Page 305 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

The contribution to the diagonal from yield is:
DIAG = DIAG + 2(0.00059) = 0.01512 + 0.00118 = 0.0163
2 2
The contribution to the ARHS from the pedigree is zero since both parents are
unknown and solutions for progeny are zero in the first round of iteration. The con-
tribution to ARHS from yield record is:
ˆ
ˆ
−1
ARHS = r (y − hd − b − uˆ − mˆ − p ˆ e )
2 np 10 2 2 3 3 3
ˆ
ˆ
−1
+ r (y − hd − b − û − mˆ − p ˆ e )
np 13 3 1 9 2 2
−1
ARHS = r (22 − (−2.567) − 33.600 − 0 − 0 − 0 )
2 np
+ r −1 (20 − 3.679 − 31.333) = −0.02818
np
Therefore:
ˆ
u = −0.02818/0.0163 = −1.729
2
After processing all animals in the pedigree and data file in the current round of itera-
tion, equations for maternal effects are set and solved as described below.
SOLUTIONS FOR MATERNAL EFFECT. Solutions for maternal effects are computed using
both the pedigree file and the data file sorted by dam. Records for the lth animal are
read in from the pedigree file and from file C if it is a dam that has progeny with a
yield record, while accumulating DIAG and ARHS. For the type 1 record in the pedi-
gree file for animal l, contributions to ARHS and DIAG according to the number of
parents known are as follows:
Number of parents known

None One (dam(d)) Both
2
22
ˆ
22
ˆ
ARHS = 0 ARHS = g (m ) ARHS = g (m + m )
ˆ
l l 3 d l s d
DIAG = g 22 DIAG = g 22 DIAG = 2g 22
4
l l 3 l
Taking into account contributions from animal effects to the ARHS due to
genetic correlation gives:
Number of parents known
None One (dam(d)) Both
ˆ
– ARHS = ARHS + (uˆ ) 2 3 g 12 ARHS = ARHS + (u + u )g 12
ˆ
l
l
s
l
d
l
d
ˆ
ˆ
ˆ
ARHS = ARHS − (u )g 12 ARHS = ARHS − (u ) 4 g 12 ARHS = ARHS − (u )2g 12
l l l l l l 3 l l l
For the type 2 record in the pedigree file for animal l, contributions to the ARHS
and DIAG according to whether the mate of animal l is known or not are:
Mate is unknown Mate is known
2
22
22
ˆ
ˆ
ARHS = ARHS + ( )g (mˆ ) ARHS = ARHS + g (m − 0.5m )
l l 3 o l l o ma
1
DIAG = DIAG + ( )g 22 DIAG = DIAG + (1/2)g 22
l l 3 l l
Solving Linear Equations 289