• The use of a genetic relationship matrix biases the best linear unbiased prediction

• # Fulltext

https://www.ias.ac.in/article/fulltext/jgen/099/0075

• # Keywords

best linear unbiased prediction; breeding values; genetic relationship matrix; numerator relationship matrix; least squares.

• # 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 inconventional 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.

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019