Page 129 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

(Continued )
Effects Solutions

Animals
Direct effects Maternal effects
1 0.564 0.262
2 −1.244 −1.583
3 1.165 0.736
4 −0.484 0.586
5 0.630 −0.507
6 −0.859 0.841
7 −1.156 1.299
8 1.917 −0.158
9 −0.553 0.660
10 −1.055 −0.153
11 0.385 0.916
12 0.863 0.442
13 −2.980 0.093
14 1.751 0.362
Permanent environment
2 −1.701
5 0.415
6 0.825
7 0.461

The solutions show little difference between the herds, but calves in pen 1 were
heavier than those in pen 2 by about 6.85 kg at birth. The solution for level i of the
fixed effect n can be calculated using Eqn 4.3 except that the sum of yields for the
level of fixed effect is corrected in addition for maternal effects. That is:
diag in
∑ y inf ∑ b ˆ inj ∑ a ˆ ink ∑ m ˆ inl ∑ pe ˆ int t
−
−
−
−
b ˆ in = f=1 j k l t (7.3)
diag in
where m is the solution for level l of genetic maternal effects within level i of the nth
inl
fixed effect and all other terms are as defined in Eqn 4.3. Thus the solution for level 1
of pen effect is:
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
b ˆ = [137 − (2hd + hd + hd ) − (a + a + a + a )
11 1 2 3 5 8 9 13
ˆ
− (2m + mˆ + mˆ ) − (2p ˆe + p ˆe + p ˆe )]/4
2 5 6 2 5 6
= [137 − 4.82 − (−0.986) − (−2.832) − (−2.162)]/4
= 34.540
ˆ
where hd is the solution for level j of herd effect.
j
From the MME, the solutions for direct and maternal effects for animal i with
progeny o are:
⎡ i u ˆ ⎤ ⎡ ( ( ⎤ −1 ⎡ u+ u ˆ ⎤
ˆ
1
1
1
=
⎢ ⎥ ⎢ n+ d + k )a 1 d + k )a 2 ⎥ ⎥ Hk 2 ⎢ s d ⎥
⎣ i ˆ m ⎦ ⎣ ( d+ k )a 2 n + d+ k )a 3 ⎦ ⎣m+ m ˆ d ⎦
ˆ
(
s
1
1
2
⎡ y − b ˆ − m ˆ − p ˆ ⎤ ⎡ aˆ − .(aˆ ) ⎤
05
+ ⎢ i i dam dam ⎥ + H k ⎢ o mate ⎥
⎢ ⎣ y o − b ˆ o − u ˆ − ˆ p i ⎥ ⎦ 3 ⎣ ˆ m o − .( ˆ m mate ⎦ ) (7.4)
−
05
o
Maternal Trait Models: Animal and Reduced Animal Models 113