Single-step Hybrid Marker Effects Models

Marker effects models (MEM) explicitly include random effects for genomic markers in the model. In typical genetic evaluations using MEM the large majority of animals involved have not been genotyped. However, when related to genotyped animals, non-genotyped animals' marker effects can be predicted by imputation of their genotypes from their genotyped relatives by regression. In the form of the MEM currently used in national cattle evaluations using MEM, this imputation is not explicit. This form is called the "hybrid model" in Fernando, et al. (2016), but is also commonly referred to as the super hybrid model.

Because of this imputation of genotypes for non-genotyped animals, the super hybrid MEM includes an effect for marker effects plus residual imputation errors for non-genotyped animals. This effect is often called the residual polygenic effect (RPE).

Current marker effects fit in the MEM do not account for all the genetic variation. Therefore, in the MEM implemented for genetic evaluations an extra polygenic effect (EPE) is often included. The EPE is fit as a tradition PBLUP with genetic covariance between animals described by the numerator relationship matrix.

The final EPD for genotyped animals is calculated as,

$EPD_{g}={\frac {M_{g}{\hat {\alpha }}+EPE_{g}}{2}}$

where $M_{g}$ is a matrix of marker values for genotyped animals (g), and ${\hat {\alpha }}$ are the predictions of the marker effects. The 2 in the denominator on the left side of the expression is because the values are solved on the breeding value scale.

The EPD for the non-genotyped animals is,

$EPD_{n}={\frac {RPE+EPE_{n}}{2}}$