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Background: Cross-validation techniques in genetic evaluations encounter limitations due to the unobservable nature of breeding values and the challenge of validating estimated breeding values (EBVs) against pre-corrected phenotypes, challenges which the Linear Regression (LR) method addresses as an alternative. Furthermore, beef cattle genetic evaluation programs confront challenges with connectedness among herds and pedigree errors. The objective of this work was to evaluate the LR method's performance under pedigree errors and weak connectedness typical in beef cattle genetic evaluations, through simulation., Methods: We simulated a beef cattle population resembling the Argentinean Brangus, including a quantitative trait selected over six pseudo-generations with a heritability of 0.4. This study considered various scenarios, including: 25% and 40% pedigree errors (PE-25 and PE-40), weak and strong connectedness among herds (WCO and SCO, respectively), and a benchmark scenario (BEN) with complete pedigree and optimal herd connections., Results: Over six pseudo-generations of selection, genetic gain was simulated to be under- and over-estimated in PE-40 and WCO, respectively, contrary to the BEN scenario which was unbiased. In genetic evaluations with PE-25 and PE-40, true biases of - 0.13 and - 0.18 genetic standard deviations were simulated, respectively. In the BEN scenario, the LR method accurately estimated bias, however, in PE-25 and PE-40 scenarios, it overestimated biases by 0.17 and 0.25 genetic standard deviations, respectively. In herds facing WCO, significant true bias due to confounding environmental and genetic effects was simulated, and the corresponding LR statistic failed to accurately estimate the magnitude and direction of this bias. On average, true dispersion values were close to one for BEN, PE-40, SCO and WCO, showing no significant inflation or deflation, and the values were accurately estimated by LR. However, PE-25 exhibited inflation of EBVs and was slightly underestimated by LR. Accuracies and reliabilities showed good agreement between true and LR estimated values for the scenarios evaluated., Conclusions: The LR method demonstrated limitations in identifying biases induced by incomplete pedigrees, including scenarios with as much as 40% pedigree errors, or lack of connectedness, but it was effective in assessing dispersion, and population accuracies and reliabilities even in the challenging scenarios addressed., Competing Interests: Declarations. Ethics approval and consent to participate: Not applicable. Consent for publication: Not applicable. Competing interests: The authors declare that they have no competing interests., (© 2024. The Author(s).)

In pig breeding, environmental challenges can affect the welfare and productivity of animals. Resilient animals have the capacity to be minimally affected by these environmental challenges. Understanding the genetic basis of sensitivity to these environmental challenges is crucial for selecting more resilient animals, thereby enhancing welfare and productivity. The aims of this study were to: (1) estimate the probability of the occurrence of an unrecorded environmental challenge at a given day using daily feed intake (DFI) data, and (2) evaluate the genetic determinism of environmental sensitivity in three pig lines bred in real selection conditions. Data comprised of 100,799, 186,247, and 304,826 DFI records from 1,618, 2,517, and 3,788 Landrace (LA), Large White (LW) and Piétrain (PI) male pigs, respectively. The pedigree included 3,730, 5,649, and 9,293 animals for LA, LW, and PI, respectively. The probabilities of the occurrence of an unrecorded environmental challenge at a given day were estimated via a mixture model. The probabilities (p) of being "high CV days" were then taken as reference and used in genetic analysis as an environmental descriptor to describe the environment. DFI records were analysed using two linear models: a linear reaction norm animal model (RNAM) and the animal model. (Co)variance components were estimated using average-information restricted maximum likelihood (AI-REML). The means of the probabilities of the occurrence of an environmental challenge for LA, LW, and PI were 0.24, 0.10, and 0.22, respectively, indicating that the probability of an environmental challenge was low for most of the days. The genetic correlations between the intercept and the slope obtained from the RNAM for LA, LW, PI were -0.52, 0.06, and -0.36, respectively. These findings suggest that selecting hypothetically for decreased DFI in non-stressful conditions would result in pigs with increased DFI in stressful conditions in the LA and PI lines, whereas it would have a minor impact on the environmental sensitivity of LW. The proportion of resilient animals for LA, LW, and PI was 75.0, 74.2, and 72.2%, respectively, implying that most of the animals were resilient. The study demonstrated that the slope of DFI is heritable and can effectively be used as an indicator of sensitivity to environmental challenges. These results are valuable in improving the resilience of livestock species to environmental challenges through genetic selection., (© The Author(s) 2024. Published by Oxford University Press on behalf of the American Society of Animal Science.)

The genetic trend of milk yield for 4 French dairy sheep breeds (Lacaune, Basco-Béarnaise, Manech Tête Noire, and Manech Tête Rousse) was partitioned in Mendelian sampling trends by categories of animals defined by sex and by selection pathways. Five categories were defined, as follows: (1) artificial insemination (AI) males (after progeny testing), (2) males discarded after progeny testing, (3) natural mating males, (4) dams of males, and (5) dams of females. Dams of males and AI males were the most important sources of genetic progress, as observed in the decomposition in Mendelian sampling trends. The yearly contributions were more erratic for AI males than for dams of males, as AI males are averaged across a smaller number of individuals. Natural mating males and discarded males did not contribute to the trend in terms of Mendelian sampling, as their estimated Mendelian sampling term is either null (natural mating males) or negative (discarded males). Overall, in terms of Mendelian sampling, females contributed more than males to the total genetic gain, and we interpret that this is because females constitute a larger pool of genetic diversity. In addition, we computed long-term contributions from each individual to the following pseudo-generations (one pseudo-generation spanning 4 years). With this information, we studied the selection decisions (selected or not selected) for females, and the contributions to the following generations. Mendelian sampling was more important than parent average to determine the selection of individuals and their long-term contributions. Long-term contributions were greater for AI males (with larger progeny sizes than females) and in Basco-Béarnaise than in Lacaune (with the latter being a larger population)., (The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).)

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., Competing Interests: Conflicts of interest: The authors declare no conflict of interest., (© The Author(s) 2023. Published by Oxford University Press on behalf of The Genetics Society of America.)

Interpopulation improvement for crosses of close populations in crops and livestock depends on the amount of heterosis and the amount of variance of dominance deviations in the hybrids. It has been intuited that the further the distance between populations, the lower the amount of dominance variation and the higher the heterosis. Although experience in speciation and interspecific crosses shows, however, that this is not the case when populations are so distant-here we confine ourselves to the case of not-too-distant populations typical in crops and livestock. We present equations that relate the distance between 2 populations, expressed as Nei's genetic distance or as correlation of allele frequencies, quadratically to the amount of dominance deviations across all possible crosses and linearly to the expected heterosis averaging all possible crosses. The amount of variation of dominance deviations decreases with genetic distance until the point where allele frequencies are uncorrelated, and then increases for negatively correlated frequencies. Heterosis always increases with Nei's genetic distance. These expressions match well and complete previous theoretical and empirical findings. In practice, and for close enough populations, they mean that unless frequencies are negatively correlated, selection for hybrids will be more efficient when populations are distant., Competing Interests: Conflicts of interest The author(s) declare no conflict of interest., (© The Author(s) 2023. Published by Oxford University Press on behalf of The Genetics Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Background: At the beginning of genomic selection, some Chinese companies genotyped pigs with different single nucleotide polymorphism (SNP) arrays. The obtained genomic data are then combined and to do this, several imputation strategies have been developed. Usually, only additive genetic effects are considered in genetic evaluations. However, dominance effects that may be important for some traits can be fitted in a mixed linear model as either 'classical' or 'genotypic' dominance effects. Their influence on genomic evaluation has rarely been studied. Thus, the objectives of this study were to use a dataset from Canadian Yorkshire pigs to (1) compare different strategies to combine data from two SNP arrays (Affymetrix 55K and Illumina 42K) and identify the most appropriate strategy for genomic evaluation and (2) evaluate the impact of dominance effects (classical' and 'genotypic') and inbreeding depression effects on genomic predictive abilities for average daily gain (ADG), backfat thickness (BF), loin muscle depth (LMD), days to 100 kg (AGE100), and the total number of piglets born (TNB) at first parity., Results: The reliabilities obtained with the additive genomic models showed that the strategy used to combine data from two SNP arrays had little impact on genomic evaluations. Models with classical or genotypic dominance effect showed similar predictive abilities for all traits. For ADG, BF, LMD, and AGE100, dominance effects accounted for a small proportion (2 to 11%) of the total genetic variance, whereas for TNB, dominance effects accounted for 11 to 20%. For all traits, the predictive abilities of the models increased significantly when genomic inbreeding depression effects were included in the model. However, the inclusion of dominance effects did not change the predictive ability for any trait except for TNB., Conclusions: Our study shows that it is feasible to combine data from different SNP arrays for genomic evaluation, and that all combination methods result in similar accuracies. Regardless of how dominance effects are fitted in the genomic model, there is no impact on genetic evaluation. Models including inbreeding depression effects outperform a model with only additive effects, even if the trait is not strongly affected by dominant genes., (© 2022. The Author(s).)

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., (© 2022. The Author(s).)

Background: Multiple breed evaluation using genomic prediction includes the use of data from multiple populations, or from parental breeds and crosses, and is expected to lead to better genomic predictions. Increased complexity comes from the need to fit non-additive effects such as dominance and/or genotype-by-environment interactions. In these models, marker effects (and breeding values) are modelled as correlated between breeds, which leads to multiple trait formulations that are based either on markers [single nucleotide polymorphism best linear unbiased prediction (SNP-BLUP)] or on individuals [genomic(G)BLUP)]. As an alternative, we propose the use of generalized least squares (GLS) followed by backsolving of marker effects using selection index (SI) theory., Results: All investigated options have advantages and inconveniences. The SNP-BLUP yields marker effects directly, which are useful for indirect prediction and for planned matings, but is very large in number of equations and is structured in dense and sparse blocks that do not allow for simple solving. GBLUP uses a multiple trait formulation and is very general, but results in many equations that are not used, which increase memory needs, and is also structured in dense and sparse blocks. An alternative formulation of GBLUP is more compact but requires tailored programming. The alternative of solving by GLS + SI is the least consuming, both in number of operations and in memory, and it uses only single dense blocks. However, it requires dedicated programming. Computational complexity problems are exacerbated when more than additive effects are fitted, e.g. dominance effects or genotype x environment interactions., Conclusions: As multi-breed predictions become more frequent and non-additive effects are more often included, standard equations for genomic prediction based on Henderson's mixed model equations become less practical and may need to be replaced by more efficient (although less general) approaches such as the GLS + SI approach proposed here., (© 2022. The Author(s).)

The use of genomic information for prediction of future phenotypes or breeding values for the candidates to selection has become a standard over the last decade. However, most procedures for genomic prediction only consider the additive (or substitution) effects associated with polymorphic markers. Nevertheless, the implementation of models that consider nonadditive genetic variation may be interesting because they (1) may increase the ability of prediction, (2) can be used to define mate allocation procedures in plant and animal breeding schemes, and (3) can be used to benefit from nonadditive genetic variation in crossbreeding or purebred breeding schemes. This study reviews the available methods for incorporating nonadditive effects into genomic prediction procedures and their potential applications in predicting future phenotypic performance, mate allocation, and crossbred and purebred selection. Finally, a brief outline of some future research lines is also proposed., (© 2022. The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature.)

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., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America.)

Inbreeding depression reduces the mean phenotypic value of important traits in livestock populations. The goal of this work was to estimate the level of inbreeding and inbreeding depression for growth and reproductive traits in Argentinean Brangus cattle, in order to obtain a diagnosis and monitor breed management. Data comprised 359,257 (from which 1,990 were genotyped for 40,678 single nucleotide polymorphisms [SNPs]) animals with phenotypic records for at least one of three growth traits: birth weight (BW), weaning weight (WW), and finishing weight (FW). For scrotal circumference (SC), 52,399 phenotypic records (of which 256 had genotype) were available. There were 530,938 animals in pedigree. Three methods to estimate inbreeding coefficients were used. Pedigree-based inbreeding coefficients were estimated accounting for missing parents. Inbreeding coefficients combining genotyped and nongenotyped animal information were also computed from matrix H of the single-step approach. Genomic inbreeding coefficients were estimated using homozygous segments obtained from a Hidden Markov model (HMM) approach. Inbreeding depression was estimated from the regression of the phenotype on inbreeding coefficients in a multiple-trait mixed model framework, either for the whole dataset or for the dataset of genotyped animals. All traits were unfavorably affected by inbreeding depression. A 10% increase in pedigree-based or combined inbreeding would result in a reduction of 0.34 to 0.39 kg in BW, 2.77 to 3.28 kg in WW, and 0.23 cm in SC. For FW, a 10% increase in pedigree-based, genomic, or combined inbreeding would result in a decrease of 8.05 to 11.57 kg. Genomic inbreeding based on the HMM was able to capture inbreeding depression, even in such a compressed genotyped dataset., (© The Author(s) 2021. Published by Oxford University Press on behalf of the American Society of Animal Science. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

We revisited, in a genomic context, the theory of hybrid genetic evaluation models of hybrid crosses of pure lines, as the current practice is largely based on infinitesimal model assumptions. Expressions for covariances between hybrids due to additive substitution effects and dominance and epistatic deviations were analytically derived. Using dense markers in a GBLUP analysis, it is possible to split specific combining ability into dominance and across-groups epistatic deviations, and to split general combining ability (GCA) into within-line additive effects and within-line additive by additive (and higher order) epistatic deviations. We analyzed a publicly available maize data set of Dent × Flint hybrids using our new model (called GCA-model) up to additive by additive epistasis. To model higher order interactions within GCAs, we also fitted "residual genetic" line effects. Our new GCA-model was compared with another genomic model which assumes a uniquely defined effect of genes across origins. Most variation in hybrids is accounted by GCA. Variances due to dominance and epistasis have similar magnitudes. Models based on defining effects either differently or identically across heterotic groups resulted in similar predictive abilities for hybrids. The currently used model inflates the estimated additive genetic variance. This is not important for hybrid predictions but has consequences for the breeding scheme-e.g. overestimation of the genetic gain within heterotic group. Therefore, we recommend using GCA-model, which is appropriate for genomic prediction and variance component estimation in hybrid crops using genomic data, and whose results can be practically interpreted and used for breeding purposes., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America.)

Inbreeding depression is associated with a decrease in performance and fitness of the animals. The goal of this study was to evaluate pedigree-based and genomic methods to estimate the level of inbreeding and inbreeding depression for 3 semen traits (volume, concentration, and motility score) in the Basco-Béarnaise sheep breed. Data comprised 16,196 (or 15,071) phenotypic records from 620 rams (of which 533 rams had genotypes of 36,464 SNPs). The pedigree included 8,266 animals, composed of the 620 rams and their ancestors. The number of equivalent complete generations for the 620 rams was 7.04. Inbreeding coefficients were estimated using genomic and pedigree-based information. Genomic inbreeding coefficients were estimated from individual SNP and using segments of homozygous SNP (runs of homozygosity, ROH). Short ROH are of old origin, whereas long ROH are due to recent inbreeding. Considering that the equivalent number of generations in Basco-Béarnaise was 6, inbreeding coefficients for ROH with a length >4 Mb refer to all (recent + old) inbreeding, those with a length >17 Mb correspond to recent inbreeding, and the difference between them indicates old inbreeding. Pedigree-based inbreeding coefficients were also estimated classically, or accounting for nonzero relationships for unknown parents, or including metafounder relationships (estimated using markers) to account for missing pedigree information. Finally, inbreeding coefficients combining genotyped and nongenotyped animal information were computed from matrix H of the single-step approach, also including metafounders. Inbreeding depression was estimated differently depending on the approach used to compute inbreeding coefficients. These 8 estimators of inbreeding coefficients were included as covariates in different animal models. No inbreeding depression was detected for sperm volume or sperm concentration. Inbreeding depression was significant for the motility of spermatozoa. The effect of old and recent inbreeding on motility was null and negative, respectively, demonstrating the existence of purging by selection of deleterious recessive alleles affecting motility. A 10% increase in inbreeding would result in a reduction in mean motility ranging between 0.09 and 0.22 points in the score (from 0 to 5). Motility is unfavorably affected by increasing recent inbreeding but the impact is very small. Runs of homozygosity and metafounders allow us to accurately estimate inbreeding depression and detect recent inbreeding., (The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).)

We investigated the effectiveness of mate allocation strategies accounting for non-additive genetic effects to improve crossbred performance in a two-way crossbreeding scheme. We did this by computer simulation of 10 generations of evaluation and selection. QTL effects were simulated as correlated across purebreds and crossbreds, and (positive) heterosis was simulated as directional dominance. The purebred-crossbred correlation was 0.30 or 0.68 depending on the genetic variance component used. Dominance and additive marker effects were estimated simultaneously for purebreds and crossbreds by multiple trait genomic BLUP. Four scenarios that differ in the sources of information (only purebred data, or purebred and crossbred data) and mate allocation strategies (mating at random, minimizing expected future inbreeding, or maximizing the expected total genetic value of crossbred animals) were evaluated under different cases of genetic variance components. Selecting purebred animals for purebred performance yielded a response of 0.2 genetic standard deviations of the trait "crossbred performance" per generation, whereas selecting purebred animals for crossbred performance doubled the genetic response. Mate allocation strategy to maximize the expected total genetic value of crossbred descendants resulted in a slight increase (0.8%, 4% and 0.5% depending on the genetic variance components) of the crossbred performance. Purebred populations increased homozygosity, but the heterozygosity of the crossbreds remained constant. When purebred-crossbred genetic correlation is low, selecting purebred animals for crossbred performance using crossbred information is a more efficient strategy to exploit heterosis and increase performance at the crossbred commercial level, whereas mate allocation did not improve crossbred performance., (Copyright © 2020 Gonzalez-Dieguez et al.)

The existence of buffering mechanisms is an emerging property of biological networks, and this results in the buildup of robustness through evolution. So far, there are no explicit methods to find loci implied in buffering mechanisms. However, buffering can be seen as interaction with genetic background. Here we develop this idea into a tractable model for quantitative genetics, in which the buffering effect of one locus with many other loci is condensed into a single statistical effect, multiplicative on the total additive genetic effect. This allows easier interpretation of the results and simplifies the problem of detecting epistasis from quadratic to linear in the number of loci. Using this formulation, we construct a linear model for genome-wide association studies that estimates and declares the significance of multiplicative epistatic effects at single loci. The model has the form of a variance components, norm reaction model and likelihood ratio tests are used for significance. This model is a generalization and explanation of previous ones. We test our model using bovine data: Brahman and Tropical Composite animals, phenotyped for body weight at yearling and genotyped at high density. After association analysis, we find a number of loci with buffering action in one, the other, or both breeds; these loci do not have a significant statistical additive effect. Most of these loci have been reported in previous studies, either with an additive effect or as footprints of selection. We identify buffering epistatic SNPs present in or near genes reported in the context of signatures of selection in multi-breed cattle population studies. Prominent among these genes are those associated with fertility (INHBA, TSHR, ESRRG, PRLR, and PPARG), growth (MSTN, GHR), coat characteristics (KIT, MITF, PRLR), and heat resistance (HSPA6 and HSPA1A). In these populations, we found loci that have a nonsignificant statistical additive effect but a significant epistatic effect. We argue that the discovery and study of loci associated with buffering effects allow attacking the difficult problems, among others, of the release of maintenance variance in artificial and natural selection, of quick adaptation to the environment, and of opposite signs of marker effects in different backgrounds. We conclude that our method and our results generate promising new perspectives for research in evolutionary and quantitative genetics based on the study of loci that buffer effect of other loci., (© The Author(s) 2020. Published by Oxford University Press on behalf of the American Society of Animal Science. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Estimates of dominance variance for growth traits in beef cattle based on pedigree data vary considerably across studies, and the proportion of genetic variance explained by dominance deviations remains largely unknown. The potential benefits of including nonadditive genetic effects in the genomic model combined with the increasing availability of large genomic data sets have recently renewed the interest in including nonadditive genetic effects in genomic evaluation models. The availability of genomic information enables the computation of covariance matrices of dominant genomic relationships among animals, similar to matrices of additive genomic relationships, and in a more straightforward manner than the pedigree-based dominance relationship matrix. Data from 19,357 genotyped American Angus males were used to estimate additive and dominant variance components for 3 growth traits: birth weight, weaning weight, and postweaning gain, and to evaluate the benefit of including dominance effects in beef cattle genomic evaluations. Variance components were estimated using 2 models: the first one included only additive effects (MG) and the second one included both additive and dominance effects (MGD). The dominance deviation variance ranged from 3% to 8% of the additive variance for all 3 traits. Gibbs sampling and REML estimates showed good concordance. Goodness of fit of the models was assessed by a likelihood ratio test. For all traits, MG fitted the data as well as MGD as assessed either by the likelihood ratio test or by the Akaike information criterion. Predictive ability of both models was assessed by cross-validation and did not improve when including dominance effects in the model. There was little evidence of nonadditive genetic variation for growth traits in the American Angus male population as only a small proportion of genetic variation was explained by nonadditive effects. A genomic model including the dominance effect did not improve the model fit. Consequently, including nonadditive effects in the genomic evaluation model is not beneficial for growth traits in the American Angus male population., (© The Author(s) 2019. Published by Oxford University Press on behalf of the American Society of Animal Science.)

The partition of the total genetic variance into its additive and non-additive components can differ from trait to trait, and between purebred and crossbred populations. A quantification of these genetic variance components will determine the extent to which it would be of interest to account for dominance in genomic evaluations or to establish mate allocation strategies along different populations and traits. This study aims at assessing the contribution of the additive and dominance genomic variances to the phenotype expression of several purebred Piétrain and crossbred (Piétrain × Large White) pig performances. A total of 636 purebred and 720 crossbred male piglets were phenotyped for 22 traits that can be classified into six groups of traits: growth rate and feed efficiency, carcass composition, meat quality, behaviour, boar taint and puberty. Additive and dominance variances estimated in univariate genotypic models, including additive and dominance genotypic effects, and a genomic inbreeding covariate allowed to retrieve the additive and dominance single nucleotide polymorphism variances for purebred and crossbred performances. These estimated variances were used, together with the allelic frequencies of the parental populations, to obtain additive and dominance variances in terms of genetic breeding values and dominance deviations. Estimates of the Piétrain and Large White allelic contributions to the crossbred variance were of about the same magnitude in all the traits. Estimates of additive genetic variances were similar regardless of the inclusion of dominance. Some traits showed relevant amount of dominance genetic variance with respect to phenotypic variance in both populations (i.e. growth rate 8%, feed conversion ratio 9% to 12%, backfat thickness 14% to 12%, purebreds-crossbreds). Other traits showed higher amount in crossbreds (i.e. ham cut 8% to 13%, loin 7% to 16%, pH semimembranosus 13% to 18%, pH longissimus dorsi 9% to 14%, androstenone 5% to 13% and estradiol 6% to 11%, purebreds-crossbreds). It was not encountered a clear common pattern of dominance expression between groups of analysed traits and between populations. These estimates give initial hints regarding which traits could benefit from accounting for dominance for example to improve genomic estimated breeding value accuracy in genetic evaluations or to boost the total genetic value of progeny by means of assortative mating.

Background: Mate allocation strategies that account for non-additive genetic effects can be used to maximize the overall genetic merit of future offspring. Accounting for dominance effects in genetic evaluations is easier in a genomic context, than in a classical pedigree-based context because the combinations of alleles at loci are known. The objective of our study was two-fold. First, dominance variance components were estimated for age at 100 kg (AGE), backfat depth (BD) at 140 days, and for average piglet weight at birth within litter (APWL). Second, the efficiency of mate allocation strategies that account for dominance and inbreeding depression to maximize the overall genetic merit of future offspring was explored., Results: Genetic variance components were estimated using genomic models that included inbreeding depression with and without non-additive genetic effects (dominance). Models that included dominance effects did not fit the data better than the genomic additive model. Estimates of dominance variances, expressed as a percentage of additive genetic variance, were 20, 11, and 12% for AGE, BD, and APWL, respectively. Estimates of additive and dominance single nucleotide polymorphism effects were retrieved from the genetic variance component estimates and used to predict the outcome of matings in terms of total genetic and breeding values. Maximizing total genetic values instead of breeding values in matings gave the progeny an average advantage of - 0.79 days, - 0.04 mm, and 11.3 g for AGE, BD and APWL, respectively, but slightly reduced the expected additive genetic gain, e.g. by 1.8% for AGE., Conclusions: Genomic mate allocation accounting for non-additive genetic effects is a feasible and potential strategy to improve the performance of the offspring without dramatically compromising additive genetic gain.

Background: Epistatic genomic relationship matrices for interactions of any-order can be constructed using the Hadamard products of orthogonal additive and dominance genomic relationship matrices and standardization based on the trace of the resulting matrices. Variance components for litter size in pigs were estimated by Bayesian methods for five nested models with additive, dominance, and pairwise epistatic effects in a pig dataset, and including genomic inbreeding as a covariate., Results: Estimates of additive and non-additive (dominance and epistatic) variance components were obtained for litter size. The variance component estimates were empirically orthogonal, i.e. they did not change when fitting increasingly complex models. Most of the genetic variance was captured by non-epistatic effects, as expected. In the full model, estimates of dominance and total epistatic variances (additive-by-additive plus additive-by-dominance plus dominance-by-dominance), expressed as a proportion of the total phenotypic variance, were equal to 0.02 and 0.04, respectively. The estimate of broad-sense heritability for litter size (0.15) was almost twice that of the narrow-sense heritability (0.09). Ignoring inbreeding depression yielded upward biased estimates of dominance variance, while estimates of epistatic variances were only slightly affected., Conclusions: Epistatic variance components can be easily computed using genomic relationship matrices. Correct orthogonal definition of the relationship matrices resulted in orthogonal partition of genetic variance into additive, dominance, and epistatic components, but obtaining accurate variance component estimates remains an issue. Genomic models that include non-additive effects must also consider inbreeding depression in order to avoid upward bias of estimates of dominance variance. Inclusion of epistasis did not improve the accuracy of prediction of breeding values.

Nonadditive effects may contribute to genetic variation of complex traits. Their inclusion in genetic evaluation models may therefore improve breeding value estimates and lead to more accurate selection decisions. In this study, we evaluated a systematic series of models accounting for additive, dominance and first-order epistatic interaction (additive by additive, GxG; additive by dominance, GxD; and dominance by dominance, DxD) on body yearling weight (YWT) of 2,550 Tropical Composite (TC) and 2,111 Brahman (BB) cattle in Australia. For both breeds, similar estimates of additive and phenotypic variances and narrow and broad-sense heritability values were obtained across the evaluated models except when GxG effect was considered. In this case, additive variance was slightly lower than that obtained in the models which do not consider this effect. The estimated dominance and epistatic variances from additive and dominance effects (AD) and additive, dominance and epistatic effects models (ADE) were greater than that ADH and ADEH models (as described above plus heterozygosity as a covariate). However, all genetic parameter estimates were associated with a large standard deviation. Averaged across ADH and ADHE models, the magnitude of dominance variance compared to the phenotypic variance of YWT was 14% (BB) and 10% (TC). The magnitude of epistasis compared to the phenotypic variance for BB and TC was 17% and 29%, respectively for GxG; 0.7% and 0% for GxD; and 0% and 0% for DxD. The inclusion of nonadditive effects slightly improves the predictive accuracy of breeding values from 0.28 for A to 0.33 for ADHEGxG and from 0.18 for A to 0.23 ADEGxD in BB and TC cattle. Models that included heterozygosity (ADH and ADHE) must be used to estimate nonadditive genetic variance components. A 1 Mb sliding window analysis identified a region on BTA 14 explaining 10.08% and 1.21% of total genetic variance (additive + dominance) of YWT in BB and TC, respectively. Our results suggest that dominance, epistasis, and heterozygosity should be included in models for genetic parameters estimation. To identify the animals with the highest additive genetic value in selection decisions, only the additive effect should be used in evaluation models.

Dominance genetic effects are rarely included in pedigree-based genetic evaluation. With the availability of single nucleotide polymorphism markers and the development of genomic evaluation, estimates of dominance genetic effects have become feasible using genomic best linear unbiased prediction (GBLUP). Usually, studies involving additive and dominance genetic effects ignore possible relationships between them. It has been often suggested that the magnitude of functional additive and dominance effects at the quantitative trait loci are related, but there is no existing GBLUP-like approach accounting for such correlation. Wellmann and Bennewitz (2012) showed two ways of considering directional relationships between additive and dominance effects, which they estimated in a Bayesian framework. However, these relationships cannot be fitted at the level of individuals instead of loci in a mixed model, and are not compatible with standard animal or plant breeding software. This comes from a fundamental ambiguity in assigning the reference allele at a given locus. We show that, if there has been selection, assigning the most frequent as the reference allele orients the correlation between functional additive and dominance effects. As a consequence, the most frequent reference allele is expected to have a positive value. We also demonstrate that selection creates negative covariance between genotypic additive and dominance genetic values. For parameter estimation, it is possible to use a combined additive and dominance relationship matrix computed from marker genotypes, and to use standard restricted maximum likelihood algorithms based on an equivalent model. Through a simulation study, we show that such correlations can easily be estimated by mixed model software and that the accuracy of prediction for genetic values is slightly improved if such correlations are used in GBLUP. However, a model assuming uncorrelated effects and fitting orthogonal breeding values and dominant deviations performed similarly for prediction., (Copyright © 2018 by the Genetics Society of America.)

In the last decade, genomic selection has become a standard in the genetic evaluation of livestock populations. However, most procedures for the implementation of genomic selection only consider the additive effects associated with SNP (Single Nucleotide Polymorphism) markers used to calculate the prediction of the breeding values of candidates for selection. Nevertheless, the availability of estimates of non-additive effects is of interest because: (i) they contribute to an increase in the accuracy of the prediction of breeding values and the genetic response; (ii) they allow the definition of mate allocation procedures between candidates for selection; and (iii) they can be used to enhance non-additive genetic variation through the definition of appropriate crossbreeding or purebred breeding schemes. This study presents a review of methods for the incorporation of non-additive genetic effects into genomic selection procedures and their potential applications in the prediction of future performance, mate allocation, crossbreeding, and purebred selection. The work concludes with a brief outline of some ideas for future lines of that may help the standard inclusion of non-additive effects in genomic selection.

Background: The quantitative genetics theory argues that inbreeding depression and heterosis are founded on the existence of directional dominance. However, most procedures for genomic selection that have included dominance effects assumed prior symmetrical distributions. To address this, two alternatives can be considered: (1) assume the mean of dominance effects different from zero, and (2) use skewed distributions for the regularization of dominance effects. The aim of this study was to compare these approaches using two pig datasets and to confirm the presence of directional dominance., Results: Four alternative models were implemented in two datasets of pig litter size that consisted of 13,449 and 11,581 records from 3631 and 2612 sows genotyped with the Illumina PorcineSNP60 BeadChip. The models evaluated included (1) a model that does not consider directional dominance (Model SN), (2) a model with a covariate b for the average individual homozygosity (Model SC), (3) a model with a parameter λ that reflects asymmetry in the context of skewed Gaussian distributions (Model AN), and (4) a model that includes both b and λ (Model Full). The results of the analysis showed that posterior probabilities of a negative b or a positive λ under Models SC and AN were higher than 0.99, which indicate positive directional dominance. This was confirmed with the predictions of inbreeding depression under Models Full, SC and AN, that were higher than in the SN Model. In spite of differences in posterior estimates of variance components between models, comparison of models based on LogCPO and DIC indicated that Model SC provided the best fit for the two datasets analyzed., Conclusions: Our results confirmed the presence of positive directional dominance for pig litter size and suggested that it should be taken into account when dominance effects are included in genomic evaluation procedures. The consequences of ignoring directional dominance may affect predictions of breeding values and can lead to biased prediction of inbreeding depression and performance of potential mates. A model that assumes Gaussian dominance effects that are centered on a non-zero mean is recommended, at least for datasets with similar features to those analyzed here.

Background: The effect of epistasis on response to selection is a highly debated topic. Here, we investigated the impact of epistasis on response to sequence-based selection via genomic best linear prediction (GBLUP) in a regime of strong non-symmetrical epistasis under divergent selection, using real Drosophila sequence data. We also explored the possible advantage of including epistasis in the evaluation model and/or of knowing the causal mutations., Results: Response to selection was almost exclusively due to changes in allele frequency at a few loci with a large effect. Response was highly asymmetric (about four phenotypic standard deviations higher for upward than downward selection) due to the highly skewed site frequency spectrum. Epistasis accentuated this asymmetry and affected response to selection by modulating the additive genetic variance, which was sustained for longer under upward selection whereas it eroded rapidly under downward selection. Response to selection was quite insensitive to the evaluation model, especially under an additive scenario. Nevertheless, including epistasis in the model when there was none eventually led to lower accuracies as selection proceeded. Accounting for epistasis in the model, if it existed, was beneficial but only in the medium term. There was not much gain in response if causal mutations were known, compared to using sequence data, which is likely due to strong linkage disequilibrium, high heritability and availability of phenotypes on candidates., Conclusions: Epistatic interactions affect the response to genomic selection by modulating the additive genetic variance used for selection. Epistasis releases additive variance that may increase response to selection compared to a pure additive genetic action. Furthermore, genomic evaluation models and, in particular, GBLUP are robust, i.e. adding complexity to the model did not modify substantially the response (for a given architecture).

Genomic prediction methods based on multiple markers have potential to include nonadditive effects in prediction and analysis of complex traits. However, most developments assume a Hardy-Weinberg equilibrium (HWE). Statistical approaches for genomic selection that account for dominance and epistasis in a general context, without assuming HWE ( e.g. , crosses or homozygous lines), are therefore needed. Our method expands the natural and orthogonal interactions (NOIA) approach, which builds incidence matrices based on genotypic (not allelic) frequencies, to include genome-wide epistasis for an arbitrary number of interacting loci in a genomic evaluation context. This results in an orthogonal partition of the variances, which is not warranted otherwise. We also present the partition of variance as a function of genotypic values and frequencies following Cockerham's orthogonal contrast approach. Then we prove for the first time that, even not in HWE, the multiple-loci NOIA method is equivalent to construct epistatic genomic relationship matrices for higher-order interactions using Hadamard products of additive and dominant genomic orthogonal relationships. A standardization based on the trace of the relationship matrices is, however, needed. We illustrate these results with two simulated F 1 (not in HWE) populations, either in linkage equilibrium (LE), or in linkage disequilibrium (LD) and divergent selection, and pure biological dominant pairwise epistasis. In the LE case, correct and orthogonal estimates of variances were obtained using NOIA genomic relationships but not if relationships were constructed assuming HWE. For the LD simulation, differences were smaller, due to the smaller deviation of the F 1 from HWE. Wrongly assuming HWE to build genomic relationships and estimate variance components yields biased estimates, inflates the total genetic variance, and the estimates are not empirically orthogonal. The NOIA method to build genomic relationships, coupled with the use of Hadamard products for epistatic terms, allows the obtaining of correct estimates in populations either in HWE or not in HWE, and extends to any order of epistatic interactions., (Copyright © 2017 by the Genetics Society of America.)

This review focuses on methods used to predict complex traits. Main characteristics of prediction approaches are given: the deterministic or stochastic nature of prediction, the objects of prediction, the sources of information and the main statistical methods. Sources of information discussed are the traditional genealogies and phenotypes, nucleotide sequences, expression data and epigenetics marks. Statistical methods are presented as successive degrees of generalization from the definition of the conditional expectation as the prediction rule, to best linear unbiased prediction, then Bayesian and, recently, machine learning methods, including meta-methods. We highlight the contributions of Daniel Gianola to this methodological evolution., (© 2017 Blackwell Verlag GmbH.)

Genomic relationships based on markers capture the actual instead of the expected (based on pedigree) proportion of genome shared identical by descent (IBD). Several methods exist to estimate genomic relationships. In this research, we compare four such methods that were tested looking at the empirical distribution of the estimated relationships across 6704 pairs of half-sibs from a cross-bred pig population. The first method based on multiple marker linkage analysis displayed a mean and standard deviation (SD) in close agreement with the expected ones and was robust to changes in the minor allele frequencies (MAF). A single marker method that accounts for linkage disequilibrium (LD) and inbreeding came second, showing more sensitivity to changes in the MAF. Another single marker method that considers neither inbreeding nor LD showed the smallest empirical SD and was the most sensible to changes in MAF. A higher mean and SD were displayed by VanRaden's method, which was not sensitive to changes in MAF. Therefore, the method based on multiple marker linkage analysis and the single marker method that considers LD and inbreeding performed closer to theoretical values and were consistent with the estimates reported in literature for human half-sibs., (© 2016 Blackwell Verlag GmbH.)

Background: Metafounders are pseudo-individuals that encapsulate genetic heterozygosity and relationships within and across base pedigree populations, i.e. ancestral populations. This work addresses the estimation and usefulness of metafounder relationships in single-step genomic best linear unbiased prediction (ssGBLUP)., Results: We show that ancestral relationship parameters are proportional to standardized covariances of base allelic frequencies across populations, such as [Formula: see text] fixation indexes. These covariances of base allelic frequencies can be estimated from marker genotypes of related recent individuals and pedigree. Simple methods for their estimation include naïve computation of allele frequencies from marker genotypes or a method of moments that equates average pedigree-based and marker-based relationships. Complex methods include generalized least squares (best linear unbiased estimator (BLUE)) or maximum likelihood based on pedigree relationships. To our knowledge, methods to infer [Formula: see text] coefficients from marker data have not been developed for related individuals. We derived a genomic relationship matrix, compatible with pedigree relationships, that is constructed as a cross-product of {-1,0,1} codes and that is equivalent (apart from scale factors) to an identity-by-state relationship matrix at genome-wide markers. Using a simulation with a single population under selection in which only males and youngest animals are genotyped, we observed that generalized least squares or maximum likelihood gave accurate and unbiased estimates of the ancestral relationship parameter (true value: 0.40) whereas the naïve method and the method of moments were biased (average estimates of 0.43 and 0.35). We also observed that genomic evaluation by ssGBLUP using metafounders was less biased in terms of estimates of genetic trend (bias of 0.01 instead of 0.12), resulted in less overdispersed (0.94 instead of 0.99) and as accurate (0.74) estimates of breeding values than ssGBLUP without metafounders and provided consistent estimates of heritability., Conclusions: Estimation of metafounder relationships can be achieved using BLUP-like methods with pedigree and markers. Inclusion of metafounder relationships reduces bias of genomic predictions with no loss in accuracy.

Accurate prediction of breeding values depends on capturing the variability in genome sharing of relatives with the same pedigree relationship. Here, we compare two approaches to set up genomic relationship matrices for precision of genomic relationships (GR) and accuracy of estimated breeding values (GEBV). Real and simulated data (pigs, 60k SNP) were analysed, and GR were estimated using two approaches: (i) identity by state, corrected with either the observed (G VR -O ) or the base population (G VR -B ) allele frequencies and (ii) identity by descent using linkage analysis (G IBD -L ). Estimators were evaluated for precision and empirical bias with respect to true pedigree IBD GR. All three estimators had very low bias. G IBD -L displayed the lowest sampling error and the highest correlation with true genome-shared values. G VR -B approximated G IBD -L 's correlation and had lower error than G VR -O . Accuracy of GEBV for selection candidates was significantly higher when G IBD -L was used and identical between G VR -O and G VR -B . In real data, G IBD -L 's sampling standard deviation was the closest to the theoretical value for each pedigree relationship. Use of pedigree to calculate GR improved the precision of estimates and the accuracy of GEBV., (© 2016 Blackwell Verlag GmbH.)

Background: Improved performance of crossbred animals is partly due to heterosis. One of the major genetic bases of heterosis is dominance, but it is seldom used in pedigree-based genetic evaluation of livestock. Recently, a trivariate genomic best linear unbiased prediction (GBLUP) model including dominance was developed, which can distinguish purebreds from crossbred animals explicitly. The objectives of this study were: (1) methodological, to show that inclusion of marker-based inbreeding accounts for directional dominance and inbreeding depression in purebred and crossbred animals, to revisit variance components of additive and dominance genetic effects using this model, and to develop marker-based estimators of genetic correlations between purebred and crossbred animals and of correlations of allele substitution effects between breeds; (2) to evaluate the impact of accounting for dominance effects and inbreeding depression on predictive ability for total number of piglets born (TNB) in a pig dataset composed of two purebred populations and their crossbreds. We also developed an equivalent model that makes the estimation of variance components tractable., Results: For TNB in Danish Landrace and Yorkshire populations and their reciprocal crosses, the estimated proportions of dominance genetic variance to additive genetic variance ranged from 5 to 11%. Genetic correlations between breeding values for purebred and crossbred performances for TNB ranged from 0.79 to 0.95 for Landrace and from 0.43 to 0.54 for Yorkshire across models. The estimated correlation of allele substitution effects between Landrace and Yorkshire was low for purebred performances, but high for crossbred performances. Predictive ability for crossbred animals was similar with or without dominance. The inbreeding depression effect increased predictive ability and the estimated inbreeding depression parameter was more negative for Landrace than for Yorkshire animals and was in between for crossbred animals., Conclusions: Methodological developments led to closed-form estimators of inbreeding depression, variance components and correlations that can be easily interpreted in a quantitative genetics context. Our results confirm that genetic correlations of breeding values between purebred and crossbred performances within breed are positive and moderate. Inclusion of dominance in the GBLUP model does not improve predictive ability for crossbred animals, whereas inclusion of inbreeding depression does.

Background: Most developments in quantitative genetics theory focus on the study of intra-breed/line concepts. With the availability of massive genomic information, it becomes necessary to revisit the theory for crossbred populations. We propose methods to construct genomic covariances with additive and non-additive (dominance) inheritance in the case of pure lines and crossbred populations., Results: We describe substitution effects and dominant deviations across two pure parental populations and the crossbred population. Gene effects are assumed to be independent of the origin of alleles and allelic frequencies can differ between parental populations. Based on these assumptions, the theoretical variance components (additive and dominant) are obtained as a function of marker effects and allelic frequencies. The additive genetic variance in the crossbred population includes the biological additive and dominant effects of a gene and a covariance term. Dominance variance in the crossbred population is proportional to the product of the heterozygosity coefficients of both parental populations. A genomic BLUP (best linear unbiased prediction) equivalent model is presented. We illustrate this approach by using pig data (two pure lines and their cross, including 8265 phenotyped and genotyped sows). For the total number of piglets born, the dominance variance in the crossbred population represented about 13 % of the total genetic variance. Dominance variation is only marginally important for litter size in the crossbred population., Conclusions: We present a coherent marker-based model that includes purebred and crossbred data and additive and dominant actions. Using this model, it is possible to estimate breeding values, dominant deviations and variance components in a dataset that comprises data on purebred and crossbred individuals. These methods can be exploited to plan assortative mating in pig, maize or other species, in order to generate superior crossbred individuals in terms of performance.

Background: In pedigreed populations with a major gene segregating for a quantitative trait, it is not clear how to use pedigree, genotype and phenotype information when some individuals are not genotyped. We propose to consider gene content at the major gene as a second trait correlated to the quantitative trait, in a gene content multiple-trait best linear unbiased prediction (GCMTBLUP) method., Results: The genetic covariance between the trait and gene content at the major gene is a function of the substitution effect of the gene. This genetic covariance can be written in a multiple-trait form that accommodates any pattern of missing values for either genotype or phenotype data. Effects of major gene alleles and the genetic covariance between genotype at the major gene and the phenotype can be estimated using standard EM-REML or Gibbs sampling. Prediction of breeding values with genotypes at the major gene can use multiple-trait BLUP software. Major genes with more than two alleles can be considered by including negative covariances between gene contents at each different allele. We simulated two scenarios: a selected and an unselected trait with heritabilities of 0.05 and 0.5, respectively. In both cases, the major gene explained half the genetic variation. Competing methods used imputed gene contents derived by the method of Gengler et al. or by iterative peeling. Imputed gene contents, in contrast to GCMTBLUP, do not consider information on the quantitative trait for genotype prediction. GCMTBLUP gave unbiased estimates of the gene effect, in contrast to the other methods, with less bias and better or equal accuracy of prediction. GCMTBLUP improved estimation of genotypes in non-genotyped individuals, in particular if these individuals had own phenotype records and the trait had a high heritability. Ignoring the major gene in genetic evaluation led to serious biases and decreased prediction accuracy., Conclusions: CGMTBLUP is the best linear predictor of additive genetic merit including pedigree, phenotype, and genotype information at major genes, since it considers missing genotypes. Simulations confirm that it is a simple, efficient and theoretically sound method for genetic evaluation of traits influenced by polygenic inheritance and one or several major genes.

Recent changes to French regulations now allow farmers to produce "foie gras" from both male and female mule ducks. The aim of this study was to assess the quality of female fatty liver and to compare, from a phenotypic and genetic point of view, liver quality in males and females. A total of 914 mule ducks (591 males and 323 females), hatched in a single pedigree batch, were reared until 86 d of age and then force-fed for 12 d, before being slaughtered. Carcasses and livers were weighed and liver quality was assessed by grading the extent of liver veining and measuring the liver melting rate, either after sterilization of 60 g of liver or pasteurization of 180 g of liver. Sexual dimorphism was observed in favor of males, with a difference of approximately 10% in carcass and liver weights and up to 54% for the liver melting rate. Moreover, one-third of female livers showed moderate to high veining, whereas this was not the case for male livers. The fatty livers of female mule ducks are, therefore, of poorer quality and could not be transformed into a product with the appellation "100% fatty liver." According to sex and parental line, heritability values ranged from 0.12 ± 0.05 to 0.18 ± 0.07 for fatty liver weight and from 0.09 ± 0.05 to 0.18 ± 0.05 for the 2 melting rate traits. The genetic correlations between the fatty liver weight and both melting rates were high (greater than +0.80) in the Muscovy population, whereas in the Pekin population, the liver weight and melting rates were less strongly correlated (estimates ranging from +0.36 ± 0.30 to +0.45 ± 0.28). Selection for lower liver melting rates without reducing the liver weight would, therefore, be easier to achieve in the Pekin population. Finally, as the 2 melting rate measurements are highly correlated (0.91 and over 0.95 for phenotypic and genetic correlations, respectively), we suggest using the easiest method, that is, sterilization of 60 g of liver.

Recent use of genomic (marker-based) relationships shows that relationships exist within and across base population (breeds or lines). However, current treatment of pedigree relationships is unable to consider relationships within or across base populations, although such relationships must exist due to finite size of the ancestral population and connections between populations. This complicates the conciliation of both approaches and, in particular, combining pedigree with genomic relationships. We present a coherent theoretical framework to consider base population in pedigree relationships. We suggest a conceptual framework that considers each ancestral population as a finite-sized pool of gametes. This generates across-individual relationships and contrasts with the classical view which each population is considered as an infinite, unrelated pool. Several ancestral populations may be connected and therefore related. Each ancestral population can be represented as a "metafounder," a pseudo-individual included as founder of the pedigree and similar to an "unknown parent group." Metafounders have self- and across relationships according to a set of parameters, which measure ancestral relationships, i.e., homozygozities within populations and relationships across populations. These parameters can be estimated from existing pedigree and marker genotypes using maximum likelihood or a method based on summary statistics, for arbitrarily complex pedigrees. Equivalences of genetic variance and variance components between the classical and this new parameterization are shown. Segregation variance on crosses of populations is modeled. Efficient algorithms for computation of relationship matrices, their inverses, and inbreeding coefficients are presented. Use of metafounders leads to compatibility of genomic and pedigree relationship matrices and to simple computing algorithms. Examples and code are given., (Copyright © 2015 by the Genetics Society of America.)

Quality control filtering of single-nucleotide polymorphisms (SNPs) is a key step when analyzing genomic data. Here we present a practical method to identify low-quality SNPs, meaning markers whose genotypes are wrongly assigned for a large proportion of individuals, by estimating the heritability of gene content at each marker, where gene content is the number of copies of a particular reference allele in a genotype of an animal (0, 1, or 2). If there is no mutation at the marker, gene content has an additive heritability of 1 by construction. The method uses restricted maximum likelihood (REML) to estimate heritability of gene content at each SNP and also builds a likelihood-ratio test statistic to test for zero error variance in genotyping. As a by-product, estimates of the allele frequencies of markers at the base population are obtained. Using simulated data with 10% permutation error (4% actual error) in genotyping, the method had a specificity of 0.96 (4% of correct markers are rejected) and a sensitivity of 0.99 (1% of wrong markers are accepted) if markers with heritability lower than 0.975 are discarded. Checking of Mendelian errors resulted in a lower sensitivity (0.84) for the same simulation. The proposed method is further illustrated with a real data set with genotypes from 3534 animals genotyped for 50,433 markers from the Illumina PorcineSNP60 chip and a pedigree of 6473 individuals; those markers underwent very little quality control. A total of 4099 markers with P-values lower than 0.01 were discarded based on our method, with associated estimates of heritability as low as 0.12. Contrary to other techniques, our method uses all information in the population simultaneously, can be used in any population with markers and pedigree recordings, and is simple to implement using standard software for REML estimation. Scripts for its use are provided., (Copyright © 2015 by the Genetics Society of America.)

Background: Estimates of dominance variance in dairy cattle based on pedigree data vary considerably across traits and amount to up to 50% of the total genetic variance for conformation traits and up to 43% for milk production traits. Using bovine SNP (single nucleotide polymorphism) genotypes, dominance variance can be estimated both at the marker level and at the animal level using genomic dominance effect relationship matrices. Yield deviations of high-density genotyped Fleckvieh cows were used to assess cross-validation accuracy of genomic predictions with additive and dominance models. The potential use of dominance variance in planned matings was also investigated., Results: Variance components of nine milk production and conformation traits were estimated with additive and dominance models using yield deviations of 1996 Fleckvieh cows and ranged from 3.3% to 50.5% of the total genetic variance. REML and Gibbs sampling estimates showed good concordance. Although standard errors of estimates of dominance variance were rather large, estimates of dominance variance for milk, fat and protein yields, somatic cell score and milkability were significantly different from 0. Cross-validation accuracy of predicted breeding values was higher with genomic models than with the pedigree model. Inclusion of dominance effects did not increase the accuracy of the predicted breeding and total genetic values. Additive and dominance SNP effects for milk yield and protein yield were estimated with a BLUP (best linear unbiased prediction) model and used to calculate expectations of breeding values and total genetic values for putative offspring. Selection on total genetic value instead of breeding value would result in a larger expected total genetic superiority in progeny, i.e. 14.8% for milk yield and 27.8% for protein yield and reduce the expected additive genetic gain only by 4.5% for milk yield and 2.6% for protein yield., Conclusions: Estimated dominance variance was substantial for most of the analyzed traits. Due to small dominance effect relationships between cows, predictions of individual dominance deviations were very inaccurate and including dominance in the model did not improve prediction accuracy in the cross-validation study. Exploitation of dominance variance in assortative matings was promising and did not appear to severely compromise additive genetic gain.

Background: "Foie gras" is produced predominantly in France and about 90% of the commercialized product is obtained from male mule ducks. The melting rate (percentage of fat released during cooking) is the main criterion used to determine the quality of "foie gras". However, up to now the melting rate could not be predicted without causing liver damage, which means that selection programs could not use this criterion., Methods: Fatty liver phenotypes were obtained for a population of over 1400 overfed male mule ducks. The phenotypes were based on two types of near-infrared spectra (on the liver surface and on ground liver) in order to predict the melting rate and liver composition (ash, dry matter, lipid and protein contents). Genetic parameters were computed in multiple traits with a "sire-dam" model and using a Gibbs sampling approach., Results: The estimates for the genetic parameters show that the measured melting rate and the predicted melting rate obtained with two near-infrared spectrometer devices are genetically the same trait: genetic correlations are very high (ranging from +0.89 to +0.97 depending on the mule duck parental line and the spectrometer) and heritabilities are comparable. The predictions based on the spectra of ground liver samples using a laboratory spectrometer correlate with those based on the surface spectra using a portable spectrometer (from +0.83 to +0.95 for dry matter, lipid and protein content) and are particularly high for the melting rate (higher than +0.95). Although less accurate than the predictions obtained using the spectra of ground liver samples, the phenotypic prediction of the melting rate based on surface spectra is sufficiently accurate to be used by "foie gras" processors., Conclusions: Near-infrared spectrometry is an efficient tool to select liver quality in breeding programs because animals can be ranked according to their liver melting rate without damaging their livers. Thus, these original results will help breeders to select ducks based on the liver melting rate, a crucial criterion that defines the quality of the liver and for which there was previously no accurate predictor.

Genomic evaluation models can fit additive and dominant SNP effects. Under quantitative genetics theory, additive or "breeding" values of individuals are generated by substitution effects, which involve both "biological" additive and dominant effects of the markers. Dominance deviations include only a portion of the biological dominant effects of the markers. Additive variance includes variation due to the additive and dominant effects of the markers. We describe a matrix of dominant genomic relationships across individuals, D, which is similar to the G matrix used in genomic best linear unbiased prediction. This matrix can be used in a mixed-model context for genomic evaluations or to estimate dominant and additive variances in the population. From the "genotypic" value of individuals, an alternative parameterization defines additive and dominance as the parts attributable to the additive and dominant effect of the markers. This approach underestimates the additive genetic variance and overestimates the dominance variance. Transforming the variances from one model into the other is trivial if the distribution of allelic frequencies is known. We illustrate these results with mouse data (four traits, 1884 mice, and 10,946 markers) and simulated data (2100 individuals and 10,000 markers). Variance components were estimated correctly in the model, considering breeding values and dominance deviations. For the model considering genotypic values, the inclusion of dominant effects biased the estimate of additive variance. Genomic models were more accurate for the estimation of variance components than their pedigree-based counterparts.

The purpose of this study was to analyze associations between polymorphisms in the PRNP gene and ewe milk traits. A total of 242,565 lactations of the Latxa breed were used. Milk, fat and protein yields, and fat and protein content from black-faced Latxa from Spanish Basque Country, black-faced Latxa from Navarra, and blond-faced Latxa were collected. To evaluate evidence of association, the different traits were analyzed using an animal model, where the PRNP genotype effect was included or not as a random effect. Adding the PRNP effect to the model improved the fitting for milk yield in black-faced Latxa from Spanish Basque Country and in blond-faced Latxa, for fat yield in black-faced Latxa from Navarra, and for protein yield in blond-faced Latxa. However, the proportion of the phenotypic variance explained by the PRNP effect for milk yield (1.0×10(-3)), fat yield (3.6×10(-3)) and protein yield (9.4×10(-4)) were near zero. The PRNP locus accounts for about 0.5, 1.5, and 0.4% of total genetic (PRNP and polygenic) variance in milk, fat, and protein yield. These values indicated that the PRNP effect is not relevant regarding genetic additive contribution. For breeding purposes, it is unlikely that selection for scrapie resistance will have an effect on the milk traits studied in the Latxa breed., (Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

In single-step genomic evaluation using best linear unbiased prediction (ssGBLUP), genomic predictions are calculated with a relationship matrix that combines pedigree and genomic information. For missing pedigrees, unknown selection processes, or inclusion of several populations, a BLUP model can include unknown-parent groups (UPG) in the animal effect. For ssGBLUP, UPG equations also involve contributions from genomic relationships. When those contributions are ignored, UPG solutions and genetic predictions can be biased. Options to eliminate or reduce such bias are presented. First, mixed model equations can be modified to include contributions to UPG elements from genomic relationships (greater software complexity). Second, UPG can be implemented as separate effects (higher cost of computing and data processing). Third, contributions can be ignored when they are relatively small, but they may be small only after refinements to UPG definitions. Fourth, contributions may approximately cancel out when genomic and pedigree relationships are constructed for compatibility; however, different construction steps are required for unknown parents from the same or different populations. Finally, an additional polygenic effect that also includes UPG can be added to the model., (© 2013 Blackwell Verlag GmbH.)

The fatty liver of mule ducks (i.e., French "foie gras") is the most valuable product in duck production systems. Its quality is measured by the technological yield, which is the opposite of the fat loss during cooking. The purpose of this study was to determine whether biochemical measures of fatty liver could be used to accurately predict the technological yield (TY). Ninety-one male mule ducks were bred, overfed, and slaughtered under commercial conditions. Fatty liver weight (FLW) and biochemical variables, such as DM, lipid (LIP), and protein content (PROT), were collected. To evaluate evidence for nonlinear fat loss during cooking, we compared regression models describing linear and nonlinear relations between biochemical measures and TY. We detected significantly greater (P = 0.02) linear relation between DM and TY. Our results indicate that LIP and PROT follow a different pattern (linear) than DM and showed that LIP and PROT are nonexclusive contributing factors to TY. Other components, such as carbohydrates, other than those measured in this study, could contribute to DM. Stepwise regression for TY was performed. The traditional model with FLW was tested. The results showed that the weight of the liver is of limited value in the determination of fat loss during cooking (R(2) = 0.14). The most accurate TY prediction equation included DM (in linear and quadratic terms), FLW, and PROT (R(2) = 0.43). Biochemical measures in the fatty liver were more accurate predictors of TY than FLW. The model is useful in commercial conditions because DM, PROT, and FLW are noninvasive measures.

Effects on prediction of analysing a multi-line chicken population as one line were evaluated. Body weight records were provided by Cobb-Vantress for two lines of broiler chickens. Phenotypic records for 183 695 and 164 149 broilers and genotypic records for 3195 and 3001 broilers were available for each line. Lines were combined to create a multi-line population and analysed using a single-step procedure combining the additive relationship matrix and the genomic relationship matrix (G). G was scaled using allele frequencies from each line, the multi-line population, or 0.5. When allele frequencies were calculated from each line, distributions of diagonal elements were bimodal. When allele frequencies were calculated from the multi-line population, the distribution of diagonal elements had one peak. When allele frequency 0.5 was used, the distribution was bimodal. Genomic estimated breeding values (GEBVs) were predicted using each allele frequency. GEBVs differed with allele frequency but had ≥ 0.99 correlations with GEBVs predicted with correct allele frequencies. Means of each line and differences in mean between the lines differed based on allele frequencies. Assumed allele frequencies have little impact on ranking within line but larger impact on ranking across lines. G may be used to evaluate multiple populations simultaneously but must be adjusted to obtain properly scaled estimates when population structure is unknown., (© 2011 Blackwell Verlag GmbH.)

Fat loss during cooking of duck "foie gras" is the main quality issue in processing plants. To better understand this phenomenon, a histological and ultrastructural study was conducted. The aim was to characterize changes in lipid droplets of duck "foie gras" related to fat loss during cooking. Ten fatty livers were sampled before and after cooking and prepared for optical and transmission electron microscopy. In raw livers, the lipid droplets were nearly spherical while after cooking, they were larger and lost their spherical shape. We also observed a decrease in the number of droplets after cooking, probably due to droplet fusion caused by the heat treatment. Before cooking, there were fewer lipid droplets and a higher osmium tetroxyde staining intensity in the fatty liver, which later gave a lower technological yield. Fat loss during cooking was higher when there was more fusion of lipid droplets before cooking., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Prediction of genetic merit or disease risk using genetic marker information is becoming a common practice for selection of livestock and plant species. For the successful application of genome-wide marker-assisted selection (GWMAS), genomic predictions should be accurate and unbiased. The effect of selection on bias and accuracy of genomic predictions was studied in two simulated animal populations under weak or strong selection and with several heritabilities. Prediction of genetic values was by best-linear unbiased prediction (BLUP) using data either from relatives summarized in pseudodata for genotyped individuals (multiple-step method) or using all available data jointly (single-step method). The single-step method combined genomic- and pedigree-based relationship matrices. Predictions by the multiple-step method were biased. Predictions by a single-step method were less biased and more accurate but under strong selection were less accurate. When genomic relationships were shifted by a constant, the single-step method was unbiased and the most accurate. The value of that constant, which adjusts for non-random selection of genotyped individuals, can be derived analytically.

Genetic parameters of traits related to hepatic lipid metabolism, carcass composition, and product quality of overfed mule ducks were estimated on both parental lines of this hybrid: the common duck line for the maternal side and the Muscovy line for the paternal side. The originality of the statistical model was to include simultaneously the additive genetic effect of the common ducks and that of the Muscovy ducks, revealing a greater genetic determinism in common than in Muscovy. Plasma metabolic indicators (glucose, triglyceride, and cholesterol contents) were heritable, in particular at the end of the overfeeding period, and heritabilities increased with the overfeeding stage. Carcass composition traits were highly heritable in the common line, with values ranging from 0.15 for liver weight, 0.21 for carcass weight, and 0.25 for abdominal fat weight to 0.32 for breast muscle weight. Heritabilities of technological outputs were greater for the fatty liver (0.19 and 0.08, respectively, on common and Muscovy sides for liver melting rate) than for the pectoralis major muscle (between 0.02 and 0.05 on both parental sides for cooking losses). Fortunately, the processing industry is mainly facing problems in liver quality, such as too high of a melting rate, than in meat quality. The meat quality appraisal criteria (such as texture and cooking losses), usually dependent on pH and the rate of decline of pH, were also very lowly heritable. This study demonstrated that genetic determinism of meat quality and ability of overfeeding is not similar in the common population and in the Muscovy population; traits related to fattening, muscle development, and BW have heritability values from 2 to 4 times greater on the common line than on the Muscovy line, which is relevant for considering different selection strategies.

This study compared models for growth (BW) before overfeeding period for male mule duck data from 7 families of a QTL experimental design. Four nonlinear models (Gompertz, logistic, Richards, and Weibull) and a spline linear regression model were used. This study compared fixed and mixed effects models to analyze growth. The Akaike information criterion was used to evaluate these alternative models. Among the nonlinear models, the mixed effects Weibull model had the best overall fit. Two parameters, the asymptotic weight and the inflexion point age, were considered random variables associated with individuals in the mixed models. In our study, asymptotic weight had a greater effect in Akaike's information criterion reduction than inflexion point age. In this data set, the between-ducks variability was mostly explained by asymptotic BW. Comparing fixed with mixed effects models, the residual SD was reduced in about 55% in the latter, pointing out the improvement in the accuracy of estimated parameters. The mixed effects spline regression model was the second best model. Given the piecewise nature of growth, this model is able to capture different growth patterns, even with data collected beyond the asymptotic BW.

Recessive dystrophic epidermolysis bullosa (RDEB) is a severe genodermatosis caused by loss-of-function mutations in COL7A1 encoding type VII collagen, the component of anchoring fibrils. As exogenous type VII collagen may elicit a deleterious immune response in RDEB patients during upcoming clinical trials of gene therapies or protein replacement therapies, we developed enzyme-linked immunosorbent assay (ELISA) and enzyme-linked immunosorbent spot (ELISPOT) assays to analyze B- and T-cell responses, to the full-length type VII collagen. The ELISA was highly sensitive and specific when tested against sera from 41 patients with epidermolysis bullosa acquisita (EBA), and the IFN-gamma ELISPOT detected a cellular response that correlated with ongoing EBA manifestations. Both tests were next applied to assess the risk of an immune response to type VII collagen in seven RDEB patients with a range of type VII collagen expression profiles. Immune responses against type VII collagen were dependent on the expression of type VII collagen protein, and consequently on the nature and position of the respective COL7A1 mutations. These immunologic tests will be helpful for the selection of RDEB patients for future clinical trials aiming at restoring type VII collagen expression, and in monitoring their immune response to type VII collagen after treatment.

A mathematical approach was developed to model and optimize simultaneous selection on 2 traits, a quantitative trait with underlying polygenic variation and a monogenic trait (e.g., resistance to a disease). A deterministic model allows global optimization of the selection scheme to maximize the frequency of the desired genotype for the monogenic trait, while minimizing the loss of genetic progress on the polygenic trait. An additive QTL or gene was considered. Breeding programs with overlapping generations, different selection strategies for males and females, and assortative mating were modeled. A genetic algorithm was used to solve this optimization problem. This modeling approach may easily be adapted to a variety of underlying genetic models and selection schemes. This model was applied to an example where selection on the Prp gene for scrapie resistance was introduced as an additional selection criterion in an already existing dairy sheep selection scheme.