Page 201 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

Table 11.1. Solutions for mean and SNP effects from various models.
Unweighted Weighted
Mean effect
9.944 11.876
SNP effects solutions
1 0.087 –0.633
2 −0.311 −3.041
3 0.262 3.069
4 −0.080 −1.267
5 0.110 2.600
6 0.139 4.447
7 0.000 0.000
8 0.000 0.000
9 −0.061 –3.240
10 −0.016 1.883

Table 11.2. Direct genomic breeding (DGV) values from various models.

Selection SNP-BLUP
SNP-BLUP GBLUP index (weighted)
Reference animals
13 0.070 0.069 0.070 –2.651
14 0.111 0.116 0.111 1.307
15 0.045 0.049 0.045 0.611
16 0.253 0.260 0.253 1.007
17 0.495 –0.500 –0.495 –5.693
18 –0.357 –0.359 –0.357 –4.358
19 0.145 0.146 0.146 0.502
20 –0.224 –0.231 –0.225 –5.718
Selection candidates
21 0.027 0.028 0.028 –0.006
22 0.114 0.115 0.115 6.513
23 –0.240 –0.240 –0.240 –3.835
24 0.143 0.143 0.143 2.701
25 0.054 0.054 0.054 3.273
26 0.354 0.353 0.353 6.350

Noting that:
2
s = s g
2
a
2Σp(
j 1 p )− j
then the matrix ZZ′ can be scaled such that:
G= ZZ ′
2 ∑ p ( 1 −p)
j
j
2
and var(a)=Gs . The above division scales G to be analogous to the numerator rela-
a
tionship matrix (A). The genomic inbreeding coefficient for individual i is G – 1, and
ii
the genomic relationship between individuals i and k, which are analogous to the
relationship coefficients (Wright, 1922), can be obtained by dividing the elements G
ij
by the square roots of the diagonals of G and G . The matrix G is generally positive
ii jj
Computation of Genomic Breeding Values and Genomic Selection 185