Page 303 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

and for non-parent records:
DIAG = DIAG + r −1
j j n
Afer reading file A, the solution for the j sex class is computed as:
−1ˆ
ARHS = ARHS − nr hd
j j ij i
ˆ
b = ARHS /DIAG
j j j
ˆ
−1
where hd is the current solution of herd i and nr is the sum of the inverse of the
i ij
residual variance for records of the jth level of sex effect in herd i. The latter is accu-
mulated while reading file A. For the example data, solutions for sex effect in the first
round of iteration are:
−1 ˆ
ˆ
−1 ˆ
(hd )/[3r + 2r ]
b = ARHS − 2r (hd ) − r (hd ) − 2r −1 ˆ −1 −1
1 1 pa 1 pa 2 np 3 pa np
−1
= (0.38134 − 2r (30.0) − r (33.638) − 2r −1 (31.333)/0.01092
−1
pa pa np
= 3.679
After obtaining solutions for fixed effects in the current round of iteration, the
solutions for animals are solved for.
SOLVING FOR ANIMAL SOLUTIONS. As described in Section 17.4.1, animal solutions are
computed one at a time as the pedigree file and file B are read. Briefly, for a type 1
record in the pedigree file for the kth animal, contributions to DIAG and ARHS
according to the number of parents known (Eqn 17.8) are:
Number of parents known

None One (sire (s)) Both
2
11
11
ˆ
ARHS = 0 ARHS = g (u ) ARHS = g (u + u )
ˆ
ˆ
k k 3 s k s d
4
DIAG = g 11 DIAG = g 11 DIAG = 2g 11
k k 3 k
ˆ
ˆ
where u and u are current solutions for direct effects for the sire and dam of the
s d
animal k.
The ARHS is augmented by contributions from the maternal effect as a result of
the genetic correlation between animal and maternal effects. These contributions are
from the sire, dam and the kth animal (see Eqn 17.9) and these are:
Number of parents known
None One (sire (s)) Both
– ARHS = ARHS + (mˆ ) 2 g 12 ARHS = ARHS + (m + m )g 12
ˆ
ˆ
k k s 3 k k s d
4
ˆ
ARHS = ARHS − (m )g 12 ARHS = ARHS − (m ) g 12 ARHS = ARHS − (m )2g 12
ˆ
ˆ
k k k k k k 3 k k k
ˆ
where m , m and m are current maternal solutions for the sire and dam of animal
ˆ
ˆ
s d k
k respectively.
Solving Linear Equations 287