Page 156 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

(Continued)
Effects Solutions
5 6.3161
6 3.0101
7 3.1085
8 3.1718
9 0.5044
10 0.0000
Fixed regression
1 16.6384
2 −0.6253
3 −0.1346
4 0.3479
5 −0.4218
Animal Regression coeffients 305-day breeding value
1 −0.0583 0.0552 −0.0442 −12.3731
2 −0.0728 −0.0305 −0.0244 −15.7347
3 0.1311 −0.0247 0.0686 28.1078
4 0.3445 0.0063 −0.3164 74.8132
5 −0.4537 −0.0520 0.2798 −98.4153
6 −0.5485 0.0730 0.1946 −118.4265
7 0.8518 −0.0095 −0.3131 184.1701
8 0.2209 0.0127 −0.0174 47.6907
Permanent environmental effects
Cow Regression coefficients 305-day solutions
4 −0.6487 −0.3601 −1.4718 −138.4887
5 −0.7761 0.1370 0.9688 −168.5531
6 −1.9927 0.9851 −0.0693 −427.2378
7 3.5188 −1.0510 −0.4048 756.9415
8 −0.1013 0.2889 0.9771 −22.6619

The solutions for HTD and fixed regression for the RRM are similar to those from
the fixed regression model. Lactation curves can be constructed from the fixed regres-
sion, as described in Section 9.2.1, and influences of different environmental factors on
the curves can be evaluated. Each animal has nr regression coefficients as solutions for
animal and permanent environmental effects. These are not useful for ranking animals
and need to be converted to breeding values for any particular day of interest. Usually,
in dairy cattle, values are calculated for 305-day yields and these have been shown above
in the table of results. The EBV from days 6 to m for animal k (EBV ) is calculated as:
km
nr
j å
u
EBV = tˆ ; with t = t = m å (9.2)
km k f ij
i=6 j=0
where t is a row vector of order nr, with the jth elements equal to the sum of the jth
ˆ
orthogonal polynomial from days 6 to m and u is vector for the regression coefficient
k
of animal k. For Example 9.2, the matrix F for days 4 to 310 has not been shown
because of the size but can be generated as described in Appendix G. Assuming 305-day
breeding values are computed from days 6 to 310, then the vector t for Example 9.2
calculated from days 6 to 310 is:
t = [215.6655 2.4414 −1.5561]

140 Chapter 9