Page 306 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

Taking into account contributions from animal effect (see Eqn 17.6) gives:

Mate is unknown Mate is known
2
12
ˆ
ARHS = ARHS + ( )g (uˆ ) ARHS = ARHS + (u − 0.5u )g 12
ˆ
l l 3 o l l o ma
1
1
ARHS = ARHS − (u )( )g 12 ARHS = ARHS − (u )( )g 12
ˆ
ˆ
l l l 3 l l l 2
For the animal l, which is a dam with progeny having yield records, DIAG and
ARHS from the pedigree is augmented with information from yield as:
DIAG = DIAG + r −1
n
and:
ˆ
ˆ
−1
ˆ
ARHS = ARHS + r (y − hd − b − u − p ˆ e )
l l pa ijklt i j k t
for parent records and:
ˆ
ˆ
−1
ARHS = ARHS + r (y − hd − b − 0.5(û + û ) − p ˆ e )
l l np ijklt i j s d t
for non-parent records.
After processing all records from pedigree and yield records for the lth animal,
the solution for the maternal effect is computed as:
ˆ
m = ARHS /DIAG
l l l
The calculation of the solution for animal 5 in the first round of iteration is as follows.
The contribution from a type 1 record in the pedigree is:
22
12
12
ARHS = (mˆ + mˆ )g + (û + û )g − (û 2g )
5 1 2 1 2 5
= (0.0217 + −1.7027)0.01261 + (0 + (−1.7294))0.00336 − ((−0.5831)(2)0.0336)
= −0.02309
DIAG = (2)0.01261 = 0.02522
5
The contribution from a type 2 record in the pedigree is:
ARHS = ARHS + (mˆ − mˆ )g + (û − û )g − (û 1 g )
12
12
22
1
1
5 5 8 2 3 8 2 3 5 2
1
= −0.02309 + (0 − (0.4587))0.01261
2
1
+ (1.4382 − (0.8960))0.00336 − ((−0.5831)( )0.00336)
1
2 2
= −0.021675
22
DIAG = DIAG + g = 0.02522 + 0.0063 = 0.03153
1
5 5 2
The contribution from yield of progeny (animal 8) for dam 5 is:
ˆ
ˆ
−1
ARHS = ARHS + r (y − hd − b − u − p ˆ e )
ˆ
5 5 pa 8 1 1 8 5
−1
= −0.021675 + r (40 − 30.00 − 3.679 − (1.4382) − 0)
pa
= − 0.007724
−1
DIAG = DIAG + r = 0.03153 + 0.002857 = 0.034387
5 5 pa
and the solution is:
ˆ
m = −0.007724/0.034387 = −0.225
5
Solutions for permanent environmental effects are solved for after processing all
animals for maternal effects in the current round of iteration.
290 Chapter 17