populations, the markers should accurately predict the relationships at the causal loci. To achieve this, it is essential that the difference in allele frequencies between populations is similar for markers and causal loci. Our results show that differences in LD phase between causal loci and markers across populations have little effect on the estimated genetic correlation.

Genomic prediction for numerically small breeds, using models with pre-selected and differentially weighted markers.

BACKGROUND: Genomic prediction (GP) accuracy in numerically small breeds is limited by the small size of the reference population. Our objective was to test a multi-breed multiple genomic relationship matrices (GRM) GP model (MBMG) that weighs pre-selected markers separately, uses the remaining markers to explain the remaining genetic variance that can be explained by markers, and weighs information of breeds in the reference population by their genetic correlation with the validation breed. METHODS: Genotype and phenotype data were used on 595 Jersey bulls from New Zealand and 5503 Holstein bulls from the Netherlands, all with deregressed proofs for stature. Different sets of markers were used, containing either pre-selected markers from a meta-genome-wide association analysis on stature, remaining markers or both. We implemented a multi-breed bivariate GREML model in which we fitted either a single multi-breed GRM (MBSG), or two distinct multi-breed GRM (MBMG), one made with pre-selected markers and the other with remaining markers. Accuracies of predicting stature for Jersey individuals using the multi-breed models (Holstein and Jersey combined reference population) was compared to those obtained using either the Jersey (within-breed) or Holstein (across-breed) reference population. All the models were subsequently fitted in the analysis of simulated phenotypes, with a simulated genetic correlation between breeds of 1, 0.5, and 0.25. RESULTS: The MBMG model always gave better prediction accuracies for stature compared to MBSG, within-, and across-breed GP models. For example, with MBSG, accuracies obtained by fitting 48,912 unselected markers (0.43), 357 pre-selected markers (0.38) or a combination of both (0.43), were lower than accuracies obtained by fitting pre-selected and unselected markers in separate GRM in MBMG (0.49). This improvement was further confirmed by results from a simulation study, with MBMG performing on average 23% better than MBSG with all markers fitted. CONCLUSIONS: With the MBMG model, it is possible to use information from numerically large breeds to improve prediction accuracy of numerically small breeds. The superiority of MBMG is mainly due to its ability to use information on pre-selected markers, explain the remaining genetic variance and weigh information from a different breed by the genetic correlation between breeds.

Genomic Prediction Within and Across Biparental Families: Means and Variances of Prediction Accuracy and Usefulness of Deterministic Equations.

A major application of genomic prediction (GP) in plant breeding is the identification of superior inbred lines within families derived from biparental crosses. When models for various traits were trained within related or unrelated biparental families (BPFs), experimental studies found substantial variation in prediction accuracy (PA), but little is known about the underlying factors. We used SNP marker genotypes of inbred lines from either elite germplasm or landraces of maize (Zeamays L.) as parents to generate in silico 300 BPFs of doubled-haploid lines. We analyzed PA within each BPF for 50 simulated polygenic traits, using genomic best linear unbiased prediction (GBLUP) models trained with individuals from either full-sib (FSF), half-sib (HSF), or unrelated families (URF) for various sizes ([Formula: see text]) of the training set and different heritabilities ([Formula: see text] In addition, we modified two deterministic equations for forecasting PA to account for inbreeding and genetic variance unexplained by the training set. Averaged across traits, PA was high within FSF (0.41-0.97) with large variation only for [Formula: see text] and [Formula: see text] [Formula: see text] For HSF and URF, PA was on average ∼40-60% lower and varied substantially among different combinations of BPFs used for model training and prediction as well as different traits. As exemplified by HSF results, PA of across-family GP can be very low if causal variants not segregating in the training set account for a sizeable proportion of the genetic variance among predicted individuals. Deterministic equations accurately forecast the PA expected over many traits, yet cannot capture trait-specific deviations. We conclude that model training within BPFs generally yields stable PA, whereas a high level of uncertainty is encountered in across-family GP. Our study shows the extent of variation in PA that must be at least reckoned with in practice and offers a starting point for the design of training sets composed of multiple BPFs.