Genomic evaluations are commonly based on models with genomic relationships. However, estimated genomic relationship matrices are often positive semi-definite and ad-hoc corrections are applied to force positive definiteness without consideration about model properties. In this contribution a hierarchical quantitative genetic model is postulated that provides a positive definite genomic relationship matrix by taking into account the amount of genetic variance captured by estimated marker effects. Based on the hierarchical formulation the proposed model also provides a system of equations to estimate marker effects and breeding values jointly without setting up and inverting covariance matrices. Further extension with pedigree information is also possible.

Gregor Gorjanc, John A Woolliams, John M Hickey

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume Genetic Improvement Programs: Selection using molecular information, , 068, 2014
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