Page 102 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

−1
Then R = diag(1/77, 1/70) and:
⎡ 0.0311 −0.0186 ⎤
−1
G = ⎢ ⎥
⎣ −0.0186 0.0445 ⎦
The MME given earlier can easily be set up using the principles discussed so far
in this chapter. Solving the MME by the direct inverse of the coefficient matrix gave
the following solutions:

Solutions
Effects Yearling weight (kg) Fat (kg)

HYS
1 411.833 193.299
2 275.955 205.344
3 – 163.315
Animal
1 −0.472 2.519
2 −3.350 0.381
3 0.856 −3.208
4 −5.142 −3.936
5 −4.778 −2.000
6 4.778 2.000
7 2.177 3.628
8 −4.940 −5.251
9 −10.234 −3.817
10 −8.842 −2.810
11 6.932 4.260
12 11.568 3.060
13 3.029 6.701
14 −6.395 −11.485
15 −2.797 −1.680
16 4.193 10.797
17 0.526 0.050

Selection of dual-purpose sires will be based on some combination of breeding
value estimates for yearling weight and fat yield. If equal weights were given to yearling
weight and fat yield, sire 1 would be the best of the three sires, followed by sire 3.

5.5.2 The multi-trait across-country evaluations (MACE)

The sire model for MACE was originally proposed by Schaeffer (1994) and involved
the analysis of the DYD of bulls in different countries as different traits, with the
number of daughters of a bull used as a weighting factor. The genetic correlations
among DYDs of bulls in different countries were incorporated. The genetic correla-
tions accounted for genotype by environment (G × E) interactions and differences in
national models for genetic evaluations among the countries. The genetic correlations
among several countries used by Interbull are usually of medium to high value.

86 Chapter 5