Page 182 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

The matrix X is formed as discussed in Example 3.1, Z is an identity matrix and
the matrix W is:
⎡11 0 0 0 0 0 0 0 0⎤
⎢ ⎥
⎢ 0 0 1 1 0 0 0 0 0 0 ⎥
W = ⎢0 0 0 0 1 1 0 0 0 0⎥
⎢ ⎥
⎢ ⎢ 0 0 0 0 0 0 1 1 0 0 ⎥
⎢ ⎣ 0 0 0 0 0 0 0 0 1 1 ⎥ ⎦

−1
−1
The matrices A and G have been calculated for the example data. The remaining
u v
matrices in the MME are calculated through matrix multiplication and addition. The
MME are too large to be shown, but solving the equations by direct inversion gives
the following results:

Effects Solutions
Sex
Male 7.357
Female 5.529
Animals Breeding values
1 0.092
2 −0.091
3 0.341
4 0.329
5 0.515
MQTL alleles of animals Additive effects
1p 0.064
1m 0.011
2p −0.065
2m −0.011
3p 0.083
3m −0.004
4p 0.028
4m 0.076
5p 0.043
5m 0.086

The additive genetic effects of the MQTL accounted for about 45% of the total
genetic merit of animals 1 and 2 but only about 20% for animals 3 and 5.
In Germany, with Holstein dairy cattle, the method used in Example 10.2 has
been used to incorporate QTL information into routine estimation of breeding values
(Szyda et al., 2003). In the study, 13 markers were used for routine genotyping of
animals, and regions representing QTL for milk, protein, fat yields and somatic cell
counts were identified on several chromosomes. The QTL information has been
incorporated into BLUP, analysing DYD as the dependent variable. As a percentage
of the polygenic variance, the variances of the MQTL in their study varied from 3 to
5% for milk, fat and protein yields in the first lactation.

166 Chapter 10