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.

Impact of interpopulation distance on dominance variance and average heterosis in hybrid populations within species.

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.

Impacts of additive, dominance, and inbreeding depression effects on genomic evaluation by combining two SNP chips in Canadian Yorkshire pigs bred in China.

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.

Genomic Prediction Methods Accounting for Nonadditive Genetic Effects.

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.

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.

Computing strategies for multi-population genomic evaluation.

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.

Estimating inbreeding depression for growth and reproductive traits using pedigree and genomic methods in Argentinean Brangus cattle.

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 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.

Genomic prediction of hybrid crops allows disentangling dominance and epistasis.

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.

Purebred and Crossbred Genomic Evaluation and Mate Allocation Strategies To Exploit Dominance in Pig Crossbreeding Schemes.

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.

Association analysis of loci implied in "buffering" epistasis.

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.

Estimating dominance genetic variances for growth traits in American Angus males using genomic models.

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.

SNP-based mate allocation strategies to maximize total genetic value in pigs.

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.

Dominance and epistatic genetic variances for litter size in pigs using genomic models.

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.

Evaluation of nonadditive effects in yearling weight of tropical beef cattle.

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.

Non-additive Effects in Genomic Selection.

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.

Genomic selection models for directional dominance: an example for litter size in pigs.

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.

Influence of epistasis on response to genomic selection using complete sequence data.

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).

Orthogonal Estimates of Variances for Additive, Dominance, and Epistatic Effects in Populations.

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 F1 (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 F1 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.