Page 110 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

and:
CD = y − m = 7.7594 − 9.036 = −1.2766
22 22 2
Parent average for sire 2 (PA ) for country i is:
2i
PA = 0.5(aˆ ) + 0.25(aˆ + gˆ ) = 0.5(7.015) + 0.25(−6.299 + (−0.067)) = 1.916
21 81 91 G51
PA = 0.5(aˆ ) + 0.25(aˆ + gˆ ) = 0.5(4.489) + 0.25(−5.059 + (−0.010)) = 0.97725
22 82 92 G52
Progeny contributions (PC) from bull 3 to sire 2 (PC ) in country i are:
32i
PC = 4(aˆ ) − 2(aˆ ) = 4(8.059) − 2(4.310) = 23.616
21 31 71
PC = 4(aˆ ) − 2(aˆ ) = 4(5.001) − 2(3.071)) = 13.862
22 32 72
1
The residual variance for bull 2 in country 1, (r ) = ( 150 )206.5 and country 2, (r ) =
22
21
1
( )148.5. Corresponding inverses were 0.72639 and 0.43771, respectively. Since both
65
= 2a +
sire and MGS of bull 2 are known and he has a maternal grandson, a bull par
4
8
= 2( 11 ) + 0.25( ) = 1.54545. Therefore:
0.25a prog 11
⎛ . 0 72630 0 ⎞ ⎛ . 0 49087 − . 0 66338 ⎞
( ′ −1 + −1 ) = +
bull ⎜ ⎟ ⎜ ⎟
⎝0 . 0 43771 ⎠ ⎝ −0.66338 . 1 05924 ⎠
.
ZR Z G a
⎛ . 1 21726 − . 0 66338 ⎞
= ⎜ ⎝ − . 0 66338 . 1 49695 ⎠ ⎟
From Eqn 5.19, the matrices of weights (W ) are:
i
0 66338 ⎞
⎛ 1 21726 − . − 1 ⎛ 0 4620 − 0 62436⎞ ⎛ 0 2007 − 0 1977⎞
.
.
.
.
.
W = ⎜ ⎝ − 0 66338 1 49695 ⎠ ⎟ ⎜ ⎝ − 0.662436 0 99693⎠ ⎟ = ⎜ ⎝ − 0 3281 0 5783⎠ ⎟
1
.
.
.
.
.
0 66338⎞
⎛ 12 . 11726 − . − 1 ⎛ . ⎞ ⎛0 7867 0 2101 ⎞
0 72639 0
.
.
W 2 = ⎜ ⎝ − . 1 49695⎠ ⎟ ⎜ ⎝ 0 0 43771⎠ ⎟ = = ⎜ ⎝0 3487 0 3855 ⎟ ⎠
.
.
.
0 66338
.
0 0124 ⎞
⎛ 1 21726 − 0 66338⎞ − 1 ⎛ 0 02887 − 0 03902⎞ ⎛ 0 0125 − .
.
.
5
.
.
.
W = =
0 02051 0 0361 ⎠
3 ⎜ ⎝ −0 66338 1 1 49695 ⎠ ⎟ ⎜ ⎝ − 0 03902 0 06231⎠ ⎟ ⎜ ⎝ − . . ⎟
.
.
.
.
The vector of proof for bull 2 is:
⎛ ˆ a ⎞ ⎛ . 1 9160⎞ ⎛ . 2 7037⎞ ⎛ 23 616⎞ ⎛ 2 176⎞
.
.
21
W
⎜ ⎝ ˆ a ⎠ ⎟ = W 1 ⎜ ⎝ . 0 9773⎠ ⎟ + W 2 ⎜ ⎝ − . 1 2766⎠ ⎟ + W 3 ⎜ ⎝ 13 862⎠ ⎟ = ⎜ ⎝ 0 403⎠ ⎟
.
.
22
Again, similar to bull 3 above, the contributions from the DRPs in both countries
accounted for much of the MACE proofs of the bull 2 in countries 1 and 2.
Recently, Interbull has modified the MACE systems to use sire and dam pedigree
instead of sire and maternal sire pedigree. Partitioning of bull proofs can be done as in
Section 5.2.3.
94 Chapter 5