Page 302 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

(Continued)
Parent/ Birth
animal Code a Animal Mate Sire Dam Herd Sex weight (kg)
7 1 12 8 8 7 3 Female 34.0
9 1 13 2 9 2 3 Male 20.0
2 1 13 9 9 2 3 Male 20.0
3 1 14 6 3 6 3 Female 40.0
6 1 14 3 3 6 3 Female 40.0
a 0, parental record; 1, non-parental record.

ITERATION STAGE
ˆ
ˆ
ˆ
The solution vectors for herd (hd), sex (b), direct animal effect (u), genetic maternal
effect (m) and permanent environmental effect (pˆe) are initially set to zero.
ˆ
SOLVING FOR FIXED EFFECTS. Data file A is read at each round of iteration one herd at
a time with ARHS and DIAG accumulated for the ith herd as:
ˆ
−1
ˆ
ARHS = ARHS + r (y − b − u − m − p ˆ e )
ˆ
i i pa ijklt j k l t
for parental records (Eqn 17.10):
ˆ
−1
ARHS = ARHS + r (y − b − 0.5(u + u ) − m − p ˆ e )
ˆ
ˆ
ˆ
i i np ijklt j s d l t
for non-parent records (Eqn 17.11):
DIAG = DIAG + r −1
i i n
−1
where r is the inverse of the residual variance of the nth record being read.
n
At the end of records for the ith herd, the solution is computed as:
ˆ
hd = ARHS /DIAG
i i i
In the first round of iteration, the solution for the first herd is:
ˆ
ˆ
ˆ
hd = [r (y − b − uˆ − mˆ − p ˆ e ) + (y − b − uˆ − mˆ − p ˆ e )
−1
1 pa 1 1 5 2 2 2 2 6 2 2
ˆ
ˆ
−1
+ (y − b − û − mˆ − p ˆ e ) + (y − b − uˆ − mˆ − p ˆ e )]/4(r )
3 2 7 6 6 4 1 8 5 5 pa
−1
= [r ((35 − 0 − 0 − 0 − 0) + (20 − 0 − 0 − 0 − 0) + (25 − 0 − 0 − 0 − 0)
pa
+ (40 − 0 − 0 − 0 − 0)]/4(r )
−1
pa
= 0.3432/0.01144 = 30.00
While reading data file A, ARHSs consisting of yield adjusted for previous animal,
maternal and permanent environmental solutions are accumulated for each level of
sex effect. Thus for the jth level of sex effect:
ARHS = ARHS + r (y − u − m − p ˆ e )
ˆ
ˆ
−1
j j pa ijklt k l t
for parent records:
−1
ˆ
ˆ
ˆ
ARHS = ARHS + r (y − 0.5(u + u ) − m − p ˆ e )
j j np ijklt s d l t
286 Chapter 17