Page 331 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

and for animals without records:
D = D
1i 0i
where D is the diagonal element for animal i in the MME and, in general, its compo-
0i
sition, depending on the amount of information available on the animal, is:
D = x + n a + n a/3 + n a/2
0i i i 1i 2i
4
where x = 1 if the animal has a record and otherwise it is zero, n equals 1 or or 2 if
i i 3
none or one or both parents are known, n and n are number of progeny with one
1i 2i
or both parents known, respectively.
2. Diagonal elements for parents (f and m) are adjusted for the fact the information
on their progeny is limited.
For each progeny i with only one parent known, adjust the diagonal element of
the parent as:

2 4
−1
D = D − a ( D )
2f 1f 9 1i
and if both parents are known, adjust the diagonal of parent f as:
2
D = D − a D −1
2f 1f 1i
Replace subscript f with m for the other parent. For animals that are not parents:
D = D
2i 1i
3. Adjustment of progeny diagonals for information on parents.
This involves initially unadjusting the diagonals of the parents for the contribu-
tion of the ith progeny in question by reversing step 2 before adjusting progeny diago-
nals for parental information. If only one parent f is known, the diagonal is unadjusted
initially as:
*
−1
2 4
D = D + a ( D )
2f 2f 9 2i
and if both parents are known as:
*
2
D = D − a D −1
2f 2f 2i
for parent f. Exchange m for f in the above equation to calculate for parent m.
Adjustment of progeny i diagonal then is:
2 4 D *−1
3i 2i 9 2f
D = D − a
if only parent f is known and:
*
*
*
*
2
2
D = D − a ((D + D − a)/(D D − a ))
1
3i 2i 2f 2m 2f 2m 4
when both parents f and m are known.
For animals with unknown parents:
D = D
3i 2i
Reliability for progeny i is calculated as:
r = const.(1 − aD )
2
−1
3i
where const. is a constant of between 0.90 and 0.95 from Meyer simulation studies
which gave the best estimate of r .
2
Appendix D 315