Page 155 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

12.0
11.0
10.0
9.0
variance (kg 2 ) 7.0
8.0

6.0

Daily 5.0
4.0
3.0
2.0
1.0
0.0
7 28 49 70 91 112 133 154 175 196 217 238 259 280 301
Days in milk

Genetic Permanent environment
Fig. 9.1. The estimates of daily genetic and permanent environmental variances by days
in milk.
−1
For all animals with records, Q′ R Q = Z′ R Z and are block diagonal. For
−1
−1
instance, Q′ R Q for the first three cows (cows 4, 5 and 6) with records is:
⎡ 1.348 0.000 0.335 0 0 0 0 0 0 ⎤
⎢ ⎥
⎢ 0.000 1.647 0.000 0 0 0 0 0 0 ⎥
⎢ 0.335 0.000 2.035 0 0 0 0 0 0 0 ⎥
⎢ ⎥
⎢ 0 0 0 1.348 0.000 0.335 0 0 0 ⎥
⎢ 0 0 0 0.000 1.647 0.000 0 0 0 ⎥
⎢ ⎥
0 ⎢ 0 0 0.335 0.0000 2.035 0 0 0 ⎥
⎢ 0.674 − ⎥
⎢ 0 0 0 0 0 0 0.648 0.167 ⎥
0 ⎢ 0 0 0 0 0 − 0.648 0.824 − 0.591⎥
⎢ ⎥
⎣ 0 0 0 0 0 0 0 0.167 − 0.591 1.018 ⎦
−1
When all animals are considered, Q′R Q is augmented by nr columns and rows per
−1
−1
ancestor without records (i.e. animals 1−3). The matrix G is then added to Q′R Q and
−1
−1
P added to Z′R Z to obtain the MME. Solving the MME by direct inversion with the
solution for level 10 of HTD effects constrained to zero gave the following results:
Effects Solutions
HTD
1 10.0862
2 7.5908
3 8.5601
4 8.2430
Continued

Analysis of Longitudinal Data 139