Estimating daily yields when not all milkings are weighed and sampled (AP Plans)

By George Wiggans
USDA-ARS-AIPL


Over the past several years, official milk testing plans have become more flexible. Most tested cows are on AM/PM programs for which data are provided from only one milking (alternately a.m. and p.m) per month. In 2003, all milkings were weighed for only 36% of cows and only 23% had component samples taken for all milkings on test day. Total daily yield must therefore be estimated for nearly two thirds of all test day records.

Milk and fat yield estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and SNF percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

For 2X Milking:

For 2X milking herds, a single milking or both milkings may be weighed. The sample may be collected at one or both of these milkings. When one milking is weighed and sampled, yield is estimated as follows:

Estimated Test-day milk yield = Measured milking yield × Milking-interval factor1 +
    (DIM-158) × Milking-interval-lactation-stage co-factor
    1For a.m. or p.m. milking time.

Table 1. Factors for estimating daily milk yield for 2X milking with one weighed/sampled milking.
Milking Interval
(hrs)
Milk adjustment factors Percent fat adjustment factors
For measured milking started in a.m. For measured milking started in p.m.
Milking-interval factor Milking-interval-lactation-stage co-factor Milking-interval factor Milking-interval-lactation-stage co-factor Milking-interval factor
<9.00 2.465 0.01566 2.594 0.00834 0.919
9.00- 9.24 2.465 0.01566 2.534 0.01069 0.927
9.25- 9.49 2.465 0.01566 2.477 0.01071 0.934
9.50- 9.74 2.411 0.01578 2.423 0.01126 0.941
9.75- 9.99 2.359 0.01600 2.370 0.01043 0.948
10.00-10.24 2.310 0.01010 2.321 0.00742 0.955
10.25-10.49 2.262 0.00879 2.273 0.00471 0.961
10.50-10.74 2.217 0.00649 2.227 0.00000 0.968
10.75-10.79 2.173 0.00492 2.183 0.00000 0.974
11.00-11.24 2.131 0.00000 2.140 0.00000 0.980
11.25-11.49 2.091 0.00000 2.099 0.00000 0.986
11.50-11.74 2.052 0.00000 2.060 0.00000 0.992
11.75-11.99 2.014 0.00000 2.022 0.00000 0.997
12.00-12.24 1.978 0.00000 1.986 0.00000 1.003
12.25-12.49 1.943 0.00000 1.951 0.00000 1.008
12.50-12.74 1.910 0.00000 1.917 0.00000 1.013
12.75-12.99 1.877 0.00000 1.884 0.00000 1.018
13.00-13.24 1.846 0.00000 1.852 -0.00418 1.023
13.25-13.49 1.815 0.00000 1.822 -0.00510 1.028
13.50-13.74 1.786 -0.00369 1.792 -0.00678 1.033
13.75-13.99 1.757 -0.00569 1.763 -0.00747 1.037
14.00-14.24 1.730 -0.00766 1.736 -0.01123 1.042
14.25-14.49 1.703 -0.00801 1.709 -0.01039 1.046
14.50-14.74 1.677 -0.00733 1.683 -0.01000 1.050
14.75-14.99 1.652 -0.00696 1.683 -0.01000 1.054
>=15.00 1.628 -0.00518 1.683 -0.01000 1.058

Milking-interval factors are calculated with the formula:
Milking-interval factor = 1 / Intercept + (Slope × Milking interval)
where the intercept and slope are as follows:
Table 2.
Trait Intercept
For measured milking started in a.m.
Intercept
For measured milking started in p.m.
Slope
Milk Yield 0.0654 0.0634 0.0363
Fat Yield 0.1965 0.1939 0.0254
The fat percent milking-interval adjustment factor is the ratio of the fat yield adjustment factor to the milk yield adjustment factor. The values for percent fat adjustment given in Table 1 are appropriate for both a.m. and p.m. milkings.

For example: Cow A is in the herd with a measured milking started at 6:30 a.m. and a milking interval of 14.25 hours. She has been in milk for 250 days. She produced 23.0 pounds of milk at the measured milking, and her sample was 4.0 % fat and 3.5 % protein.

Test-day milk yield = (1.703 × 23.0#) + (-0.00801) × (250d - 158)
= 38.4 pounds of milk
     
Test-day fat percentage = 1.046 × 4.0
  = 4.2% fat
     
Test-day fat yield = 0.042 × 38.4#
  = 1.61 pounds of fat
     
Test-day protein percentage = 3.5% protein
     
Test-day protein yield = 0.035 × 38.4#
    1.34 pounds of protein

If both milkings are weighed, but only one is sampled, daily milk weight is the sum of weighed milkings, and fat percent is calculated as above. Fat and protein yield are calculated using the total daily milk weight.

For 3X Milking:

For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking.

These AP factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. (See DHIA Fact Sheet G-2.)


Milking-interval factors are calculated using the same formula with the intercept and slope as follows:
Table 3.
Trait Intercept
Slope
For measured milking started between 2 a.m. and 9:59 a.m For measured milking started between 10 a.m. and 5:59 p.m. For measured milking started between 6:00 p.m. and 1:59 a.m.
Milk Yield 0.077 0.068 0.066 0.0329
Fat Yield 0.186 0.186 0.182 0.0186
When 2 milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings.
Milking-interval factor = 1 / (Intercept 1 + Intercept 2)+ (Slope × (Milking interval 1 + Milking interval 2)
 

Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

For Example: Cow B is in a herd that had 2 of 3 milkings weighed of which 1 was sampled. She produced 16.0 pounds of milk at a 5 a.m. milking and 12.0 pounds of milk at a noon milking. Her sample at the 5 a.m. milking was 4.0 % fat and 3.5 % protein. The milking preceding the 5 a.m. milking started at 7 p.m. the evening before.

Milk-yield factor = 1 / {0.077 + 0.068 + [0.0329 × (10h + 7h)]}
  = 1 / 0.704
  = 1.42
     
Test-day milk yield = 1.42 × (16.0# + 12.0#)
= 39.8 pounds of milk
     
Percent-fat factor = [0.077 + (0.0329 × 10h)] / [0.186 + (0.0186 × 10h)]
  = 0.406 / 0.372
  = 1.09
     
Test-day fat percentage = 1.09 × 4.0
  = 4.4 % fat
     
Test-day fat yield = 0.044 × 39.8
  = 1.75 pounds of fat
     
Test-day protein percentage = 3.5% protein
     
Test-day protein yield = 0.035 × 39.8
    1.39 pounds of protein

For 4X - 6X Milking:

The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X. See http://aipl.arsusda.gov/reference/freqadj.pdf for further explanation of the 3X AP factors.