### 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

For additive gene-action, the statistical models BayesB [4] with π = 0.995, BayesCπ [5] and GBLUP (G1) with relationship matrix created according to [6] were applied. To examine dominance gene-action, a both additive and dominance SNP effects were fitted for every locus using BayesCπ:

{y}_{i}=\mathbf{\mu}+{\sum}_{j=1}^{k}\left({X}_{ij}{a}_{j}+{W}_{ij}{d}_{j}\right)+{e}_{i}

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 σ^{2} ({\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

In the Bayesian methods, QTL positions were identified based on the absolute value of estimated SNP effects, the posterior inclusion probability (or model frequency) for each SNP, and the variance of GEBV (or window variance) for any 10 consecutive SNP standardized by dividing by the total variance of GEBV in the population. The QTL were mapped to the SNP that explained the largest proportion of the total variance of GEBV within the significant overlapping windows, whose variances were in top \left(1-\widehat{\pi}\right)\times 100\% in BayesCπ or visually remarkably higher than the background window variances in BayesB. In GBLUP model G1, allele substitution effects were estimated following [2]:

\mathbf{\alpha}={\sigma}_{\alpha}^{2}{\mathbf{Z}}^{\prime}{\mathbf{G}}^{-1}\widehat{\mathbf{a}}

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.