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.     

Mixed Model Methods for Genomic Prediction and Variance Component Estimation of Additive and Dominance Effects Using SNP Markers

We established a genomic model of quantitative trait with genomic additive and dominance relationships that parallels the traditional quantitative genetics model, which partitions a genotypic value as breeding value plus dominance deviation and calculates additive and dominance relationships using pedigree information. Based on this genomic model, two sets of computationally complementary but mathematically identical mixed model methods were developed for genomic best linear unbiased prediction (GBLUP) and genomic restricted maximum likelihood estimation (GREML) of additive and dominance effects using SNP markers. These two sets are referred to as the CE and QM sets, where the CE set was designed for large numbers of markers and the QM set was designed for large numbers of individuals. GBLUP and associated accuracy formulations for individuals in training and validation data sets were derived for breeding values, dominance deviations and genotypic values. Simulation study showed that GREML and GBLUP generally were able to capture small additive and dominance effects that each accounted for 0.00005–0.0003 of the phenotypic variance and GREML was able to differentiate true additive and dominance heritability levels. GBLUP of the total genetic value as the summation of additive and dominance effects had higher prediction accuracy than either additive or dominance GBLUP, causal variants had the highest accuracy of GREML and GBLUP, and predicted accuracies were in agreement with observed accuracies. Genomic additive and dominance relationship matrices using SNP markers were consistent with theoretical expectations. The GREML and GBLUP methods can be an effective tool for assessing the type and magnitude of genetic effects affecting a phenotype and for predicting the total genetic value at the whole genome level.     

Including Dominance Effects in the Genomic BLUP Method for Genomic Evaluation

We evaluated the performance of GBLUP including dominance genetic effect (GBLUP-D) by estimating variances and predicting genetic merits in a computer simulation and 2 actual traits (T4 and T5) in pigs. In simulation data, GBLUP-D explained more than 50% of dominance genetic variance. Moreover, GBLUP-D yielded estimated total genetic effects over 1.2% more accurate than those yielded by GBLUP. In particular, when the dominance genetic variance was large, the accuracy could be substantially improved by increasing the number of markers. The dominance genetic variances in T4 and T5 accounted for 9.6% and 6.3% of the phenotypic variances, respectively. Estimates of such small dominance genetic variances contributed little to the improvement of the accuracies of estimated total genetic effects. In both simulation and pig data, there were nearly no differences in the estimates of additive genetic effects or their variance between GBLUP-D and GBLUP. Therefore, we conclude GBLUP-D is a feasible approach to improve genetic performance in crossbred populations with large dominance genetic variation and identify mating systems with good combining ability.     

Improvement of Prediction Ability for Genomic Selection of Dairy Cattle by Including Dominance Effects

Dominance may be an important source of non-additive genetic variance for many traits of dairy cattle. However, nearly all prediction models for dairy cattle have included only additive effects because of the limited number of cows with both genotypes and phenotypes. The role of dominance in the Holstein and Jersey breeds was investigated for eight traits: milk, fat, and protein yields; productive life; daughter pregnancy rate; somatic cell score; fat percent and protein percent. Additive and dominance variance components were estimated and then used to estimate additive and dominance effects of single nucleotide polymorphisms (SNPs). The predictive abilities of three models with both additive and dominance effects and a model with additive effects only were assessed using ten-fold cross-validation. One procedure estimated dominance values, and another estimated dominance deviations; calculation of the dominance relationship matrix was different for the two methods. The third approach enlarged the dataset by including cows with genotype probabilities derived using genotyped ancestors. For yield traits, dominance variance accounted for 5 and 7% of total variance for Holsteins and Jerseys, respectively; using dominance deviations resulted in smaller dominance and larger additive variance estimates. For non-yield traits, dominance variances were very small for both breeds. For yield traits, including additive and dominance effects fit the data better than including only additive effects; average correlations between estimated genetic effects and phenotypes showed that prediction accuracy increased when both effects rather than just additive effects were included. No corresponding gains in prediction ability were found for non-yield traits. Including cows with derived genotype probabilities from genotyped ancestors did not improve prediction accuracy. The largest additive effects were located on chromosome 14 near DGAT1 for yield traits for both breeds; those SNPs also showed the largest dominance effects for fat yield (both breeds) as well as for Holstein milk yield.     

On the Additive and Dominant Variance and Covariance of Individuals Within the Genomic Selection Scope

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.     

Unraveling Additive from Nonadditive Effects Using Genomic Relationship Matrices

The application of quantitative genetics in plant and animal breeding has largely focused on additive models, which may also capture dominance and epistatic effects. Partitioning genetic variance into its additive and nonadditive components using pedigree-based models (P-genomic best linear unbiased predictor) (P-BLUP) is difficult with most commonly available family structures. However, the availability of dense panels of molecular markers makes possible the use of additive- and dominance-realized genomic relationships for the estimation of variance components and the prediction of genetic values (G-BLUP). We evaluated height data from a multifamily population of the tree species Pinus taeda with a systematic series of models accounting for additive, dominance, and first-order epistatic interactions (additive by additive, dominance by dominance, and additive by dominance), using either pedigree- or marker-based information. We show that, compared with the pedigree, use of realized genomic relationships in marker-based models yields a substantially more precise separation of additive and nonadditive components of genetic variance. We conclude that the marker-based relationship matrices in a model including additive and nonadditive effects performed better, improving breeding value prediction. Moreover, our results suggest that, for tree height in this population, the additive and nonadditive components of genetic variance are similar in magnitude. This novel result improves our current understanding of the genetic control and architecture of a quantitative trait and should be considered when developing breeding strategies.     

Efficient Markov chain Monte Carlo implementation of Bayesian analysis of additive and dominance genetic variances in noninbred pedigrees

Accurate and fast computation of quantitative genetic variance parameters is of great importance in both natural and breeding populations. For experimental designs with complex relationship structures it can be important to include both additive and dominance variance components in the statistical model. In this study, we introduce a Bayesian Gibbs sampling approach for estimation of additive and dominance genetic variances in the traditional infinitesimal model. The method can handle general pedigrees without inbreeding. To optimize between computational time and good mixing of the Markov chain Monte Carlo (MCMC) chains, we used a hybrid Gibbs sampler that combines a single site and a blocked Gibbs sampler. The speed of the hybrid sampler and the mixing of the single-site sampler were further improved by the use of pretransformed variables. Two traits (height and trunk diameter) from a previously published diallel progeny test of Scots pine (Pinus sylvestris L.) and two large simulated data sets with different levels of dominance variance were analyzed. We also performed Bayesian model comparison on the basis of the posterior predictive loss approach. Results showed that models with both additive and dominance components had the best fit for both height and diameter and for the simulated data with high dominance. For the simulated data with low dominance, we needed an informative prior to avoid the dominance variance component becoming overestimated. The narrow-sense heritability estimates in the Scots pine data were lower compared to the earlier results, which is not surprising because the level of dominance variance was rather high, especially for diameter. In general, the hybrid sampler was considerably faster than the blocked sampler and displayed better mixing properties than the single-site sampler.     

The use of linear mixed models to estimate variance components from data on twin pairs by maximum likelihood.

It is shown that maximum likelihood estimation of variance components from twin data can be parameterized in the framework of linear mixed models. Standard statistical packages can be used to analyze univariate or multivariate data for simple models such as the ACE and CE models. Furthermore, specialized variance component estimation software that can handle pedigree data and user-defined covariance structures can be used to analyze multivariate data for simple and complex models, including those where dominance and/or QTL effects are fitted. The linear mixed model framework is particularly useful for analyzing multiple traits in extended (twin) families with a large number of random effects.     

Dominance Genetic Variance for Traits Under Directional Selection in Drosophila serrata

In contrast to our growing understanding of patterns of additive genetic variance in single- and multi-trait combinations, the relative contribution of nonadditive genetic variance, particularly dominance variance, to multivariate phenotypes is largely unknown. While mechanisms for the evolution of dominance genetic variance have been, and to some degree remain, subject to debate, the pervasiveness of dominance is widely recognized and may play a key role in several evolutionary processes. Theoretical and empirical evidence suggests that the contribution of dominance variance to phenotypic variance may increase with the correlation between a trait and fitness; however, direct tests of this hypothesis are few. Using a multigenerational breeding design in an unmanipulated population of Drosophila serrata, we estimated additive and dominance genetic covariance matrices for multivariate wing-shape phenotypes, together with a comprehensive measure of fitness, to determine whether there is an association between directional selection and dominance variance. Fitness, a trait unequivocally under directional selection, had no detectable additive genetic variance, but significant dominance genetic variance contributing 32% of the phenotypic variance. For single and multivariate morphological traits, however, no relationship was observed between trait–fitness correlations and dominance variance. A similar proportion of additive and dominance variance was found to contribute to phenotypic variance for single traits, and double the amount of additive compared to dominance variance was found for the multivariate trait combination under directional selection. These data suggest that for many fitness components a positive association between directional selection and dominance genetic variance may not be expected.     

Genomic prediction of hybrid performance in maize with models incorporating dominance and population specific marker effects

Identifying high performing hybrids is an essential part of every maize breeding program. Genomic prediction of maize hybrid performance allows to identify promising hybrids, when they themselves or other hybrids produced from their parents were not tested in field trials. Using simulations, we investigated the effects of marker density (10, 1, 0.3 marker per mega base pair, Mbp(-1)), convergent or divergent parental populations, number of parents tested in other combinations (2, 1, 0), genetic model (including population-specific and/or dominance marker effects or not), and estimation method (GBLUP or BayesB) on the prediction accuracy. We based our simulations on marker genotypes of Central European flint and dent inbred lines from an ongoing maize breeding program. To simulate convergent or divergent parent populations, we generated phenotypes by assigning QTL to markers with similar or very different allele frequencies in both pools, respectively. Prediction accuracies increased with marker density and number of parents tested and were higher under divergent compared with convergent parental populations. Modeling marker effects as population-specific slightly improved prediction accuracy under lower marker densities (1 and 0.3?Mbp(-1)). This indicated that modeling marker effects as population-specific will be most beneficial under low linkage disequilibrium. Incorporating dominance effects improved prediction accuracies considerably for convergent parent populations, where dominance results in major contributions of SCA effects to the genetic variance among inter-population hybrids. While the general trends regarding the effects of the aforementioned influence factors on prediction accuracy were similar for GBLUP and BayesB, the latter method produced significantly higher accuracies for models incorporating dominance.     

Dissecting total genetic variance into additive and dominance components of purebred and crossbred pig traits

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.     

Analysis of cytoplasmic and maternal effects. II. Genetic models for triploid endosperms

Genetic models for quantitative traits of triploid endosperms are proposed for the analysis of direct gene effects, cytoplasmic effects, and maternal gene effects. The maternal effect is partitioned into maternal additive and dominance components. In the full genetic model, the direct effect is partitioned into direct additive and dominance components and high-order dominance component, which are the cumulative effects of three-allele interactions. If the high-order dominance effects are of no importance, a reduced genetic model can be used. Monte Carlo simulations were conducted in this study for demonstrating unbiasedness of estimated variance and covariance components from the MINQUE (0/1) procedure, which is a minimum norm quadratic unbiased estimation (MINQUE) method setting 0 for all the prior covariances and 1 for all the prior variances. Robustness of estimating variance and covariance components for the genetic models was tested by simulations. Both full and reduced genetic models are shown to be robust for estimating variance and covariance components under several situations of no specific effects. Efficiency of predicting random genetic effects for the genetic models by the MINQUE (0/1) procedure was compared with the best linear unbiased prediction (BLUP). A worked example is given to illustrate the use of the reduced genetic model for kernel growth characteristics in corn (Zea mays L.).     

Estimating Additive and Non-Additive Genetic Variances and Predicting Genetic Merits Using Genome-Wide Dense Single Nucleotide Polymorphism Markers

Non-additive genetic variation is usually ignored when genome-wide markers are used to study the genetic architecture and genomic prediction of complex traits in human, wild life, model organisms or farm animals. However, non-additive genetic effects may have an important contribution to total genetic variation of complex traits. This study presented a genomic BLUP model including additive and non-additive genetic effects, in which additive and non-additive genetic relation matrices were constructed from information of genome-wide dense single nucleotide polymorphism (SNP) markers. In addition, this study for the first time proposed a method to construct dominance relationship matrix using SNP markers and demonstrated it in detail. The proposed model was implemented to investigate the amounts of additive genetic, dominance and epistatic variations, and assessed the accuracy and unbiasedness of genomic predictions for daily gain in pigs. In the analysis of daily gain, four linear models were used: 1) a simple additive genetic model (MA), 2) a model including both additive and additive by additive epistatic genetic effects (MAE), 3) a model including both additive and dominance genetic effects (MAD), and 4) a full model including all three genetic components (MAED). Estimates of narrow-sense heritability were 0.397, 0.373, 0.379 and 0.357 for models MA, MAE, MAD and MAED, respectively. Estimated dominance variance and additive by additive epistatic variance accounted for 5.6% and 9.5% of the total phenotypic variance, respectively. Based on model MAED, the estimate of broad-sense heritability was 0.506. Reliabilities of genomic predicted breeding values for the animals without performance records were 28.5%, 28.8%, 29.2% and 29.5% for models MA, MAE, MAD and MAED, respectively. In addition, models including non-additive genetic effects improved unbiasedness of genomic predictions.     

The Contribution of Quantitative Trait Loci and Neutral Marker Loci to the Genetic Variances and Covariances among Quantitative Traits in Random Mating Populations

Using Cockerham's approach of orthogonal scales, we develop genetic models for the effect of an arbitrary number of multiallelic quantitative trait loci (QTLs) or neutral marker loci (NMLs) upon any number of quantitative traits. These models allow the unbiased estimation of the contributions of a set of marker loci to the additive and dominance variances and covariances among traits in a random mating population. The method has been applied to an analysis of allozyme and quantitative data from the European oyster. The contribution of a set of marker loci may either be real, when the markers are actually QTLs, or apparent, when they are NMLs that are in linkage disequilibrium with hidden QTLs. Our results show that the additive and dominance variances contributed by a set of NMLs are always minimum estimates of the corresponding variances contributed by the associated QTLs. In contrast, the apparent contribution of the NMLs to the additive and dominance covariances between two traits may be larger than, equal to or lower than the actual contributions of the QTLs. We also derive an expression for the expected variance explained by the correlation between a quantitative trait and multilocus heterozygosity. This correlation explains only a part of the genetic variance contributed by the markers, i.e., in general, a combination of additive and dominance variances and, thus, provides only very limited information relative to the method supplied here.     

Genetics of tassel branch number in maize and its implications for a selection program for small tassel size

Summary Tassel branch numbers of six crosses of maize (Zea mays L.) were analyzed to determine inheritance of this trait. Generation mean analyses were used to estimate genetic effects, and additive and nonadditive components of variance were calculated and evaluated for bias due to linkage. Both narrow-sense and broad-sense heritabilities were estimated. Additive genetic variance estimates were significant in five of the six crosses, whereas estimates of variance due to nonadditive components were significant in only three crosses. Additionally, estimates of additive variance components usually were larger than corresponding nonadditive components. There was no evidence for linkage bias in these estimates. Estimates of additive genetic effects were significant in four of six crosses, but significant dominance, additive × additive and additive × dominance effects also were detected. Additive, dominance, and epistatic gene action, therefore, all influenced the inheritance of tassel branch number, but additive gene action was most important. Both narrow-sense and broadsense heritability estimates were larger than those reported for other physiological traits of maize and corroborated conclusions concerning the importance of additive gene action inferred from analyses of genetic effects and variances. We concluded that selection for smalltasseled inbreds could be accomplished most easily through a mass-selection and/or pedigree-selection system. Production of a small-tasseled hybrid would require crossing of two small-tasseled inbreds. We proposed two genetic models to explain unexpected results obtained for two crosses. One model involved five interacting loci and the other employed two loci displaying only additive and additive × additive gene action.Journal Paper No. J-9231 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa 50011. Project No. 2152     

作物品种间杂种优势遗传分析的新方法

本文提出了分析双列杂交试验资料的两个遗传模型。第一个模型包括加性、显性和母体效应;第二个模型只包括简单的加性和显性效应。还介绍了分析杂种优势、估算遗传方差分量以及预测遗传效应值的相应统计分析方法。用所介绍的遗传模型和分析方法以及常用的Griffing配合力分析方法,分析了棉花6个品种双列杂交的产量性状,并进一步比较了不同方法的分析结果。采用本文所介绍的遗传模型和分析方法,可以克服用Griffing的配合力模型及其方法分析杂种优势和配合力遗传表现所存在的局限性。     

Estimation of variance components of quantitative traits in inbred populations

Use of variance-component estimation for mapping of quantitative-trait loci in humans is a subject of great current interest. When only trait values, not genotypic information, are considered, variance-component estimation can also be used to estimate heritability of a quantitative trait. Inbred pedigrees present special challenges for variance-component estimation. First, there are more variance components to be estimated in the inbred case, even for a relatively simple model including additive, dominance, and environmental effects. Second, more identity coefficients need to be calculated from an inbred pedigree in order to perform the estimation, and these are computationally more difficult to obtain in the inbred than in the outbred case. As a result, inbreeding effects have generally been ignored in practice. We describe here the calculation of identity coefficients and estimation of variance components of quantitative traits in large inbred pedigrees, using the example of HDL in the Hutterites. We use a multivariate normal model for the genetic effects, extending the central-limit theorem of Lange to allow for both inbreeding and dominance under the assumptions of our variance-component model. We use simulated examples to give an indication of under what conditions one has the power to detect the additional variance components and to examine their impact on variance-component estimation. We discuss the implications for mapping and heritability estimation by use of variance components in inbred populations.     

The use of genetic correlations to evaluate associations between SNP markers and quantitative traits

Open-pollinated progeny of Corymbia citriodora established in replicated field trials were assessed for stem diameter, wood density, and pulp yield prior to genotyping single nucleotide polymorphisms (SNP) and testing the significance of associations between markers and assessment traits. Multiple individuals within each family were genotyped and phenotyped, which facilitated a comparison of standard association testing methods and an alternative method developed to relate markers to additive genetic effects. Narrow-sense heritability estimates indicated there was significant additive genetic variance within this population for assessment traits ( $ {\widehat{h}^{{2}}} = 0.{28}\;{\text{to}}\;0.{44} $ ) and genetic correlations between the three traits were negligible to moderate (r _G?=?0.08 to 0.50). The significance of association tests (p values) were compared for four different analyses based on two different approaches: (1) two software packages were used to fit standard univariate mixed models that include SNP-fixed effects, (2) bivariate and multivariate mixed models including each SNP as an additional selection trait were used. Within either the univariate or multivariate approach, correlations between the tests of significance approached +1; however, correspondence between the two approaches was less strong, although between-approach correlations remained significantly positive. Similar SNP markers would be selected using multivariate analyses and standard marker-trait association methods, where the former facilitates integration into the existing genetic analysis systems of applied breeding programs and may be used with either single markers or indices of markers created with genomic selection processes.     

Non-additive genetic variation in growth,carcass and fertility traits of beef cattle

Background

A better understanding of non-additive variance could lead to increased knowledge on the genetic control and physiology of quantitative traits, and to improved prediction of the genetic value and phenotype of individuals. Genome-wide panels of single nucleotide polymorphisms (SNPs) have been mainly used to map additive effects for quantitative traits, but they can also be used to investigate non-additive effects. We estimated dominance and epistatic effects of SNPs on various traits in beef cattle and the variance explained by dominance, and quantified the increase in accuracy of phenotype prediction by including dominance deviations in its estimation.

Methods

Genotype data (729 068 real or imputed SNPs) and phenotypes on up to 16 traits of 10 191 individuals from Bos taurus, Bos indicus and composite breeds were used. A genome-wide association study was performed by fitting the additive and dominance effects of single SNPs. The dominance variance was estimated by fitting a dominance relationship matrix constructed from the 729 068 SNPs. The accuracy of predicted phenotypic values was evaluated by best linear unbiased prediction using the additive and dominance relationship matrices. Epistatic interactions (additive × additive) were tested between each of the 28 SNPs that are known to have additive effects on multiple traits, and each of the other remaining 729 067 SNPs.

Results

The number of significant dominance effects was greater than expected by chance and most of them were in the direction that is presumed to increase fitness and in the opposite direction to inbreeding depression. Estimates of dominance variance explained by SNPs varied widely between traits, but had large standard errors. The median dominance variance across the 16 traits was equal to 5% of the phenotypic variance. Including a dominance deviation in the prediction did not significantly increase its accuracy for any of the phenotypes. The number of additive × additive epistatic effects that were statistically significant was greater than expected by chance.

Conclusions

Significant dominance and epistatic effects occur for growth, carcass and fertility traits in beef cattle but they are difficult to estimate precisely and including them in phenotype prediction does not increase its accuracy.     

Modeling additive and non-additive effects in a hybrid population using genome-wide genotyping: prediction accuracy implications

Hybrids are broadly used in plant breeding and accurate estimation of variance components is crucial for optimizing genetic gain. Genome-wide information may be used to explore models designed to assess the extent of additive and non-additive variance and test their prediction accuracy for the genomic selection. Ten linear mixed models, involving pedigree- and marker-based relationship matrices among parents, were developed to estimate additive (A), dominance (D) and epistatic (AA, AD and DD) effects. Five complementary models, involving the gametic phase to estimate marker-based relationships among hybrid progenies, were developed to assess the same effects. The models were compared using tree height and 3303 single-nucleotide polymorphism markers from 1130 cloned individuals obtained via controlled crosses of 13 Eucalyptus urophylla females with 9 Eucalyptus grandis males. Akaike information criterion (AIC), variance ratios, asymptotic correlation matrices of estimates, goodness-of-fit, prediction accuracy and mean square error (MSE) were used for the comparisons. The variance components and variance ratios differed according to the model. Models with a parent marker-based relationship matrix performed better than those that were pedigree-based, that is, an absence of singularities, lower AIC, higher goodness-of-fit and accuracy and smaller MSE. However, AD and DD variances were estimated with high s.es. Using the same criteria, progeny gametic phase-based models performed better in fitting the observations and predicting genetic values. However, DD variance could not be separated from the dominance variance and null estimates were obtained for AA and AD effects. This study highlighted the advantages of progeny models using genome-wide information.