Deregressing estimated breeding values and weighting information for genomic regression analyses

TLDR

Genomic prediction of breeding values relies on training analyses that regress phenotypic or breeding value information on marker genotypes, yet researchers inconsistently use EBV or deregressed data and vary weighting methods to account for heterogeneous variance. The study proposes a systematic method for genomic prediction that specifies how to weight heterogeneous data and how to deregress EBV by removing parent averages. The method uses EBV/r² as deregressed breeding values, weights them with the ratio (1–h²)/[(c+(1–r²)/r²)h²] instead of reliability or prediction error variance, and allows combining phenotypic and deregressed data with appropriate weighting.

Abstract

Genomic prediction of breeding values involves a so-called training analysis that predicts the influence of small genomic regions by regression of observed information on marker genotypes for a given population of individuals. Available observations may take the form of individual phenotypes, repeated observations, records on close family members such as progeny, estimated breeding values (EBV) or their deregressed counterparts from genetic evaluations. The literature indicates that researchers are inconsistent in their approach to using EBV or deregressed data, and as to using the appropriate methods for weighting some data sources to account for heterogeneous variance. A logical approach to using information for genomic prediction is introduced, which demonstrates the appropriate weights for analyzing observations with heterogeneous variance and explains the need for and the manner in which EBV should have parent average effects removed, be deregressed and weighted. An appropriate deregression for genomic regression analyses is EBV/r2 where EBV excludes parent information and r2 is the reliability of that EBV. The appropriate weights for deregressed breeding values are neither the reliability nor the prediction error variance, two alternatives that have been used in published studies, but the ratio (1 - h2)/[(c + (1 - r2)/r2)h2] where c > 0 is the fraction of genetic variance not explained by markers. Phenotypic information on some individuals and deregressed data on others can be combined in genomic analyses using appropriate weighting.