Allele coding in genomic evaluation

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.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.There has been growing interest in the use of marker-based models [1] in recent years. In studies using these models, descriptions of the effect of allele coding system on inference and computations are often vague or missing. By allele coding, we refer to the coefficients in the marker matrix of marker-based models. Coefficients, commonly used for allele coding of a marker is 0 when the individual is homozygous for the first allele, 1 when the individual is heterozygous, and 2 when the individual is homozygous for the second allele. Depending on which of the alleles has been chosen as the first allele, the coefficients are different. Thus, this allele coding method does not give unique regression coefficients.There are other allele coding methods such as the one that use coefficients -1, 0, and 1 instead of 0, 1, and 2, resp