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.R. Schaeffer et al. Livestock Production Science 65 2000 219 –227
producing cows, so they continue to demand a high milk weight is recorded, but fat and protein content
level of supervised testing. are not necessarily determined for that sample. Thus,
A growing segment of the Canadian dairy industry a method to predict 24 h yields needs to incorporate
includes herds that milk cows three-times per day phenotypic correlations between milk, fat, and pro-
3 3 versus the traditional two-times per day 2 3 . tein yields.
Many 3 3 herds have not enrolled in milk recording An important feature in 3 3 herds is the interval
because of a lack of adjustment factors to estimate between milkings. In practice, time between startup
total 24 h yields from just one or two of the three of the milking machines is known, and this interval
milkings. With the increased flexibility in milk is assumed to be the same for all cows in a herd.
recording schemes, there are many possible scenarios However, in a milking parlour situation, the intervals
with 3 3 herds on a given test day. These combina- for individual cows could vary markedly. A cow
tions are shown in Table 1 along with the combina- may enter the parlour first out of 20 cows at one
tions for 2 3 herds in terms of availability of milk, milking and last out of 20 cows in the next milking.
fat, and protein yields. The word sample denotes one If the herd is large, then the cow may not enter the
of the three milkings in a 3 3 herd or one of the two holding pen in the same order every milking. Thus,
milkings in a 2 3 herd. At the time of sampling, a there could be significant deviations from the mean
interval between machine startups for many indi- viduals.
Stage of lactation of the cow has been shown to be
Table 1
important in predicting 24 h yields Schaeffer and
Possible data situations for cows on 3 3 and 2 3 milkings
Rennie, 1976; Lee and Wardrop, 1984. Also, parity
Number of Which
Number of Which
a
and season of calving may have effects on yield
milk weights milkings
fat and protein milkings
predictions. With these considerations in mind, the
determinations
objectives of this study were to develop a model for
3 3 Milkings
estimating 24 h milk and component yields, to
3 111
3 111
estimate the parameters to adjust sample yields, and
2 110
101
to verify the factors in terms of accuracy of predic-
011
tions for both 2 3 and 3 3 testing schemes.
1 100
010 001
2. Material and methods
2 110
2 110
1 100
010
2.1. Three-times-a-day data
101 2
101 1
100
Data were collected from three Ontario and one
001
Alberta Holstein herds from 1996 through 1998 and
011 2
011 1
010
included 3857 test day records from 996 cows. Cows
001
were milked three-times per day. The first milking of
1 100
1 100
the day was defined as the milking that occurred
1 010
1 010
after 0 h on a 24 h clock. Samples for milk, fat, and
1 001
1 001
protein yield were taken at each milking and the
23 Milkings
milking start time was recorded for each cow. The
2 AM PM
2 AM PM
phenotypic means and variances are given in Table
1 AM
2.
1 PM
1 AM
1 AM
2.2. Model for three-times data
1 PM
1 PM
a
Indicates when samples were taken, for 33 milkings, the
For the 3 3 data, 24 h yields were calculated as
three digit code correspond to mornings, afternoon, and evening milkings, and 0 means no samples were taken at that milking.
the sum of the milk, fat, or protein weights from the
L .R. Schaeffer et al. Livestock Production Science 65 2000 219 –227
221 Table 2
third and later, and season of calving October to
Means and variances of 24 h test day yields kg
April and May to September for a total of 72
Trait Cows
Records Mean
Variance
subclasses. The days in milk DIM classes are shown in Table 3. The intervals for the 3 3 data
23 data Milk yield
2384 14 013
27.0 81.60
were expressed as deviations from 480 min. Recall
Fat yield 2378
13 899 0.983
0.0981
that the intervals for each cow were known.
Protein yield 2380
13 929 0.873
0.0659
The model was modified to fit the possible combi- nations given in Table 1 by removing the appropriate
33 data
covariates. For example, the situation when there are
Milk yield 996
3857 32.8
84.66 Fat yield
988 3592
1.116 0.1154
only two sample weights for milk, fat, and protein
Protein yield 988
3592 1.041
0.0600
and these are from the first two milkings, then b INT , b Milk , b Fat , and b Prot would
3 3
6 3
9 3
12 3
be removed from the model, and the other parame- ters would be estimated.
three milkings. Milk, fat, and protein yields were Cow effects were random, but the ratio of residual
analyzed separately. The general model for a 24 h to cow variances was never estimated due to the
yield was small size of the data set. The assumed ratio was 1.0,
corresponding to a repeatability of 0.5. Cows were y
5 HTD 1 Cow
ijkm i
j
also assumed to be genetically unrelated for these 1 [b 1 b INT 1 b INT 1 b INT
1 1
2 2
3 3
analyses. 1 b Milk 1 b Milk 1 b Milk
4 1
5 2
6 3
2.3. Two-times-a-day data 1 b Fat 1 b Fat 1 b Fat
7 1
8 2
9 3
1 b Prot 1 b Prot 1 b Prot ]
10 1
11 2
12 3 k
Data were collected from 19 Holstein herds in 1 e
,
ijkm
Alberta, Manitoba, British Columbia, and Ontario. where
Morning AM and evening PM milk weights and their corresponding fat and protein percentages were
y is the m-th 24 h yield milk, fat, or
obtained for 2395 cows over their completed lacta-
ijkm
protein made by tions. Out of 14 878 test day records, 4989 were
cow j in herd-test date subclass i at days from first lactation cows, 3572 were from second
in milk, parity, lactation cows, and 6407 were from third and later
and season of calving subclass k, lactation cows. Records were collected from 1991
HTD is a fixed effect of herd-test date,
i
Cow is a random effect of cow j includes
j
genetic and permanent environmental effects,
Table 3 Definition of days in milk classes
INT is the interval before the t-th milking,
t
Milk is the sample milk weight at the t-th
Class Range
t
milking,
1 30 d
Fat is the sample fat weight at the t-th
t
2 31–50 d
milking,
3 51–70 d
4 71–90 d
Prot is the sample protein weight at the t-th
t
5 91–110 d
milking,
6 111–130 d
and
7 131–150 d
e is the residual effect.
ijkm
8 151–180 d
9 181–220 d
10 221–260 d
Note that the regression coefficients were nested
11 261–300 d
within subclasses that were formed on the basis of
12 . 300 d
days in milk 12 classes, parity first, second, or
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.R. Schaeffer et al. Livestock Production Science 65 2000 219 –227
through 1993. All herds had automated milking For the 3 3 data set, the same data that were used
systems so that milk yields between supervised test to estimate the regression coefficients were used to
days were available. The data were previously used calculate accuracies of prediction. Hence the derived
by Schaeffer and Jamrozik 1996. The raw pheno- regression coefficients should perform better than
typic means and variances are given in Table 2. any factors that may have been derived from other
The data were split into two subsets, where one data. Further data need to be collected for a true
was used to estimate the factors for predicting 24 h verification analysis.
yields, and the other data set was used to verify the The current official milk recording program uti-
accuracy of the factors. Data set 1 contained 10 288 lizes adjustment factors for 2 3 and 3 3 herds. For
test day records from 1672 cows in 14 herds, with 2 3 herds with either AM or PM yields measured,
each of the four provinces represented by at least one the factors used were derived by Lee and Wardrop
herd. Data set 2 contained the other five herds with 1984. These factors multiplicatively adjust milk
4590 test day records also from 1672 cows. The start yields for milking interval and stage of lactation, and
of milking times for AM and PM milkings were only multiplicatively adjust fat percentage for milking
available on a herd basis on that test day and the interval, but there are no factors for protein per-
intervals were expressed as deviations from 720 min. centage. For 3 3 data, there is a requirement that
two of the three samples have milk weights and one or both of these have fat and protein composition
2.4. Model for two-times data known. The same procedure and factors as reported
by Wiggans 1986 are used to multiply the totals The model for 2 3 data set 1 was the same as for
from two milkings. These factors were applied to the the 3 3 data set, except that the number of covari-
complete set of 2 3 data and to the 3 3 data in this ables was reduced because there were only two
study for comparison. milkings rather than three in these data. Also, only
No tests were conducted to test whether more or one interval needs to be known because the two
less than 72 subclasses of prediction equations were intervals sum to 24 h. The intervals were only known
needed. A reduction in the number of subclasses for each herd-test date rather than for each cow.
should be possible without sacrificing accuracy of predictions. This can be done safely only after more
2.5. Verification data are collected. In the current study, an average of
23 cows or 63 test day records per subclass were in The analyses provided regression coefficients for
the 2 3 data sets, and only 13 cows and 53 test day predicting 24 h yields in various situations of
records in the 3 3 data set. Thus, standard errors on missing information, and for the 72 subclasses of
regression coefficients for some subclasses could be days in milk, parity, and season of calving. For the
very large. 2 3 data set, the 24 h yields were predicted in data
set 2 from the regression coefficients estimated from data set 1. The predicted 24 h yields were compared
3. Results and discussion
