Genetic evaluation methods for populations with dominance and inbreeding (original) (raw)
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PloS one, 2014
The traditional quantitative genetics model was used as the unifying approach to derive six existing and new definitions of genomic additive and dominance relationships. The theoretical differences of these definitions were in the assumptions of equal SNP effects (equivalent to across-SNP standardization), equal SNP variances (equivalent to within-SNP standardization), and expected or sample SNP additive and dominance variances. The six definitions of genomic additive and dominance relationships on average were consistent with the pedigree relationships, but had individual genomic specificity and large variations not observed from pedigree relationships. These large variations may allow finding least related genomes even within the same family for minimizing genomic relatedness among breeding individuals. The six definitions of genomic relationships generally had similar numerical results in genomic best linear unbiased predictions of additive effects (GBLUP) and similar genomic REM...
Journal of Animal Breeding and Genetics, 2002
Inbreeding depression estimates obtained by regression of the individual performance on the inbreeding were studied by stochastic simulation under various genetic models (solely additive, partial dominance, overdominance and epistasis), and mating strategies (random mating versus selection). In all models, inbreeding depression estimates based on the individual pedigree inbreeding coef®cients were compared with estimates based on the true level of autozygosity. For the model with partial dominance and selection, the estimates of inbreeding depression from pedigree information were more negative (lower) than those based on true inbreeding coef®cients whereas, in contrast, they were less negative (higher) for the models with overdominance and selection. The difference in the variation of true and pedigree individual inbreeding coef®cient indicated that biased estimates might occur even in random mating populations. The estimation of inbreeding depression was further complicated when epistatic effects were present. The sign and the magnitude of the inbreeding effect (depression) estimates might be rather heterogeneous if additive by dominance effects are present because they are strongly dependent on the gene frequency. It was also shown that inbreeding depression is possible in models with negative additive by dominance effects. In models with dominance by dominance inheritance it was dif®cult to assess the non-linear relationship between performance and inbreeding, while at the same time, non-linear estimates based on pedigree information were extremely biased. The results obtained indicate that new or additional methodologies are required if reliable conclusions about consequences of inbreeding depression are needed.
Bias and precision of estimates of genotype-by-environment interaction: A simulation study
Aquaculture, 2010
Re-ranking of genotypes across environments is a form of genotype-by-environment (G × E) interaction with serious consequences for breeding programmes. The degree of such G × E interaction can be estimated using the genetic correlation (r g ) between measurements in two environments for a given trait. When r g is lower than 0.8, G × E interaction is commonly considered to be biologically significant. Here a stochastic simulation was used to study the impact of population structure on bias and precision of genetic correlation estimates between two environments. Simulated populations resulted from a nested mating design (1 sire to 2 dams). Simulated r g was 0.0, 0.5, or 0.8. A trait with heritability (h 2 ) of either 0.3 or 0.1 in both environments was simulated. Simulation results show that genetic correlation estimates are biased downward especially when the simulated r g is 0.8, heritability is 0.1, and family size is less than 10. A downward biased genetic correlation estimate incorrectly suggests the existence of G × E interaction. This can lead to the erroneous conclusion that a multi-environment breeding programme is needed. The optimal design with the lowest mean square error for r g for a trait with low h 2 requires a large family size (20-25) and a low number of families (100-80 or 50-40 for population size fixed to 2000 and 1000 animals, respectively). For traits with moderate h 2 , the optimal family size is 10 with 200 or 100 families for population size fixed to 2000 and 1000, respectively. We also studied the effect of selective mortality on G × E estimates. However, schemes with unequal family sizes due to differences between families in survival produced similar results for the optimum design as schemes with equal family sizes. Equal-family-size design can thus be used to determine the optimal design for estimating G × E interaction. Our study can be used as a guideline for estimating a genetic correlation for practical breeding programmes.
Genetics Selection Evolution, 2005
Selection programmes are mainly concerned with increasing genetic gain. However, short-term progress should not be obtained at the expense of the within-population genetic variability. Different prediction models for the evolution within a small population of the genetic mean of a selected trait, its genetic variance and its inbreeding have been developed but have mainly been validated through Monte Carlo simulation studies. The purpose of this study was to compare theoretical predictions to experimental results. Two deterministic methods were considered, both grounded on a polygenic additive model. Differences between theoretical predictions and experimental results arise from differences between the true and the assumed genetic model, and from mathematical simplifications applied in the prediction methods. Two sets of experimental lines of chickens were used in this study: the Dutch lines undergoing true truncation mass selection, the other lines (French) undergoing mass selection with a restriction on the representation of the different families. This study confirmed, on an experimental basis, that modelling is an efficient approach to make useful predictions of the evolution of selected populations although the basic assumptions considered in the models (polygenic additive model, normality of the distribution, base population at the equilibrium, etc.) are not met in reality. The two deterministic methods compared yielded results that were close to those observed in real data, especially when the selection scheme followed the rules of strict mass selection: for instance, both predictions overestimated the genetic gain in the French experiment, whereas both predictions were close to the observed values in the Dutch experiment.
The value of genomic relationship matrices to estimate levels of inbreeding
Genetics Selection Evolution, 2021
Background Genomic relationship matrices are used to obtain genomic inbreeding coefficients. However, there are several methodologies to compute these matrices and there is still an unresolved debate on which one provides the best estimate of inbreeding. In this study, we investigated measures of inbreeding obtained from five genomic matrices, including the Nejati-Javaremi allelic relationship matrix (FNEJ), the Li and Horvitz matrix based on excess of homozygosity (FL&H), and the VanRaden (methods 1, FVR1, and 2, FVR2) and Yang (FYAN) genomic relationship matrices. We derived expectations for each inbreeding coefficient, assuming a single locus model, and used these expectations to explain the patterns of the coefficients that were computed from thousands of single nucleotide polymorphism genotypes in a population of Iberian pigs. Results Except for FNEJ, the evaluated measures of inbreeding do not match with the original definitions of inbreeding coefficient of Wright (correlation...
Additional considerations to the use of single‐step genomic predictions in a dominance setting
Journal of Animal Breeding and Genetics, 2019
Recent publications indicate that single-step models are suitable to estimate breeding values, dominance deviations and total genetic values with acceptable quality. Additive single-step methods implicitly extend known number of allele information from genotyped to non-genotyped animals. This theory is well derived in an additive setting. It was recently shown, at least empirically, that this basic strategy can be extended to dominance with reasonable prediction quality. Our study addressed two additional issues. It illustrated the theoretical basis for extension and validated genomic predictions to dominance based on single-step genomic best linear unbiased prediction theory. This development was then extended to include inbreeding into dominance relationships, which is a currently not yet solved issue. Different parametrizations of dominance relationship matrices were proposed. Five dominance single-step inverse matrices were tested and described as C 1 , C 2 , C 3 , C 4 and C 5. Genotypes were simulated for a real pig population (n = 11,943 animals). In order to avoid any confounding issues with additive effects, pseudo-records including only dominance deviations and residuals were simulated. SNP effects of heterozygous genotypes were summed up to generate true dominance deviations. We added random noise to those values and used them as phenotypes. Accuracy was defined as correlation between true and predicted dominance deviations. We conducted five replicates and estimated accuracies in three sets: between all (S 1), non-genotyped (S 2) and inbred non-genotyped (S 3) animals. Potential bias was assessed by regressing true dominance deviations on predicted values. Matrices accounting for inbreeding (C 3 , C 4 and C 5) best fit. Accuracies were on average 0.77, 0.40 and 0.46 in S 1 , S 2 and S 3 , respectively. In addition, C 3 , C 4 and C 5 scenarios have shown better accuracies than C 1 and C 2 , and dominance deviations were less biased. Better matrix compatibility (accuracy and bias) was observed by re-scaling diagonal elements to 1 minus the inbreeding coefficient (C 5).
Journal of Dairy Science, 2014
The observed low accuracy of genomic selection in multibreed and admixed populations results from insufficient linkage disequilibrium between markers and trait loci. Failure to remove variation due to the population structure may also hamper the prediction accuracy. We verified if accounting for breed origin of alleles in the calculation of genomic relationships would improve the prediction accuracy in an admixed population. Individual breed proportions derived from the pedigree were used to estimate breed-wise allele frequencies (AF). Breed-wise and across-breed AF were estimated from the currently genotyped population and also in the base population. Genomic relationship matrices (G) were subsequently calculated using across-breed (G AB) and breed-wise (G BW) AF estimated in the currently genotyped and also in the base population. Unified relationship matrices were derived by combining different G with pedigree relationships in the evaluation of genomic estimated breeding values (GEBV) for genotyped and ungenotyped animals. The validation reliabilities and inflation of GEBV were assessed by a linear regression of deregressed breeding value (deregressed proofs) on GEBV, weighted by the reliability of deregressed proofs. The regression coefficients (b 1) from G AB ranged from 0.76 for milk to 0.90 for protein. Corresponding b 1 terms from G BW ranged from 0.72 to 0.88. The validation reliabilities across 4 evaluations with different G were generally 36, 40, and 46% for milk, protein, and fat, respectively. Unexpectedly, validation reliabilities were generally similar across different evaluations, irrespective of AF used to compute G. Thus, although accounting for the population structure in G BW tends to simplify the blending of genomic-and pedigree-based relationships, it appeared to have little effect on the validation reliabilities.