Page 296 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

ITERATION STAGE
ˆ
ˆ
Let b and a be vectors of solutions for sex and animal effects. Starting values for sex
and animal effect are assumed to be the same as in Example 17.1.
SOLVING FOR FIXED EFFECTS. In each round of iteration, file A is read one level of sex
effect at a time with adjusted right-hand sides (ARHS) and diagonals (DIAG) accu-
mulated for the ith level as:
ARHS = ARHS + y − uˆ
i i ik k
DIAG = DIAG + 1
i i
At the end of the ith level, the solution for the level is computed as:
ˆ
b = ARHS /DIAG
i i i
The above step essentially involves adjusting the yields for animal effects using previous
solutions and calculating solutions for each level of sex effect. For example, the solution
for level one of sex effect in the first round of iteration is:
ˆ
b = [(4.5 − 0.167) + (3.5 − (−0.833)) + (5.0 − 0.667)]/3 = 4.333
1
After calculating solutions for fixed effect in the current round of iteration, file B and
the pedigree file are processed to compute animal solutions.

SOLVING FOR ANIMAL SOLUTIONS. DIAG and ARHS are accumulated as data for each ani-
mal and read from the pedigree file or from both the pedigree file and file B for animals with
records. When processing type 1 records in the pedigree file for the kth animal, the contri-
bution to the DIAG and ARHS according to the number of parents known is as follows:

Number of parents known
None One (sire (s)) Both
2
ARHS = 0 ARHS = ( )a(u ) ARHS = a(u + u )
ˆ
ˆ
ˆ
k k 3 s k s d
4
k k 3 k
DIAG = a DIAG = ( )a DIAG = 2a
ˆ
ˆ
where u and u are current solutions for the sire and dam, respectively.
s d
When processing type 2 records in the pedigree file for the kth animal, the contri-
bution to the DIAG and ARHS according to whether the mate of animal k is known
or not is as follows:
Mate unknown Mate known
2
ˆ
ˆ
ARHS = ARHS + ( )a(uˆ ) ARHS = ARHS + a(u − 0.5u )
k k 3 o k k o m
1 1
2
k
3
k
k
k
DIAG = DIAG + ( )a DIAG = DIAG + ( )a
ˆ
where u and u are current solutions for the progeny and mate, respectively, of
ˆ
o m
the kth animal. If the kth animal has a yield record:
ARHS = ARHS + y − b ˆ
k k ik i
DIAG = DIAG + 1
k k
280 Chapter 17