Abstract
The best linear unbiased prediction (BLUP), derived from the linear mixed model (LMM), has been popularly used to estimate animal and plant breeding values (BVs) for a few decades. Conventional BLUP has a constraint that BVs are estimated from the assumed covariance among unknown BVs, namely conventional BLUP assumes that its covariance matrix is a \( \lambda K \), in which \( \lambda \) is a coefficient that leads to the minimum mean square error of the LMM, and \( K \) is a genetic relationship matrix. The uncertainty regarding the use of \( \lambda K \) in conventional BLUP was recognized by past studies, but it has not been sufficiently investigated. This study was motivated to answer the following question: is it indeed reasonable to use a \( \lambda K \) in conventional BLUP? The mathematical investigation concluded: (i) the use of a \( \lambda K \) in conventional BLUP biases the estimated BVs, and (ii) the objective BLUP, mathematically derived from the LMM, has the same representation as the least squares.
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Kim, B. The use of a genetic relationship matrix biases the best linear unbiased prediction. J Genet 99, 75 (2020). https://doi.org/10.1007/s12041-020-01220-y
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DOI: https://doi.org/10.1007/s12041-020-01220-y