Page 85 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

(Continued )
Effects Solutions
7 −1.667
8 −2.334
9 3.925
10 2.895
11 −1.141
12 1.525
13 0.448
14 0.545
15 −3.819
Common environment
2 −1.762
4 2.161
5 −0.399

The equation for the solution of the i level of fixed, animal and common envi-
ronmental effects under this model are the same as those given for fixed (Eqn 4.3),
animal and permanent environmental effects (Eqn 4.4), respectively, in Example 4.1.
The inclusion of common environmental effects in the model allows for accurate
prediction of breeding values of animals. Assuming each dam reared her progeny and
full-sib families were kept under similar environmental conditions, the estimates of
common environmental effects indicate that dam 4 provided the best environment for
her progeny compared with dams 2 and 5. Also, dam 4 has the highest breeding value
among the dams and would therefore be the first dam of choice, whether selection is
for dams of the next generation on the basis of breeding value only or selection is for
future performance of the dams in the same herd, which will be based on some com-
bination of breeding value and estimate of common environmental effect.
The environmental covariance among full-sibs or maternal half-sibs might be due
to influences from the dam (mothering ability or maternal effect); therefore, differ-
ences in mothering ability among dams would cause environmental variance between
families. For instance, resemblance among progeny of the same dam in body weight
could be due to the fact they share the same milk supply and variation in milk yield
among dams would result in differences between families in body weight. This varia-
tion in mothering ability of dams has a genetic basis and, to some degree, is due to
genetic variation in some character of the dams. In Chapter 7, the genetic component
of maternal effect is examined and the appropriate model that accounts for the genetic
component in genetic evaluation is presented.

Models with Random Environmental Effects 69