Genomic breeding value prediction and QTL mapping of QTLMAS2011 data using Bayesian and GBLUP methods

Data

The simulated population included 20 sires, 10 dams per sire and 15 full-sib progeny per dam. The genome consisted of 5 chromosomes of 1 Morgan and 1,998 evenly spaced SNPs. Sources of information for analysis included 2 generations of pedigree, genotypes for all individuals and phenotypic records for 10 progeny per family. More detailed description of the dataset is available at [3].

Methods to predict GEBV

where X _ij is the copy number of a given allele of animal i at SNP j, W _ij is the dummy variable indicating whether the genotype for SNP j of animal i is heterozygous, a _j (additive effect) is half the difference between homozygotes for SNP j, and d _j (dominance effect) is the difference between heterozygote and the mean of homozygotes for SNP j. The priors for a _j and d _j were mixtures of normals as described in [5], with effect specific values for π (π _a and π _d ) and variance σ² (${\sigma }_a^2$and ${\sigma }_d^2$). Gibbs sampling was used to sample the posterior distribution of model parameters. SNP effects were estimated by the mean of the sampled values. GEBVs were predicted as the linear combination of the SNP substitution effects. GenSel [7] was used to implement the Bayesian methods.

In GBLUP the presence of dominance was investigated using a model with an additional random dominance effect (G2) for each animal. The variance-covariance matrix for this effect was created similar to the genomic relationship matrix G, except genotypes were coded as 1 for heterozygotes and 0 for both homozygotes. The third model (G3) had an additional random additive-by-additive epistatic effect for each animal, with G ² as the variance-covariance matrix. GEBV were estimated using models G1 to G3 with variance components estimated using ASReml [8].

Methods to map QTL

where α is the vector of allele substitution effects, ${\sigma }_{\alpha }^2={\sigma }_a^2/2\sum {\mathsf{\text{p}}}_{\mathsf{\text{i}}}\left(1-{\mathsf{\text{p}}}_{\mathsf{\text{i}}}\right)$ where ${\sigma }_{\mathsf{\text{a}}}^2$ is additive genetic variance, Z is the genotype matrix with dimensions equal to the number of individuals by the number of SNPs, and â is the vector of GEBV obtained from GBLUP. Given the estimated SNP effects, QTL were mapped to the positions where the SNP had visually significant effects on the trait.

Estimated variance components

QTL mapping

Figure 1 shows the estimated SNP effects and single SNP model frequencies for BayesCπ with the additive model. Two regions showed strong evidence of association, indicating QTL. The additive signals of SNP from the dominance model of BayesCπ shown in Figure 2 confirm the results of the additive model and suggest the absence of dominance. The top 10-SNP window variances were markedly higher than the background window variances (Figure 3). While the top 10-SNP window variances agreed with the significant regions found by single SNP signals (Figure 2), the moderate single SNP signals towards the end of the genome were absent in the window variances. BayesB gave similar results to BayesCπ thus the results are not shown. However, the selection of significant windows in BayesB was more subjective. GBLUP resulted in more signals and larger noise, which increased the probability of false positives (Figure 4). It turned out that BayesB detected 6 QTL, BayesCπ 5 and GBLUP 4, out of 8 simulated QTL regions. Except for one false positive on chromosome 1, all QTL identified by BayesB and BayesCπ were in the true simulated QTL regions. Under the additive model, a QTL region on chromosome 4 was successfully detected by BayesB, and at the cost of some false positives by GBLUP, but missed by BayesCπ. This QTL, however, turned out to be an imprinted QTL. None of the methods found the two simulated epistatic QTL on chromosome 5.

Predictive accuracy of GEBV