Page 64 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

The solutions to the MME by direct inversion of the coefficient matrix are:

Sex effects Sires

Males Females 1 3 4
4.336 3.382 0.022 0.014 −0.043

The difference between solutions for sex subclasses, L′b, where L is [1 − 1], is the
same as in the animal model. However, sire proofs and differences between sire
proofs (s − s ) are different from those from the animal model, although the ranking
i j
for the three sires is the same in both models. The differences in the proofs are due to
the lack of adjustment for breeding values of mates in the sire model and differences
in progeny contributions under both models. In this example, most of the differences
in sire solutions under both models are due to differences in progeny contributions.
The proofs for these sires under the animal model are based on their progeny contri-
butions, since their parents are unknown. This contribution from progeny includes
information from progeny yields and those of grand-offspring of the sires. However,
in the sire model, progeny contributions include information from only male grand-
offspring of the sires in addition to progeny yields. The effect of this difference on sire
proofs under the two models is illustrated for two bulls below.
From the calculations in Section 3.3.1, the proportionate contribution of calves 4
and 6 to the proof of sire 1 in the animal model are −0.003 and 0.102, respectively.
Using Eqn 3.8, the contribution of information from the different yield records to sire 1
under the sire model are as follows.
Contributions (CONT) from yields for calves 4 and 6 are:
CONT = n (0.082) = 0.010
4 2
CONT = n (0.259) = 0.031
6 2
where n = 2/16.667.
2
Contributions from yield record for male grand-progeny (calf 7) through animal 4
(progeny) is:
CONT = n (−0.086) = −0.019
7 3
where n = 3.667/16.667.
3
Therefore:
s = CONT + CONT + CONT = 0.022
1 4 6 7
In the sire model the sum of CONT and CONT is equivalent to the contribution
4 7
from calf 4 to the sire proof in the animal model. Thus the main difference in the
proof for sire 1 in the two models is due largely to the lower contribution of calf 6 in
the sire model. This lower contribution arises from the fact the contribution is only
from the yield record in the sire model while it is from the yield and the progeny of
calf 6 in the animal model.
Similar calculations for sire 3 indicate that the proportionate contributions from
its progeny are −0.088 for calf 5 and 0.047 for calf 8 in the animal model. However,
in the sire model the contributions are −0.037 and 0.051, respectively, from the
yield of these calves. Again, the major difference here is due to the contribution from
calf 5, which contains information from her offspring (calf 7) in the animal model.

48 Chapter 3