Improved Scalar Deregression of Estimated Breeding Values

Background

In genomic studies of animals and plants, analyses are often split into two stages. In the first stage, the average phenotype of each genotyped candidate is calculated from its estimated breeding value (EBV). This average is adjusted for all other effects and is known as the deregressed breeding value. Scalar deregression removes the inherent shrinkage from the original EBVs candidate-by-candidate, rather than for a vector of EBVs. A previously published standard method is easy to apply but implicitly assumes no inbreeding.

Results

An improved method uses each candidate’s and its parents’ inbreeding coefficients and the three-by-three prediction error covariance matrix of their EBVs. The candidate’s effective number of observations can be derived as the root of a second-order polynomial, and the deregressed EBV is then obtained. Two mathematically equivalent polynomials differed in numerical stability.

Applications to small examples demonstrated that the improved method produced deregressed EBVs unbiased by inbreeding, whereas the standard method underestimated their absolute magnitude. The same prediction error covariance matrix also allows filtering out uninformative candidates if their estimated Mendelian sampling term has zero reliability.

Conclusions

The improved method requires access to selected off-diagonal elements of the inverted coefficient matrix of the mixed model equations. The resulting deregressed EBVs and their appropriate weights are unbiased by inbreeding, thereby improving the baseline for the second stage of the analysis. Additionally, uninformative observations can be reliably filtered out. Studies involving traits with low heritability or sparsely recorded phenotypes are expected to benefit most.