Best linear unbiased prediction (BLUP) is a standard method for estimating random effects of a

mixed model. This method was originally developed in animal breeding for estimation of breeding

values and is now widely used in many areas of research. In the process of developing of new cultivars

as well as the recommendation of newly released varieties require a selection to be made among a

larger set of candidate genotypes, thereby the estimation of genotypic values is at the heart of any

breeding effort.


A desirable feature of BLUP is its ability to borrow strength from relatives by exploiting

genetic correlation arising from the pedigree. The closer the genetic correlation with relatives, the

more information can be extracted from phenotypic information on relatives. The most common

approach to exploiting pedigree information involves use of the so-called numerator relationship

matrix (Mrode 1996), computed from the coefficient of coancestry.


During 2007, the pedigree-based kinship in widely used software package, such as

MTDFREML, was replaced by the marker-based kinship. Soon after, a computationally efficient

algorithm was developed to derive the marker-based kinship (Van Raden 2008). Due to the advantages

of fast computing times and similarity to the existing models and software, this marker-based kinship

approach was well known as genomic BLUP or genomic best linear unbiased prediction (gBLUP) and

quickly adapted as the practical method for genomic selection (Hayes et al. 2009).

Oliveira et al. (2016) conducted a study to evaluate the prediction efficiency of hybrid maize

by using diallel analysis and the best linear unbiased predictor (BLUP). Eight synthetic varieties were

crossed in a diallel scheme to produce inter-varital hybrids and were then evaluated in three separate

environments along with parents; both combining ability and predicted breeding values (BLUPs) were

estimated. Correlations between the BLUP and combining abilities were also obtained. Combining

ability analysis revealed that both additive and non-additive types of gene action were important in the

studied traits. There was a moderate to high correlation between the mean square of the combining

ability and the predicted breeding values. This shows that BLUP can be used to select the best parents

for different traits, especially for ear height and ear position, which had the highest correlations.

Bauer et al. (2006) reported that for breeding self-pollinated crops the widely used coefficient

of coancestry has disadvantages especially when pedigree information is not complete. This study was

conducted to determine whether, coefficient of co-ancestry can be replaced by genetic similarities

calculated from DNA marker data in the prediction of BLUP values. Three selection strategies based

on BLUP (BLUP[E]) = including environmental effects, BLUP[E+A] = including environmental

effects and pedigree data, BLUP[E+GS] = including environmental effects and genetic similarities)

were compared to the commonly used selection among adjusted line means. They generated a

“virtual” parental population where heritability and amount of missing data in the data were varied. A

tight association between coefficient of coancestry and genetic similarities under roughly unbiased

conditions indicates that genetic similarities could be used in BLUP of self-pollinated crops.

Wang et al. (2018) reported two ways to change the kinship derivation in the BLUP method

that improve prediction accuracy while maintaining the computational advantage. First, using the

settlement under progressively exclusive relationship (SUPER) algorithm, by substituting all available

markers with estimated quantitative trait nucleotides (QTNs) to derive kinship. Second, they

compressed individuals into groups based on kinship, and then used the groups as random effects

instead of individuals. The two methods were named as SUPER BLUP (sBLUP) and compressed

BLUP (cBLUP). Analyses on both simulated and real data demonstrated that these two methods offer

flexibility for evaluating a variety of traits, covering a broadened realm of genetic architectures. For

traits controlled by small numbers of genes, sBLUP outperforms Bayesian LASSO (least absolute

shrinkage and selection operator). For traits with low heritability, cBLUP outperforms both gBLUP

and Bayesian LASSO methods.

References:

Bauer, A. M., Reetz, T. C. and Léon, J., 2006, Estimation of breeding values of inbred lines using best linear unbiased prediction (BLUP) and genetic similarities. Crop Sci., 46(6): 2685-2691.

Hayes, B. J., Visscher, P. M. and Goddard, M. E., 2009, Increased accuracy of artificial selection by using the realized relationship matrix. Genetics Res., 91(1): 47-60.

Mrode, R. A., 1996, Linear models for the prediction of animal breeding values. CAB Int., Wallingford.

Oliveira, G. H., Buzinaro, R., Revolti, L., Giorgenon, C. H., Charnai, K., Resende, D. and Moro, G. V., 2016, An accurate prediction of maize crosses using diallel analysis and best linear unbiased predictor (BLUP). Chilean J. of Agril. Res., 76(3): 294-299.

Van Raden, P. M., 2008, Efficient methods to compute genomic predictions. J. of Dairy Sci., 91(11): 4414-4423.

Wang, J., Zhou, Z., Zhang, Z., Li, H., Liu, D., Zhang, Q., Bradbury, P. J., Buckler, E. S. and Zhang, Z., 2018,

Expanding the BLUP alphabet for genomic prediction adaptable to the genetic architectures of complex traits. Heredity, 121(6): 648-662.