Single-step Hybrid Marker Effects Models

Marker effects models[1][2][3] (MEM) explicitly include random effects for genomic markers. 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, 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 traditional PBLUP with genetic covariance between animals described by the numerator relationship matrix.

The final EPD for genotyped animals is calculated as,

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

where ${\displaystyle M_{g}}$ is a matrix of marker values for genotyped animals (g), and ${\displaystyle {\hat {\alpha }}}$ 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,

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

A more detailed description of how the MEM are used in US national beef cattle evaluations can be found in Golden, et al. (2018)[4]

References

1. Fernando, R. L., H. Cheng, B. L. Golden, and D. J. Garrick. 2016. Computational strategies for alternative single-step Bayesian regression models with large numbers of genotyped and non-genotyped animals. Genet. Sol and Evol. 46:96 DOI: 10.1186/s12711-016-0273-2.
2. Fernando RL. Genetic evaluation and selection using genotypic, phenotypic and pedigree information. In: Proceedings of the 6th World Congress on Genetics Applied to Livestock Production: 11–16 January 1998. vol. 26. Armidale; 1998. pp. 329–36.
3. Meuwissen THE, Hayes BJ, Goddard ME. Prediction of total genetic value using genome-wide dense marker maps. Genetics. 2001;157:1819–1829. [PMC free article] [PubMed]
4. Golden, B. L., M. L. Spangler, W. M. Snelling, and D. J. Garrick. 2018. Current single-step national beef cattle evaluation models used by the American Hereford Association and International Genetic Solutions, computational aspects, and implications of marker selection. In Proc. Beef Improvement Federation 11th genetic prediction workshop refining genomic evaluation and selection indices. Pp 14-22.