Simulation of functional additive and non-additive genetic effects using statistical estimates from quantitative genetic models.

Stochastic simulation software is commonly used to aid breeders designing cost-effective breeding programs and to validate statistical models used in genetic evaluation. An essential feature of the software is the ability to simulate populations with desired genetic and non-genetic parameters. However, this feature often fails when non-additive effects due to dominance or epistasis are modeled, as the desired properties of simulated populations are estimated from classical quantitative genetic statistical models formulated at the population level. The software simulates underlying functional effects for genotypic values at the individual level, which are not necessarily the same as effects from statistical models in which dominance and epistasis are included. This paper provides the theoretical basis and mathematical formulas for the transformation between functional and statistical effects in such simulations. The transformation is demonstrated with two statistical models analyzing individual phenotypes in a single population (common in animal breeding) and plot phenotypes of three-way hybrids involving two inbred populations (observed in some crop breeding programs). We also describe different methods for the simulation of functional effects for additive genetics, dominance, and epistasis to achieve the desired levels of variance components in classical statistical models used in quantitative genetics.

Prediction of additive, epistatic, and dominance effects using models accounting for incomplete inbreeding in parental lines of hybrid rye and sugar beet.

Genomic models for prediction of additive and non-additive effects within and across different heterotic groups are lacking for breeding of hybrid crops. In this study, genomic prediction models accounting for incomplete inbreeding in parental lines from two different heterotic groups were developed and evaluated. The models can be used for prediction of general combining ability (GCA) of parental lines from each heterotic group as well as specific combining ability (SCA) of all realized and potential crosses. Here, GCA was estimated as the sum of additive genetic effects and within-group epistasis due to high degree of inbreeding in parental lines. SCA was estimated as the sum of across-group epistasis and dominance effects. Three models were compared. In model 1, it was assumed that each hybrid was produced from two completely inbred parental lines. Model 1 was extended to include three-way hybrids from parental lines with arbitrary levels of inbreeding: In model 2, parents of the three-way hybrids could have any levels of inbreeding, while the grandparents of the maternal parent were assumed completely inbred. In model 3, all parental components could have any levels of inbreeding. Data from commercial breeding programs for hybrid rye and sugar beet was used to evaluate the models. The traits grain yield and root yield were analyzed for rye and sugar beet, respectively. Additive genetic variances were larger than epistatic and dominance variances. The models' predictive abilities for total genetic value, for GCA of each parental line and for SCA were evaluated based on different cross-validation strategies. Predictive abilities were highest for total genetic values and lowest for SCA. Predictive abilities for SCA and for GCA of maternal lines were higher for model 2 and model 3 than for model 1. The implementation of the genomic prediction models in hybrid breeding programs can potentially lead to increased genetic gain in two different ways: I) by facilitating the selection of crossing parents with high GCA within heterotic groups and II) by prediction of SCA of all realized and potential combinations of parental lines to produce hybrids with high total genetic values.

Statistical model and testing designs to increase response to selection with constrained inbreeding in genomic breeding programs for pigs affected by social genetic effects.

BACKGROUND: Social genetic effects (SGE) are the effects of the genotype of one animal on the phenotypes of other animals within a social group. Because SGE contribute to variation in economically important traits for pigs, the inclusion of SGE in statistical models could increase responses to selection (RS) in breeding programs. In such models, increasing the relatedness of members within groups further increases RS when using pedigree-based relationships; however, this has not been demonstrated with genomic-based relationships or with a constraint on inbreeding. In this study, we compared the use of statistical models with and without SGE and compared groups composed at random versus groups composed of families in genomic selection breeding programs with a constraint on the rate of inbreeding. RESULTS: When SGE were of a moderate magnitude, inclusion of SGE in the statistical model substantially increased RS when SGE were considered for selection. However, when SGE were included in the model but not considered for selection, the increase in RS and in accuracy of predicted direct genetic effects (DGE) depended on the correlation between SGE and DGE. When SGE were of a low magnitude, inclusion of SGE in the model did not increase RS, probably because of the poor separation of effects and convergence issues of the algorithms. Compared to a random group composition design, groups composed of families led to higher RS. The difference in RS between the two group compositions was slightly reduced when using genomic-based compared to pedigree-based relationships. CONCLUSIONS: The use of a statistical model that includes SGE can substantially improve response to selection at a fixed rate of inbreeding, because it allows the heritable variation from SGE to be accounted for and capitalized on. Compared to having random groups, family groups result in greater response to selection in the presence of SGE but the advantage of using family groups decreases when genomic-based relationships are used.

Phenotypically Selective Genotyping Realizes More Genetic Gains in a Rainbow Trout Breeding Program in the Presence of Genotype-by-Environment Interactions.

Selective genotyping of phenotypically superior animals may lead to bias and less accurate genomic breeding values (GEBV). Performing selective genotyping based on phenotypes measured in the breeding environment (B) is not necessarily a good strategy when the aim of a breeding program is to improve animals' performance in the commercial environment (C). Our simulation study compared different genotyping strategies for selection candidates and for fish in C in a breeding program for rainbow trout in the presence of genotype-by-environment interactions when the program had limited genotyping resources and unregistered pedigrees of individuals. For the reference population, selective genotyping of top and bottom individuals in C based on phenotypes measured in C led to the highest genetic gains, followed by random genotyping and then selective genotyping of top individuals in C. For selection candidates, selective genotyping of top individuals in B based on phenotypes measured in B led to the highest genetic gains, followed by selective genotyping of top and bottom individuals and then random genotyping. Selective genotyping led to bias in predicting GEBV. However, in scenarios that used selective genotyping of top fish in B and random genotyping of fish in C, predictions of GEBV were unbiased, with genetic correlations of 0.2 and 0.5 between traits measured in B and C. Estimates of variance components were sensitive to genotyping strategy, with an overestimation of the variance with selective genotyping of top and bottom fish and an underestimation of the variance with selective genotyping of top fish. Unbiased estimates of variance components were obtained when fish in B and C were genotyped at random. In conclusion, we recommend phenotypic genotyping of top and bottom fish in C and top fish in B for the purpose of selecting breeding animals and random genotyping of individuals in B and C for the purpose of estimating variance components when a genomic breeding program for rainbow trout aims to improve animals' performance in C.

Genetic analysis on body weight at different ages in broiler chicken raised in commercial environment.

A multivariate model was developed and used to estimate genetic parameters of body weight (BW) at 1-6 weeks of age of broilers raised in a commercial environment. The development of model was based on the predictive ability of breeding values evaluated from a cross-validation procedure that relied on half-sib correlation. The multivariate model accounted for heterogeneous variances between sexes through standardization applied to male and female BWs differently. It was found that the direct additive genetic, permanent environmental maternal and residual variances for BW increased drastically as broilers aged. The drastic increase in variances over weeks of age was mainly due to scaling effects. The ratio of the permanent environmental maternal variance to phenotypic variance decreased gradually with increasing age. Heritability of BW traits ranged from 0.28 to 0.33 at different weeks of age. The direct genetic effects on consecutive weekly BWs had high genetic correlations (0.85-0.99), but the genetic correlations between early and late BWs were low (0.32-0.57). The difference in variance components between sexes increased with increasing age. In conclusion, the permanent environmental maternal effect on broiler chicken BW decreased with increasing age from weeks 1 to 6. Potential bias of the model that considered identical variances for sexes could be reduced when heterogeneous variances between sexes are accounted for in the model.