Page 209 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

0.762 0.209 0.093 0.096 −0.137 0.149 −0.330 0.091 −0.176
0.209 0.801 0.394 −0.690 0.152 0.170 −0.307 0.380 0.114
0.093 0.394 0.839 −0.537 −0.232 0.592 −0.154 −0.004 −0.270
G = 0.096 −0.690 −0.537 2.217 −0.497 −0.211 0.115 −0.537 −0.268
−0.137 0.152 −0.232 −0.497 1.184 −0.445 0.686 0.840 0.572
0.149 0.170 0.592 −0.211 −0.445 0.684 −0.368 −0.216 −0.483
−0.330 −0.307 −0.154 0.115 0.686 −0.368 1.067 0.378 0.380
0.091 0.380 −0.004 −0.537 0.840 −0.216 0.378 0.836 0.264
−0.176 0.114 −0.270 −0.268 0.572 −0.483 0.380 0.264 1.107

The H for this example was constructed from the inverses of A in Example 11.1, of
−1
G and A shown above. The matrices in Eqn 11.19 have all been defined and solving
22
these equations with a = 245/35.241 = 6.952 gives the following solutions:
Mean effects
6.895
EBVs for animals with records
13 3.114
14 1.697
15 4.200
16 3.842
17 2.861
GEBV for genotyped animals
18 1.477
19 1.410
20 0.572
21 0.691
22 1.526
23 0.036
24 0.564
25 1.765
26 0.527

It is not possible to compare these results with the other models considered so far in
this chapter as the data structure was modified.

11.8 Bayesian Methods for Computing SNP Effects

The assumption of equal variance explained by all loci in the SNP-BLUP or GBLUP
model has the advantage that only one variance has to be estimated. However, this
may be unrealistic across all traits, which may have different genetic architecture.
Also, one of the problems with GBLUP is that it does not allow for moderate to large
QTL effects; if these are actually present they will be severly reduced. The other prob-
lem is that with GBLUP, SNP effects cannot be zero, they always have (often very
small) effects. Meuwissen et al. (2001) presented a Bayesian method that assumes
t distributions at the level of the SNP effect, modelled using different genetic variances
for each SNP (the so-called BayesA method) and another method in which some SNPs
are assumed to have effects following a t-distribution, and others have zero effects

Computation of Genomic Breeding Values and Genomic Selection 193