Page 157 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

The breeding value for 305-day yield for animal 4, for instance, can be calculated as:
⎛ . 0 3445 ⎞
⎜
tˆ u = [215 .6655 . 2 4414 − . 1 5561 ] 0 .0063 ⎟ ≈ 74..81
4 ⎜ ⎟
⎝ − . 0 3164⎠
Over the lactation length, daily breeding values can be computed for each animal
from the random regression coefficients. Genetic lactation curves can be obtained for
each animal by plotting these daily breeding values against DIM and differences
between curves for different animals can then be studied. Let v be a vector containing
daily breeding values for days 6 to 310, then v can be calculated as:
310 nr
v = Tu ˆ ; with T = t = ∑ ∑
k ij f ij
= i 6 = j 0
The plots of the daily breeding values for animals 2, 3 and 8 are shown in Fig. 9.2.
The plots indicate that the animal with the highest 305-day breeding value for fat
yield also had the highest daily breeding values along the lactation length.
If the trait being analysed is milk yield, persistence breeding values can be calculated
from the daily breeding values. For instance, persistence predicted transmitting ability
(PS ) for milk yield can be calculated (Schaeffer et al., 2000) as:
PTA
PTA − PTA + y
PS PTA = 280 60 280 ( 100)
y 60
where PTA and PTA are predicted transmitting abilities for day milk yield for an
60 280
animal at days 60 and 280, respectively, and y and y are the average milk yields
60 280
of cows in the genetic base at days 60 and 280, respectively.

0.25

0.2
0.15
Daily breeding values (kg) 0.05
0.1

0

–0.05

–0.1

–0.15
7 28 49 70 91 112 133 154 175 196 217 238 259 280 301
Days in milk

Animal 2 Animal 3 Animal 8
Fig. 9.2. The estimates of daily breeding values for some animals by days in milk.

Analysis of Longitudinal Data 141