Genetic Evaluation

EPD

Basic Models

ssGBLUP (Suggested writer: Daniela Lourenco)

Single-step genomic BLUP (ssGBLUP) is a method developed to enable the inclusion of marker genotypes into the well-known BLUP machinery. The idea of ssGBLUP came from the fact that only a small portion of the animals in the pedigree is genotyped. In this way, one approach to account for all animals (i.e., genotyped and non-genotyped) in the evaluation would be to combine pedigree and genomic relationships and use this as the covariance structure in the BLUP mixed model equations. Thus, ssGBLUP uses marker information to construct genomic relationships.

Legarra et al. (2009) stated that genomic evaluations would be simpler if genomic relationships were available for all animals in the model. Then, their idea was to look at the pedigree relationship as a priori relationship and at the genomic relationship as the observed relationship. Based on that, they showed the genomic information could be extended (i.e., imputed) to non-genotyped animals. This means that in ssGBLUP pedigree relationships for non-genotyped animals are enhanced by the genomic information of their relatives. The relationship matrix that combines information for genotyped and non-genotyped animals is represented by H:

$H={\begin{bmatrix}A_{11}+A_{12}A_{22}^{-1}(G-A_{22})A_{22}^{-1}A_{21}&A_{12}A_{22}^{-1}G\\GA_{22}^{-1}A_{21}&G\end{bmatrix}}$

Where the subscripts 1 and 2 refer to non-genotyped and genotyped animals, respectively. A is the pedigree relationship matrix and G is the genomic relationship matrix computed based on markers. If M is a matrix of marker genotypes centered for allele frequency (p) and has the dimension of number of animals by number of SNP (n), G is computed as :

$G={\frac {MM^{'}}{2\sum _{i=1}^{n}p_{i}(1-p_{i})}}$

Although H is very complicated, H^-1 is quite simple :

$H^{-1}=A^{-1}+{\begin{bmatrix}0&0\\0&G^{-1}-A_{22}^{-1}\end{bmatrix}}$

If we replace A^{-1} by H^{-1} in the BLUP mixed model equations, we have ssGBLUP:

${\begin{bmatrix}{X^{'}X}&{X^{'}Z}\\{Z^{'}X}&{Z^{'}Z}+H^{-1}{\lambda }\end{bmatrix}}{\begin{bmatrix}{b}\\{u}\end{bmatrix}}={\begin{bmatrix}{X^{'}y}\\{Z^{'}y}\end{bmatrix}}$

Where b and u are vectors of fixed effects and breeding values, respectively; X and Z are incidence matrices for the effects in b and u; y is a vector of phenotypes, and λ is the ratio of residual to additive genetic variance.

As a combined relationship is used in ssGBLUP, the output for each animal is automatically a genomic EBV, and the mixed model equations above can be simplistically represented as:

The genomic EPD is then calculated as:

${genomic\,EPD}={\frac {genomic\,EBV}{2}}$

When the subject is genetic evaluation, one of the most common questions is “What is the main difference among ssGBLUP, BLUP, and genomic BLUP (GBLUP)?” In a nutshell, ssGBLUP uses phenotypes, pedigree, and genotypes for both genotyped and non-genotyped animals, whereas BLUP uses phenotypes and pedigree for all animals and GBLUP uses phenotypes and genotypes only for genotyped animals.

In the US, ssGBLUP has been used for genomic evaluation of beef and dairy cattle, pigs, chickens, and fish. For more information about ssGBLUP for beef cattle evaluation check Lourenco et al. (2015), Lourenco et al. (2017), and Misztal & Lourenco (2018) .

Marker effects in ssGBLUP

Although the marker information in ssGBLUP is used to construct genomic relationships, it is possible to calculate SNP effects once we obtain genomic EBV (Wang et al., 2012, Lourenco et al., 2015). Marker effects can be then used to calculate predictions based only on marker genotypes for young genotyped animals that are not yet or will never make into an official evaluation.

Connectivity (Suggested writer: Ron Lewis)

Measures of (Suggested writer: Ron Lewis)

==Impact on GE== (Suggested Writer: Ron Lewis)