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Table 1

Possible data situations for cows on $3\times$ and $2\times$ milkings. For $3\times$ milkings, the code (ijk) under the heading "Which Milkings" indicates when the samples were taken during the three milkings where i,j,k correspond to morning, afternoon, and evening milkings, respectively, and 0 means no samples were taken at that milking and 1 means that they were.

Number of Which Number of Which
milk weights milkings fat and protein milkings
    determinations  
$3\times$ Milkings    
3 111 3 111
    2 110
      101
      011
    1 100
      010
      001
       
2 110 2 110
    1 100
      010
  101 2 101
    1 100
      001
  011 2 011
    1 010
      001
       
1 100 1 100
1 010 1 010
1 001 1 001
$2\times$ Milkings    
2 AM PM 2 AM PM
    1 AM
    1 PM
       
1 AM 1 AM
1 PM 1 PM

Table 2

Means and variances of 24 h test day yields (kg).

Trait   Cows Records Mean Variance
$2\times$ data        
  Milk yield 2,384 14,013 27.0 81.60
  Fat yield 2,378 13,899 0.983 0.0981
  Protein yield 2,380 13,929 0.873 0.0659
           
$3\times$ data        
  Milk yield 996 3,857 32.8 84.66
  Fat yield 988 3,592 1.116 0.1154
  Protein yield 988 3,592 1.041 0.0600

Table 3

Definition of days in milk classes.

Class Range
1 $\leq 30$ d
2 31 to 50 d
3 51 to 70 d
4 71 to 90 d
5 91 to 110 d
6 111 to 130 d
7 131 to 150 d
8 151 to 180 d
9 181 to 220 d
10 221 to 260 d
11 261 to 300 d
12 >300 d

Table 4

Prediction equations for fat and protein yields for first lactation Holsteins calving between October to April for $2\times$ milking herds.

Milk Fat, Days in Inter   AM PM AM PM AM PM
Samples Prot. Milk -cept INT Milk Milk Fat Fat Prot Prot
Fat Yields                
AM,PM AM $\leq 30$d 0.0705 0.0001 -0.0255 0.0380 1.4198   0.2315  
    91-110d 0.1255 -0.0001 -0.0331 0.0276 1.2625   0.7443  
    221-260d 0.0496 0.0004 -0.0215 0.0343 1.4370   0.1372  
                     
AM,PM PM $\leq 30$d 0.0405 0.0002 0.0346 -0.0345   1.3776   0.5893
    91-110d 0.0262 0.0001 0.0329 -0.0261   1.3869   0.3294
    221-260d 0.0900 0.0001 0.0305 -0.0387   1.4529   0.5732
                     
AM AM $\leq 30$d 0.2358 -0.0001 0.0104   1.2490   -0.0607  
    91-110d 0.3059 -0.0005 -0.0060   1.1396   0.4050  
    221-260d 0.2235 -0.0007 0.0005   1.4419   -0.0011  
                     
PM PM $\leq 30$d 0.2623 0.0000   0.0079   1.3281   -0.1241
    91-110d 0.2206 -0.0005   0.0051   1.2927   0.0709
    221-260d 0.2208 -0.0006   -0.0055   1.3750   0.3035
                     
Protein Yields                
AM,PM AM $\leq 30$d 0.0083 0.0000 -0.0249 0.0303 0.0551   1.7390  
    91-110d 0.0106 0.0000 -0.0209 0.0325 -0.0156   1.6345  
    221-260d 0.0117 -0.0001 -0.0207 0.0328 -0.0282   1.6607  
                     
AM,PM PM $\leq 30$d 0.0156 0.0000 0.0300 -0.0269   -0.0099   1.8679
    91-110d 0.0050 0.0000 0.0326 -0.0310   0.0179   1.9048
    221-260d -0.0023 -0.0002 0.0323 -0.0328   0.0549   1.9454
                     
AM AM $\leq 30$d 0.1430 -0.0001 0.0040   -0.0893   1.4914  
    91-110d 0.2105 -0.0005 0.0099   -0.1395   1.2869  
    221-260d 0.1740 -0.0012 -0.0004   -0.0202   1.5544  
                     
PM PM $\leq 30$d 0.2145 -0.0002   0.0100   -0.0471   1.2242
    91-110d 0.1997 -0.0007   -0.0003   -0.0765   1.6556
    221-260d 0.1366 -0.0009   0.0022   -0.0232   1.6581

Table 5

Variance of the difference of estimated 24 h yield from actual 24 h yields for fat and protein and their accuracies from data set 2 for $2\times$ milking schemes.

Milk weights Fat, protein Var(dif) Accuracy
taken on taken on Fat Prot Fat Prot
AM PM AM 0.0069 0.0003 0.93 0.995
AM PM PM 0.0086 0.0005 0.92 0.99
           
AM AM 0.0123 0.0059 0.89 0.92
PM PM 0.0140 0.0069 0.88 0.91
           
None AM 0.0120 0.0057 0.89 0.92
None PM 0.0136 0.0068 0.88 0.91
           
None AM fat only 0.0131   0.88  
None PM fat only 0.0134   0.88  
           
None AM prot only   0.0057   0.92
None PM prot only   0.0069   0.91

Table 6

Variance of the difference of estimated 24 h yield from actual 24 h yields for fat and protein and their accuracies from the complete data for $2\times$ milking schemes.

Milk weights Fat, protein Var(dif) Accuracy
taken on taken on Milk Fat Prot Milk Fat Prot
AM PM AM 0.000 0.0059 0.0003 1.00 0.94 0.995
AM PM PM 0.000 0.0074 0.0004 1.00 0.93 0.99
AM AM 4.546 0.0112 0.0048 0.95 0.90 0.93
PM PM 4.702 0.0122 0.0050 0.95 0.89 0.93
AM None 4.658     0.95    
PM None 4.882     0.94    
None AM   0.0111 0.0048   0.90 0.93
None PM   0.0121 0.0050   0.89 0.93
None AM fat only   0.0123     0.89  
None PM fat only   0.0122     0.89  
None AM prot only     0.0049     0.93
None PM prot only     0.0051     0.93

Table 7
Variance of the difference of estimated 24 h yield from actual 24 h yields for milk, fat and protein and their accuracies from the complete data for $2\times$ milking schemes using the current official factors.

Trait Sample Var(dif) Accuracy
Milk AM 5.053 0.94
  PM 7.573 0.92
       
Fat AM 0.0166 0.86
  PM 0.0193 0.84
       
Protein AM 0.0054 0.92
  PM 0.0081 0.89

Table 8

Prediction equations for fat and protein yields for first lactation Holsteins calving between October to April for $3\times$ milking herds.

Milk Fat, Days in Inter     1st 2nd 1st 2nd 1st 2nd
Samples Prot. Milk -cept INT1 INT2 Milk Milk Fat Fat Prot Prot
Fat Yields                  
110 110 $\leq 30$d 0.1405 0.0004 0.0016 -0.0148 0.0223 1.0783 1.1410 0.0537 0.2326
    91-110d 0.1994 -0.0002 -0.0004 0.0439 -0.0275 0.9733 1.1700 -1.2844 0.9995
    221-260d 0.1906 -0.0004 -0.0012 0.0059 0.0096 0.8596 0.9137 0.2845 -0.0637
                       
110 100 $\leq 30$d 0.1830 0.0008 0.0015 -0.0491 0.0538 1.4476   1.1285  
    91-110d 0.3106 0.0001 -0.0005 -0.0202 0.0348 1.6150   -0.0353  
    221-260d 0.2438 -0.0010 -0.0017 0.0130 0.0417 1.1973   -0.5177  
                       
110 010 $\leq 30$d 0.2109 0.0004 0.0018 0.0216 0.0016   1.6640   0.2387
    91-110d 0.2576 -0.0005 -0.0006 0.0407 -0.0111   1.6989   -0.4395
    221-260d 0.3268 -0.0007 -0.0004 0.0519 -0.0289   1.0240   0.3238
Protein Yields                  
110 110 $\leq 30$d 0.1269 0.0002 0.0010 0.0212 -0.0043 -0.1701 0.1380 0.4753 1.6475
    91-110d 0.1189 -0.0007 -0.0009 -0.0001 0.0059 -0.0401 -0.0844 1.2578 1.3423
    221-260d 0.1135 -0.0004 -0.0008 0.0046 0.0127 -0.0127 -0.2501 1.2456 1.1862
                       
110 100 $\leq 30$d 0.1684 0.0003 0.0010 -0.0278 0.0514 -0.1249   1.8863  
    91-110d 0.1360 -0.0006 -0.0010 -0.0276 0.0447 -0.1310   2.1861  
    221-260d 0.1254 -0.0003 -0.0011 -0.0238 0.0487 -0.1021   1.9838  
                       
110 010 $\leq 30$d 0.1414 0.0004 0.0007 0.0324 -0.0127   -0.0487   2.0092
    91-110d 0.1320 -0.0006 -0.0007 0.0381 -0.0192   -0.0983   2.1391
    221-260d 0.1076 -0.0005 -0.0007 0.0481 -0.0193   -0.2835   2.1262

Table 9

Variance of the difference of estimated 24 h yield from actual 24 h yields for milk, fat, and protein and their accuracies for $3\times$ milking schemes.

Milk weights Fat, protein Var(dif) Accuracy
taken on taken on Milk Fat Prot Milk Fat Prot
111 111 0.000 0.002 0.000 1.00 1.00 1.00
               
  110   0.007 0.001   0.94 0.98
  101   0.006 0.001   0.95 0.98
  011   0.007 0.001   0.94 0.98
               
  100   0.018 0.002   0.87 0.97
  010   0.015 0.001   0.89 0.98
  001   0.018 0.001   0.87 0.97
               
110 110 2.573 0.011 0.003 0.97 0.91 0.95
  100   0.021 0.004   0.85 0.94
  010   0.020 0.004   0.85 0.94
               
101 101 2.192 0.008 0.003 0.97 0.94 0.95
  100   0.020 0.003   0.85 0.95
  001   0.019 0.003   0.86 0.95
               
011 011 2.223 0.010 0.003 0.97 0.92 0.95
  010   0.019 0.003   0.86 0.95
  001   0.023 0.003   0.83 0.95
               
100 100 8.328 0.027 0.008 0.91 0.81 0.88
010 010 8.120 0.026 0.009 0.91 0.82 0.87
001 001 8.357 0.028 0.009 0.91 0.80 0.87

Table 10

Variance of the difference of estimated 24 h yield from actual 24 h yields for fat and protein and their accuracies for $3\times$ milking schemes when considered separately.

Samples Var(dif) Accuracy
  Fat Protein Fat Protein
111 0.003 0.000 1.00 1.00
         
110 0.012 0.003 0.91 0.95
101 0.009 0.003 0.93 0.95
011 0.013 0.003 0.90 0.95
         
100 0.027 0.009 0.81 0.87
010 0.026 0.009 0.82 0.87
001 0.029 0.009 0.80 0.87

Table 11

Variance of the difference of estimated 24 h yield from actual 24 h yields for milk, fat, and protein and their accuracies for $3\times$ milking schemes using the current official factors.

Milk weights Fat, protein Var(dif) Accuracy
taken on taken on Milk Fat Prot Milk Fat Prot
110 100 3.256 0.028 0.004 0.96 0.80 0.94
  010   0.027 0.004   0.81 0.94
               
101 100 2.510 0.031 0.004 0.97 0.79 0.94
  001   0.025 0.003   0.82 0.95
               
011 010 2.687 0.025 0.004 0.97 0.82 0.94
  001   0.027 0.003   0.81 0.95


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This LaTeX document is available as postscript or asAdobe PDF.

Larry Schaeffer
1999-07-05