Derivation of Factors to Estimate Daily Milk Yield

1. Derivation of Factors to Estimate Daily Milk Yield from Single Milkings for Holsteins Milked Two or Three Times Daily M.M. Schutz, J.M. Bewley Department of Animal Sciences, Purdue University and H.D. Norman USDA-ARS, Animal Improvement Programs Laboratory

2. Introduction • Increasing number of herds utilizing AP testing plans • Cost • Convenience • Necessity in herds milking around the clock • AP programs easier for DHI service providers to test large herds • Large herds have variable milk pick-up times

3. Background • Present factors to estimate daily milk from a single milking for milking interval (MI) in herds milked 2x (DeLorenzo and Wiggans, 1986). • Factors derived from total milk yields • Bulk tank component samples • Used milking start and end times • Accounted for differences in DIM • Allow prediction by either look-up table or regression equations.

4. Background • Method extended to prediction of daily yield from one or two milkings in 3x herds (Wiggans, 1986). • Based on 7 PA and 5 UT herds • Factors allow prediction of daily yield by application of regression equations.

5. Background • Liu et al., 2000 explored several approaches to estimating daily yields from a single milking. 0. DeLorenzo factors (no adjustment for DIM). 1. MD = 2MP (MD = daily milk, MP = partial milk) 2. MD = b0 + b1MP 3. MD = b0 + b1MP + b2MI 4. MD = b0 + b1MP (by MIclass) 5. MD = b0 + b1MP + b2(DIM – 158) (by MIclass) 6. MD = b0 + b1MP (by parity x MIclass x DIMclass)

6. Objective • To derive preliminary factors to estimate daily yields from: • One record for 2x milking • One or two records from 3x milking • Focus in this presentation on one record and Holsteins • Compare factors derived by several methods for their accuracy in predicting true daily production

7. Data • Records were from 9 herds (5-2x and 4-3x) in IN, KS, IA, MI, and MN. • Herds used Automatic Milk Recording, records processed through DRMS (except MN). 2X 3X 1 83,690 1842 5 2+ 143,670 2957 5 1 41,657 779 4 Parity number Test-d records Cows Herds 2+ 84,131 1999 4

8. Method 1 • DeLorenzo and Wiggans Method Factor = Σy / Σx For each Milking Interval x Parity subclass. 24 MI classes (approx 9-15 h for 2x, 5-10.5 for 3x) 2 Parity classes (1, 2+) Factors smooth by weighted regression of their reciprocals on MI. Residuals regressed on DIM to develop stage of lactation adjustment.

9. Method 2 • DeLorenzo and Wiggans Alternative Method Factor = Σ (y / x) / n For each Milking Interval x Parity subclass. 24 MI classes (approx 9-15 h for 2x, 5-10.5 for 3x) 2 Parity classes (1, 2+) Factors smooth by weighted regression of their reciprocals on MI. Residuals regressed on DIM to develop stage of lactation adjustment.

10. Method 3 • Liu et al. Model [6] • MD = b0 + b1MP (by parity x MI class x DIM class) For each Parity x MI x DIMclass). 2 Parity classes (1, 2+) 7 MI classes (approx 9-14 h for 2x, 6 to 10 for 3x) 12 DIM classes (≤30, ≤60, … ≤330, ≥330) Factors are not smooth. Adjustment uses regression coefficients.

11. Distribution of numbers of cow-test-days with intervals prior to AM or PM milkings Holstein Observations Milking Interval

12. Distribution of numbers of cow-test-days with intervals prior to 1st, 2nd, or 3rd milkings Holstein Observations Milking Interval

13. Current and Method 2 factors by parity for AM milking Holstein 2x Factor Milking Interval

14. Current and Method 2 factors by parity for PM milking Holstein 2x Factor Milking Interval

15. Current and Method 2 factors by parity for Milking 1 Holstein 3x Factor Milking Interval

16. Current and Method 2 factors by parity for Milking 2 Holstein 3x Factor Milking Interval

17. Current and Method 2 factors by parity for Milking 3 Holstein 3x Factor Milking Interval

18. Method 3 results for 12.5 to 13 h interval for AM milking by milk weight for DIM classes Holstein 2x Predicted Daily Milk (kg) Milking 1 Weight (kg)

19. Method 3 results for 11.0 to 11.5 h interval for PM milking by milk weight for DIM classes Holstein 2x Predicted Daily Milk (kg) Milking 1 Weight (kg)

20. Method 3 results for <10 h interval for PM milking by milk weight for DIM classes Holstein 2x Predicted Daily Milk (kg) Milking 1 Weight (kg)

21. Method 3 results for 180-210 DIM class for milking 1 by milk weight for interval classes Predicted Daily Milk (kg) Holstein 3x Milking 1 Weight (kg)

22. Measures of variation and goodness of estimation of daily yield from AM yield for Holsteins Correlation With true .955 .956 .956 .957 .964 .964 .964 .965 Parity 1 Current Method 1 Method 2 Method 3 Parity 2+ Current Method 1 Method 2 Method 3 SD of Estimates 18.76 18.59 18.82 17.03 26.48 26.39 26.74 24.30 Absolute Error 3.78 3.62 3.80 3.58 4.94 4.87 5.16 4.71 Root MSE 5.614 5.449 5.591 5.175 7.080 6.999 7.263 6.572 Abs. Diff. Current NA 0.90 0.67 1.71 NA 0.55 1.06 2.13

23. Measures of variation and goodness of estimation of daily yield from PM yield for Holsteins Correlation With true .908 .945 .944 .947 .931 .954 .954 .955 Parity 1 Current Method 1 Method 2 Method 3 Parity 2+ Current Method 1 Method 2 Method 3 SD of Estimates 18.52 18.72 18.91 16.85 25.10 25.98 26.23 24.05 Absolute Error 7.01 4.05 4.12 3.90 8.09 5.41 5.49 5.36 Root MSE 9.070 6.149 6.272 5.724 10.583 7.827 7.973 7.443 Abs. Diff. Current NA 5.39 6.04 5.51 NA 5.83 5.49 5.92

24. Measures of variation and goodness of estimation of daily yield from single milking yield for Parity 1 Holsteins milked 3x Current Method 2 Method 3 Current Method 2 Method 3 Current Method 2 Method 3 Correlation With true .937 .937 .938 .931 .931 .934 .926 .926 .930 SD of Estimates 19.60 19.70 17.38 20.35 20.70 17.29 19.54 20.10 17.22 Absolute Error 4.57 4.66 4.51 4.78 5.01 4.60 4.77 5.04 4.79 Root MSE 6.865 6.961 6.408 7.415 7.7.4 6.633 7.439 7.708 6.827 Abs. Diff. Current NA 0.64 2.11 NA 1.27 2.71 NA 2.11 2.37 Milking 1 Milking 2 Milking 3

25. Measures of variation and goodness of estimation of daily yield from single milking yield for Parity 2+ Holsteins milked 3x Current Method 2 Method 3 Current Method 2 Method 3 Current Method 2 Method 3 Correlation With true .940 .939 .942 .936 .935 .939 .933 .933 .938 SD of Estimates 29.41 29.69 26.31 30.84 31.03 26.21 29.01 30.50 26.21 Absolute Error 6.95 7.24 6.85 7.59 7.79 6.88 7.16 7.76 6.90 Root MSE 10.029 10.368 9.365 11.065 11.305 9.621 10.669 11.249 9.645 Abs. Diff. Current NA 1.66 3.06 NA 0.85 4.49 NA 4.58 3.68 Milking 1 Milking 2 Milking 3

26. Conclusions • Method 3 (regression within parity x MI x DIM subclasses) estimates of daily yield consistently had highest correlation with true daily yields, and smallest errors compared to actual daily yield. • Measures of differences between estimated and actual yields were greater for parity 2. • Error terms were greater for PM than AM milkings for 2x herds but similar across milkings for 3x herds.

27. Implications and Future Work • Data collection is ongoing to acquire • more milk weight records for Jersey herds • More test-day records for fat, protein, and SCC. • While derived factors performed better than current factors for these herds, factors will need to be compared for robustness on more herds before new factors are implemented.

28. Acknowledgments • Animal Improvement Programs Laboratory, provided financial support for data collection and analyses. • Dairy Records Management Services (John Clay and Tammie Guyer) assisted in data file management. • DHI Affiliate Managers, DHI Supervisors, and Herd Owners are also recognized for their contributions.