Page 203 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

21 0.887 0.100 0.120 −0.526 −0.183 0.100 −0.728 −0.567 2.280
22 −0.789 0.402 −0.708 −0.506 −0.446 −0.163 0.140 −0.264 −0.526 1.190
23 −0.203 −0.143 0.160 0.362 0.140 0.140 0.160 0.604 −0.224 −0.486 0.665
24 −0.143 0.483 −0.345 −0.708 −0.648 −0.365 −0.345 −0.183 0.120 0.705 −0.405 1.068
25 −0.829 0.362 −0.748 −0.264 −0.486 0.079 0.382 −0.022 −0.567 0.867 −0.244 0.382 0.826
26 −0.264 0.362 −0.466 −0.264 −0.486 −0.203 0.100 −0.304 −0.284 0.584 −0.526 0.382 0.261 1.109
For the purposes of comparison, the G matrix computed from 41866 SNPs (G ) with
all
2Σp (1 – p ) = 15555.80 and the A computed from a five-generation pedigree are
j j
shown below:
G =
all
13 0.957
14 −0.108 0.973
15 0.452 −0.116 1.182
16 0.209 −0.058 0.424 1.025
17 0.234 −0.083 0.425 0.312 1.037
18 −0.040 0.438 0.097 −0.047 −0.043 1.151 symmetric
19 −0.089 0.458 0.039 −0.067 −0.070 0.426 1.175
20 −0.093 0.460 0.053 −0.058 −0.063 0.432 0.707 1.183
21 0.077 −0.082 0.064 0.104 0.082 −0.071 −0.069 −0.069 1.031
22 −0.056 0.418 0.093 −0.046 −0.038 0.408 0.355 0.342 −0.044 1.139
23 −0.005 0.464 −0.038 −0.035 −0.038 0.206 0.223 0.215 0.011 0.280 0.993
24 −0.070 0.468 0.075 −0.027 −0.053 0.403 0.521 0.550 −0.079 0.424 0.260 1.198
25 −0.052 0.416 0.098 −0.009 −0.031 0.386 0.363 0.342 −0.038 0.370 0.219 0.419 1.125
26 −0.070 0.493 −0.084 −0.039 −0.044 0.258 0.241 0.270 −0.072 0.253 0.178 0.259 0.214 1.009
A =
13 1.008
14 0.033 1.037
15 0.545 0.021 1.041
16 0.288 0.021 0.536 1.016
17 0.285 0.031 0.541 0.293 1.020
18 0.047 0.580 0.036 0.028 0.032 1.062
19 0.033 0.613 0.021 0.021 0.031 0.365 1.095 symmetric
20 0.033 0.613 0.021 0.021 0.031 0.365 0.613 1.095
21 0.099 0.031 0.082 0.118 0.074 0.028 0.031 0.031 1.021
22 0.046 0.586 0.032 0.031 0.039 0.351 0.373 0.373 0.044 1.068
23 0.096 0.569 0.067 0.043 0.047 0.329 0.357 0.357 0.042 0.338 1.050
24 0.041 0.574 0.027 0.019 0.026 0.331 0.406 0.406 0.028 0.335 0.335 1.056
25 0.033 0.548 0.035 0.039 0.039 0.315 0.336 0.336 0.037 0.321 0.310 0.310 1.029
26 0.035 0.588 0.023 0.024 0.039 0.337 0.376 0.376 0.036 0.347 0.341 0.348 0.325 1.070
The matrix A is more similar to G than to G, thus with more SNPs, the genomic
all
relationship matrix captures more relationships.
The matrices required for Eqn 11.9 have been described. Solving Eqn 11.9 gives
the DGVs directly for both the reference and selection animals and these are shown
in Table 11.2. The solution for the mean effects was 9.944. Thus the model gave the
same results as the SNP model.

11.5.3 Equivalent models: selection index approach

VanRaden (2008) presented a selection index approach which is equivalent to Eqn 11.9.
The method is of limited use in practice as it is assumed that the solutions of the vec-
ˆ
tor of fixed (b) effects are known. It does, however, demonstrate the equivalence of
the selection index approach to GBLUP.

Computation of Genomic Breeding Values and Genomic Selection 187