Page 198 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

(Continued)
Unweighted analysis Weighted analysis
Reference animals
DGV Polygenic DGV Polygenic
13 2.834 −0.299 7.070 −0.001
14 0.293 0.256 1.464 0.000
15 0.081 0.142 2.726 0.000
16 3.554 0.254 4.711 0.002
17 −2.460 −0.085 −2.880 −0.001
18 −3.787 0.271 −3.176 0.002
19 1.620 −0.092 1.760 −0.002
20 −2.460 −0.181 −2.880 −0.002
Selection animals
DGV Polygenic DGV Polygenic
25 0.900 0.000 4.119 0.000
26 −0.314 0.128 −1.191 0.000
27 −2.460 0.128 −2.880 0.000
28 0.293 0.128 1.464 0.000
29 −0.314 0.128 −1.191 0.000
30 2.227 0.128 4.415 0.000
With this small amount of data, it seems that when records are properly weighted,
polygenic effects were very close to zero. The GEBV for reference and selection ani-
ˆ
mals equals Zgˆ + u. This would be equal to 2.535 for animal 13 for instance. The Z
has been given for reference animals and for the selection candidates the correspond-
ing matrix Z is:
2
⎛ 1 357 − . − .
0 714⎞
.
0 357
⎜ − 0 643 − 0 357 − 0 714 ⎟
.
.
.
⎜ ⎟
.
.
.
Z = ⎜ − 0 643 0 643 0 286⎟
2 ⎜ 03577 − . − . ⎟
0 357
0 714
.
⎜ ⎟
⎜ − . − . − .
0 714 ⎟
0 357
0 643
⎜ ⎝ 0 357 − . 0 286⎠ ⎟ ⎠
.
0 357
.
11.5 Mixed Linear Model for Computing SNP Effects
Several methods that fit SNP effects as random have been presented by various
researchers (Meuwissen et al., 2001; VanRaden et al., 2008; Habier et al., 2011). The
most common random model used in the national evaluation centres for genomic
evaluation, especially of dairy animals, assumes the effect of the SNP are normally
distributed and all SNP are from a common normal distribution (e.g. the same genetic
variance for all SNPs). There are two equivalent models with these assumptions:
1. A model fitting individual SNP effects simultaneously. In this model (SNP-BLUP),
DGVs for selection candidates are calculated as DGV = Zg, where g are the estimates
ˆ
ˆ
2
of random SNP effects. This method involves knowing s , but this may not be the
g
2
2
case in practice, and s may have to be approximated from s , the additive genetic
g a
variance. In such situations, this method is also referred as ridge regression.
182 Chapter 11