Page 142 - Linear Models for the Prediction of Animal Breeding Values

The matrix Z that relates an individual to other members of the same group is:
S
⎛ 0 1 1 0 0 0 0 0 0⎞
⎜ 1 0 1 0 0 0 0 0 0 ⎟
⎜ ⎟
⎜ 1 1 0 0 0 0 0 0 0⎟
⎜ ⎟
⎜ 0 0 0 0 1 1 0 0 0 ⎟
⎜
Z = 0 0 0 1 0 1 0 0 0⎟
S
⎜ ⎟
⎜ 0 0 0 1 1 0 0 0 0 ⎟
⎜ 0 0 0 0 0 0 0 0 1 1⎟
⎜ ⎟
⎜ 0 0 0 0 0 0 1 0 1 ⎟
⎜ ⎝ 0 0 0 0 0 0 1 1 0⎠ ⎟
Setting up the MME therefore follows a similar pattern to that described in previous chap-
ters. Solving the MME (Eqn 8.6) for this example gives the following set of solutions. The
results from an analysis that ignored associative effects but fitted random animal and com-
mon environmental effects and fixed effects of sex of pigs and pen effects are also presented.
Model with no
Model with associative effects associative effects a
Sex of pig effects
Male 6.006 0.000
Female 8.241 2.169
Animal effects
DBV SBV TBV
1 0.298 −0.044 0.210 0.336
2 −0.487 0.028 −0.431 −0.478
3 0.189 0.016 0.221 0.142
4 0.298 −0.044 0.210 0.336
5 −0.487 0.028 −0.431 −0.478
6 0.189 0.016 0.221 0.142
7 0.129 −0.075 −0.022 0.279
8 0.527 −0.098 0.330 0.652
9 −0.878 0.010 −0.858 −0.738
10 0.538 −0.003 0.531 0.412
11 −0.494 0.083 −0.328 −0.628
12 0.400 0.059 0.517 0.216
13 −0.578 0.019 −0.539 −0.547
14 0.156 0.004 0.164 0.162
15 0.201 0.002 0.204 0.192
Common environment effects
1 0.325 0.327
2 −0.504 −0.465
3 0.178 0.139
Group effects
1 −0.275
2 0.367
3 −0.092

DBV, direct EBV; SBV, associative EBV; TBV, total EBV = (DBV + (n − 1)SBV).
a Model also fitted pen effects, and solutions were 5.160, 7.131 and 5.838 for pens 1, 2 and 3, respectively.

126 Chapter 8