bayesian methods

This study aimed to compare different methods of genomic evaluation using the criteria of correlation (ρ), regression (β), mean square error (MSE), and selection effectiveness (SE). For this purpose, nine different scenarios were designed based on different levels of heritability (0.1, 0.3, and 0.5) and different numbers of QTLs (20, 200, and 1000). To simulate different scenarios, five generations with a size of 1000 animals were simulated, of which the first two generations were considered as the reference population and the next three generations as the validation population. For each animal, a genome of 500 centimorgans with a marker density of 10000 SNP consisting of five chromosomes was simulated. Genomic breeding values were predicted using three statistical methods GBLUP, Bayes A, and Bayes B. The results showed that with increasing generation interval from the reference population, the accuracy of genomic breeding values decreased for three statistical methods, although Bayesian methods performed better in terms of continuity of accuracy. Based on the criteria of correlation, regression, and selection effectiveness, with increasing the levels of heritability, improved accuracy was observed, but the criterion of mean squares error showed the opposite trend. Bayesian methods performed better in low QTLs, but differences in different genomic evaluation methods were minimized in high QTLs. The results of selection effectiveness in comparison with the accuracy of genomic breeding value showed that accuracy can’t always be a suitable criterion for determining the superior method of genomic evaluation.

The aim of this study was to estimate genetic components and parameters of retained placenta and dystocia traits in FOKA dairy farm. The non-genetic factors affecting these traits were evaluated using logistic regression implemented in GENMOD procedure of SAS 9.1 software. In order to do genetic evaluations, 5 Bayesian threshold models of repeat records and a Bayesian bivariate model were used. The genetic model parameters were obtained using Bayesian and Gibbs sampling method implemented in THRGIBBS1F90B software. The results shown effects that the season and year of birth were significant on the retained placenta; however, only effect of the birth year was significant for the dystocia. For both traits, the best fitted model was selected using DIC measure. Direct heritability, maternal genetic effect, maternal permanent environmental effect and repeatability estimates for retained placenta using best fitted model on repeated records were obtained as 0.15(0.002), 0.03(0.007), 0.14(0.01) and 0.29(0.02), respectively. In multivariate analysis, these parameters were estimated as 0.005(0.003), 0.001(0.030), 0.002(0.001) and 0.008(0.002) respectively. These parameters for dystocia trait using best fitted model over repeated records were as 0.03(0.001), 0.02(0.002), 0.27(0.003) and 0.30(0.01), respectively. In multivariate analysis, aforementioned parameters were estimated as 0.003(0.01), 0.005(0.002), 0.004(0.001) and 0.007(0.002), respectively. The results of this research showed that, considering the economic importance of these two traits on the profitability of FOKA dairy farm, and on the other hand, estimated a low direct, maternal heritability and different correlations i.e. direct genetic (0.41), maternal genetics (0.18), phenotypic (0.55), environmental (0.58) permanent environment (0.81), much attention should be paid on management of environmental factors affecting these traits. In this regards, it is not expected that manipulating of direct and maternal genetic would be crucial on aforementioned traits.

The aim of this study was to compare different methods of Bayesian (parameteric) approaches for predicting genomic breeding values of traits with different genetic architecture in different distribution of gene effects, number of quantitative traits loci, heritability and the number of reference population using simulated data. A genome contained 3 chromosomes, with the length of 100 cM and 1000 evenly spaced single nucleotide polymorphisms (SNP) on each chromosome was simulated. For hypotheses simulation attributes, different distribution of gene effects (uniform, normal and gamma), 3 levels of QTL (50, 200 and 400), 2 levels of heritability (0.16 and 0.5) and 2 levels of the reference population (1000 and 2000) was considered. In order to predict breeding values of individuals in the population of reference and verification, 5 Bayesian methods including Bayes Ridge regression (BRR), A, LASSO (L), Cπ and B were used. As the distance between reference population and selection candidates increased, due to disruption of linkage phase, the accuracy of genomic breeding values in all methods decreased. As heritability increased from 0.16 to 0.5, all methods showed an increase of about 0.2 in accuracy of genomic breeding values. When the number of reference population had increased from 1000 to 2000, all methods showed increased accuracy by nearly 0.18. When the distribution of gene effects was gamma, the Bayes A method showed a clear preference along with both levels of heritability compared with other methods. When the distribution of gene effects was uniform, all methods showed similar accuracy. For high heritability traits, the accuracy of prediction reduced as the number of QTL increased from 50 to 200. Conversly, in low heritability traits, there was no visible influence in accuracy of genomic breeding values.

Advances in high-throughput assays for genotyping single nucleotide polymorphisms (SNP) led to using these dense markers for predicting genomic breeding values, called genomic selection, and have been revolutionized both animal and crop breeding programs. The accuracy of genomic predictions is determined by the size of the reference population, extent of relationships between selection candidates and the reference population, linkage disequilibrium among markers and QTLs, the method used to estimate marker effects, and genetic architecture of the trait. Most of stuides on this topic focus on continuous traits, but some of economical important traits in livestock are threshold. Therefore, a stochastic simulation was used to compare 125 different scenarios for a threshold trait based on five 10, 50, 150, 500 and 2000 underlying QTL numbers, five normal, uniform, t, gamma and Laplace distributions for QTL effects and five BayesA, BayesB, BayesC, BayesL and BayesR methods for estimation of marker effects.
In order to compare the different methods, R software were used to simulate datasets. Simulation started with a base population of 100 animals, including 50 male and 50 female, which randomly mated for subsequent 50 generations. Generations were discrete and number of animals for each generation fixed at 100 animals. Thereafter, by randomly mating of animals in generation 50, reference population generation with 1000 animals were obtained and a threshold trait was simulated for each of them. Finally, Next validation population generation was produced by randomly mating of animals from the previous generation. Simulated genome for each animal consisted of 10 chromosomes with equal 1 Morgan lengths, each having 1000 evenly spaced SNPs. In each scenario QTLs were randomly distributed on genome and their substitution effects were drawn from one of five normal, uniform, t, gamma and Laplace distributions. Marker effects were estimated in reference population using five different Bayesian methods that differ with respect to assumptions regarding distribution of marker effects, including: Bayes A, Bayes B, Bayes C, Bayes L and Bayes R. These estimated markers effects were used for genomic breeding value predictions of animals in validation population which did not have any phenotype. The accuracy of the different methods was calculated as correlation between true and estimated genomic breeding values.
Results of this study showed that Bayes A, Bayes B and Bayes C predictions was affected by QTL numbers and distributions, while Bayes L and Bayes R had almost same accuracies for all scenarios. Scenario with gamma distribution for QTL effects and number of 10 QTLs had highest accuracy for Bayes A, Bayes B and Bayes C methods. Bayes C method was the best method when number of QTL was low. Increases in number of QTL from 10 to 150 were decreased accuracy of Bayes A, Bayes B and Bayes C methods and after that accuracy of different methods was constant and same. When distributions of QTL effects was uniform lower accuracy achieved rather than other distributions for same QTL number, instead distributions with unequal QTL variance like gamma increased accuracy of Bayes A, Bayes B, and Bayes C methods. These results were because of different extent of shrinkage of estimates of effects for different methods. Methods like Bayes B induced differential shrinkage of estimates relative to methods like Bayes R and Bayes L lead to higher accuracy for scenarios with low QTL number and unequal QTL variance.
Conclusion in a nutshell, different studied methods had diverse results for various QTL number and distribution, and its difficult to suggest a method that best in all situations. However, it is better to use methods like Bayes B when the number of QTLs was low and each QTL had not equal contribution to the trait of interest.

The current study was carried out to evaluate accuracy of some Bayesian methods for genomic breeding values prediction for threshold traits with different types of genetic architecture based on distribution of gene effect and QTL numbers. A genome consisted of 3 chromosomes of 100 CM with 2000 single nucleotide polymorphisms (SNP) was simulated. The QTL numbers were 0.01, 0.05 and 0.1 of total number of SNPs whose effects were simulated by uniform, normal and gamma distributions. The studied threshold traits were either one-threshold (survival) or two-threshold (litter size). Genomic estimated breeding values were predicted by five regression methods including Bayesian Ridge Regression (BRR), Bayes A, Bayes B, Bayes C, and Bayes LASSO. Comparison of prediction accuracy of these methods (correlation between real and estimated breeding value) showed that Bayesian methods are powerful for genomic evaluation and there were no significant differences among them. The proficiency of these methods for one-threshold trait was significantly higher compared to two-threshold trait. Non-significant and irregular variance was observed in accuracy of prediction these methods between different QTL numbers and statistical distributions. Also the results showed that increasing in distance (generation) between reference and target populations will lead to decline in accuracy of prediction due to breakdown of LD between QTL and marker.

The objective of this study was to compare six statistical methods for prediction of genomic breeding values for traits with different genetic architecture in term of gene effects distributions and number of Quantitative Traits Loci (QTLs). A genome consisted of 500 bi-allelic single nucleotide polymorphism (SNP) markers distributed over a chromosomes with 100 cm length was simulated. Three different gene effects distributions (uniform، normal and gamma) were considered. Number of QTLs varied from 50 to 200. Finally، nine quantitative traits with different genetic architecture were generated. The performance of six statistical methods of genomic prediction that differ with respect to assumptions regarding distribution of marker effects، including i) Genomic Best Linear Unbiased Prediction (GBLUP)، ii) Ridge Regression Best Linear Unbiased Prediction (RRBLUP)، iii) Bayes A، iv) Bayes B، v) Bayes C، and vi) Bayesian least absolute shrinkage and selection operator (Bayes L) are presented. The accuracy of prediction declined significantly over generations (P< 0. 05) but Bayesian methods outperformed GBLUP and RRBLUP in persistence of accuracy of genomic estimated breeding values over generations. Bayesian methods were superior to GBLUP and RRBLUP when the gene effects distribution generated from gamma distribution. The highest accuracy of genomic breeding values was observed when the gene effects come from normal distribution. In all statistical evaluation methods with increasing the number of QTLs towards 200، the accuracy of predicted genomic values has been decreased. In general، Bayesian and GBLUP methods performed better in prediction than RRBLUP method. These results gave some evidences that when the genetic architecture of quantitative traits deviated from infinitesimal model assumptions، Bayesian methods usually perform better than GBLUP and RR-BLUP.