Background: Genomic data are used in animal breeding to assist genetic evaluation. Several models to estimate genomic breeding values have been studied. In general, two approaches have been used. One approach estimates the marker effects first and then, genomic breeding values are obtained by summing marker effects. In the second approach, genomic breeding values are estimated directly using an equivalent model with a genomic relationship matrix. Allele coding is the method chosen to assign values to the regression coefficients in the statistical model. A common allele coding is zero for the homozygous genotype of the first allele, one for the heterozygote, and two for the homozygous genotype for the other allele. Another common allele coding changes these regression coefficients by subtracting a value from each marker such that the mean of regression coefficients is zero within each marker. We call this centered allele coding. This study considered effects of different allele coding methods on inference. Both marker-based and equivalent models were considered, and restricted maximum likelihood and Bayesian methods were used in inference.
Results: Theoretical derivations showed that parameter estimates and estimated marker effects in marker-based models are the same irrespective of the allele coding, provided that the model has a fixed general mean. For the equivalent models, the same results hold, even though different allele coding methods lead to different genomic relationship matrices. Calculated genomic breeding values are independent of allele coding when the estimate of the general mean is included into the values. Reliabilities of estimated genomic breeding values calculated using elements of the inverse of the coefficient matrix depend on the allele coding because different allele coding methods imply different models. Finally, allele coding affects the mixing of Markov chain Monte Carlo algorithms, with the centered coding being the best.
Conclusions: Different allele coding methods lead to the same inference in the marker-based and equivalent models when a fixed general mean is included in the model. However, reliabilities of genomic breeding values are affected by the allele coding method used. The centered coding has some numerical advantages when Markov chain Monte Carlo methods are used.