Multiple-Trait Prediction of Lactation Yields for Dairy Cows by a62nh

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									                                GENETICS, BREEDING, AND MODELING
Multiple-Trait Prediction of Lactation
Yields for Dairy Cows
                                                                              L. R. SCHAEFFER and J. JAMROZIK'
                                                                                    Centre for Genetic Improvement of Livestock,
                                                                                       Department of Animal and Poultry Science,
                                                                            University of Guelph, Guelph, ON, Canada N l G 2W1



                         ABSTRACT                               in the most current methods for calculating 305-d
                                                                lactation totals.
   A multiple-trait procedure is described for predict-             The test interval method (TIM) has been a stan-
ing 305-d lactation yields for milk, fat, and protein           dard method for calculating 305-d lactation yield from
that incorporates information about standard lacta-             test day yields that are at approximately 30-d inter-
tion curves and covariances between yields for milk,            vals through the lactation (5, 11). With special ad-
fat, and protein. Test day yields are weighted by their         justments for first and last test day yields, TIM has
relative variances, and standard lactation curves of            been an unbiased measure of actual 305-d yields.
cows from similar breed, region, lactation number,              With TIM, yields of milk, fat, and protein are
age, and season of calving are used for the estimation          processed separately, ignoring information from the
of lactation curve parameters for each cow, Accuracies
                                                                other two traits.
of the test interval method and the multiple-trait                  In the Netherlands, yields are estimated for every
procedure were comparable. In addition, the multiple-
                                                                20-d lactation period, utilizing standard lactation
trait procedure can handle long intervals between test
                                                                curves based on cows with production characteristics
days as well as test days with milk only recorded and
                                                                that are similar t o those of the cow being evaluated
can make 305-d predictions on the basis of just one
                                                                ( 9 , 15). Each trait is also processed separately with
test day record per cow. The procedure also lends
itself to the calculation of peak yield, day of peak            this procedure, but this algorithm incorporates
yield, yield persistency, and expected test-day yields,         specific prior information about other cows to predict
which could be useful management tools for a                    yields better for a single cow.
producer on a milk recording program.                               Lactation yields have been analyzed with mathe-
( Key words: lactation curves, multiple traits, predic-         matical functions of various types (1, 3, 4, 8, 12, 13,
tion)                                                            14, 16), and usually a minimum of four or five test
                                                                day yields are needed t o obtain an accurate prediction
Abbreviation key: MTP = multiple-trait prediction,              of yields for a 305-d lactation for individual cows.
TIM = test interval method.                                     Archer ( 2 ) used a multiple-trait version of Wood's
                                                                model ( 1 4 ) without incorporating standard curves.
                      INTRODUCTION                              The multiple-trait method was not significantly bet-
                                                                ter than TIM, when data were available for all tests,
   Test day yields (24-h measurements) for milk, fat,           but showed that accurate predictions of 305-d fat and
and protein are the components used for calculation of          protein yields could be attained even if fat and pro-
standard 305-d lactation yields. Test day yields are            tein information was missing for some test days. No
affected by a number of production characteristics,              study has utilized a curve function to obtain standard
including geographical region, breed, herd manage-              curves for groups of cows with the same production
ment, lactation number, age at calving, month of                characteristics and then utilized that information to
calving, and number of days in lactation. Correlations          assist in predicting the curve for a single cow. Also, no
of yields on consecutive test days are generally high,          study has incorporated phenotypic correlations among
depending on the interval between tests (1, 12).                yields of milk, fat, and protein into the prediction
Correlations between yields of milk, fat, and protein           procedure.
on a given test day are also high but are not utilized              In the future, cows may not be officially tested
                                                                every 30 d but may have much longer test intervals.
                                                                These longer intervals, however, may be offset by
   Received January 12, 1996.                                   more frequent weighings by the owner for milk yield
   Accepted May 13, 1996.                                       during the lactation. There will also be herds with
   'On leave from Department of Genetics and Animal Breeding,
Agricultural Academy, al. Mickiewicza 24128, 30-059 Krakow,      automated milking systems that could provide data
Poland.                                                         on milk yields throughout the lactation. Also, herds

1996 J Dairy Sci 79:2044-2055                              2044
                                               PREDICTION OF LACTATION YIELDS                                            2045

that pay for milk recording services expect more infor-        these correlations. Use of an MTP would allow for the
mation in return, such as management data, yield               prediction of yields even if data were not available on
persistency, peak yields, and day of peak yield. Thus,         each test day for a cow. The vector of parameters to
the calculation of 305-d lactation yields may become           be estimated for one cow are designated:
more complex and may be based on combinations of                                         In AM
official1.y supervised tests and tests supplied by own-
                                                                                         BM
ers. Fat and protein yields may only be available from                                   CM
official tests. Therefore, the prediction of 305-d yield                                 In AF
requires an accuracy figure associated with the                                      c = BF
predictions of milk, fat, and protein individually.                                      CF
Predictions that exceed a specified minimum accuracy                                     In Ap
could be labeled as an official record. All predictions                                  BP
                                                                                         CP
could be used for genetic evaluations as long as ac-
curacies are known and the method incorporates                 where M, F, and P represent milk, fat, and protein,
them, unless a test day model is employed for genetic          respectively. Vector c is to be estimated from the
evaluation ( 7 , 10).                                          available test day records. Let C O represent the cor-
   The objectives of this study are to describe a              responding parameters estimated across all cows with
multipletrait prediction ( MTP) procedure that uti-            the same production characteristics as the cow in
                                                               question. Let
lizes Wood's function ( 1 4 ) and information from
groups of cows sharing the same production charac-
teristics, to illustrate the calculations by an example;
to compare MTP to TIM for accuracy, to study the
effect of missing fat and protein yields on accuracy,          be the vector of natural logarithms of the yield traits
and to demonstrate the information that can be ob-             on test k at day t of the lactation. The incidence
tained from MTP as part of a milk recording program.           matrix, xk, is constructed as follows:

                                                                                1 l n t t O O     0 0 0
               THE MTP PROCEDURE                                                0 0     O l l n t t 0 0
                                                                                0 0     0 0 0
   The IMTP method is based upon Wood's model ( 1 4 )
in conjunction with an approach incorporating stan-            The equations for MTP are by Henderson (6):
dard c-urve parameters for cows with the same
production characteristics. In this paper, production
characteristics are determined by region of the coun-
try, breed, lactation number, age at calving, and sea-         where
son of (calving. Wood's model for one trait is

                    y = AtB expCt

where y is yield on day t of lactation, A is related t o       and
the peak yield, and B and C are related to the shape
of the lactation curve. This equation is usually linear-
ized by taking logarithms to give

            l n ( y ) = In A   +B   In t   +   Ct.             and n is the number of tests for that cow. Rk is a
                                                               matrix of order 3 that contains the variances and
                                                               covariances among the log yields on test k of the
   The parameters In A, B, and C must be estimated             lactation at day t of lactation. The elements of this
for each yield trait. The yield traits have high pheno-        matrix were derived from regression formulas based
typic correlations, and an MTP would incorporate               on fitting phenotypic variances and covariances of log
                                                                                 Journal of Dairy Science Vol. 79, No. 11, 1996
2046                                                 SCHAEFFER AND JAMROZIK

yields to models, and t and t2 were covariables. Thus,           TABLE 2. Calculated logarithm values for example test day yields.
element ij of R k would be determined by                         DIM          In DIM        In Milk     In Fat                In Protein
                                                                  15          2.708         3.360       .   .   I             ...
                                                                  54          3.989         3.374        0.113                -0.139
                                                                 188          5.236         3.165       -0.030                -0.248
   G is a 9 x 9 matrix containing variances and                  250          5.521         3.035       ...                   ...
covariances among the parameters in c and
represents the variation between cows in these
parameters, which include genetic and permanent en-
vironmental effects. The parameters for G and Rk                 G-l) -l for the In A parameters, based on 15 tests per
vary depending on the region and breed, but must be              lactation spaced at regular 20-d intervals, was used
known. Estimation of G is described later.                       as lower limit values. The diagonal elements of
   If a cow has a test, but only milk is reported, then          (X'R-IX + G-l)-l for any particular cow based on
                                                                 fewer tests would be greater than those based on 15
                                                                 equally spaced tests. Dividing the lower limit values
                                                                 by those for a particular cow provided the accuracy of
and                                                              the 305-d predictions relative to a cow with 15 tests,
                                                                 If the diagonals of the inverse based on 305 tests per
                                                                 lactation were used as the lower limit values, then a
                                                                 lactation based on 10 tests would be only 70% ac-
                             0        0 01                       curate by this method. Thus, the lower limits were
                                                                 defined by a cow having 15 tests evenly spaced a t 20
The inverse of Rk is the regular inverse of the nonzero          d so that lactations based on 10 tests would have 98%
submatrix within Rk, ignoring the zero rows and                  relative accuracy rather than 70%.
columns. Thus, missing fat or protein yields can be
accommodated in the multiple-trait procedure.
   Because MTP uses Bayesian estimation for                      Example Calculations
parameters of each cow, lactation curve parameters                  Four test day records for a 25-mo-o1d, Holstein cow
can be obtained with only one test day record. In                in Ontario are given in Table 1. Two tests did not
addition, using Wood's function for the lactation                have fat and protein yields, and two did. Intervals
curve, the test day records of a cow do not need t o be          between tests were irregular and large. The first step
spaced evenly through the lactation t o enable good
                                                                 was to take the necessary logarithms of yields and
prediction of 305-d lactation totals. Special factors for
first and last test days also are not needed. Therefore,         DIM as shown in Table 2. The vector of standard
MTP can handle any number of test day records from               curve parameters based on all available comparable
1t o 305 per lactation. When no test day records exist,          cows, was
then 6 = CO.
   The accuracy of the predicted 305-d lactation totals                                         2.722 -
mainly depends on the number of test day records                                                0.177
during the lactation and the days in lactation that are                                       -0.00 2 77
associated with each test. Thus, any prediction proce-                                        -0.188
dure requires reliability figures to be reported with                                  CO   = 0.056                 .
all predictions, especially if fewer tests at very irregu-                                    -0.00 144
lar intervals are going to be frequent in milk record-                                        -0.575
ing. The average of diagonal elements from ( X'R-lX +                                           0.188
                                                                                             ,-0.00181-

                                                                    The R k matrices for each test day needed to be
TABLE 1. Example test day yields for a cow.
                                                                 constructed. These matrices were derived from regres-
Test         DIM          Milk         Fat           Protein     sion equations. The equations for Ontario Holsteins
(no.)                                         (kg)               were derived to be as follows:
1             15          28.8         ...           ...
2             54          29.2         1.12          0.87               rMM(t) 0.758 - 0.0036t
                                                                             =                                  +       0.000012t2.
3            188          23.7         0.97          0.78
4            250          20.8         ...           ...                 rMF(t)= 0.313       -   0.0026t        + 0.000010t2.
Journal of Dairy Science Vol. 79, No. 11, 1996
                                            PREDICTION OF LACTATION YIELDS                                                  2047


                 = 0.321 - 0.0020t     + 0.000008t2.            rFF(t, = 0.401 - 0.0027t       + 0.000010t2.
       rF,Jt) = 0.292 - 0.0023t        + 0.000009t2.            rpp(t) = 0.315   -   0.0019t   + 0.000008t2.
  The residual variance-covariance matrices for the log yields for the 4 test days were as follows:

                                       0.597 0.204 0.236               0.489 0.185 0.2361      [:.580            0 01
                                       0.204 0.285 0.196               0.185 0.240 0.185 , R4 = 0                0 0.
                                       0.236 0.196 0.234               0.236 0.185 0.229                         0 0
  The matrix G was assumed to be the same for all cows of the same breed and region:

                 -0.435   0       0             0.350   0       0             0.394    0       0
                  0       0.035   0             0       0.026   0             0        0.032   0
                  0       0       5.0463 - 6    0       0       4.2213 - 6    0        0       4.5593 - 6
                  0.350   0       0             0.695   0       0             0.371    0       0
                  0       0.026   0             0       0.054   0             0        0.029   0
                  0       0       4.22 1E - 6   0       0       6.27 2E - 6   0        0       4.2143 - 6
                  0.394   0       0             0.371   0       0             0.477    0       0
                  0       0.032   0             0       0.029   0             0        0.038   0
                  0       0       4.5593 - 6    0       0       4.2143 - 6    0        0       4.8643 - 6

Note that many covariances between different parameters of the lactation curves were assumed to be zero.
When all covariances were included, the prediction errors for individual cows were very large, possibly because
the covariances were highly correlated to each other within and between traits. Including only covariances
between the same parameter among traits gave much smaller prediction errors.
  The elements of the MTP equations for this cow were

             -      10.0    45.8    1,370.5      0.1        0.9       45.3    -7.1   -34.0                          -98 1.5'
                   45.8    219.2    7,058.0      0.9        5.3      248.0  -34.0   -164.5                        -4,959.8
                 1370.5 7058.0 260,582          45.3     248.0     9,676.2 -981.5 -4,959.8                      -165,245
                     0. 1      0.9     45.3     19.4       91.1    2,537.4  -16.0    -75.6                        -2,116.5
                     0.9     5.3      248.0     91.1     436.1    12,732.3 -75.6    -362.6                       -10,630.5
                   45.3    248.0    9,676.2 2537.4 12,732.3 417,544 -2 116.5 -10,630.5                          -349,374
                   -7.1    -34.0     -981.5    -16.0     -75.6    -2,116.5    29.1    136.7                         3,789.4
                  -34.0   -164.5   -4,959.8    -75.6    -362.6 -10,630.5     136.7   653.5                         18,996.0
                 -981.5 -4959.8. -165,245   --2116.5 --10,630.5 -349,374   3789.4 18,996.0                       621,563


                                33.75.                                            30.29-
                               154.05                                              9.58
                              4542.37                                         -1465.01
                                 4.21                                             -2.54
                                20.39                                             -1.80 .
                               614.35                                            199.16
                               -29.42                                           -24.26
                              -139.70                                             -3.53
                             -3990.72                                           828.50




                                                                                     Journal of Dairy Science Vol. 79, No. 11, 1996
2048                                                SCHAEFFER AND JAMROZIK

   The solution vector for this cow was                   at least 50 daily milk yields with 2 daily milk yields
                                                          before 40 DIM and 2 daily milk yields after 210 DIM.
                          - 2.778 -                       This constraint resulted in 1495 lactations with milk
                            0.181                         yields only and 769 lactations with yields of milk, fat,
                           -0.002 9                       and protein with a mean of 270 daily yields per
                           - 0.106                        lactation. Percentages of fat and protein were only
                     i5 = 0.070 .                         available from test day records. Yields of fat and
                           -0.0015                        protein were estimated by fitting Wood's function to
                           -0.528                         the percentages and multiplying predicted percen-
                            0.122                         tages times the actual milk yields for the daily
                           -0.0019                        records. Percentages were fitted rather than yields
                                                          because percentages were generally less variable ( 2 I .
   To predict 305-day yields, Y305, Wood's model,         Lactation curves for percentage traits were inverted
                                                          relative to lactation curves for yield traits, but Wood's
                                                          model can be used for either expression ( 2 ) .
                                                             The variances and covariances between the
                                                          logarithms of yields for milk, fat, and protein on
                                                          different DIM were calculated from the records and
was used separately for each trait (milk, fat, and were regressed on the linear and quadratic terms for
protein). The results for this cow were 7539 kg of DIM to derive prediction equations. The resulting Rk
milk, 305 kg of fat, and 241 kg of protein. Table 3 matrices were checked for positive definiteness for all
presents the diagonal elements for In A of ( X'R-IX + DIM from 1 t o 305 d.
G-l)-l for the cow and the lower limit values based          The MTP procedure required known parameters
on 15 tests during the lactation for milk, fat, and for the standard lactation curves of various groups of
protein to derive relative accuracies.                    cows and known variance-covariance matrix, G, for
                                                          cow effect for different breeds and regions of Canada.
             MATERIALS AND METHODS                        Standard lactation curves were estimated for Ontario
                                                          Holstein cows born during 1989 and later from
                                                          1,401,793 test day records of 214,999 lactations with
Parameter Estimation
                                                          a minimum of four tests per lactation. The DIM were
   In this section, a test day record refers t o a super- restricted to be between 5 and 305 d. Test day data
vised weighing at the farm with milk yield and fat were required to be between 1.5 and 90 kg for milk
and protein contents recorded expressed on a yield, between 1.5 to 8.5% for fat percentage, and
24-h basis. A daily yield refers t o any unsupervised between 1.5 and 7.5% for protein percentage.
milk weighing with only milk yield recorded ex- Nineteen age groups were created within lactation 1,
pressed on a 24-h basis.                                  17 groups within lactation 2, and 12 groups within
   Phenotypic variances and covariances between lactation 3 or greater. Each lactation-age group was
natural logarithms of milk, fat, and protein were split into two seasons of calving (September to Febru-
estimated from data collected between 1991 and 1993 ary and March t o August). Each subclass had a mini-
from 28 herds with automated milking systems. The mum of 1000 cows. Standard parameters for lactation
Holstein herds were located in Ontario, Alberta, curves were estimated by fitting a fixed regression
Manitoba, and British Columbia and supplied model across cows within each subclass separately.
965,997 daily records of milk yield for 8178 lactations.     To estimate G, only cows with a minimum of 9 test
The same herds and cows had 54,978 test day records day records in a lactation were used (40,242 lacta-
on 6620 lactations. Not all lactations had complete tions). Curve parameters were estimated for each cow
information for daily milk yield. Lactations of cows as
were required to have at least 5 test day records and

TABLE 3. Diagonal elements of equations for the example cow ( A )   and simple variances and covariances of the elements
and for a cow with 15 equally spaced tests ( B ) as well as the
relative accuracy (Acc) of 305-d predictions for the example cow.   of i5 across cows were calculated to obtain G.
Trait           A                B               Acc
                                                                    Comparison with TIM
Milk            0.250            0.227           0.91
Fat             0.397            0.306           0.77                  From the data for estimation of the standard lacta-
Protein         0.245            0.223           0.91               tion curves, the subset of cows with at least 10 test
Journal of Dairy Science Vol. 79, No. 11, 1996
                                        PREDICTION OF LACTATION YIELDS                                             2049

day records were selected to compare MTP with TIM.        calculated by TIM and were based on all 10 test day
This criterion provided data for 5174 first lactations,   records. The MTP generally produced smaller percen-
2354 second lactations, and 498 third and later lacta-    tages for differences from true 305-d yields for all
tions. The usual TIM procedure, as implemented by         traits than TIM, although TIM was better for a few
the Canadian Milk Recording Board for routine milk        situations during the early part of lactations. The
recording, was used to estimate 305-d lactation totals    standard deviations showed that MTP and TIM were
for milk, fat, and protein. The usual procedure was t o   very similar for variability of predictions for each test
estimate the cumulative yields up to the last test day    day. Generally, correlation was high between the
and then to apply projection factors to predict the       MTP prediction and the TIM prediction (0.991 to
305-d yield. The MTP procedure automatically              0.997). Correlations of MTP and TIM with true
provided 305-d yields without the additional need for     305-d yields increased as the number of tests in-
projection factors. The TIM 305-d yields based on all     creased. The MTP seemed to have slightly, but not
10 test day records were used as the basis for all        significantly, larger correlations between the 2nd to
comparisons and were referred to as the true              5th test days with true yield. The conclusion from this
305-d yields.
                                                          comparison was that MTP and TIM did not differ
   For each consecutive test day from 1 to 9, the MTP
                                                          significantly when tests were regularly spaced and
and TIM methods were used to predict 305-d lactation
                                                          each test included yields for milk, fat, and protein.
yields for each cow. The differences in the predicted
                                                          Thus, a change to MTP would not be detrimental to
yields from true 305-d yields, expressed as a percen-
tage of the true 305-d yields averaged over all cows in   current milk recording predictions of lactation yields.
each lactation group, were used to compare TIM and           As used in this study, TIM included the projection
MTP. The standard deviations of the percentages           factors for obtaining 305-d yields from cumulative
were used to estimate the variability among cows.         yields, and therefore the comparison was not MTP
Finally, the correlations between predicted and true      versus TIM, but rather MTP versus the projection
305-d yields were calculated.                             factors and TIM methodology. If the projection factors
                                                          were inappropriate, then TIM may have been a t a
Effect of Missing Data                                    disadvantage compared with MTP. However, with
for Fat and Protein                                       current practices and factors used for milk recording,
                                                          MTP and TIM did not differ significantly.
    The previous comparisons were made for cows that         The MTP may have had a slight advantage over
had yields for milk, fat, and protein for each test day.  TIM because the cows used in the comparisons were
The MTP was expected t o outperform TIM when fat          included in the data to derive the standard lactation
and protein may not be available for each test day        curves for MTP. In practice, the standard curves
( 2 1. Six schemes were created t o simulate missing fat  would be applied to future records of cows, but the
and protein data on different test days using the same    standard lactation curves would be updated annually.
data as in the previous section. Milk yield was in-       This advantage might have been counteracted by us-
cluded from every test. The following plans had fewer     ing the TIM 305-d yields as the true 305-d yields for
fat and protein yields than milk yields and on differ-    comparisons.
ent test days in the lactation, as follows: plan 1, on
tests 1, 3, 5, 7, and 9; plan 2, on tests 2, 4, 6, and 8;
plan 3, on tests 1, 4, and 7; plan 4, on tests 2, 5, and Effect of Missing Data
8; plan 5, on tests 3, 6, and 9; and plan 6, no fat or for Fat and Protein
protein yields during the entire lactation.
                                                             Correlations of predicted 305-d yields from MTP
    The MTP was applied to cows for each plan. Corre-
                                                          with true 305-d yields under different frequencies of
lations of predicted 305-d yields with the true
305-d yields (i.e., TIM using all 10 tests for milk, fat, testing for fat and protein are given in Tables 7, 8,
and pr'otein) were used to compare results.               and 9. The correlations for milk yields were very
                                                          similar for all six testing schemes and were similar to
                                                          values in Table 4, and correlations are shown in the
              RESULTS AND DISCUSSION
                                                          last column of Table 7. Milk yields were available for
                                                          each test. For fat and protein yields, however, correla-
Comparison with TIM
                                                          tions with true yield had a smaller increase, except
    The statistics for comparing MTP with TIM are when another test with fat and protein yields was
gven in Tables 4, 5 , and 6. The true 305-d yields were included in MTP. For example, for lactation 1,plan 1,
                                                                           Journal of Dairy Science Vol. 79, No. 11, 1996
2050                                                  SCHAEFFER AND JAMROZIK

the correlation was 0.62 for fat yield after the first                was the correlation of the predicted yields with true
test. Correlation only increased t o 0.67 after the se-               yields.
cond test because another fat yield was not available                    In the future, herds may supply data for milk
for that test. Another fat yield was reported on the                  yields to milk recording agencies at more frequent
third test, and the correlation increased to 0.83,                    intervals during the year on an unsupervised basis,
which was less than the 0.85 when data for fat yield                  and, at the same time, may choose to have fewer
were available for all three tests. The next substan-                 supervised weighings per year. The MTP is necessary
tial increase in correlation for fat yield came after the             to keep these herd owners enrolled in a milk record-
fifth and seventh tests.                                              ing system. Thus, for a given lactation, there could be
   For plan 2, the initial correlation for fat yield was              perhaps 20 or more unsupervised records of milk yield
0.52 and was based entirely on the correlations be-                   (every 2 wk, for example) and 4 supervised weigh-
tween milk and fat yields because a fat yield was not                 ings with yields of milk, fat, and protein. With MTP,
present on the first test. In the extreme case, with no               milk recording agencies could be more flexible in the
fat or protein yields on any test days (plan 61, the                  types of recording schemes from which herd owners
correlation of the fat yield prediction after nine tests              could select. The number of unsupervised weighings
was only 0.74, but, for protein yield prediction, the                 and number of supervised weighings should be
correlation was 0.94. Protein yields were more consis-                reported for each cow along with the accuracies of the
tent throughout the lactation than for fat yields, and,               prediction. A cow with 40 unsupervised weighings
thus, the accuracy of the predictions for protein were                could have a much more accurate prediction of
greater than for fat yield. In general, the fewer tests               305-d yields than a cow with only 8 supervised weigh-
there were with fat and protein yields, then the lower                ings.



                 TABLE 4. Mean percentages and standard deviations of percentage differences between predicted and
                 true 305-d milk yields, and correlations (Corr.) between predicted and true yields by the multiple-trait
                 procedure ( M T P ) and by the test interval method ( T I M ) .
                                               Mean                           SD                            Corr.
                 Tests                 MTP            TIM             MTP          TIM               MTP            TIM
                 (no.)                                                    Lactation 1
                 1                     -2.2           -6.4            14.8         16.9              0.65           0.64
                 2                     -0.3            5.8            11.6         12.4              0.80           0.82
                 3                       0.4           5.4             9.3         10.1              0.87           0.87
                 4                       0.3           3.5             7.4          8.0              0.92           0.92
                 5                       0.1           2.1             5.9          6.3              0.95           0.95
                 6                     -0.1            0.9             4.8          4.8              0.97           0.97
                 7                     -0.4            0.2             3.7          3.4              0.98           0.98
                 8                     -0.5           -0.1             2.9          2.3              0.99           0.99
                 9                     -0.7           -0.2             2.3          1.3              0.99           1.00
                                                                          Lactation 2
                                       -4.5            3.6            14.1         17.7              0.65           0.64
                                       -3.3           12.9            11.2         13.5              0.79           0.80
                                       -2.8            9.0             9.4         11.4              0.86           0.85
                                       -2.5            5.6             8.0          9.3              0.90           0.90
                                       -1.7            3.6             6.5          6.9              0.94           0.94
                                       -1.2             1.7            5.4          5.3              0.96           0.96
                                       -0.9            0.7             4.3          3.8              0.97           0.98
                                       -0.7            0.0             3.3          2.4              0.98           0.99
                                       -0.8           -0.3             2.7          1.3              0.99           1.00
                                                                          Lactation 3
                                       -5.0            3.2            16.0         19.3              0.56           0.58
                                       4.3            13.2            11.0         12.7              0.80           0.82
                                       -3.4            9.9             9.2         11.1              0.87           0.87
                                       -2.7            6.0             7.7          8.9              0.92           0.91
                                       -1.7            4.1             6.5          7.1              0.94           0.94
                                       -1.1            2.0             5.3          5.1              0.96           0.97
                                       -0.8            0.7             4.1          3.9              0.98           0.98
                                       -0.7            0.0             3.1          2.4              0.99           0.99
                                       -0.6           -0.2             2.6          1.3              0.99           1.00

Journal of Dairy Science Vol. 79, No. 11, 1996
                                                 PREDICTION OF LACTATION YIELDS                                                      2051

Daily Yields                                                           protein but maintain the positive definiteness of the
                                                                       matrix.
   The assumption has been that MTP utilized
24-h yields of milk, fat, and protein; that is, a cow has
been mi1:ked two times in 24 h and supervised at each                  Cows that Change Herds
milking. However, there are alternating a.m. and                          Usually, when cows change herds during a lacta-
p.m. weighing schemes in which only one milking                        tion, the cumulative yield to the last test in the first
within a 24-h period is supervised, and some cows                      herd is transferred to the new herd. The test weigh-
may be milked three times in 24 h. There are availa-                   ings in the new herd can be used to estimate the
ble numerous tables of factors for converting single                   curve parameters for that cow in the new herd. Sup-
milkings t o a 24-h, twice daily basis. The expected                   pose the cow had milked for 100 d in the first herd
24-h, twice daily yields, however, are less accurate                   with a cumulative yield of X kg. First, the curve
than an (actual 24-h, twice daily yield. If the accuracy               parameters estimated in the new herd would be used
of a predicted 24-h, twice daily yield is known, then                  to compute the expected yield from d 101 to 305, and
these predicted values can be incorporated into the                    then the X kg from the first herd would be added to
MTP procedure. For example, if a cow has a predicted                   that total to derive the 305-d predicted yields. If the
24-h milk yield and accuracy is 0.7, the variance for                  accuracy of the cumulative yield was reported t o be
milk yield in Rk should be greater than that indicated                 0.99, and the accuracy of the predicted yield from d
by the regression formula. Thus, the predicted vari-                   101 to 305 was 0.60, then the accuracy of the
ance, rMlvl() , can be divided by 0.7. The covariances
           t                                                           305-d predicted yield could be approximated by
are not changed. The higher variances automatically
lower the correlations between yields of milk, fat, and                           [100(0.99j      +   205(0.60)1/305 = 0.73.



               TABLE 5. Mean percentages and standard deviations of percentage differences between predicted and
               true 305-d fat yields, and correlations ( C o r r . ) between predicted and true yields by the multiple-trait
               procedure ( M T P ) and by the test interval method ( T I M ) .
                                              Mean                             SD                              Corr.
               Tests                  MTP            TIM               MTP          TIM                MTP             TIM
               (no.)                                                       Lactation 1
               1                        2.0           0.5              20.0         20.5               0.62            0.64
               2                        1.4           0.5              15.1         15.5               0.77            0.75
               3                        0.7          -0.2              11.5         12.5               0.85            0.82
               4                      -0.1           -1.1               9.1         10.0               0.90            0.88
               5                      -0.3           -1.2               7.2          7.9               0.94            0.92
               6                      -0.3           -1.2               5.8          6.0               0.96            0.95
               7                      -0.2           -1.0               4.6          4.3               0.97            0.97
               8                      -0.2           -0.7               3.6          2.9               0.98            0.99
               9                      -0.3           -0.4               2.7          1.6               0.99            1.00
                                                                           Lactation 2
                                      -1.2           11.7              19.8         23.3               0.61            0.61
                                      -2.8            5.9              15.0         17.5               0.75            0.71
                                      -3.0            3.3              11.9         14.8               0.83            0.78
                                      -2.5             1.7              9.8         12.0               0.88            0.85
                                      -1.5            0.9               7.9          8.8               0.93            0.91
                                      -0.8            0.0               6.4          6.7               0.95            0.94
                                      -0.3           -0.3               5.0          4.6               0.97            0.97
                                        0.0          -0.5               3.9          3.0               0.98            0.99
                                      -0.2           -0.5               2.9          1.6               0.99            1.00
                                                                           Lactation 3
                                      -1.6           13.4              20.9         25.4               0.56            0.56
                                      4.2             6.0              13.9         17.0               0.78            0.75
                                      4.0             3.7              12.0         15.1               0.84            0.80
                                      -3.0            2.0               9.7         12.3               0.89            0.87
                                      -1.7             1.5              8.3          9.6               0.92            0.90
                                      -0.4            0.9               6.4          6.3               0.95            0.95
                                        0.1           0.0               4.8          4.8               0.97            0.97
                                        0.2          -0.3               3.6          2.8               0.98            0.99
                                      -0.1           -0.4               2.9          1.7               0.99            1.00

                                                                                             Journal of Daily Science Vol. 79, No. 11, 1996
2052                                                  SCHAEFFER AND JAMROZIK

Long Lactations                                                      management aids. The day of peak milk yield can be
                                                                     calculated for each cow as well as the peak milk yield,
   Some cows lactate beyond 305 d. How many days
                                                                     which can be derived by estimating the daily yields
beyond 305 d does the MTP procedure apply? A
                                                                     for each day from d 5 to the point at which the daily
proposal is that MTP would be used for all tests from
d 5 to the first test after 305 d. After that point, TIM             yield begins to decrease from the yield of the previous
would be used to calculate lactation to date totals. For             day.
tests after 305 d, if the fat and protein yields were not               The mean of the curve parameters, e, of all cows in
measured, then they could be estimated by using the                  each lactation number within a herd can be used to
fat and protein percentages for 305-d lactations times               plot curves for herd lactation. The overall mean
the daily milk yield. Although the lactation curve                   curves for herd lactation for a breed and region can be
continues to decline after 305 d, and Wood’s function                superimposed on the curves within a herd.
seems to fit this decline, some cows begin producing                    Let persistency be defined as the difference be-
at higher levels once again and can be milked for up                 tween daily yields on d 60 and d 280 of lactation,
to 700 d. Woods function fits these types of data                    estimated based on parameters of the lactation curve.
poorly. By using the first test after 305 d as the cutoff            For each cow, persistency is compared with that of a
for MTP, the 305-d predictions no longer change with                 cow with the same standard lactation curve, and the
subsequent tests, but the lactation to date totals can               difference is multiplied by 110 to determine the gain
continue to increase.                                                or loss in yield from persistency between d 60 to 280.
                                                                     For example, a standard cow might have a drop of 9
Additional information                                               kg from d 60 to 280, and a particular cow might have
  The MTP procedure allows other variables to be                     a drop of only 7.5 kg. Thus, the latter cow would have
calculated to provide milk recording agencies with                   a drop of 1.5 kg less and would be classified as being

                 TABLE 6. Mean percentages and standard deviations of percentage differences between predicted and
                 true 305-d protein yields, and correlations (Corr.) between predicted and true yields by the multiple-
                 trait procedure ( M T P ) and by the test interval method (TIM).
                                               Mean                          SD                            Corr.
                 Tests                 MTP            TIM            MTP          TIM              MTP             TIM
                 (no.)                                                   Lactation 1
                 1                     -1.1           -8.3           16.2         15.4              0.62           0.63
                 2                     -0.9           -3.0           12.2         12.1              0.80           0.79
                 3                     -0.2           -0.7            9.7         10.3              0.87           0.85
                 4                       0.2          -0.3            7.8          8.3              0.91           0.90
                 5                       0.5          -0.3            6.2          6.7              0.94           0.93
                 6                       0.6          -0.5            5.0          5.2              0.96           0.96
                 7                       0.5          -0.6            3.8          3.7              0.98           0.98
                 8                       0.3          -0.5            2.8          2.5              0.99           0.99
                 9                     -0.1           -0.4            2.1          1.4              0.99           1.00
                                                                         Lactation 2
                 1                     -2.3            3.1           15.6         16.9              0.62           0.63
                 2                     -3.2            3.0           11.8         13.1              0.77           0.76
                 3                     -2.8            2.4            9.9         11.5              0.84           0.81
                 4                     -1.9            1.6            8.5          9.5              0.89           0.87
                 5                     -0.7            1.2            6.9          7.2              0.93           0.92
                 6                     -0.1            0.2            5.5          5.5              0.95           0.95
                 7                       0.3          -0.2            4.3          3.9              0.97           0.97
                 8                       0.4          -0.4            3.2          2.6              0.98           0.99
                 9                       0.0          -0.5            2.3          1.4              0.99           1.00
                                                                         Lactation 3
                 1                     -2.8            2.3           18.0         19.4              0.54           0.56
                 2                     4.2             2.8           11.5         12.3              0.79           0.79
                 3                     -3.2            3.0            9.5         11.0              0.87           0.85
                 4                     -2.0            2.0            8.1          9.1              0.91           0.90
                 5                     -0.4             1.9           6.8          1.2              0.94           0.93
                 6                       0.4           0.8            5.6          5.3              0.96           0.96
                 7                       0.7           0.1            4.2          4.0              0.97           0.98
                 8                       0.5          -0.4            3.1          2.6              0.99           0.99
                 9                       0.2          -0.4            2.3          1.4              0.99           1.00

Journal of Dairy Science Vol. 79, No. 11, 1996
                                                 PREDICTION OF LACTATION YIELDS                                                        2053

more persistent. Multiplying yield lost or gained by                    day model for genetic evaluation and the MTP should
110 gives 165 kg of additional milk yield because of                    utilize the same lactation curve functions, but, at this
greater persistency between d 60 and 280 than for an                    time, the covariables for the test day model are not
average cow. This measure of persistency is free of                     finalized. When the covariables for the test day
the absolute yield of the cow. Ratios of yield during                   models are set, then efforts to harmonize MTP with
the last 100 d of lactation to yield during the first 100               the test day models can occur.
d are usually more dependent on absolute yields but                        The MTP procedure and methods for its implemen-
could also be used as a measure of persistency. In-                     tation in a milk recording program have been
stead of using standard lactation curves as the com-                    described. Separate curve parameters should be esti-
parison, the curves for mean herd lactation could be                    mated for each lactation of the cow. First lactation
used to make within-herd comparisons.                                   curves are generally very different from later lacta-
                                                                        tion curves. The standard lactation curves would need
                       CONCLUSIONS                                      to be updated, which could be done annually by milk
                                                                        recording agencies. The G matrix could be updated in
   Prediction of 305-d lactation yields are necessary                   a similar manner by calculating variances and covari-
for producers for management purposes even if test                      ances between cows among the curve parameters for
day models are utilized in the future for genetic                       milk, fat, and protein. The Rk matrices are not ex-
evaluation purposes. The test day model proposed by                     pected to change greatly over time, but could be re-
Jamrozik and Schaeffer ( 7 ) does not use Woods                         estimated every 10 yr, for example.
model as the basis for covariables in the random                           The MTP is computationally more complex than
regression model. To be consistent, perhaps the test                    TIM, but modern computers are able to accommodate



               TABLE 7. Correlations between predicted and true 305-d milk yields by the multiple-trait procedure
               for various testing schemes.'
                                                      Tests with fat and protein recorded
               Test           Plan 1 2       Plan 2         Plan 3         Plan 4          Plan 5         Plan 6        All
               (no.)                                                    Lactation 1
               1              0.65           0.66           0.65           0.66            0.66           0.66          0.65
               2              0.79           0.80           0.79           0.80            0.81           0.81          0.80
               3              0.87           0.87           0.87           0.87            0.88           0.88          0.87
               4              0.92           0.92           0.92           0.92            0.92           0.92          0.92
               5              0.95           0.95           0.95          0.95             0.95           0.95          0.95
               6              0.97           0.97           0.98           0.97            0.97           0.97          0.97
               7              0.98           0.98           0.98          0.98             0.98           0.98          0.98
               8              0.99           0.99           0.99           0.99            0.99           0.99          0.99
                                                                        Lactation 2
                              0.65           0.67           0.65           0.67            0.67           0.67          0.65
                              0.79           0.79           0.79           0.79            0.81           0.81          0.79
                              0.86           0.86           0.86           0.86            0.86           0.87          0.86
                              0.90           0.90           0.90           0.90            0.90           0.91          0.90
                              0.94           0.94           0.94           0.94            0.94           0.94          0.94
                              0.96           0.96           0.96           0.96            0.96           0.96          0.96
                              0.97           0.97           0.97           0.97            0.97           0.97          0.97
                              0.98           0.98           0.98           0.98            0.98           0.98          0.98
                                                                        Lactation 3
                              0.56           0.62           0.56           0.62            0.62           0.62          0.56
                              0.77           0.80           0.77           0.80            0.81           0.81          0.80
                              0.87           0.87           0.86           0.87            0.87           0.87          0.87
                              0.92           0.92           0.92           0.92            0.92           0.92          0.92
                              0.94           0.94           0.94           0.94            0.94           0.94          0.94
                              0.96           0.96           0.96           0.96            0.96           0.96          0.96
                              0.98           0.98           0.98           0.98            0.98           0.98          C.98
                              0.99           0.99           0.99           0.99            0.99           0.99          0.99
                  1Milk yields were available on each test day. Fat and protein yields were not available each test day.
                  2Plan 1,tests 1, 3, 5, 7, and 9; plan 2, tests 2 , 4 , 6, and 8; plan 3, tests 1, 4, and 7; plan 4,tests 2, 5,
               and 8; plan 5, tests 3 , 6, and 9; and plan 6, none.

                                                                                               Journal of Dairy Science Vol. 79, No. 11, 1996
2054                                                    SCHAEFFER AND JAMROZIK

MTP. The MTP procedure, written in FORTRAN 77                             statistics that could have economic significance to
and tested on a 486 microcomputer, was able to calcu-                     herd owners. The curves may also be useful for detect-
late results as fast as data could be read. Thus, input                   ing test day yields that are too high or too low com-
and output, not calculation, was the limiting factor.                     pared with previous tests. This aspect has not yet
The best strategy seems to be to recalculate com-                         been studied. There may as yet be problems with
pletely the lactation curve parameters after a new                        MTP that have not been identified but that will be-
test day yield is added rather than saving the MTP                        come known as MTP is used in a routine milk record-
equations for each cow and updating them with the                         ing environment. The MTP is being implemented into
latest test day information. The speed of the calcula-                    the new milk recording software for Canada for 1997.
tions offsets the extra storage that would be needed
for the MTP equations. This strategy also allows test                                          ACKNOWLEDGMENTS
day information to be corrected, if necessary, between
test days and to have the corrected data incorporated                       The authors acknowledge the financial support of
into the next predictions.                                                the Ontario Ministry of Agriculture, Food, and Rural
   The potential for calculating more statistics for                      Affairs and the collaboration of the Canadian Milk
management purposes of the herd owner is an attrac-                       Recording Board, Don Lazenby of the Ontario Dairy
tive feature of MTP. Yield persistency, peak yields,                      Herd Improvement Corporation, and Jack Dekkers of
day of peak yield, and herd lactation curves are                          the Centre for Genetic Improvement of Livestock.



                 TABLE 8. Correlations between predicted and true 305-d fat yields by the multiple-trait procedure for
                 various testing schemes.'
                                                       Tests with fat and Drotein recorded
                 Test          Plan   12      Plan 2          Plan 3         Plan 4         Plan 5         Plan 6        All
                 (no.)                                                   Lactation 1
                 1             0.62           0.52            0.62          0.52            0.52           0.52          0.62
                 2             0.67           0.73            0.67          0.73            0.63           0.63          0.77
                 3             0.83           0.75            0.69          0.75            0.79           0.67          0.85
                 4             0.84           0.90            0.87          0.77            0.80           0.70          0.90
                 5             0.91           0.88            0.88          0.90            0.81           0.72          0.94
                 6             0.92           0.93            0.89          0.91            0.91           0.73          0.96
                 7             0.95           0.93            0.95          0.91            0.91           0.73          0.97
                 8             0.95           0.96            0.95          0.95            0.92           0.74          0.98
                 9             0.97           0.96            0.95          0.95            0.95           0.74          0.99
                                                                         Lactation 2
                 1             0.61            0.51           0.61          0.51            0.51           0.51          0.61
                 2             0.64            0.70           0.64          0.70            0.60           0.60          0.75
                 3             0.79            0.73           0.66          0.73            0.74           0.63          0.83
                 4             0.80            0.83           0.83          0.74            0.76           0.66          0.88
                 5             0.90            0.84           0.85          0.89            0.77           0.69          0.93
                 6             0.90            0.90           0.86          0.89            0.88           0.70          0.95
                 7             0.94            0.91           0.93          0.90            0.89           0.72          0.97
                 8             0.95            0.95           0.94          0.94            0.89           0.74          0.98
                 9             0.97            0.95           0.94          0.95            0.94           0.75          0.99
                                                                         Lactation 3
                 1             0.56            0.47           0.56          0.47            0.47           0.47          0.56
                 2             0.62            0.74           0.62          0.74            0.63           0.63          0.78
                 3             0.79            0.76           0.65          0.76            0.76           0.66          0.84
                 4             0.81            0.86           0.86          0.77            0.77           0.69          0.89
                 5             0.88            0.87           0.87          0.87            0.78           0.70          0.92
                 6             0.89            0.92           0.88          0.88            0.90           0.73          0.95
                 7             0.94            0.93           0.95          0.89            0.91           0.75          0.97
                 8             0.95            0.95           0.95          0.94            0.91           0.76          0.98
                 9             0.97            0.95           0.95          0.94            0.94           0.76          0.99
                    1Milk yields were available on each test day. Fat and protein yields were not available each test day.
                    2Plan 1, tests 1, 3, 5, 7, and 9; plan 2, tests 2, 4, 6, and 8; plan 3, tests 1, 4. and 7; plan 4,tests 2, 5.
                 and 8; plan 5, tests 3, 6, and 9; and plan 6, none.

Journal of Dairy Science Vol. 79, No. 11, 1996
                                                 PREDICTION       OF LACTATION YIELDS                                                   2055

               TABLE 9. Correlations between predicted and true 305-d protein yields by the multiple-trait procedure
               for various testing schemes.'
                                                     Tests with fat and protein recorded
               Test           Plan   12     Plan 2         Plan 3         Plan 4         Plan 5          Plan 6       All
               (no.)                                                   Lactation 1
               1              0.62          0.62           0.62          0.62            0.62            0.62         0.62
               2              0.73          0.79           0.73          0.79            0.77            0.77         0.80
               3              0.86          0.83           0.79          0.83            0.85            0.84         0.87
               4              0.89          0.90           0.91          0.86            0.88            0.88         0.91
               5              0.94          0.92           0.92          0.93            0.90            0.90         0.94
               6              0.95          0.95           0.93          0.94            0.95            0.92         0.96
               7              0.97          0.96           0.97          0.95            0.96            0.93         0.98
               8              0.98          0.98           0.98          0.98            0.97            0.94         0.99
               9              0.99          0.98           0.98          0.98            0.98            0.94         0.99
                                                                       Lactation 2
               1              0.62          0.62           0.62          0.62            0.62            0.62         0.62
               2              0.71          0.76           0.71          0.76            0.75            0.75         0.77
               3              0.83          0.81           0.78          0.81            0.82            0.81         0.84
               4              0.87          0.88           0.88           0.84           0.85            0.85         0.89
               5              0.92          0.90           0.90          0.92            0.87            0.88         0.93
               6              0.94          0.94           0.92          0.93            0.94            0.90         0.95
               7              0.97          0.95           0.96           0.94           0.95            0.91         0.97
               8              0.97          0.97           0.97           0.98           0.96            0.92         0.98
               9              0.99          0.98           0.98           0.98           0.98            0.93         0.99
                                                                       Lactation 3
               1              0.54          0.60            0.54          0.60            0.60           0.60         0.54
               2              0.68          0.80            0.68          0.80            0.78           0.78         0.79
               3              0.86          0.83            0.76          0.83            0.85           0.83         0.87
               4              0.89          0.90            0.90          0.87            0.88           0.86         0.91
               5              0.93          0.92            0.91          0.93            0.90           0.88         0.94
               6              0.94          0.95            0.93          0.95            0.95           0.90         0.96
               7              0.97          0.96            0.97          0.95            0.96           0.92         0.97
               8              0.98          0.98            0.97          0.98            0.96           0.93         0.99
               9              0.99          0.98            0.98          0.98            0.98           0.93         0.99
                  1Milk yields were available on each test day. Fat and protein yields were not available each test day.
                  2Plan 1,tests 1, 3, 5, 7, and 9; plan 2, tests 2, 4,6, and 8; plan 3, tests 1. 4, and 7; plan 4, tests 2. 5,
               and 8; plan 5, tests 3, 6, and 9; and plan 6, none.




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                                                                                                Journal of Dairy Science Vol. 79, No. 11, 1996

								
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