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APPLICATION OF A MULTITRAIT ANIMAL MODEL TO PREDICT
NEXT TEST-DAY MILK PRODUCTION

BY

FLORAH NGWERUME

A DISSERTATION

Submitted to
Michigan State University
for the degree of

DOCTOR OF PHILOSOPHY

Department of Animal Science

1994

ABSTRACT

APPLICATION OF A MULTITRAIT ANIMAL MODEL TO PREDICT
NEXT TEST-DAY MILK PRODUCTION

BY

FLORAH NGWERUME

Effects of six seasons of calving, three herd production levels, and three
lactations on test-day milk yield were studied using test-day records from Holstein
cows. Lactation curves were estimated within each herd level-lactation-season
subclass by fitting a regression model with a sixth degree polynomial to days in
milk least square means. Significant (P< .001) season differences were detected
with summer calving season depressing peak test-day milk production, total
lactation yield and time to attain peak test-day production. First lactation cows
had typical lower peaks and were more persistent than later lactation cows.
Curves shifted upwards with herd production level with narrower differences at
the end of lactation.

After assessing effects of the above factors; lactation data consisting of
171,922 test-day milk records for first lactation Holstein cows tested in 600
Michigan herds from 1988 to 1992 were divided into ten stages of lactation. Each
stage was a 30-day days in milk (DIM) interval. With ten stages treated‘as

separate traits, a multiple trait animal model was used to estimated the phenotypic

variances and covariances among these traits within three herd production levels.

The model for each trait contained fixed effects of season of calving by DIM,
season of test by temperature-humidity index and age at calving, and random
additive genetic effects. Phenotypic (co)variances between traits were used to
predict next test-day milk yield deviations for individual cows. Test-day milk
deviations were predicted using either 1, 2 or 3 previous test-day deviations for a
cow.

Biases in predicting test-day deviations averaged near zero when 3 previous
test-day deviations were used. Biases were greatest when using only 1 previous
test-day deviation. For the low herd production level, overall population mean
biases were -.311, -.132 and -.005 kg when using either 1, 2 or 3 previous test
deviations respectively. The corresponding root mean square errors did not differ
much (3.32, 3.12, and 3.19, respectively). The traits or days in milk intervals
predicted most accurately were between 120-270 days. Biases and root mean

square errors were similar for medium and high production herd groups.

DEDICATION

This work is dedicated to my wonderful sister Rosemany Ngwerume who passed

away on April 24, 1994, just before my final exam.

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to Dr. T. A. Ferris, my
academic advisor, for his advice, encouragement and unselfish contribution of
support and time during my graduate program.

I thank Dr. I. L. Mao, Dr. J. L. Gill, Dr. A. L. Skidmore and Dr. W. G.
Bickert, members of my graduate committee.

My heart felt appreciation goes to Michigan DHIA for supplying the data
and supporting this project and to USDA for use of their computers. I want to
especially acknowledge Dr. George Wiggans at USDA for his help and support.
His counsel and willingness to convey his knowledge was greatly appreciated. I
would also like to thank Dr. F. Nurnberger for supplying the climatological data
used in this study.

I wish to express my sincere gratitude to my wonderful friends who have
been a pillar of support during my study. In particular, Faith and Chad Gandiya
and their kids, Lawrence Mutenda, Connie Sewani, Best Mbadzo, Joe Siegle,
Peter Saama and Shan Chung. They have all made the hard times a little easier to
get through.

I owe a tremendous debt to my wonderful family; mom, sisters, brothers,

and relatives for their love and unwavering support throughout my study.

ii

TABLE OF CONTENTS

List of Tables ................................................... iv
List of Figures .................................................. ix
1. Introduction ................................................ 1
2. Objectives .................................................. 8
2.1 Lactation Curves ...................................... 8
2.2 Predicting Test-day Milk Production ........................ 8
3. Review of Literature ......................................... 9
3.1 Introduction ....................................... 9
3.2 Environmental factors affecting a cow's production ........... 9
3.2.1 Effect of Cow’s Age ............................. 9
3.2.2 Season of Calving ............................. 12
3.2.3 Stage of Lactation ............................. 14
3.2.3.1 Mathematical functions for describing
lactation curves ..................... 15
3.2.4 Effect of Gestation ............................ 19
3.2.5 Heat Stress .................................. 21
3.2.6 Herd and Herd Level .......................... 23
3.2.7 Bovine Somatotropin ........................... 24
3.3 Modelling Test-day Production vs Modelling 305-day Production 25
3.3.1 Analyzing 305-day yield ......................... 25
3.3.1.1 USDA projection factors .............. 27
3.3.2 Analyzing test-day records ....................... 28
3.3.2.1 Predicting next test-day production ...... 31

iii

3.4 Animal Models. .................................... 34
3.4.1 Advantages of multiple trait analysis. ............... 39
3.4.2 Disadvantages of Multiple trait Analysis. ............ 41

Assessing the effects of herd production level, lactation number and season
of freshening on shape of lactation curves for test-day milk, energy corrected

milk, and milk components. ................................ 42
4.1 Abstract ............................................ 43
4.2 Introduction ......................................... 44
4.3 Materials and Methods ................................. 48
4.3.1 Data ..................................... 48
4.3.2 Model ...................................... 50
4.4 Results and Discussion ................................ 52
4.4.1 Season of freshening. ......................... 52
4.4.2 Herd Production Level ......................... 69
4.4.3 Lactation number ............................. 70
4.5 Conclusion ......................................... 81
Application of a multitrait animal model to predict next test-day milk
production. ............................................ 83
5.1 Abstract ......................................... 84
5.2 Introduction ...................................... 85
5.3 Materials and Methods .............................. 88
5.3.1 Data ....................................... 88
5.3.2 Model ...................................... 89
5.3.2.1 Estimating (co)variances between test
intervals .......................... 90
5.3.2.2 Predicting next test-day production ...... 94
5.3.2.3 Prediction of next test-day using lactation
curve slopes ........................ 97
5.4 Results and Discussion ................................ 98
5.4.1 Age at calving ................................ 98
5.4.2 Season of test by temperature—humidity index ......... 98
5.4.3 Phenotypic and Residual correlation among DIM
interval traits ................................ 103
5.4.4 Predicting current test-day milk using one, two or three previous
TD records .................................. 107
5.4.4.1 Low Producing Herds .............. 107
5.4.4.2 Medium Producing Herds ......... .. . . . 112
5.4.4.3 High Producing Herds ............... 113
5.5 Conclusions ...................................... 121

iv

6. Summary .............................................. 122
7. Appendices. ............................................ 125

8. List of References ....................................... 153

LIST OF TABLES

Review of literature

Table 1. Average constant estimates and SE for the effects of age at
calving on lactation yield and test-day yields of milk in kg for
Swedish Red and White dairy breed. .................... 12
Study 1
Table 1. Number of test-day records (N) and mean for test-day milk,
ECM, fat and protein for three lactation groups in three herd
production levels (HPL) ............................. 51
Table 2. Day of peak milk production for the different season of calving
groups by herd production level ......................... 53
Table 3. Predicted Peak Test-Day Production for First Lactation
cows for different seasons of calving by herd production
level (HPL) ....................................... 59
Table 4. Predicted Peak Test-Day Production for Second Lactation cows
for different seasons of calving by herd production level
(HPL) ........................................... 60

Table 5. Predicted Peak Test-Day Production for Third and later
Lactation cows for different seasons of calving by herd

production level (HPL) .............................. 61
Table 6. Ratio of lactation production for calving seasons to July-August
calving season by lactation number, season of freshening and

Herd Production Level .............................. 68

Table 7.

Table 1:

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Standard lactation test-day values for 150 days in milk for
second lactation cows calving in November-December used as
base for standardized 150 days in milk within three herd

production levels ...................................

Study 2

Phenotypic variances (diagonal), covariances (above diagonal)
and correlations (below diagonal) among TD milk weights in
ten 30—day days in milk intervals for first lactation cows in low

80

producing herds. ................................... 104

Residual variances (diagonal), covariances (above diagonal) and
correlations (below diagonal) among TD milk weights in ten 30-
day days in milk intervals for first lactation cows in low

producing herds. ................................... 104

Phenotypic variances (diagonal), covariances (above diagonal)
and correlations (below diagonal) among TD milk weights in
ten 30—day days in milk intervals for first lactation cows in

medium producing .................................. 105

Residual variances (diagonal), covariances (above diagonal) and
correlations (below diagonal) among TD milk weights in ten 30-
day days in milk intervals for first lactation cows in medium

producing herds. ................................... 105

Phenotypic variances (diagonal), covariances (above diagonal)
and correlations (below diagonal) among TD milk weights in
ten 30-day days in milk intervals for first lactation cows in high

producing herds. ................................... 106

Residual variance (diagonal), covariances (above diagonal) and
correlations (below diagonal) among TD milk weights in ten 30-
day days in milk intervals for first lactation cows in high

producing herds. ................................... 106

Mean biases and root mean square errors (RMSE) for
predicting current test-day deviations from either 1, 2, or 3
previous test-day deviations for first lactation cows

in low producing herds ........................... I. . . . 109

vii

Table 8.

Table 9.

Table 10.

Table 11.

Table 12.

Table 13

Table 14.

Table 15.

Biases along with Mean and SD of actual and predicted test-day
milk yields predicted from the previous test-day record of first
lactation cows in 50 low producing herds over five years using
a slope of a standard lactation curve estimated by a model that
considers additive genetic effects. ...................... 110

Biases along with, Mean and SD of actual and predicted test-day milk
yields predicted from the previous test-day records of first lactation
cows in 50 low producing herds over five years using a slope of a
standard lactation curve fit estimated by a regression model that did
not include additive genetic effects ....................... 111

Mean biases and root mean square errors (RMSE) for predicting
current test-day deviations from using either 1, 2, or 3 previous test-day
deviations for first lactation cows in 50 medium producing herds over
five years ......................................... 114

Biases along with Mean and SD of actual and predicted test-day milk
yields predicted from the previous test-day record of first lactation cows
in medium producing herds using a slope of a standard lactation curve
estimated by a model that considers additive genetic effects. . . . 115

Biases along with Mean and SD of actual and predicted test-day
milk yield predicted from the previous test-day records of first
lactation cows in medium producing herds using a slope of a
standard lactation curve estimated by a regression model that
did not include additive genetic effects. ................... 116

Mean biases and root mean square errors (RMSE) for predicting
current test-day deviations from either 1, 2, or 3 previous test-day
deviations for first lactation cows in 50 high production herds . . 118

Biases along with Mean and SD of actual and predicted test-day
milk yields predicted from the previous test-day record of first
lactation cows in 50 high producing herds over five years using
a slope of a standard lactation curve estimated by a model that
considers additive genetic effects. ...................... 119

Biases along with Mean and SD of actual and predicted test-day
milk yield predicted from the previous test-day records of first
lactation cows in 50 high producing herds over five years using
a slope of a standard lactation curve fit estimated by a
regression model that did not include additive genetic effects. . . 120

viii

Table II. 1.

Table II. 2.

Table II. 3.

Table II. 4.

Table II. 5.

Table II. 6.

Table II. 7.

Table II. 8.

Table II. 9.

Table II. 10

Appendix 11

Number of records, cows, sires and dams, Mean and SD for
test-day milk yield by herd production level. ............... 138

Age at calving solutions (SOL) and SE for test-day milk production of
first lactation cows by herd production level ............... 138

N, min, max, mean for daily dry bulb and dew point
temperature and temperature-humidity index for a five year
period, 1988-1992 from five weather stations in Michigan. ..... 139

Min, Max, Mean and SD of observed deviations and predicted
deviations using deviations from the previous test-day record of
first lactation cows in low producing herds ............... 140

Min, Max, Mean and SD of observed deviations and predicted
deviations using deviations from the two previous test-day
records of first lactation cows in low producing herds ....... 141

MIN, MAX, Mean and SD of observed deviations and predicted
deviations using deviations from three previous test-day records
of first lactation cows in low producing herds .............. 142

Min, Max, Mean and SD of observed deviations and predicted
deviations using deviations from the previous test-day record of
first lactation cows in medium producing herds ............ 143

Min, Max, Mean and SD of observed deviations and predicted
deviations using deviations from the two previous test-day
records of first lactation cows in medium producing herds ..... 144

Min, Max, Mean and SD of observed deviations and predicted
deviations using deviations from three previous test—day records
of first lactation cows in medium producing herds ........... 145

Min, Max, Mean and SD of observed deviations and predicted
deviations using deviations from the previous test-day record of first
lactation cows in high producing herds .................. 146

Table II. 11. Min, Max, Mean and SD of observed deviations and predicted
deviations using deviations from the two previous test-day
records of first lactation cows in high producing herds ....... 147

Table II. 12. Min, Max, Mean and SD of observed deviations and predicted
deviations using deviations from three previous test-day records
of first lactation cows in high producing herds ............. 148

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

LIST OF FIGURES

Study 1

Test-day milk season curves for second lactation cows in
low producing herds .................................. 54

Test-day milk season curves for second lactation cows
in medium producing herds ............................ 55

Test-day milk season curves for second lactation cows
in high producing herds ............................... 56

Test-day milk season curves for second lactation cows
in medium producing herds for two years (01 and 02) ........ 57

Test-day ECM season curves for second lactation cows
in medium producing herds ........................... 63

Test-day protein % season curves for second lactation cows
in medium producing herds ............................ 64

Test—day fat % season curves for second lactation cows
in medium producing herds ............................ 65

Test-day milk and ECM production curves for second
lactation cows calving in MAR-APR, JUL-AUG or
NOV-DEC in medium producing herds ................... 66

Test-day milk , ECM, fat % and protein % curves for second
lactation cows calving in NOV-DEC in medium producing
herds ............................................ 67

Test-day milk curves for first lactation cows calving in
NOV-DEC in low, medium, and high producing herds ......... 71

xi

Figure 11.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Test-day protein % curves for first and second lactation cows
calving in NOV-DEC in low, medium, and high
producing herds .................................... 72

Test-day fat % curves for first and second lactation cows calving
in NOV-DEC in low, medium, and high producing
herds ............................................. 73

Test-day milk curves for first, second, and third or later lactation
cows calving in NOV-DEC in medium producing herds ...... 74

Test-day ECM curves for first, second, and third or later lactation

cows calving in NOV-DEC in medium producing herds ........ 75

Test-day protein % curves for first, second, and third or
later lactation cows calving in NOV-DEC in medium

producing herds .................................... 76

Test-day fat % curves for cows calving in medium producing

herds ............................................ 77
Study 2

Predicting test-day milk production from previous test—day
deviations ........................................ 96

Effect of age at calving on test-day milk production of
first lactation cows in low, medium, or high producing
herds ............................................ 102

Effect of temperature-humidity index within season of
test on milk production of first lactation cows in
low producing herds .................................. 103

Effect of temperature-humidity index within season
of test on milk production of first lactation cows in
medium producing herds .............................. 104

Effect of temperature-humidity index within season

of test on milk production of first lactation cows in
high producing herds ................................. 105

xii

1. INTRODUCTION

Dairy managers need to accurately evaluate milk production responses
resulting from management changes or the implementation of new technologies to
determine if they are cost effective. Evaluating production responses is critical to
maintain long-run profitability. Because comparison with control groups is often
not possible on farms, this task is difficult. In addition there may be periods
when no specific changes or multiple management changes are made, that require
monitoring production trends in order to effectively evaluate general management
and herd health status. Without control groups, producers are forced to assess
production change of the entire herd or a group of cows from period to period.
This is difficult because cows in a herd or group contributing to a day's production
vary as cows freshen or dry off between periods being assessed. In addition, a
cow's test-day yield is influenced by systematic environmental effects such as
season of calving, season of test and herd, and physiological factors such as stage
of lactation, age and number of days open. Importantly, stage of lactation, season
of test and days open change between periods for each cow. A within herd
standardization of test-day yields for all these effects allows comparison between
periods and between individual cows within a herd. Making these adjustments is

useful for management and selection purposes. In the Netherlands, for example,

2

test-day yields of cows recorded prior to 250 days in milk are standardized for age

and season of calving and stage of lactation. The standardized tests are averaged

to give a herd index which is used as a management guide by producers (Wilmink,

1987).

A cow’s performance can be llustrated by the following general model for

the phenotypic expression of a quantitative trait:

where Pij

p.

Pu=n+G,+PE,+TEu

is the jth test-day record of the ith animal.

is a test-day constant level of performance for a group of animals
which can be thought of as the average value that a group in a
population have in common including the average level of
management for the group. The term ,u. would, therefore, represent
major identifiable fixed environmental effects that affect a cow’s
test-day record such as herd, management level, age of the animal at
calving, the year and the season of calving, days in milk after calving
and season of test. Since some fixed effects would change
throughout a cow’s lactation, p. might be different for each test-day
record of an individual cow.

is the sum of the genetic values which includes both additive and
non—additive genetic effects. An additive genetic effect is the effect
of a single allele at one locus on the expression of the trait of

interest. The sum total of these additive genetic effects from all loci

PE-

3

give the additive genetic value (A) of an individual. A random
sample half of the alleles will be transmitted to progeny of that
animal. The non-additive genetic effects include dominance and
epistasis. Dominance genetic effects are caused by the combination
of a pair of alleles at one locus. Dominance genetic effects are not
transmitted to progeny from one parent, but arise due to the
particular combination of alleles received from both parents. The
dominance genetic value of an animal is the sum total of all
dominance genetic effects over all loci. Epistatic genetic effects are
the result of interactions among additive and dominance effects.
Epistatic genetic effects are commonly assumed to be non-significant
in genetic evaluation problems and measurement of such effects is
difficult.

is the sum of effects of environmental factors which permanently
influence the performance of animal i, i.e. influence all subsequent
observations made on an individual. For example, the feeding
regime used to raise dairy heifers, if extreme (poor feeding or
excessive energy), can influence mammary development, hence
becoming a permanent environmental effect influencing all
lactations. If a cow is preferentially treated during all her lactations,
then preferential treatment can be a permanent environmental

effect.

4

TB. is the sum of random environmental effects which affect the jth
record of animal i and thus are temporary. A temporary
environmental effect may influence one or more observations on the
individual but is not repeated for every observation. Whether or not
an individual receives a particularly favorable or unfavorable
influence is assumed to be by chance for each observation.

The underlying assumptions for the above model are:

i. Pii is random and normally distributed

ii. the expected value of Pi is p.

iii. expected value of G,, PEi and TEii is zero

iv. the covariances among G,, PEi and TEii are zero

Since Gi and PEi repeat in every record, then the sum of the permanent

effects, termed real producing ability (RPA) of an animal, can be denoted as
follows:
RPA, = G, 4» PE,
Further test-day producing ability (TDPA) of an animal can then defined as:
TDPA, = RPA. + TEu
To monitor herd or individual cow performance, attention needs to be paid to
TEii which can increase or decrease. Dairy producers would be interested in
improving TEii through management changes. A method to predict TEii for ’
comparison to actual test-day performance of individual cows which is the focus of

this study would be desirable. This would allow producers to determine if cows

5

performed better than expected on a test-day as a result of management. Use of
animal models has been a breakthrough in that both G, and PEi (RPA) for an
individual animal can be estimated and results in more accurate estimation of
fixed effects. The RPA has been computed for total lactation yields. Estimation
of TDPA of a cow has not been done because of lack of methods to predict TE“.

Daily milk yields can provide a useful measure of a herd's current
performance and as an indication of management and disease problems.
Producers, veterinarians and feed consultants make numerous decisions based
upon weekly or monthly changes in daily milk averages within a herd. Such
comparisons are often used to evaluate new management practices, feed changes,
or feed additives. However, comparison of changes in average daily milk based
upon milk tank comparisons does not account for addition of fresh or removal of
dry and antibiotic treated cows, changes in stage of lactation or seasonal
differences between periods of measurement.

Often, subgroups such as the high producer strings are of interest, requiring
individual milk weights. Changes in monthly test-day daily milk averages provided
by Michigan DHIA and a number of other DHIA organizations do not account
for changes in stage of lactation and normal seasonal trends which, jointly, can
result in more than a 10% change in daily milk production for a cow over a 30-
day period. As a result, comparison of daily milk averages are crude, potentially,
resulting in inaccurate assessment of management changes and health status of

herds. Methods are necessary to adjust daily milk weights for test-day comparison.

6

Currently, several methods are being used to account for stage of lactation
by adjusting milk to 150 days in milk (McCraw and Butcher, 1976; Steuernagel,
1988; Nordlund, 1987). Steuernagel also adjusts for age and parity. However,
season of calving, which also influences production peak and rate of decline was
only considered by (McCraw and Butcher, 1976). Herd production level may also
influence rate of lactation decline.

Summarizing test-day records into a single measure, lactation yield, as is
common practice has some deficiencies. Adjustments of a 305-day cumulative
value for systematic environmental effects such as herd, season and age of calving
can be done but it would be difficult to adjust for systematic effects specific to
each individual test day making up the 305 day record. Such factors include the
effects of temperature, relative humidity, pregnancy, use of bST and disease. It
would require accurate start and stop times for disease, use of bST, etc., to get
accurate test interval estimates of milk production from which to compute 305-day
production.

Many methods have been developed to predict total lactation yield or 305
day milk yield. For monitoring management changes one method has been to
compare projected 305 day Mature Equivalent (ME) values from one test day to
the next test-day (Galligan and Ferguson, 1991; Eicker et al., 1993). This accounts
for age, season of calving and herd level but it is difficult to quantify change in
305 ME values to change in daily milk. Prediction of short production periods,

such as to the next test-day, would likely be more accurate compared to predicting

7

longer periods as is done in projecting 305-day records. Further, prediction of
test-day production or the next test-day production in lieu of predicting 305-day
yield would be more useful in monitoring cow and herd production change
resulting from changes in management such as ration modification or use of bST.
The problem of accurately comparing daily milk production has resulted in
requests by a number of feed consultants and veterinarians for a better system to
monitor production changes in dairy herds. A useful system would predict
production for the next test day while accounting for physiological changes in each
cow and season of test or change in the environment. The predicted values could
then be compared to the actual values for that test day to determine if there is a
significant change in production. When predicting unobserved test-day records, it
is desirable to make maximum use of the predictability of the lactation curve and

to minimize the error of prediction from a sample of daily records.

8
2. Objectives

2.1 Lactation Curves (Study one)

The objectives of this study were 1) to assess the effect of six seasons, three
herd production levels and parity on the shape of lactation curves, 2) to derive
factors that can be used to estimate herd mean production at 150 days
postpartum.

2.2 Predicting Test-day Milk Production (Study 2)

The objectives of this study were to 1) estimate phenotypic, additive
genetic and residual (co)variances of test-day milk production for ten 30-d days in
milk intervals treated as separate traits; 2) predict next test-day milk production

deviations using deviations from the previous 1, 2, or 3 tests (traits).

3. Review of Literature.

3.1 Introduction

Milk production is influenced by a number of non-genetic factors. When
attempts are made to estimate the genetic value of an animal, the effects of some
of these factors have to be removed. Adjusting records for known causes of
variation is a must in making accurate culling and selection decisions.

The non-genetic or environmental factors affecting milk yield are
documented in numerous investigations reported in the literature. Problems of
estimating a number of these effects, their magnitude and mutual interrelations
have been thoroughly investigated. Some of the environmental factors that affect
milk production will be reviewed in this section. A review on the advantages of
modelling test-day production vs 305-day lactation yield is also given.

3.2 Environmental factors affecting a cow's production
3. 2.1 Efiect of Cow's Age

Age at calving of a cow is one of the main factors affecting milk, protein
and fat yields in dairy cattle. Yield increases with age at a decreasing rate and
reaches a maximum at maturity. Yield then decreases as cows become still older.
Auran (1973) reported that age explains about 20-40 % of the total variation in
milk production. Influence of month of calving on production records is also well
established. 80, in Canada, an age-month adjusted record is known as 3 Breed

Class Average (BCA) and in the United States the adjusted records are known as

10
Mature Equivalents (ME). In a review, Freeman (1971) reported the history and

basic problems both of estimating age effects and their practical application as
adjustment factors. Unbiased estimates of age effects require simultaneous
consideration of herd, year, season of calving, age and cow effects together with
their interactions (Daniel, 1981, 1982a).

Several workers showed that the influence of age at calving on monthly
test-day yields decreased with advancing lactation, accounting for about 41% to
50% of total variation of first monthly test to about 2% to 5% for the last three
test-days (Auran, 1973; Dannel, 1981). Ronningen (1967) showed 5.7% of the
variation in maximum daily yield in first lactation was due to age at calving.

Dannel (1981) studied the effects of age at calving on both total lactation
production and individual test—day yields of milk and fat percentages. Lactation
milk yields increased with increasing age at calving for the Swedish Red and White
(SRB) and Swedish Friesian (SLB) dairy breeds. Effects of age at calving on 305
day milk production and test-day milk production of SRB breed reported by
Danell (1981) are in Table 1. Younger cows (20 to 25 months) gave 150-200 kg
more for each month of age while older cows (26 to 33 months) had a smaller
(only 25-33 kg) increase in yield with increasing age. There is a trend of 50 kg /
month in the interval between 24 and 33 months of age. Although test-day fat
percentages were also affected by age at calving, the effects were far less than milk
yield. Younger calving cows had lower fat % values than those calving older.

Effects of age of the cow on a test-day have been studied (Ng-Kwai-Hang et al.,

11
1984; Stanton et al., 1992). Ng-Kwai-hang et al. (1984) indicated that milk

production increased markedly between two and five years of age and then
increased at a slower rate between five and six years of age. Percentage of fat in
milk increased linearly between two and five years followed by a drop between five
and six years. Stanton et al. (1992) used a test day model to study the effects of
age on test-day production and concluded that age at calving would account for
more variation in test—day production than age on test-day.

Effects of age on milk production has also been examined in terms of
lactation number or parity. Wood (1967) showed the effect of parity on the
lactation curve parameter. The constant 3 representing average daily production
on a log scale was 3.53, 3.72, 3.97, 3.86 for first, second, third and fourth or
greater parities respectively. The increase may result from successive parities
promoting udder development and from a cow's physiological development in
general.

Parity differences have been shown in terms of persistence, with first
lactation cows being more persistent than later lactations. Keown et al. (1986)
reported similar persistence of fat % and protein %. Wiggans and Van Vleck

(1979) reported parity to have little effect on projection factors for protein yield.

Table l.

12

Average constant estimates and SE for the effects of age at calving
on lactation yield and test-day yields of milk In kg for Swedish Red
and White dairy breed.

 

AGE

20-21
22-23
24-25
26-27
28-29
30-31
32-33
34-35

305-d 1

-530.3 -2.14
-249.5 -1.09
-108.6 -0.41
-14.2 0.07
76.3 0.37
188.2 0.74
287.3 1.08
350.7 1.37

2

-2.15
-1.02
-0.43
0.01
0.34
0.76
1.12
1.38

3

-2.05

4

-1.77

-.0.94 0.95

-0.42
-0.04
0.30
0.63
1.07
1.43

—0.39
-0.05
0.23
0.61
1.02
1.30

-1.66
-0.79
-0.34
-0.08
0.20
0.55
0.94
1.18

-1.78
-0.73
-0.27
-0.05
0.18
0.57
0.93
1.15

-1.48
-0.65
-0.31
-0.1 1
0.12
0.53
0.88
1.01

-1.49
-0.61
-0.33
-0.13

0.21
0.57
0.84
0.94

9

-1.26
-0.63
-0.36
-0.12

10

-1.05
-0.58
-0.34
-0.07

0.26 0.29
0.56 0.55
0.73 0.59
0.81 0.61

 

Source:

Dannel ( 1981).

3.2.2 Season of Calving

the cow's milk production. The relationship of yield with month of calving is

The effect of season or month of calving exerts a considerable influence on

caused in part by the seasonal variations in feeding and care. The quality and

quantity of feed or pasture seems to be of particular importance. In countries

where the grazing system is short and cows are housed and fed indoors for most

of the year, the highest lactation is given by cows calving during the autumn and

early winter (Danell, 19823).

Auran (1973) used test-day records to study the influence of month of

calving on individual test-days. The effects of monthly and cumulative yield

13

showed that month of calving was not as important as age at calving. Month of
calving accounted for about 1.8% of the total variation in the first test-day and
about 7.8% in the seventh and eighth test-days. Thus, contrary to the age effects,
the effect of month of calving is largest towards the end of lactation. At the early
stage of lactation, body reserves can supply part of the energy requirements and
the production may therefore be less influenced by month of calving. Danell
(1981) also reported findings similar to those found by Auran in using test-day
records from Swedish dairy herds. When calving occurred in September for
example, the yield was below average in the first month but above average in the
last month of lactation. This suggested an interaction between month of calving
and stage of lactation which makes the shape of the lactation curve dependent
upon month of calving. Miller et al. (1967) ranked this interaction as the second
most important source of variability in developing factors for monthly records.
Effect of month of calving can vary in different years, herds, regions, although the
general pattern seems to be the same overall (Auran, 1973; Dannel, 1981).

In addition to test-day milk yield, milk components are influenced by
season of calving. Fat% showed seasonal variation which was the reverse of the
effect on test-day milk yield. The month with the highest milk yield had the lowest
fat test results (Danell, 1981; Schultz et al., 1990). Schultz et al. (1990) showed
that test-day fat and protein percent were highest for cows calving from April .
through August and lowest for cow calving from September through March.

Month of test also affects test-day production (Sysrtad, 1965; Dannel, 1981;

14
Ng-Kwai-Hang et al., 1984). Lindgren et al. (1980) did a comprehensive study on

the effect of non-genetic factors on monthly protein records of individual cows.
Month of test was significant for all stages of lactation. During the period 2-9
months after calving, 6-8% of the variation in protein content was attributed to
month of test. During the first month only 2 % was due to month of test, partly a
result of larger overall variation in protein content during that period. Lindgren
et al. (1980) concluded that a cow's production is less affected by month of testing
immediately after calving than later in the lactation. Protein % showed steady
increasing values during winter and decreasing values during summer a similar
trend observed on Norwegian data by Sysrtad (1965, 1977). The low values in
summer could be due to change in feed as cows generally were put out to pasture
during summer, leading to an unfavorable balance between energy and protein in
the diet.
3. 2.3 Stage of Lactation

This is one of the several factors that change during lactation of a cow.
Parity, age at calving, season of calving are fixed for a given lactation. Effects of
stage of lactation are well documented. In general, daily milk yield increases to a
peak a few weeks (30 to 90 days) after calving and then gradually declines to dry
off. The graph of daily milk production against time (usually for 305 days) post
calving is a lactation curve. Methods which characterize lactation curves allow for
statistical comparison of milk production for the entire lactation and avoid

restriction to the linear phase post-peak. This would include the critical first

15

months of lactation in nutritional or physiological experiments. Knowledge of the
lactation curve shape in dairy cattle is important because the pattern of how a cow
produces milk over time could determine her biological and economical efficiency
for purposes of feeding and selection. The shape of a lactation curve could be
incorporated into the process of extending lactations. Sire and cow genetic
ranking can be based on extended lactation records. An evaluation of sires could
use the parameters derived from lactations of daughters. For a herd, three major
uses of lactation curves would be i) to compare herd values to reference values, ii)
to compare animals within herd, and iii) to monitor production after a
management change.
3. 2. 3. 1 Mathematical fimctions for describing lactation curves

Since the 1920's there has been considerable interest in mathematical
description and analysis of the lactation curve in dairy cattle. Mathematical
functions descrrbed below have been used to depict the shape of the lactation.
Usefulness of these parameters has however been limited because of systematic
divergence from typical lactation curves. Wood (1967) noted that the gamma
curve approximated the lactation curve for milk yield. Wood‘s equation of the
form

yll = anbe’cu

is the non-linear form of the incomplete gamma function and ya is production on
day 11, a is the scaling factor and b and c are coefficients that define shape of the

lactation curve before and after peak, respectively. Woods equation implicitly

16

assumes more variable production at the peak than at extremes of the curve thus
requiring a logarithmic transformation of the gamma curve to achieve
homogenous variances. A group of cows usually have higher variance of
production around the first two months than around eight months. Kellogg et al.
(1977) suggested that other than random variation contributing to this comparison
of variance two factors also cause such variation; i) cows have different lactation
curves so individuals following different curves will differ much more at the second
than the eight month and ii) the actual days post-partum for the second record of
monthly production can range from about 35 to 70 days in milk for a group of
cows. Therefore, early production records reflect a time period when production
is changing more rapidly. Kellogg et al., (1977) suggested that techniques of
intrinsically non-linear regression would fulfil the assumption of equal variance
throughout a lactation. Using data from 4 lactations of 36 cows, Kellogg and
coworkers (1977) found variances of deviation from the estimated curves were
approximately equal after the first month of lactation thus supporting the use of
non-linear equation of the untransformed Wood's (1967) equation using
techniques of intrinsically non-linear regression.

Cobby and LeDu (1978) compared 3 regression methods to estimate
parameters of the incomplete gamma function. Analysis of the residuals indicated
that each method tended to overpredict actual data during early and late lactation.
As such, reparameterization of the incomplete gamma function was proposed.

They reported a 14% reduction in residual mean square when using non-linear

17

techniques as opposed to linear regression on the logarithm transformed equation.

Using the incomplete gamma function, Congleton and Everett (1980)
predicted daily and cumulative yield to 305 days post-calving and compared
predictions to actual 305 day records. They found that fitting the log transformed
incomplete gamma function by linear regression to monthly observations of daily
milk gave a prediction with a bias of -15.1 kg and a root mean square of 183.4 kg
in predicting 305 day cumulative milk.

Grossman et al. (1986) modified Wood's equation by multiplication with
sine and cosine coefficients to account for other seasonal effects other than season
of calving. The following equation was used

yn=an"e'“‘[1- u sin(x) + v cos(x)]
where a, b, c, u and v are coefficients to be estimated, it is the day of lactation
and x is the day of year computed as radians. The log transformation of the
above equation was used in the form of a multiple regression model. Grossman
and Koops (1988) proposed yet another lactation curve model, the multiphasic
function which considers milk yield resulting from several phases of lactation. The

multiphasic function has the form:

v. =2 aMl -tanh’(b.(t-c.))l

where;

y( = milk yield at time t ( t = days in milk)

n = number of phases

ai = half asymptotic total yield for phase i

bi = rate of yield relative to ai (per day for phase i)

18

ci = time of yield in days for phase i
The multiphasic model was fit to 17,607 complete lactation records from the
Dutch Friesland Black and White in the Netherlands by Grossman and Koops
(1988). The authors observed that the optimal model was the diphasic function
(n=2) for which six parameters must be estimated. The diphasic function proved
to be superior to the incomplete gamma function (Wood, 1967) in terms of less
correlated residuals. For example, it was observed that the incomplete gamma
function tended to over-predict milk yield from 30 through 110 days, underpredict
from 130 to 230 days and again overpredict throughout the end of lactation.
Residuals were also highly correlated and ranged from -.91 to .37 with a standard
deviation of .37.

Since lactation curves represent amount of milk or milk components
produced on each days in milk (DIM), they have also been estimated by solving
for the least square estimates for DIM. Seasonal effects on production and
reproduction influence both the amount of milk produced per day and duration of
lactation. Therefore solving for DIM solutions requires accounting for variation
due to season. Keown et al. (1986) estimated lactation curves for six seasons of
freshening within 5 production groups and three lactation groups by solving for
least square estimates for DIM. Curves were formed by adding an overall mean
to season-stage of lactation subclasses. A similar approach was later used by
Schultz et al. (1990) who estimated lactation curves for three parity groups and

three breeds. In this study, lactation curves were smoothed by medians of five and

19

repeated means of pairs. In estimating lactation curves by solving for the DIM
least square estimates, Stanton and coworkers (1992) used a test-day model that
included test-day effects to solve for DIM solutions.

3. 2.4 Efi'ect of Gestation

The relationship between reproductive efficiency and production has been
reported in many investigations. As early as 1955, Carman attributed the negative
correlation between lactation and reproductive efficiency to the depressing
influence of high production on fertility. Lee et a1. (1961) however assumed that
this negative correlation was caused by the inhibitory action of gestation on
production. Milk yield is depressed by gestation towards the end of lactation as
demonstrated in many investigations reviewed by Gustafson (1972 cited by Auran,
1974). The influence of placental homomes was considered to be responsible.
Reece (1958) explained this relationship with the theory that progesterone inhibits
the stimulatory effect of estrogen on secretion of pituitary lactogen during
lactation.

The variables that have been used to study the influence of gestation on
production include calving interval (CI), days open (DO), days carried calf (DCC)
and days dry (DD). Calving interval can however, be divided into two periods,
DO and the gestation period with most of the variation in CI determined by the
variation in DO.

Lactation yield increases as days open increases. The study done by

Weller et al. (1985), defined length of period affecting annualized milk as:

20
[(Total Lactation yield)/CI] " 365.

He found maximum milk yield was at 75 to 91 days open for heifers and at 61 to
75 days open for cows. Influences of present lactation DO and previous lactation
DO were examined simultaneously by Funk et al. (1987). As present DO
increased from 20 to 300 days, lactation yields for F CM, milk, and milk fat
increased approximately 1250, 1350 and 45 kg respectively. As previous DO
increased from 20 to 300 days, lactation yields for F CM, milk and milk fat
increased approximately 625, 650, and 25 kg. A study on Israeli cows (Bar-Anan
and Seller, 1979) indicated that longer days open in previous lactation also
increased lactation yield. These findings confirm the reports by previous authors
(Auran, 1974; Oltenacu et al., 1980; Sehaeffer & Henderson, 1972;). However,
first lactation cows are less affected by days open than later parity yields (Auran,
1974).

A few researchers have studied the influence of DCC on lactation
performance. The yield falls off about 100 days after conception amounting to 3-5
kg per day as the interval from conception to calving increases (Dannel, 1981).
Keown and Everett (1986) studied the effects of days carried calf (DCC) on 305
day actual milk, fat and protein yield by lactation. In this study, maximum loss of
lactation yield in first lactation cows was 510 kg milk, 15.2 kg fat, and 17.1 kg
protein which occurred at 221 to 230 DCC. Milk, fat and protein yields in 305 d
decreased continually from less than 41 DCC through 221-230 DCC after which

the trend reversed for all three traits. Reasons for this reversal is however

21

unknown. In the same study, estimates for second and third lactations were more
similar than estimates for first lactation cows. The effect of DCC is more
significant for milk than fat or protein for all lactations. Fat and protein are more
persistent than milk and maybe less influenced by these factors than milk yield.

Funk et al. (1987) reported that cows dry 60 to 90 days gave the most milk
the following lactation. Sehaeffer and Henderson (1972) also indicated effects of
days dry on subsequent production with dry periods of about 60 days resulting in
the greatest subsequent production. Days dry have a larger impact on second
lactation cows compared with later lactations (Wilton et al., 1967).

Heritability for DO is less than 10%, with most estimates close to zero.
Therefore, adjustment of milk records for days open (DO) has been suggested
since 305 day milk yields increase as number of DO increases (Sehaeffer, Everett
& Henderson, 1973). For adequate adjustment in milk records for D0 or DCC
breeding dates must be reported accurately. However, losses of information from
missing breeding dates are normally very large. This is probably the major reason
why adjustments of lactations for D0 or DCC have not been incorporated into
many genetic evaluation systems. One scheme that currently includes DCC is the
Northeast Multiple Trait AI summary (Everett and Schmitz, 1993).

3.2.5 Heat Stress
It is apparent that performance, well being and health of the animal are
influenced by biometeorologieal factors. The most important climatological factors

are heat stress during the hot season and the wind chill factor during the cold

22

winter. Buffington et al. (1981) defined heat stress as any combination of
environmental parameters producing conditions that are higher than the
temperature range of the animal's neutral zone. The survival and performance of
an animal during heat stress periods depends on several weather factors especially
temperature and humidity (Linvill and Pardue, 1992).

Heat stress increases the length of the estrus cycle, shortens the period of
estrus, reduces conception, and increases embryo mortality with a corresponding
decrease in fertility and placental malfunction. Further, fetal growth is retarded,
gestation period is lengthened and calves show a corresponding lower birth mass
as well as decreased ability to survive (Brody et al., 1948; Fuquay ct al., 1979;
Thatcher et al., 1974). Heat stress results in decreased feed intake, particularly
roughage intake. Decreases in roughage intake maybe responsible for the
decrease in the percentage butterfat in milk (Dupreeze et al., 1990). In a study
by Roussel et al. (1969), milk production and nonfat milk solids were significantly
decreased by thermal stress.

Due to vulnerability of dairy cows to heat stress caused by hot, humid
weather, dairy cows can benefit from the micro-climate modifications to improve
their comfort zone and performance. Appropriate facilities to protect cattle from
climatic extremes are of cardinal importance for optimal performance. Protection
includes location of the farm, shade, modification of dairy facilities, direct wetting
of cattle by sprinkling combined with other supplemental cooling designs such as

air fans (Dupreez et al., 1990). These practices ensure evaporative cooling which

23
is ideal for protection against heat stress (Harn, 1981). Thatcher et al. (1974)

studied milk production and breeding efficiency under climatically controlled
conditions. Cows in air conditioned facilities produced 10% to 40% more FCM
than cows in facilities that were not air conditioned. Studies by Romen et al.
(1977) revealed that cows placed under shade to remove solar radiational heating
produced more milk and have higher conception rates than unshaded cows.
Ngwerume et al. (1991) looked at the effect of curtain walled freestall housing on
milk production during summer in Michigan. Results suggested that using curtain
walls that can be rolled up during summer to allow more air movement in the
barn, alleviated milk decline due to heat stress.
3. 2.6 Herd and Herd Level

For lactation milk yield, Van Vleck and Henderson (1961a) estimated that
the variation due to herd accounted for 35% of the total variation. The influence
of herd on milk production is mostly due to management within a given herd.
Herd management includes such aspects as calf raising methods, age at first
calving practices, feeding practices and herd health program to mention a few
aspects. Auran (1973) studied the effects of herd on monthly test-day milk
production. It was found that herd effects accounted for approximately 25-45% of
the total sums of squares in monthly test-day yield and 30 to 42% in cumulative
milk yield. The easiest way to remove herd effects of cows is to compare
individuals within herds. Auran (1973) also looked at the influence of herd

production level by analyzing three herd average levels. Herd level accounted for

24
5-23% of the total sums of squares in test-day yield with 74 to 89% of the herd

effects in the first eight test-day yields and about 11 to 36% in the ninth and
tenth. Wiggans (1980) reported that herd average was most important is early
lactation for projecting lactation records since it provided a reference point for
sample day production and accounted for the subsequent higher production in
higher producing herds.
3. 2. 7 Bovine Somatotropin

A significant increase in milk, fat and protein yields due to treatment of
cows with bovine somatotropin (bST) has been documented. Increases in milk
yield to bST have been variable with increases in lactation yield between 15 to 20
% (Burton et al., 1987) and the increase being dose dependent (Thomas et al.,
1991). Despite the controversy surrounding the use of bST commercially, it was
finally approved for commercial use in the United States. Based on research over
several lactations, Burton et al., (1987), recommended that bST be initiated when
the cow is in positive energy balance and pregnant, i.e. 90 to 120 d of lactation.
Due to its approval there is increasing concern about its potential effects on milk
records and consequently sire and cow evaluations. Potentially, how then can bST
be handled using the current mathematical models for genetic evaluations.
Additional challenges would occur in the case of ignorance of the real status of
the cows treated or not treated which would arise due to poor reporting (Colleau,
1989). The results of a simulation study conducted by Colleau (1989) indicated

that the reduction in genetic gains was 1-10%. When bST was allocated to the

25

best cows, large biases of up to 30% in the evaluations were observed. To
accurately model lactation records from bST treatments, information such as
dosage administered, dates individual cows began and ceased receiving bST and
time when it was administered will be needed along with good statistical models.
3.3 Modelling Test-day Production vs Modelling 305-day Production

The above section has attempted to give a brief overview of some of the
environmental factors that influence a cow's production record. In this section, the
advantages and disadvantages of modelling 305-day milk production and the
possrbility of modelling actual test-day milk production will be discussed.
3.3.] Analyzing 305-day yield

Genetic evaluation of dairy sires has been based, for many years, on the
analysis of 305 day (305-d) lactation yields. The basis of 305-d yield is a set of test-
day yields taken at approximately 30 day intervals. This standard length allows
records to be compared without concern for the length of the production period.
However, one difficulty is that a cow must have the opportunity to complete 305
days in milk before this measure of her productive ability exists. For cows that are
sold or die, this information not available (Wiggans and Van Vleck, 1979)
meaning that the 305-d yield must be estimated. In many cases 305-d lactation
yields are estimated from lactations that are in progress. There are several
advantages of extending records to 305-d production. The prediction of total
lactation is important for early estimates of breeding values and individual cow

performance which aid in management decisions. As a result, producers are able

26

to identify low producing cows earlier and make culling decisions sooner.
Prediction of 305-d records for lactations in progress and culled cows provides
data from more daughters for evaluating dairy sires (Congleton and Everett, 1980;
Wilmink, 1987; Wiggans and Van Vleck, 1979; Danell, 1982b). Danell (1982b)
pointed out that extending part lactations to 305-d offers the potential of
shortening the generation interval. Also, it is possible to reduce breeding
program costs by culling progeny tested bulls with low breeding values for milk up
to a half year earlier than when using completed 305-d lactations (Henderson and
Van Vleck, 1961c, 1961d). However, the accuracy of extending records to a 305—
day yield will depend on the number of test-days involved and the method used to
project these test-day records.

Many researchers have developed factors for extending records in progress
to a complete 305-d lactation. Examples include single regression of the
remaining part of the record on the last known test-day yield; multiple regression
of the unknown part on known test-day yields; and use of functions describing the
lactation ( Van Vleck and Henderson, 1961b, Miller et al., 1971, 1972; Keown and
Van Vleck, 1973; Auran, 1976; Sehaeffer et al., 1977; Wiggans and Van Vleck,
1979; Congleton and Everett, 1980; Wilmink, 1987). In general, the last known
test-day yield provides the most information about yield in the remaining lactation.
3. 3. 1.1 USDA projection factors

The projection procedure currently used by USDA is based on the yield

for the number of days the cow actually milked, plus an estimate for the

27

remainder of the 305-day lactation derived from the last available sample-day
yield. For records of 155 d or less, the ME herd average for cows calving in the
same herd 1 to 2 years prior to the record's last sample day is incorporated into
the computed projection factors. The use of ME herd average was reported by
Wiggans and Van Vleck (1979) to increase the accuracy of the projection by
providing information on the normal yield level of the herd. Separate factors
have been developed for 4 seasons of freshening, two lactation groups (first and
second or later), three US. regions, and five breeds. The four calving seasons are
1) December through February, 2) March through May, 3) June through August
and 4) September through November. The projection procedure for milk or fat is

as follows:

A

Y305 = YDIM + (YD) (305 - DIM)

where

{(306 is projected 305-day yield, Yum is yield for the partial record, a?!)

is estimated average daily yield for the remainder of the lactation and (305 - DIM)
is days remaining.

For records with greater than 155 days:

it, = ta. + unmet.) + a, + BP(DIM)

28

where a is an intercept, s is sample day , B is a slope, Y, is sample-day yield, F is
the DIM factor. For records with 155 days in milk or less estimated average daily

milk yield is as follows:

YD = Id, + [3,(D1M)l(Y.) + [an + BADMIWH)

where Y" is actual herd-average yield.
3. 3.2 Analyzing test-day records

Prediction of 305-d production is not without error (Sehaeffer and
Burnside, 1976). There is still a quest to improve methods for extending part
lactations to 305-d production. Recently, Trus and Buttazzoni (1990) proposed a
method that describes the lactation curve as a series of correlated traits. This
model predicts the residuals for each trait that can be added to the expected
values to estimate a missing test-day record which can then be summed with other
test-day yields to give lactation yield. This method is currently being used in Italy.

As mentioned in the above section, major emphasis is placed on
standardized lactation production when selecting dairy cattle. Summarizing test-
day records into a single measure is a common practice. However, adjusting this
cumulative record for environmental effects such as herd, season and age of
calving eliminates the possibility of adjusting for those effects peculiar to
individual test-day records. With 305-d yields such effects which are test-day '
specific are assumed to be random and to average out over the lactation. These

effects may be quite different from the average effects for the lactation, hence

29
they may not average out (Meyer et al., 1989; Stanton et al., 1992). Meyer et al.

(1989) reported low heritabilities for milk (.17), fat (.15), and protein (.13) yields.
These low values were partly attributed to short-term environmental variation
affecting daily performance which could not be accurately accounted for by
modelling lactation totals.

Modelling individual test-day records for both genetic evaluations and
management purposes might eliminate some of the problems of extending records
to 305-day yield, as well as the problems associated with accurately modelling 305-
day yields. When modelling individual test-day records, a linear model that is
assumed to explain test-day records is important. This model shall be referred to
as a "Test-day Model". By definition, a test-day (TD) model is a method of
evaluating daily production of milk, fat, protein and somatic cell count considering
effects for each test-day in place of one set of fixed effects over the 305-day
lactation. A TD model would need to incorporate the general shape of the
lactation curve (Sehaeffer et al., 1977; Trus and Buttazzoni, 1990; Stanton et al.
1992) and accurately account for the test-day environmental effects affecting all
cows on the same test-day and along with effects specific to each particular cow
such as days carried calf, days open and disease. Analyzing test-day records may
provide a valuable tool for herd management as well as genetic evaluations. In
terms of management, dairy producers are interested in accurate evaluation of
their feeding and management practices so their best programs can be repeated

(Everret and Schmitz, 1993). On the other hand, geneticists desire accurate

30

estimates of these environmental effects and management programs so that they
can be eliminated or properly adjusted when evaluating animals for breeding
purposes. Research which looks at the prediction of future test-day records and
adjustments for test-day effects will be beneficial.

Few studies utilizing TD models are reported in literature. Meyer et al.,
(1989) used a TD model to compute genetic parameters using test-day records of
first lactation cows. In this study, test-day records were split into 30-day intervals
and yield in each interval was analyzed separately by either using a model with
herd-year-season (HYS) subclasses or a model with herd-test-day effects (HTD).
Fitting HTD effects which accounted for the environmental effects specific to the
day of test reduced residual variances as compared to fitting HYS. The proportion
of total sums of squares for milk yield explained by HTD ranged from 36% to
86% for three regions. Ptak and Sehaeffer (1992) used a test-day model for
genetic evaluation of 576 sires. The breeding values for the same sires were also
estimated using 305-day lactation yield. The rank correlations between the two
methods ranged from .889 to .96. Although these results do not suggest which
method is better, at least the results show that using a test-day model ranks the
animals differently. However, Ptak and Sehaeffer showed that when using HTD
effects in the model, residual variances were greatly reduced as compared to
adjusting for HYS effects only. Further research using simulated records is
needed.

Everett and Schmitz (1993) developed a herd test-day model which

31

corrects for the effects of age on test-day, days carried calf, days in milk, month of
calving and herd test-day milk within each herd. In this model an auto-correlation
structure was assumed for the residual (co)variance matrix structure. The
advantages of the test-model developed by Everett and Schmitz (1993) over the
conventional 305-d production models is that it permits age, month of calving and
DIM effects to vary by herd and includes a herd-testday effect that adjusts for
differing effects of sampling dates. Since this is a fixed effect model, the residuals
are summed for cows and used for genetic evaluations.

3. 3. 2. I Predicting next test-day production

In North Carolina, McCraw and Butcher (1976) estimated lactation curves
that can be used to determine expected production of lactating cows based on
breed, age, month of calving and stage of lactation. A fifth degree polynomial was
used to construct lactation curves within breed-age-season subclasses. A dramatic
seasonal influence was observed. Cows calving in summer months peaked at a
much lower level of production and had flatter lactation curves. However, in the
North Carolina system, herd production level is not considered.

Nordlund (1987) developed a method to adjust test-day milk to a 150 days
in milk value to assess management effects from month to month. The value was
termed Adjusted Corrected Milk (ACM) with the formula as below:

ACM = (0432*le milk) +(16.23*(lbs milk‘%fat/100)) + (((ADIM-ISO)

*.0029)"lbs milk)

32

where

ADIM is average days in milk, .29% is the average decline rate per day

and FCM = (432*le milk) + (16.23 " lbs fat).

Nordlund's formula however ignores season of calving which has a significant
influence on milk production and assumes a fixed percentage of first lactation
cows. The ACM assumes a constant slope for the whole lactation curve which is
not correct.

In Minnesota, Steurnergal (1988) developed a formula for management
level milk (MLM) which can be used to monitor production and to determine
management changes from the previous month. MLM was derived by adjusting
milk, fat %, and protein % production for lactation number and stage of lactation
for each cow. Using MLM factors, cow values are adjusted to 150 days in milk
and a second lactation base. However, MLM might not give a good indication of
management changes since season of calving is not considered.

Stanton and Jones (1993) used a simplified version of Everett and Schmitz
(1993) test-day model for developing standard lactation curves for projecting test-
day records in New York dairy herds. In this method, if an animal does not have
a previous record, the predicted current test-day milk will be the standard curve
value. In the case of cows with previous test-day records;

future test-day production = previous test-day production +
(solution for future test-day minus solution for previous test-day).

Using this procedure to project lactations, the mean differences between

33

predicted and actual test-day values for milk yield, fat % and protein % averaged

approximately .158 lb, .004% and .006% and root mean squares of 11.65 lbs, .69%

and .25% respectively. In this study, incorporating previous test-day information

appeared to be more accurate than just using reference curves alone to project

lactations.

Better methods to predict test-day production and to monitor daily

production are still needed.

Advantages of modelling actual test records using test-day models can be

summarized as follows:

i.

ii.

iii.

i.v.

vi.

Methods to project records to 305-day yield will not be necessary.
If cows are grouped according to production on a test-day, such
grouping, if known, can be included in the models describing test-
day records.

For genetic purposes, cows can be evaluated as long as they have at
least one test-day measurement.

The use of BST, if recorded, can be accounted for as an effect on a
specific test-day.

Comparison of performance of cows within herd based on test-day
will be more accurate as animals will be compared on the same test-
day and as such would have experienced the same environment.
Using a TD model would account for variable amounts of

information from different lactations.

34

vii. TD models permit estimates of fixed effects to vary across herds,

stages of lactation.

viii. Differing effects of sampling date can be considered.

ix. A test-day model has the potential to reduce residual variances

which may lead to better genetic estimates.
The disadvantages of using test-day yields would be: the need to adjust for days in
milk; the need to store all of the individual test-day yields on a cow; the
computation of genetic evaluations may take more time due to the increased
number of observations (test-day yields) and more complex statistical models that
might be used for test-day yields.
3.4 Animal Models.

Statistical models applied to data obtained from animals attempt to
describe biological processes and effects quantitatively. The goal is to fit a
practical model that describes the biological situation as closely as possible. By
describing all the factors that may influence the observation on an individual, the
researcher will likely develop a good ideal model.

Henderson (1988) notes that an animal model can take many different
forms depending on the number of measurements per animal, the objectives of the
study and whether genetic relationships exist among the animals in the data. As
such, an animal model can account for repeated records, multiple traits, non
additive genetic effects, litter effects and in addition, a number of environmental

effects.

35

An additive genetic model is an integral part of the mixed linear models
assumed for virtually all animal breeding applications of best linear unbiased
prediction (BLUP). The general form of mixed linear models with one random

factor is as follows

y = Xb + Zu + e [1]
where y = N x 1 vector of observations,

b = p x 1 vector of fixed effects associated with y,

u = q x 1 vector of random effects associated with y,

X & Z = known
incidence matrices of order N x p and
N x q respectively that relate elements of b
and u to elements of y and

e = an N x 1 vector of residual effects with

E(y) = Xb, E(u) = 0 and E(e) = 0 and

'y‘ 'ZGZ’+R ZG R-
V 11 = 62’ G 0
to o R,

 

 

 

 

36

The elements of u can contain additive genetic effects, non additive genetic
effects, maternal effects and permanent environmental effects. The mixed model
equations for the BLUE of the estimable functions of b and for BLUP of u are

therefore:

X’R“X X’R"Z
Z’R"X Z’R“Z+G '1

X’R’ly
Z’R"'y

 

 

Lil =

All multitrait linear models are special cases of the above general linear model.
Suppose there are t traits, one random factor and observations are ordered within

traits then:

y, = 01,325,, ° ° ”Yb

U, ' (111’, “2,, ° ' °’ utl)
e’ - (ell, ez’, . . ., e,’)
111 gul guI . . . gnI
u2 g12I 322I ° ° ° 32:1
V(u)=V' =G=' ' =I>I<G0
_ut, 31:1 g2tI ' ° ° gal,

 

 

 

 

37

811 812 ° - - 811
812 822 ° - ° 82¢

_g1t g2t ° ' ° gttj

 

 

This model assumes no relationships are considered. Therefore, the numerator
relationship matrix A = I. The model also assumes the genetic covariance
between traits for the random variable 11 is not zero. Similarly the residual

(co)variance matrix is as follows:

1

r111 r121 . . . rnI

r121 r221 . . . r2tI

V(e)=R=° ' I>1<R0

tI r2tI . . . ral‘

 

 

hrl

A common feature of all animal models, although they take the above form, is

the use of the additive genetic relationship matrix (A). Diagonal elements of A

38

assuming no epistasis, equal 1+F, where F, is a coefficient of inbreeding for
animal i. When multiplied by the additive genetic variance (0,2), Ao,2 describes
the variance-covariance structure among additive genetic (breeding) values of
animals. From the above general mixed linear model, the mixed model for the

multiple trait individual animal model are as follows (Sehaeffer, 1984, Meyer,

1985).
X/R'IX X’R‘lz b" X’R—IY
= 141

Z’R'lX Z’R'1Z+A‘1* G,‘1 a Z’R’IY
with

.31. rgllA gle ° ' ° gltA-

a2 :8le 822A ° ° ° 321A
V(a)=v'=' ' =A*Go

_atj LgltA thA ° ' ° 311A,

 

 

 

 

where A is the numerator relationship matrix among animals.

The additive genetic animal models have become accepted as the models of

39
choice for the genetic evaluation of animals by utilizing BLUP. Fitting the

additive genetic effect for each animal allows males and females to be evaluated
simultaneously taking into account all relationships between animals. Then, genetic
values of animals without records such as sires or dams, are predicted by
augmenting the mixed model equations with function of the inverse of the
relationship matrix.

3. 4.] Advantages of multiple trait analysis.

Multitrait models are useful to improve the accuracy of genetic evaluations,
especially of lowly heritable traits and to account for selection effects. While
univariate analysis assumes that all correlations between traits are zero, joint
analyses of correlated traits utilizes all traits to obtain estimates for each trait and
is therefore likely to yield more accurate results. Multitrait analysis (MTA)
improves accuracy of parameter estimates by reducing or eliminating bias due to
selection. Usually in animal breeding, one or more traits have undergone
selection. For example in sequential selection, observations on one trait are used
for selection and the selected group of animals is then measured for subsequent
traits. As such, evaluation of the second trait by single trait analysis is potentially
biased by selection on the first trait.

Pollack et al. (1984) and Walter and Mao (1985) examined the ability of
MTA to reduce or eliminate bias due to either sequential selection or selection on
correlated traits. Results indicated that in both cases bias in the single trait 9

evaluation was eliminated by MTA. Sehaeffer (1984) also noted the increase in

40

accuracy of genetic evaluations by MTA as demonstrated by the reduction in
variance of prediction errors (PEV). The ability of MTA to reduce PEV depends
on error and genetic correlations used for the analysis.

A second advantage of MTA is that it allows every animal to be evaluated
for all traits without actually being observed for all traits (Sehaeffer, 1984). This is
due to non-zero genetic and residual covariances among traits that are
incorporated into the analysis. The correlation between errors for the different
traits has a direct effect on the contribution from an observation on a trait
(Sehaeffer, 1984). As the absolute value of the correlation increases, the weight
on observations from other traits also increases. As such, multiple trait
evaluations can be greatly different from single trait evaluations due to
correlations among traits.

A third advantage of MTA is the estimation of variance and covariance
when different variables are observed on different experimental units and the
same linear model is not possible for both traits. Usually components of variances
are estimated between traits measured on the same individual when the same
linear model is assumed for each trait. For example, the genetic covariance
between milk and fat production in dairy cattle is obtained from measurement of
both milk and fat on each cow and the covariances is estimated using the sum of
the crossproduct of the two traits. Sometimes, however, crossproducts of the traits
do not exist. Yearling weight, for example, is measured on male and female

offspring in beef cattle, thus requiring a different model for each offspring.

41

Sehaeffer et al. (1978) demonstrated a procedure for estimation of covariance
components when sums of crossproducts between the traits do not exist.
3.4.2 Disadvantages of Multiple trait Analysis.

The major limitations of MTA is the increased number of equations to be
solved. Costs could be greater because of the time needed to construct and solve
a large set of equations iteratively. The complexity of multiple trait models
increases rapidly beyond two traits. Convergence might be slow as the number of
traits increases. A cost-benefit justification for multiple trait models would be
dependent on the particular model and whether shortcuts can be applied to

calculations.

4.

Assessing the effects of herd production level, lactation number and season
of freshening on shape of lactation curves for test-day milk, energy
corrected milk, and milk components.

42

43
4.1 ABSTRACT

Test-day records of 150,000 Holstein cows from Michigan herds tested
between January 1989 and December 1991 were used to estimate lactation curves
for milk, energy corrected milk (ECM), fat% and protein% in milk. Lactation
curves were estimated for three parity groups; first, second and third or later
lactation within six seasons of calving and three herd production levels resulting in
54 curves for each trait. A fixed classification model considering days in milk
(DIM), age at calving, herd, and season of calving was used. Estimated least
square means for days in milk (DIM) were smoothed by a regression model using
a six degree polynomial.

Differences due to season of calving were significant (P< .001) for all
traits. Peak test-day milk production was depressed by summer calving seasons
with production being lowest for the July-August calving season. Total lactation
yield was depressed for cows calving in summer seasons. For each lactation,
November-February were the best months for calving to maximize total 305 day
milk production.

Time to peak milk production differed with herd production level. Cows in
high production herds tended to peak later compared to low production herds.
For first lactation cows, days to peak milk production after calving was 58, 61, and
67 for low, medium and high production herds respectively. Peak production
increased with herd production level reflecting good management in high A

production herds.

44

The standard lactation curves produced by fitting a sixth degree polynomial
were used to derive factors for adjusting test-day production to 150 days in milk
postpartum. The base group used was second lactation cows calving during
November-December. Adjusting test-day milk for season of calving, lactation and
days-in-milk provides dairy producers with test-day milk averages that can be used

to monitor production changes in a herd from test day to test day.

4.2 INTRODUCTION

Dairy producers enrolled in production recording schemes are aware of the
benefits of monitoring herd and individual cow performance. Dairy production is
enhanced by identifying the downward trends in performance and taking corrective
action to alleviate any decline in performance. Evaluating response to altered
herd management or new technology is critical not only in the short term but for
maintaining long run profitability.

Production can be monitored in different ways e.g., rolling herd average,
daily production, or production per day of life. Unless such indicators are
adjusted for environmental and animal variables, they might not be very accurate
in the diagnosis of herd performance.

Nordlund (1987) developed adjusted fat corrected milk (ACM) to account
for lactation shape and use to monitor production from month to month to
evaluate management changes. The ACM is a crude adjustment for days in milk.

It adjusts test-day FCM to 150 days in milk. The formula for computing ACM is:

45
ACM = (.0432 x lbs milk) +(16.23 x (lbs milk x %fat/100)) + (((ADIM-

150) x .0029) x lbs milk)
where

ADIM is average days in milk,

.29% is the average decline rate per day

and FCM is (.432 x Ibs milk) + (16.23 x lbs fat).

Nordlund's formula, ignores season of calving and assumes a constant decline rate
for lactation which is not correct. Since variation due to season of calving is not
adjusted, estimated changes in management may be in error possibly resulting in
incorrect management decisions.

Steurnergal (1988) developed a formula for management level milk (MLM)
which also is used to monitor production changes from the previous months.
MLM is computed by adjusting milk, fat%, and protein% production for lactation
number and stage of lactation for each cow and computing a herd average. The
base group is second lactation at 150 days in milk. MLM is an improvement over
Nordlund's crude estimate but also ignores variation due to season of freshening.

Lactation curves describe the effect of days in milk and with proper use
can be used to evaluate a herd, to evaluate subgroups within a herd and to
monitor performance changes. Lactation curves generally have two features. The
first one is that curves for different production levels are parallel and secondly
younger cows are more persistent than older cows. The curve for a mature cow

generally declines linearly until advanced pregnancy causes a sharper decline

46
(Kellogg et al., 1977).

Several mathematical functions have been used to describe lactation curves.
Wood (1967) approximated the lactation curve for milk yield with an incomplete
gamma function with three parameters; a associated with the average daily
production, and b and c being coefficients that define the shape of the lactation
curve pre and post peak, respectively. Grossman et al. (1986) modified Wood's
equation by multiplying with sine and cosine coefficients to account for seasonal
effects other than season of calving. In 1988, Grossman and Koops proposed
another lactation curve model, a multiphasic function which considers milk yield
resulting from several phases of lactation.

Lactation curves have been estimated by solving for the least square
estimates for DIM (Keown et al., 1986; Stanton et al., 1992; Shultz et al., 1990).
Seasonal effects on production and reproduction influence both the amount of
milk produced per day and duration of lactation. Therefore, variation due to
season must be adjusted when solving for DIM solutions. McCraw and Butcher
(1976) estimated lactation curves that can be used to determine expected
production of lactating cows based on breed, age (<36 and :36 months), month
of calving and stage of lactation. A fifth degree polynomial was fitted to the DIM
means to construct lactation curves within breed-age-season-subclasses. A
dramatic seasonal influence was observed. Cows calving in summer months
peaked at a much lower level of production and had flatter lactation curves. This

study did not consider herd production level.

47

Keown et al. (1986) estimated lactation curves by solving for least square
estimates for DIM by six seasons of freshening within five herd production groups
and for three lactation groups. Curves were formed by adding an overall mean to
season-stage subclasses. A similar approach was later used by Schultz et al. (1990)
who estimated lactation curves for three parity groups and three breeds. In this
study lactation curves were smoothed by medians of five and repeated means of
pairs. Stanton and Jones (1993) used a model that included herd test-day effects
to solve for DIM solutions for milk, fat and protein for three lactation groups,
three herd production levels and two seasons of calving. Currently such lactation
curves are being utilized in North-Eastern dairy herds to project future test-day
production.

The effect of season or month of calving exerts a considerable influence on
a cow's milk production. The relationship of yield with month of calving is
caused in part by the seasonal variations in feeding and environmental factors such
as heat stress. The quality and quantity of feed or pasture is important for some
countries. In countries where the grazing season is short and cows are housed
indoors for most of the year, the highest lactation yield is produced by cows
calving during autumn and early winter (Danell, 1981). Wunder & McGilliard
(1971), using dairy records from Michigan Dairy Herd Improvement Association
(DHIA), reported that for second or later lactations cows, yield was more for
January to April calvings and less for May to October calvings. I

Since season of calving is an important source of variation in test-day

48

production, it is important to include it in the derivation of projection factors that
either project test—day records to 305-day production or predict individual test-day
records.

Herd and herd production level also have a tremendous influence on the
performance of dairy cows. The effect of herd on production is mainly due to
management which varies from herd to herd. Wiggans (1980) reported on the
importance of considering herd production level when extending lactation records.

The objective of this study was to compute lactation curves for cows calving
in different herd production levels, parities and seasons. The curves will be used
to compute 150-d days in milk adjustment factors that can be used to standardize

test-day milk averages for individual herds to second lactation at 150 days in milk.

4.3 MATERIALS AND METHODS
4.3.1 Data
Test-day records of milk, fat % and protein % of 150,000 holstein cows in
1,800 Michigan Dairy Herds tested from January 1989 to December 1991 were
used in this analysis. Data were supplied by Michigan DHIA. The following
criteria were used for screening records:
i. Age at calving was restricted to 18-36 months for first lactation cows,
30-48 months for second lactation cows and greater than 42 months
for third and greater parities.

ii. Records of herds involved in bST research herds were dropped.

49

iii. First test-day record of a cow's lactation must be less than 60 days in
milk otherwise the cow was dropped from the data set.

iv. lactation must be greater than 180 days in milk.
Tests beyond 305 days were dropped. The decision of restricting the lactation
length to 305 days was based on the fact that test-day records past 305 days in
lactation were scarce and therefore, the lactation curves may not be adequately
smoothed after 305 days in milk.

After editing, ECM was computed for each test-day to give an indication of

the energy value of milk. The following formula was used (Tyrell and Reid, 1965):

ECM = .72 x (Protein% x milk lbs/100) +12.95 (fat% x milk lbs/100)
+.327 x milk lbs.

Preliminary analysis showed the significant (P< .001) effects of herd
production level, season of test and parity on test-day milk production. Therefore,
test-day records were grouped by herd production level (HPL) and six seasons of
calving. Season of calving was defined by two month intervals with January and
February being the first class and November-December being the sixth class.
Three HPL were defined according to the 1990 annual ME milk herd averages.
The year 1990 was chosen based on the fact that it was the middle year of the
data set. The HPL groups were low (<7,718 kg ME milk average), medium
(7,718-9,535 kg ME milk average) and high ( >9,535 kg ME milk average). I

Number of records and means for the three HPL are shown in Table 1.

50
4.3.2 Model

To estimate DIM solution, the following mixed linear model was used for

the univariate analysis of test-day milk yield, ECM yield, fat or protein percentage.

ywm = p. + H, + YRj + DIMk + b,(AGE) + b2(AGE2) + C6,, +
e,,,dm

where

yijklm = TD milk, ECM, fat % or protein %;

H, = Herd, 1,2,..., N;

YRi = Year of Calving, 1988-1991;

DIMk = Days in milk, 1,2,...,299;

Age,jkllru = Age at calving as a covariate with b1 and b2 being the linear

and quadratic age coefficients, respectively;
C0,, = random cow effect with C distributed as N(0, 16,2);
e,ilkmn = random residual with e distributed as N(0, 103).

The Statistical Analysis System (SAS) was used for analyzing the data.
Analysis was done within each HPL-Parity-Season subclass giving a total of 54
estimated lactation curves. Within each of the 54 subsets, days in milk (DIM) was
divided into one day interval classes starting from day 7 to 305. The single day
class interval was used to estimate daily solutions for DIM.

Herd-year and random cow effects were absorbed. An overall mean was
added to DIM solutions to form the DIM least square estimates. The DIM
means were smoothed by fitting a sixth degree polynomial. The predicted DIM

values from the polynomial equation were used as the standard lactation curve

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values for the production traits.
4.4 RESULTS AND DISCUSSION

A sixth degree polynomial was fit to DIM solutions to estimate lactation
curves for test-day milk, ECM yield and fat and protein percentage. The R-square
values ranged from .90 to .9958% for milk and ECM and ranged from .60 to .98
for fat and protein percentage.

4.4.1 Season of freshening.

Table 2 shows the days in milk for peak milk production for the 54 milk
lactation curves that were estimated. Day of peak milk varied with season of
freshening, lactation number and HPL. Peak milk production seemed to occur
early for summer calvings (May-August). Figures 1, 2, and 3 show seasonal milk
curves and demonstrate the variation in time of peak and production due to
season of freshening for second lactation cows calving in low, medium and high
production herds. Depression of daily milk production and the days to peak as
well as amount of peak milk produced for cows calving in summer months is, in
part, due to heat and humidity (Figure 4). This trend was also observed by
Keown et al. (1986). Figure 4 demonstrates some indication of simultaneous
changes in slopes influenced by season of year for cows in various stages of

lactation.

53

Table 2. Day of peak milk production for the different season of calving
groups by herd production level.

 

HERD PRODUCTION LEVEL

 

 

 

SEASON of < 7,718 kg 7,718-9,535 kg > 9,535 kg
CALVING

Days Days Days
Lactation 1
Jan-Feb 58 61 67
Mar-Apr 49 57 63
May-Jun 44 53 58
Jul-Aug 43 53 62
Sep-Oct 51 59 67
Nov-Dec 51 60 67
Lactation 2
Jan-Feb 42 48 49
Mar-Apr 39 45 49
May-Jun 35 41 46
Jul-Aug 36 37 48
Sep-Oct 37 42 47
Nov-Dec 39 43 47
Lactation 3+
J an-Feb 43 48 49
Mar-Apr 41 47 51
May-Jun 39 47 52
J ul-Aug 39 47 52
Sep-Oct 39 46 52

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For example, the decline in production increases between 6/30 and 8/29 for cows
calving in J anuary-February, March-April and May-June. This increase in decline
might be more consistent if calving groups were based on one month, not two
month groupings. Tables 3, 4 and 5 contain peak values for the four traits by herd
level and season of calving for lactations 1, 2 and 3 or greater, respectively.
Figures 5, 6 and 7 show the differences in season curves for ECM, protein
percent and fat percent, respectively for second lactation cows in medium
producing herds. Both protein and fat percent dropped from calving to a nadir 30
to 60 days postpartum. There is also a clearly defined low production point for
both fat and protein percentage later in lactation (about 120 to 180 days
postpartum) for cows calving in fall, winter and early spring (Figures 6 and 7).
Fat% peaked at the beginning of lactation while protein peaked either at the
beginning or end of lactation. Fall and winter seasons tended to promote higher
protein peaks in these herds. For example, peak protein % was 3.67% for
November-December calvings and 3.51% for the July-August (Figure 6) and for
low producing herds, peak protein % for J anuary-F ebruary calvings was 3.76% vs
3.49% in July-August (Table 4). For second lactation cows in all herd production
levels, summer calvings depressed protein % in early lactation. Again low
production in summer could be due to heat stress that results in decreased feed
and reduced roughage intake. However, later into lactation, cows calving in
summer months had higher protein levels (Figure 6). For example, at aboutlSO

days postpartum, protein percentage averaged 3.375 % for July-August calvings

Tal

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59

Table 3. Predicted Peak Test-Day Production for First Lactation
cows for different seasons of calving by herd production
level (HPL)

 

 

 

PEAK
Season Milk (kg) ECM(kg) Fat % Protein %
HPL < 7,718 kg
Jan-Feb 24.32 24.82 4.44 3.72
Mar-Apr 24.39 24.63 4.23 3.61
May-Jun 22.92 23.09 4.11 3.60
Jul-Aug 22.39 22.70 4.25 3.38
Sep-Oct 23.07 23.94 4.26 3.52
Nov-Dec 24.19 25.13 4.38 3.60
HPL 7,718-9,535 kg
Jan-Feb 29.16 29.64 4.53 3.68
Mar-Apr 28.74 28.71 4.34 3.59
May-Jun 27.88 27.70 4.14 3.55
Jul-Aug 26.69 26.93 4.15 3.44
Sep-Oct 27.43 28.28 4.34 3.49
. Nov-Dec 28.76 29.62 4.51 3.62
HPL > 9,535 kg
Jan-Feb 33.58 33.70 4.63 3.61
Mar-Apr 33.06 32.78 4.38 3.55
May-Jun 32.02 31.68 4.29 3.49
Jul-Aug 30.58 30.71 4.25 3.39
Sep-Oct 31.86 32.55 4.53 3.47
Nov-Dec 32.78 33.34 4.66 3.58

 

60

Table 4. Predicted Peak Test-Day Production for Second Lactation cows for
different seasons of calving by herd production level (HPL)

 

 

 

PEAK
Season Milk (kg) ECM (kg) Fat % Protein %
HPL < 7,718 kg
Jan-Feb 31.44 33.44 4.54 3.76
Mar-Apr 31.31 32.46 4.39 3.74
May-Jun 30.03 31.18 4.20 3.59
Jul-Aug 28.71 29.46 5.09 3.49
Sep-Oct 28.31 30.18 4.41 3.63
Nov-Dec 31.03 33.28 4.56 3.72
HPL 7,718-9,535 kg
Jan-Feb 40.11 41.54 4.52 3.60
Mar-Apr 38.38 39.90 4.57 3.65
May-Jun 36.34 37.06 4.20 3.60
Jul-Aug 34.06 34.66 4.23 3.51
Sep-Oct 34.98 36.71 4.37 3.51
Nov-Dec 37.38 39.38 4.66 3.67
HPL > 9,535 kg
J an-Feb 43.86 45.13 4.75 3.66
Mar-Apr 44.43 45.50 4.73 3.55
May—Jun 41.97 41.97 4.32 3.52
Jul-Aug 40.33 40.60 4.24 3.46
Sep-Oct 41.58 43.00 4.56 3.57
Nov-Dec 43.10 44.65 4.72 3.65

 

61

Table 5. Predicted Peak Test-Day Production for Third and later
Lactation cows for different seasons of calving by herd
production level (HPL)

 

 

 

PEAK
Season Milk (kg) ECM(kg) Fat % Protein %
HPL < 7,718 kg
Jan-Feb 33.61 35.59 4.70 3.71
Mar-Apr 33.58 35.06 4.59 3.66
May-Jun 31.61 32.89 4.35 3.58
Jul-Aug 30.13 31.03 4.30 3.52
Sep-Oct 31.01 33.08 4.49 3.62
Nov-Dec 33.35 35.84 4.66 3.69
HPL 7,718-9,535 kg
Jan-Feb 40.06 41.76 4.76 3.67
Mar-Apr 39.42 40.72 4.69 3.62
May-Jun 37.32 38.00 4.44 3.53
Jul-Aug 35.78 36.45 4.40 3.50
Sep-Oct 37.49 39.38 4.67 3.60
Nov-Dec 41.63 41.63 4.84 3.68
HPL > 9,535 kg
J an-Feb 44.13 44.96 4.61 3.56
Mar-Apr 45.94 46.44 4.63 3.53
May-Jun 43.66 43.60 4.58 3.47
Jul-Aug 42.19 42.57 4.41 3.51
Sep-Oct 42.88 44.86 4.91 3.70
Nov-Dec 46.65 47.94 4.81 3.54

 

62

and 3.2% per day for November-December season of freshening for second
lactation cows in medium producing herds. Animals calving in July-August would
be lactating in December and January at 150 DIM, obviously during cooler
months. Fat % also showed a similar pattern (Figure 7). In Table 4 for low
producing herds, July-August season of calving had the highest peak fat %
production. Peaks for fat% tend to occur at the beginning of lactation (Figure 7)
while protein peaks tend to occur at the end of lactation (Figure 6). Higher peaks
are associated with greater lactation mean percentages.

Milk and ECM curves for three seasons, March-April, July-August and
November-December are shown in Figure 8. For all three calving seasons milk
production trailed behind ECM production although both traits followed a similar
trend. Peaks for ECM were greater than milk. Lactation curves for all four traits
are shown on Figure 9 for November-December month of freshening for second
lactation cows in medium herd production level. This gives a visual comparison
between milk, ECM and, fat and protein percentages.

The relationship of yield with month of calving is influenced by the
seasonal variations in feeding and heat stress. To determine the best season for
calving in terms of total lactation for milk production for the Michigan herds, the
DIM values were summed to 305-day value and a ratio for each season of calving
to July-August season was computed. The ratios show the benefit of winter
calving (Table 6). Our findings agree with others (Dannel, 1981; Keown et al.,

1986; Stanton et al., 1992) that highest lactation production is given by cows

63

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Table 6. Ratio of lactation production for calving seasons to July-August
calving season by lactation number, season of freshening and Herd
Production Level

 

 

 

Season Herd Production Level

<7,718 kg 7,718-9535 kg > 9,535 kg

RATIO

Lactation 1
J an-Feb 1.024 1.042 1.050
Mar—Apr 1.008 1.014 1.031
May-Jun .991 1.007 1.020
Jul-Aug 1.000 1.000 1.000
Sep-Oct 1.035 1.027 1.047
Nov-Dec 1.042 1.049 1.050
Lactation 2
Jan-Feb 1.069 1.156 1.056
Mar-Apr 1.025 1.091 1.074
May-June 1.015 1.031 1.020
Jul-Aug 1.000 1.000 1.000
Sep-Oct 1.010 1.033 1.042
Nov-Dec 1.075 1.075 1.055
Lactation 3+
Jan-Feb 1.092 1.096 1.030
Mar-Apr 1.057 1.053 1.051
May-Jun 1.020 1.021 1.017
Jul-Aug 1.000 1.000 1.000
Sep-Oct 1.046 1.080 1.019
Nov-Dec 1.110 1.144 1.017

 

69

calving during the autumn and early winter. For first and third or later
lactations, November-December season was the best season for freshening to
maximize total milk production. Similarly, for the second lactation cows in low
producing herds November-December was also a good season but January-
February was the best for the medium and high producing herds. Wunder and
McGilliard (1971) used data from Michigan to study the influence of season on
milk production. In this study of second and later lactations, January to April
calvings resulted in greater production than May to October season of calving.
4.4.2 Herd Production Level

Time of peak milk production increased with herd production level within
lactation group as shown on Table 2. First lactation cows in low producing herds
calving in NOV-DEC peaked earlier (51 days postpartum) when compared to first
lactation cows in high producing herds (67 days postpartum). The same was
observed for the other lactation groups. Since cows peak higher in high producing
herds, it may take them longer to peak. On the other hand, if feed intake is not
adequate in low producing herds, peaks may occur earlier as body reserves are
used up more rapidly.

Tables 3, 4 and 5 show the actual peak production for all the traits
examined by herd level and season of calving for lactation 1, 2 and 3+,
respectively. Peak milk and ECM production increased with herd level as
expected. For example, for third or later lactations, peak milk production was

33.35, 41.63 and 46.65 for low, medium and high producing herds, respectively, for

70

the November-December season of calving. For protein and fat % it was difficult
to discern a trend for all three herd production levels for the three lactation
groups. Lack of a defined trend could be due to the fact that the herd production
levels were based on milk ME average. For example, peak fat % increased with
herd production level; 4.56, 4.66 and 4.72 % for second lactation cows calving in
November-December in low, medium and high production herds respectively.
However, for July-August season of calving, peak fat % was 5.09, 4.23 and 4.24 %
for low, medium and high producing herds respectively. Such results indicate the
significant interaction between herd management and season of calving for
component percentages. However, some drop in component percentages is likely
resulting from increases in production since they are antagonistic.

Figure 10 demonstrates milk lactation curves within the three herd levels
for first and second lactation cows calving in November-December. As expected,
curves shift upwards from low to high production levels. The curves are closer at
the end of lactation than at peak indicating the interaction between herd level and
days in milk. Figures 11 and 12 demonstrate that fat and protein curves follow
similar patterns across herd levels, but percentages decrease with increase in herd
production level.

4.4.3 Lactation number

When examining the period of peak across lactations, first lactation cows

tended to peak latest and second lactation cows peaked earliest for milk and ECM

(Figures 13 and 14). Lactation curves for milk and ECM were flatter for first

71

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lactation cows, demonstrating their high persistency. This results in first lactation
cows producing more at the end of lactation than second and third or later
lactation cow. Protein % is lower for third or later lactations (Figure 15) while fat
% is lower for first lactation (Figure 16).

4.4.4 Adjusting milk to 150 DIM

For management purposes, dairy producers want to assess their herd’s
production from month to month. In order to do this using daily milk, test-day
production has to be adjusted for stage of lactation, season of calving and
lactation number and then standardized to a common base with a mean computed
for daily milk which can be monitored from month to month. Reference lactation
curves are a useful tool for this purpose. Some DHI organizations in the US
adjust test-day milk to a 150 day DIM value and compute a herd mean for this
adjusted daily milk value. As mentioned above, Steurnegal (1988) and Nordlund
(1987) developed methods to adjust test-day production to 150 days in milk.
However, their methods do not consider season of freshening and herd production
level.

Factors to adjust records to 150 days in milk were developed from the
standard curves computed in this study. Sixth degree polynomial regressions for
the 54 curves are in Appendix I. The second lactation group calving in NOV-
DEC was chosen as the base group. An example of how to use these factors to

adjust a cow's record to the base group at 150 days in milk is illustrated below.

79

4.4.4.1 Illustration of how to compute factors to adjust test day production
to 150 DIM standardized to second lactation cows calving in
November-December.

Cow Amanda is in Parity 1 at 47 days in milk and calved in April in a herd with
an annual ME average > 9,535 kg milk.
Let her test-day (TD) yield = 30.50 kg.

Adjusting her Record to 150 DIM as if she was in her 2nd lactation and calved in
November-December (base group).

Adjusted 150 day production = (TD yield) x Factor
Factor = 36.08 / Standard DIM Yield for
Amanda’s lactation class. (36.08 is from
Table 7)

From Appendix I, Table 9.

Standard yield at 47 DIM = 20.096926 + 0.579507(D) - O.009521(D2) +
0.000073851(D3) - 0.000000307(D‘) +
6.541044E-10(D5) - 5.59630E-13(D6)

= 32.61 kg where D = 47 days in milk

Factor = 36.08/32.61
= 1.106
Adjusted 150 day production = 30.50 x 1.106 = 33.75 kg

Table 7 shows the standard 150 DIM test-day means for second lactation

cows calving in November-December for all three herd production levels.

80

Table 7. Standard lactation test-day values for 150 days in milk for second
lactation cows calving in November-December used as base for
standardized 150 days in milk within three herd production levels.

 

 

Trait Herd Production Level

< 7,718 kg 7,718-9,535 kg >9,535
Milk (kg) 25.51 30.52 36.08
ECM (kg) 26.56 31.41 36.67
Fat % 3.73 3.65 3.58

Protein % 3.22 3.20 3.15

 

81
4.5 CONCLUSIONS

Lactation curves were estimated by fitting a 6th degree polynomial to least
square means for three lactation groups, three herd production levels and six
seasons of freshening. The R-square values ranged from .90 to .9958 for milk and
ECM and ranged from .60 to .99 for protein and fat %.

Season of calving had a significant effect on the shape of lactation curves.
Calving in summer months depressed both time to reach peak milk production
and peak production. For components, a nadir was reached earlier by cows
calving in July-August compared to other calving seasons. November-December
seemed to be the best season for calving for the Michigan Dairy herds in terms of
total lactation yield for milk. July-August season had the lowest total lactation
production for milk. The low production for summer calvers is probably due, in
part, to the depressing effects of heat stress.

Milk and ECM lactation curves did not coincide. Milk tended to trail
behind ECM although following the same shape or trend. Peak milk and ECM
production coincided with the nadir in protein and fat %.

First lactation cows had lower peaks and flatter, more persistent lactation
curves compared to second and third or later lactation cows. For protein and fat
%, third lactation cows exhibited low values when compared to first and second
lactation cows, which were similar in component percentages.

Milk and ECM curves shifted upward with herd production level group.

However, less differences for milk and ECM and were at the end of lactation than

82

at peak for the three herd production groups. Protein and fat % differed little
with increased production levels. Small differences could be due to the fact that
herd production levels were based on ME milk herd average. Breaking these
levels by fat or protein production would enhance the observed differences for
components. This study supports the need to develop separate adjustment factors
for parity, herd production levels and season of calving to account for these

environmental and physiological factors that influence daily milk yields.

5.

Application of a multitrait animal model to predict next test-day milk
production.

83

84
5.1 ABSTRACT

Lactation data consisting of 171,922 test-day milk records for first lactation
Holstein cows tested in 600 Michigan herds from 1988 to 1992 were divided into
ten stages of lactation. Each stage was a 30—day days in milk interval (DIM).
With stages treated as ten separate traits, a multiple trait animal model (MT A)
was used to estimated the phenotypic variances and covariances among these traits
within three herd production levels. The model for each trait contained fixed
effects of season of calving by DIM, season of test by temperature-humidity index
and age at calving, and random additive genetic effects. Phenotypic (co)variances
between traits were used to predict next test-day milk yield deviations for
individual cows from standardized lactation curve values. This method was
evaluated using 50 randomly selected herds within each herd production level.
Test-day milk deviations were predicted using either 1, 2 or 3 previous test-day
deviations for a cow. Predicted test-day production was the sum of the predicted
deviation and the expected standard lactation curve value.

Biases in predicting test-day deviations averaged near zero for the overall
population of 50 herds and within herd-testdays when 3 previous test-day
deviations were used. Biases were greatest when using only 1 previous test-day
deviation. For the low herd production level, overall population mean biases
were -.311, -.132 and -.005 kg when using either 1, 2 or 3 previous test deviations
respectively. The corresponding root mean square errors did not differ much-

(3.32, 3.12, and 3.19, respectively). The traits or days in milk intervals predicted

85

most accurately were between 120-270 days. Biases and root mean
square errors were similar for medium and high production herd groups.

Same predictions were made using slopes of standard lactation
curves and the previous test-day weight. These predictions resulted in larger
mean biases with greater root mean square errors. For low producing herds, the
overall mean bias was .487 kg with a root mean square error of 3.87 kg when
using a slope from a curve estimated from season of calving by DIM solutions
using an animal model. The bias was even larger (1.13 kg) with predictions from
the slope of a standard curve which was fit by a sixth degree polynomial model
and ignored additive genetic effects. Results were similar for the medium and

high herd production levels.

5.2 INTRODUCTION

Dairy managers need to accurately evaluate milk production responses
resulting from management changes or the implementation of new technologies to
determine if they are cost effective. This is critical to maintaining long-run
profitability, but because comparison with control groups is often not possible on
farms, this task is difficult. In addition, there may be periods when no specific
changes or multiple management changes are made, that require monitoring
production trends in order to effectively evaluate general management and herd
health status. Without control groups, producers are forced to assess produCtion

change of the entire herd or a group of cows from period to period. This is

86

difficult because cows in a herd or group contributing to a day's production vary as
cows freshen or dry off between periods being assessed. In addition, a cow's test-
day yield is influenced by systematic environmental effects such as season of
calving, season of test and herd, and physiological factors such as stage of
lactation, age and number of days open. Importantly, stage of lactation, season of
test and days open change between periods for each cow. A within herd
standardization of test-day yields for all these effects allows comparison between
periods and between individual cows within a herd. Making these adjustments is
useful for management and selection purposes.

Currently, several methods are being used to account for stage of lactation
by adjusting daily milk to 150 days in milk (McCraw and Butcher, 1976;
Steuernagel, 1988; Nordlund, 1987). Steuernagel also adjusts for age and parity.
Only McCraw and Butcher (1976) included season of calving, which influences
production peak and rate of decline. None included herd production level which
may also influence rate of lactation decline.

Summarizing test-day records into a single measure, lactation yield, as is
common practice has some deficiencies. Adjustments to a 305-day cumulative
value for systematic environmental effects such as herd, season and age of calving
can be done but it would be difficult to adjust for systematic effects specific to
individual test days making up the 305 day record. Such factors include the effects
of temperature, relative humidity, pregnancy, use of bST and disease. It would

require accurate start and stop times for disease, use of bST, etc., to get accurate

87
test interval estimates of milk production from which to compute 305-day

production.

The problem of accurately comparing daily milk production has resulted in
requests by feed consultants and veterinarians for a better system to monitor
production changes in dairy herds. A useful system would predict production for
the next test day while accounting for physiological changes in each cow and
season of test or change in the environment. The predicted values could then be
compared to the actual values for that test day to determine if there is a
significant change in production.

When predicting unobserved test-day records, it is desirable to make
maximum use of the predictability of the lactation curve and to minimize the error
of prediction from a sample of daily records. Many mathematical models have
been proposed to model lactation production (Wood, 1967; Grossman and Koops,
1988, Deboer et al., 1989, Weigel et al., 1992). Stanton et al. (1992) used standard
lactation curves derived from a test-day model that considers herd level, age at
calving, days in milk, season of calving and herd-testday to predict next test-day
production from the slope and previous test-day weight. Trus and Buttazzoni
(1990) proposed a multitrait model that can be used to estimate missing test-day
weights to compute total lactation production. Their approach subdivided
lactation into ten 30—day periods, treating each period as a trait. For the purpose
of computing total lactation, they used the (co)variances between traits to ‘

compute values for missing test-days (traits). Estimation of a missing last test-day

88

in a lactation was a unique case in their method in which only prior tests are used
to estimate the missing last test. This method provides the basis to estimate next
test-day production at any point in the lactation using (co)variances from prior
observed individual test yields. There are several advantages to using multitrait
models. The major advantage being simultaneous consideration of more than one
trait to obtain the phenotypic, additive or residual relationships between the traits.
The objective of this study was to use phenotypic (co)variances computed
between ten 30—d stages of lactation classes to predict phenotypic production
deviations for individual cows for the next test day using either 1, 2 or 3 previous

test-day deviations.

5.3 MATERIALS AND METHODS

5.3.1 Data

Data were 171,922 test-day milk records of first lactation Holstein cows
calving in 600 Michigan herds and tested between 1988 and 1992. Herds with less
than 80 cows were not used. Cows with completed 305 d lactations were used
with test-day (TD) yields greater than 305 days in milk (DIM) excluded.
Lactation records were deleted if first reported test-day had greater than 60 DIM
or age at calving was different from 18 to 36 months. Records with highly
improbable TD yield were deleted. Herds were grouped into three herd
production levels based on 1990 annual ME milk herd averages as defined in

section 4.3. A summary of the number of observations and means for TD milk

89
yield are given in Appendix II, Table 1.

Weather data was obtained from the Michigan State University
Climatology Center and merged with test-day data. The weather data included
hourly observations of dry bulb and dew point temperature.

5.3.2 Model

To determine the fixed effects of season of calving, age and temperature-
humidity index on test-day milk yield, a single trait animal model was run within
each of three herd production levels. Six, two-month season of calving classes
were defined as J anuary-February ,..., November-December. Classes of days in
milk were formed by 3-day intervals up to day 150 and then S-day intervals up to
305 days in milk. Nine classes for age at calving in months were defined as 18-20;
21-22; 23-24; 25-26; 27-28; 29-30; 31-32; 33-34; and 35—36. Three seasons of test
were defined as December to April; May to August and September to November.
Temperature-humidity index (THI) ( Standards, American Society of Agriculture
Engineers, 1991) was computed from the following formula:

THI = 41.2 + tdb + .36 x tdp
where: tdb = mean daily dry bulb temperature (°C)

t,1p = mean daily dew point temperature (°C)
Mean daily temperatures were averages of 24 hourly measurements. THI provides
a reasonable measure of the combined effects of humidity and air temperature.
Seven classes of THI were defined as : < 30, 30-40, >40-50, >50-65, >65-70,

>70-75 and >75. Preliminary analysis showed that previous day THI had more

90
influence on test-day yield than THI for the day of test. Therefore, THI was

lagged by one day. The single trait animal model used was:

yijump = p. + HYRi + SDIMi + SO'I'I‘HIk + AGEl + am + pn
+ cijldmnp [1]
where
yijklmnp = the pth test-day milk record for a cow in HYR i;
HYRi = the ith herd-year subclass;
SDIMi = the jth season of calving by days in milk subclass for a
cow on the pth test-day with j = 1,2,...,468;
SOTI‘HIk = the kth season of test by THI subclass for a cow on
the pth test-day with k = 1,2,...,20;
AGE, = 1th age at calving for a cow with l = 1,2,...,9;
a,m = random additive genetic effects pertaining to cows,
sires and dams, with a as N(0, A0,,2 );
pm = random permanent environmental effects for each cow
with p as N(0, lo”) and
eijklmnp = random residual effects with e as N(0, 10,”)
5.3.2.1 Estimating (co)variances between test intervals

DHIA test-day records making up a cow's lactation where classified into ten
30-day days in milk intervals. Test-day yields within each interval were treated as
separate traits. A second model, a multitrait animal model, was used to estimate

the (co)variance between the ten intervals. This second model included the fixed

91

effects used in the single trait model [1]. Ten traits were defined but they could
not be analyzed simultaneously. Simultaneous analysis of more than two traits in
multitrait models could not be run because the number of equations to solve
increased and convergence was not be reached. Since, the objective was to
predict any test-day using information from 3 or less previous tests, traits were

grouped into groups of four as shown below.

TRAIT
TRAIT l 2 3 4 5 6 7 8 9 10
l x x x x
2 x x x x
3 x x x x
4 x x x x
5 x x x x
6 x x x x
7 x x x x

Then, (co)variances for each set of four trait combinations were computed two
traits at a time. For example, in the first set, the 2 trait combinations were trait 1
and 2, trait 1 and 3, and trait 1 and 4. The sampling variance of trait 1 was
estimated by averaging the three variances. Fixed effect classes (days in milk,
season of test and THI) differed for the ten traits of a cow since these effects

were test-day specific.

92

The multitrait model was:

 

 

 

y = Xb +20: +6 [2]
where
y = yi is a vector of test-day milk records on traits i and j;
yi
bi . . . .
b = 1s a vector of constants for traits 1 and j;
3;
Xi 0 . . . . . . .
x .-. IS a deSIgn matrix corresponding to fixed effects of tralts 1
O X.
l
andj;
“i
a = is a random vector of additive genetic effects for traits i
a.
J o
andj;
2i 0 '
Z = is a design matrix corresponding to the random
0 j
additive effects of traits i and j and
Ci
6 = is a random vector of residuals for traits i and j.
C

vectors a and e were from multivariate normal distributions with expected values

E(y) = Xb, E(a) = 0 E(e) = 0 and

93

3i A811 A812
aj Ag12 Ag22

A is the numerator relationship matrix among animals. The relationships

considered were based on sires and dams. Inbreeding was not considered.

Similarly
e Ir Ir

R = V i = n ij = 1*R0
ej Irij Irjj

 

 

The mixed mode] equations for the multiple trait individual animal models are:

X’R"X X’R"Z
Z’R"X Z’R"Z+A"1*G'1

(3

6t

_ X’R’ly'
- Z’R‘ly

 

The above models were solved by a Derivative-Free Restricted Maximum
Likelihood (DFREML) algorithm (Meyer, 1989b). The DFREML procedure
relies on the repeated use of Gaussian elimination in conjunction with sparse
matrix techniques to evaluate the log likelihood function (L) using a convergence
criterion of 108. Number of iterations to reach convergence varied from 100 to

300.

5.3.2.2

94
Predicting next testoday production

From the solutions of the above equations, the population parameter

estimates R and b are used for prediction of test-day production of a cow using

the following procedure:

First compute:

where

e0 = Yo ' E(yo) = Yo'Xb

eo is a vector of 1,2, 3 observed deviations for previous test-day yields of a
cow.

yo is a vector of 1, 2 or 3 previous TD milk yields (traits) of a cow.

E(yo) or Xb is the expected yield for the previous 1, 2 or 3 traits for an
average cow in a cow's herd subgroup class.

Let ep be a vector of unknown or predicted deviations for the next test-day
and yp be the predicted TD milk yield. So previous or observed phenotypic
deviations were defined as the difference between the expected
standardized TD yield (Xb) and the previous observed TD milk yield (yo).
The expected standard TD yield for each test-day of a cow is the sum of
her class solutions for season of calving by DIM, age at calving and season
of test by THI, plus a herd deviation. So Xb is a within herd subclass
average. The herd deviation is a five year herd average computed as the
mean of individual cow TD milk yields minus solutions from the three fixed

effects (season of calving by DIM; age at calving and season of test by

95
THI). The addition of this deviation to Xb makes Xb specific for a herd as

the deviation accounts for the difference between a herd's production level
and the average production for the herd production level group of the
herd. As a result,
E (yo - Xb) = 0 and
E (yp - Xb) = cl, = 0 for the average of all cows in a herd on a
test-day, i.e., the expected average of previous and predicted
deviations for cows in a herd is zero.
If average ep varies from zero, this suggests a change has occurred, possibly a
management change which has influenced the production of cows in the herd.

Henderson (1988) demonstrated the following procedure to predict missing

residuals:
e = R I R 'le l3]
P 0P 00 0
where Rop = submatrix of the residual (co)variance matrix (R)
corresponding to intervals with missing observations
R00 = submatrix of R corresponding to observed records

This method can be used to predict the deviation (ep) for the next test day from
one, two or three previous observed test-day records. Since the goal was to
estimate phenotypic deviations, the phenotypic (co)variances are used. An

unobserved test-day record was therefore predicted as:

yp = x6+ep [4]

96
In practice the test-day yield being predicted would be today's yield or a recent

yield so that the one day lagged THI is available and the actual yield for the test-
day is known.
Figure 1 illustrates 3 previous deviations (traits 1-3) for a cow in a herd

and the comparison of the predicted TD milk yield (trait 4) with the actual test-

 

 

  
   
  
     

 

 

 

 

 

 

 

 

 

 

 

day yield.
30
7 Previous tests I
A 25 for cow I
O) c .
f.
i Ii
20 U . 4,_ I Actual I 7
.. a <—| Predicted |
15 i i : : : I
1 2 3 4 5
, Test day (Trait)
-- Herd Standard -a- Previous milk
at Predicted milk -0- Actual milk

 

 

 

Frigu 1. Prdctg s iolroc from deavions.

To test this method of prediction, prediction biases were computed for

cows in 50 randomly selected herds within each herd production level using the

97

five year data set. Biases for each cow were computed as observed deviation
minus predicted deviation:
bias = e,- e, [5]

Root means square errors (RMSE) of the prediction were approximated as the
standard deviation of the mean biases (Stanton et al., 1992). Mean biases and
RMSE were computed 1) across herds, DIM intervals (traits) and Herd-TD, 2)
within herd across all cows and traits; 3) within herd test-days and 4) within each
trait across herds. Since the objective of the study is to assess how well this
method predicts the herd's current test-day average, the within Herd-TD biases
will be critical to evaluate.
5.3.2.3 Prediction of next test-day using lactation curve slopes

TD production was also predicted in a more traditional way using the slope
of standard lactation curves. First, the slope was computed between the previous
and current test-day by dividing by the standard TD milk (from a standard curve)
for the current DIM of a particular cow by the standard milk for the previous test-
day DIM of the cow. Standard curves represented six seasons of calving and three
herd production levels. The previous TD production was then multiplied by the
slope to predict the current TD record.

In this study, standard curves were computed from the method discussed

previously in section 4.3.2 and from the single trait animal model in section 5.3.2.

98
5.4 RESULTS AND DISCUSSION

5.4.1 Age at calving

Figure 2 shows the effect of age at calving on milk production for the three
herd production levels. The solutions are shown in Appendix II, Table 2. In all
cases, age effects on milk tended to increase with increasing age at calving.
However, the age solutions for the low herd production level were much smaller
as compared to those of the medium and high production levels. This shows the
need to develop separate age adjustment factors for different production levels.
Everett and Schmitz (1993) showed that within herd age effects were different
from global population age effects. He developed a TD model that will compute
intra-herd age effects.
5.4.2 Season of test by temperature-humidity index

Appendix II, Table 3 shows the temperature and the THI ranges for the
twelve months of the year averaged over five years. Figures 3, 4 and 5
demonstrate the influence of season of test-THI on test-day milk for low, medium
and high production herd levels, respectively. For the December to April season,
drop in milk production was highest for THI class 6 and 7 (>65-70 and > 70-75)
For May-August, the threshold THI was 70. Beyond a THI of 70, TD milk
production started to decline. However, the same THI class tended to be more
favorable in high producing herds for September-November test-season as seen by
the increase from .01 to 2.5 kg/day. This season class had few test-days with THI

above 70. Classes in the extremes for each season of test had fewer observations.

99

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:oil 2:.omzl 26...;
025.20 2 mg

 

on vn mm cm mm em um NN
_ _ _ _ _ L _ _

 

IIII

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(5)1) Noun'los )l'llW cu

100

 

SEP-NOV

 

    
       

 

 

 

 

 

 

 

 

 

(5x) NOIin‘IOS )I'IIW or

/,, .—

Temperature-Humidity Index Class

idity index within season of test on milk

production of first lac

perature-hum

re 3. Effect of tem
producing herds

101

 

 

 

SEP—NOV

. MAY-AUG

DEC-APR

 

Mi
i
.

.
//«

- /_

 

/c
/.

///////// i

 

lass
milk production of first lacta

mperature-Humidity Index C

i.

idity index within season of test on

gum 4. Effect of temperature-hum
medium producing herds

~

(6») NOan'IOS mm or

 

 

 

 

102

 

 

 

 

 

 

 

   

 

 

(6x) NOIln‘IOS mm or

5
E
3i
‘3
g
E
,,
5i:
E

5 6
Temperature-Humidity Index Class

4

Figure 5. Effect of temperature-humidity index within season of test on milk production of first lactation cows in

high producing herds

103
5.4.3 Phenotypic and Residual correlation among DIM interval traits

Table 1 shows the phenotypic variances, covariances and correlations
among the DIM interval traits for TD records from cows in low producing herds.
Phenotypic variances tended to be higher for the first two tests and tended to
increase towards the end of lactation. Phenotypic covariances were higher for
adjacent traits and decreased for traits further apart. Phenotypic correlations
followed a similar trend. For example, the phenotypic correlation between traits
one and two was .60 and .51 between traits one and four. The estimated
correlations were, however, lower than the correlations reported by Trus and
Buttazzoni (1990). The differences could be due to different models used. Trus
and Buttazoni (1990) used a fixed effect model which ignored the random effects.
Highest correlations for adjacent traits were observed after peak production or 90
DIM (traits 4 to 8).

Residual (co)variances and correlations are shown in Table 2 for the low
herd production level. Residual correlations tended to be lower for early lactation
and slightly increased in magnitude for later tests. The magnitude of the residual
correlations were similar to those obtained by Trus and Buttazoni (1990).
Residual covariances tended to be lower for traits further apart. This probably
suggests there will not be much gain in predictions using traits that are far apart

as the strength of their correlations is weaker.

104

Table 1: Phenotypic variances (diagonal), covariances (above

diagonal) and correlations (below diagonal) among TD
milk weights in ten 30-day days in milk intervals for first
lactation cows in low producing herds.

 

 

 

 

 

TRAIT
TRAIT 1 2 3 4 5 6 7 8 9 10
1 22.86 13.02 10.54 11.66
2 .60 20.54 12.33 11.32 10.8
3 .50 .62 19.25 12.28 11.03 10.24
4 .51 .58 .64 19.71 12.71 12.70 10.45
5 .55 .58 .67 18.74 12.72 11.84 10.58
6 .56 .67 .68 19.28 16.18 14.33 10.20
7 .58 .63 .74 19.06 13.70 11.88 10.87
8 .59 .70 .72 18.49 15.74 12.19
9 .59 .68 .75 18.57 12.25
10 .57 .65 .69 19.75
Table 2. Residual variances (diagonal), covariances (above diagonal) and
correlations (below diagonal) among TD milk weights in ten 30-day
days in milk intervals for first lactation cows in low producing
herds.
TRAIT
TRAIT 1 2 3 4 5 6 7 8 9 10
1 16.97 5.94 9.37 5.93
2 .41 16.38 10.10 8.32 7.78
3 .52 .59 15.98 9.11 8.67 7.65
4 .39 .50 .65 14.29 9.47 9.46 7.32
5 .52 .56 .71 12.02 8.72 5.15 5.92
6 .48 .71 .69 15.22 9.81 8.24 7.82
7 .53 .44 .64 14.12 7.59 9.60 6.64
8 .45 .69 .59 12.58 9.39 5.46
9 .62 .63 .65 14.46.1033
10 .57 .46 .69 15.21

 

105

 

 

 

 

 

Table 3. Phenotypic variances (diagonal), covariances (above diagonal) and
correlations (below diagonal) among TD milk weights in ten 30-day
days in milk intervals for first lactation cows in medium producing
herds.

TRAIT

TRAIT 1 2 3 4 5 6 7 8 9 10

1 24.27 13.97 11.23 10.70

2 .58 24.63 14.04 12.17 16.71

3 .49 .64 21.80 1437 14.03 12.16

4 .45 .57 .67 23.61 16.31 22.37 13.16

5 .59 .62 .69 22.90 14.76 13.76 12.08

6 .58 .74 .70 22.23 15.46 13.78 12.39

7 .61 .64 .71 20.89 14.71 13.84 12.45

8 .58 .66 .70 21.34 15.23 15.30

9 .59 .65 .71 21.73 16.02

10 .56 .64 .70 24.97

Table 4. Residual variances (diagonal), covariances (above diagonal) and
correlations (below diagonal) among TD milk weights in ten 30-day
days in milk intervals for first lactation cows in medium producing
herds.

TRAIT

TRAIT 1 2 3 4 5 6 7 8 9 10

1 19.21 5.76 5.42 4.38

2 .37 18.31 12.09 5.71 11.25

3 .33 .65 13.90 9.12 7.61 5.98

4 .30 .38 .59 15.51 11.22 15.61 5.28

5 .54 .59 .79 14.94 6.62 6.35 7.72

6 .41 .69 .52 15.37 6.40 8.96 8.32

7 .39 .46 .52 15.92 9.98 10.36 9.22

8 .48 .57 .61 16.30 11237.85

9 .50 .59 .64 16.30 12.90

10 .56 .50 .67 19.76

 

106

Table 5. Phenotypic variances (diagonal), covariances (above diagonal) and
correlations (below diagonal) among TD milk weights in ten 30-day
days in milk intervals for first lactation cows in high producing

 

 

 

 

 

herds.
TRAIT
TRAIT 1 2 3 4 5 6 7 8 9 10
1 24.26 14.23 11.70 9.45
2 .57 26.27 16.31 13.79 12.66
3 .48 .64 23.78 15.58 14.58 13.18
4 .40 .56 .66 23.41 16.25 14.41 14.66
5 .51 .61 .68 24.22 17.05 16.30 14.95
6 .55 .63 .69 24.71 17.59 16.68 18.13
7 .59 .65 .71 25.20 18.13 17.02 15.98
8 .60 .67 .72 25.11 18.95 18.24
9 .61 .66 .73 25.84 19.53
10 .58 .66 .73 29.88
Table 6. Residual variance (diagonal), covariances (above diagonal) and
correlations (below diagonal) among TD milk weights in ten 30-day
days in milk intervals for first lactation cows in high producing
herds.
TRAIT
TRAIT 1 2 3 4 5 6 7 8 9 10
1 21.99 11.47 8.15 7.40
2 .53 21.72 11.12 10.88 9.04
3 .40 .55 19.37 10.28 10.64 9.40
4 .36 .51 .56 19.10 12.45 9.75 7.64
5 .43 .54 .62 19.55 11.72 10.30 10.66
6 .48 .53 .62 18.83 118310.94 10.91
7 .45 .56 .63 18.62 13.15 11.86 10.30
8 .54 .57 .66 19.84 13.34.1216
9 .54 .58 .66 20.06 12.03
10 .49 .57 .62 22.58

 

107
Although phenotypic and residual variances tended to be higher for medium and

high producing herds (Tables 3, 4, 5, and 6), the correlations were of the same
magnitude and followed a similar trend as those estimated for low producing
herds. For all herd production levels, highest residual correlations between

adjacent residuals tended to occur at the center of lactation.

5.4.4 Predicting current test-day milk using one, two or three previous TD
records
5.4.4.1 Low Producing Herds

Table 7 shows the mean biases from five years of data from the 50 herds in
the low production level when deviations were predicted from either one, two or
three previous test deviations. Overall means reflect the average bias for cows
across all herds for 5 years, 1988-1992. Herd means reflect average bias for cows
within herds across all years and Herd-TD reflects averages within herd-testday.
Root mean squares errors are averages for within Herd and within Herd-TD.

Using only the previous test to predict the current TD deviation was less
accurate than using two or three previous tests (Table 7). Mean biases were
smaller when three previous tests were used and largest when only one previous
test. Overall population bias was reduced by about 96% when three previous TD
deviations were used instead of using only two tests. Within HERD-TD biases
averaged -.352 kg, -.210 kg, and -.037 kg when predicting from one two or three
tests, respectively. The negative signs show that there was a tendency of the
method to overestimate the deviations. Although the bias was improved by. using

more information to predict, the RMSE from using either one, two or three

108

previous tests did not differ much. So the variance of prediction within Herd-TD
deviations was similar when using one, two or three previous tests. As expected
the variance is less for within Herd-TD than within Herd or for the overall
population. The expectation is that the average bias for a herd on a test—day is
zero. This is because Xb was adjusted for average production of the herd over
time. Therefore, herd average c9 and c0 on test day are expected to be zero with
a difference between the two or bias of zero. However, the expected deviation of
individual cows would depend on their performance in a herd. If previous
deviations of each cow were adjusted to average zero, their ep would have an
expectation of zero. This likely would reduce RMSE for within Herd-TD.

Within trait biases and RMSE are also shown on Table 7. Trait 7 to 9
(181-270 DIM) were predicted more accurately than other parts of the lactation
curve. Prediction of early and peak production which occurred at 60-90 DIM was
least accurate as reflected by bias and RMSE. This is probably because in early
lactation the correlation among the DIM intervals were lower than after peak.
Variation in physiological events in early lactation likely contributes to lower
correlations.

Appendix 11, Tables 4, 5 and 6 show the minimum, maximum, mean and
SD of the observed and predicted test-day deviations when using either one, two
or three previous tests for low producing herds.

Tables 8 and 9 show the prediction biases obtained by using the slope of

standard curves estimated by an animal model and a multiple regression model

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112

that did not consider animal relationships. The results show that smaller biases
are obtained by using standard lactation curves from an additive genetic animal
model (Table 8) suggesting that considering the additive genetic effects provides
more precise estimates for the fixed effects. When mean biases where compared
to the prediction from the multitrait animal model (MTA) (Table 7), the results
show that the MTA is a more accurate method. The one advantage of this MTA
method is that a cow's previous performance on 1, 2 or 3 separate test-days is
used to predict current test-day performance and this performance can be adjusted
for effects specific to each test-day such as temperature-humidity index.

5.4.4.2 Medium Producing Herds

Table 10 shows the mean biases and the RMSE for prediction done in
medium producing herds using the MTA method. Again for this group using
three previous TD deviations resulted in lower biases. However, RMSE were
larger when using three previous tests versus one or two previous tests. The
RMSE were larger than in low producing herds.

When looking at individual traits, traits 3 through 6 (61-180 DIM) had the
lowest mean bias and RMSE. Trait seven (181-210 DIM) was poorly predicted,
and had the highest RMSE when 3 previous traits were used. The reason for such
poor prediction for trait seven is unknown. However, one can speculate that the
poor prediction is due to the phenotypic (co)variances used for prediction of this
trait. The increased RMSE of trait seven is contributing to the increase in RMSE

for the overall population, Herd and Herd-TD. Potentially, the RMSE would be

113

in line with values for the low herd production group if trait seven had a RMSE
similar to other traits. The bias for trait ten (270-305 DIM) was also higher. The
magnitude of the observed and predicted deviations from using one, two or three
previous tests are shown in Appendix 11 (Tables 7, 8 and 9).

Results from predictions of test—day deviations using slopes from standard
curves are shown in Tables 11 and 12. Results were similar to those from the low
herd production group. Using a slope from lactation curves estimated from an
animal model was more accurate than slope estimated from a model ignoring
additive genetic effects. The MTA method was most accurate but the RMSE
resulting from using three previous deviations was larger than values from the two
slope methods.
5.4.4.3 High Producing Herds

Tables 13, 14 and 15 show the results of the prediction for high producing
herds. In this group, the trend was similar to the other two groups. There was a
tendency for the MT A method to slightly overestimate the actual production or
deviations. The poorest method again was predicting from a slope resulting from
a model that ignores additive genetic effects. Appendix 11, Tables 10, 11, and 12
contain the magnitude of the observed and predicted deviations from using one,
two, or three previous tests.

Few results have been reported on the use of a MTA approach to predict
test-day production. Trus and Buttazzoni used the same method to predict

missing TD records, but their model was a fixed effect model and also included

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117

DCC. They found that adjacent residuals tended to do a better job of predicting
missing observations. The method, however, also tended to overpredict total
production as seen in this study. Deviation of 90-100 kg from observed total
lactation yields were reported. Herd production level was not considered.

Stanton et al. (1992) projected test-day records using standard lactation
curves and a previous record. This is similar to the approach in this study using
slopes. In their study, a TD record was predicted by a adding the difference in
pounds between the current and previous DIM solutions of the standard curve to
the previous TD record of a cow. For the cows with no previous record the TD
record was estimated by the lactation curve. In their study the mean bias was
.158 lbs and the standard deviation of the bias averaged 11.65 lbs. Again, the
prediction were not done within herd production level. Applying the method to
all herds might be misleading as the method might be less precise for certain herd
production levels.

Everett and Schmitz (1993) developed a method that projects management
level milk within a herd. However, Everett considered herd-testday effects and
DCC. Fixed effects are unique within herds. In our study global fixed effect
solutions are used for individual herd. If individual herd solutions can be used,

the MTA method might be more precise.

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121
5.5 CONCLUSIONS

Lactation test-day milk yields were classified into ten traits based on 30-day
DIM intervals. A multitrait animal model was used to estimate the (co)variances
among these traits. A procedure of Henderson (1988) for estimating residuals for
missing records was used to estimate the phenotypic deviations for next test-day
yield of cows using either one, two or three previous tests. Using three previous
tests was most accurate with one test being the least accurate in predicting next
test-day deviation. Thus more information used to predict the current test, the
better the prediction.

The study included the fixed effect of THI to accurately account for the
temperature-humidity influence on test-day production.

Traditional methods that predict next test-day yields from slopes were less
accurate than the MTA approach. The study showed that an animal model
probably gives better estimates of the fixed effects thereby estimating lactation
curves more accurately. Biases from predictions using a slope from curves
estimated with models that ignore additive genetic effects were much larger as

compared to slopes from curves estimated by an animal model.

122
6. SUMMARY

This research assessed the influence of herd production level, season of
calving, age at calving, season of test and temperature-humidity index on test-day
milk production of first lactation cows.

The first study revealed the influence of season of calving, herd production
level and parity on lactation curve shapes. Lactation curves were estimated as
least square means for days in milk (DIM) fit with a sixth degree polynomial for
six seasons of calving within three lactation groups and three herd production
levels resulting in 54 curves. Lactation curves for cows calving in the summer
season classes showed lower peaks as compared to other seasons. The time to
peak was also reduced for cows calving in summer. November-December was the
best season for calving in the Michigan dairy herds to maximize total lactation
yield for milk. For milk fat and protein percentages, a nadir was reached earlier
by cows calving in July-August as compared to other calving seasons.

First lactation cows were more persistent, peaked later and had flatter
curves as compared to second, third or later lactations. Cows in high producing
herds peaked higher than those in lower herd production levels.

From this study it is obvious that when extending part lactations, different
factors are needed for different seasons of calving, herd production levels and
lactation groups. The results of the first study helped in the design of the
second study in which the objective was to use a multitrait animal model (MTA)

method to predict next test-day milk using either 1, 2 or 3 previous test-day

123

records. The uniqueness of this approach was the use of MTA and the inclusion
of a test—day's temperature-humidity index in the model.

Age at calving effects on test-day milk differed for the three herd
production levels. T est-day milk production tended to increase with increasing age
at calving. Effects were much smaller for lower production herds than for
medium and high production herds.

The interaction between season of test and temperature-humidity index was
significant. For the December to April season of test, THI above 65-70 causes a
decrease in milk yields. For the May to August season, the threshold occurred
beyond 70.

The MTA method of predicting test-day production was compared to
prediction using slopes computed from two methods. The MT A method was
superior in the three herd production levels. With the MTA, using three previous
tests to predict current test-day was more accurate than including one or two
previous tests.

Of the two methods used to compute slopes, the method that used an
animal model gave more precise estimates of the fixed effects and less bias in
predicting test-day production.

The MTA method can be recommended because it:

1. allows for inclusion of effects specific to a test-day, i.e., temperature

humidity index;

2 allows the inclusion of effects specific to a cow on a test-day, i.e.,

124

bST and pregnancy status;

3. accounts for additive genetic effects in the estimate of fixed effects

and

4. Allows for the inclusion of more information on a cow, i.e., more

than one previous test.

From the MT A model, average TD deviations for a cow could be used for
culling. With this model, genetic parameters of the different parts of the lactation
curve are also obtained. However, results from selecting for a specific stage of
lactation are not known.

The MTA model gives the potential to use estimated individual cow
additive genetic effects and permanent environmental effects. If these are
computed, a more accurate comparison of individual cows for culling purposes will
be possible.

In the future, it is recommended to assess the inclusion of reproductive
parameters such as days carried calf and days open as they may improve
predictions. Days carried calf (DCC) depresses milk production from about 240
days until the end of lactation (Everett and Schmitz, 1993). Therefore its
inclusion in the MTA method may improve the accuracy of prediction of test-day
records at the end of lactation. In addition, adjusting previous observed test-day
deviations on individual cows to average zero would result in an expectation for
their predicted test-day deviation (ep) of zero. This adjusts for cow's ability within

herd. This would likely result in lower RMSE for within Herd-TD.

7. APPENDICES

125

JAN -FEB
MAR-APR
MAY-J UN E
J UL-AUG
SEP-OCI'

NOV-DEC

J AN-FEB

MAR-APR

MAY-JUNE

JUL-AUG

SEEP-OCT

NOV-DEC

JAN-FEB

MAR-APR

MAY-JUNE

J UL—AUG

SEP-OCT

NOV-DEC

126

! APPENDIX I
Days in milk polynomial regression coefficients for
milk, ECM, fat % and protein %

MILK (kg) : HERD MEAVG < 17000 lbs
PARI'I'Y l

18.560200 + 0.26977703) - 0.004552036) + 0.000035725036) . 0.000000156 (136) +
3.59363510036) - 3.36825513036)

17.450885 + 0.36739803) . 0006773(D6) + 0.000054021036) - 0000000223036)
+ 4.605589510036) - 3.76038513036)

18.904490 + 0.23389503) - 0.004697036) + 0000040285(D6) - 0.000000181036)
+ 4.141675510036) - 3.83373513036)

17.721787 + 0.28291903) - 0.005987036) + 0.000054770036) - 0000000254036)
+ 5.805767510036) — 5.22181513036)

18.562957 + 023901703) - 0004512036) + 0.000038046036) - 0.000000165036) +
3.507899510(D6) - 3.507899510(D6)

17.504233 + 036448403) - 0007211036) + 0000065637036) - 0.000000308036)
+ 7.114372510036) - 637785513036)

PARI'I'YZ

25.844901 + 033732003) - 0.006915036) + 0000059100036) - 0.000000265036) +
5937625510036) - 520445513036)

23.387810 + 051191203) - 0.011282036) + 0000104036) - 0.000000487036) +
1.135116559036) - 1.0349512(D6)

25.146559 + 034077703) - 0.007935036) + 0000073650036) - 0.000000353036) +
8.447547510036) - 7.99941513036)

23.164802 + 038723403) - 0.009074036) + 0000085296036) - 0.000000399036) +
9.066441510036) — 7.96913513036)

24.492228 + 025281303) - 0005579036) + 0.000048794036) - 0.000000214036) +
4.5641510(D6) - 373672513036)

24.032090 + 046557703) - 0010667036) + 0.000103036) - 0000000508036) +
1216224859036) -1.1328E-12(D‘)

PARITY 3 +
26.436420 + 042220003) - 0.008536036) + 0.000073439036) - 0.000000333036)
+ 7.57916510036) - 6.78889513036)

25.285906 + 051254303) - 0.010804036) + 0000095008036) - 0000000432036) +
9747421510036) - 8.6045513036)

26.626050 + 030984503) - 0006347036) + 0000050694036) - 0000000212036) +
4516075510036) - 3.85783513036)

24.197644 + 0.381015(D) - 0008205036) + 0000070968036) - 0.000000310036)
+ 6671917510036) - 5.58441513036)

25.392358 +.364694(D) -.00779840:36) + 0000071081036) - 0000000322036) +
7.194993510036) - 6.34615513036)

26.055479 + 046960003) - 0010392036) + 0000097264036) - 0000000465036) +
109165659036) - 10003512036)

JAN -FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

JAN-FEB

MAR—APR

MAY-JUNE

JUL-AUG

SEP-OCT

NOV-DEC

JAN-FEB

MAR-APR

MAY-J UNE

JULA-AUG

SEP-OCT

NOV-DEC

127

ECM (kg) : HERD MEAVG < 17000 lbs

PARITYI

22.778425 + 008984603) - 0001189036) + 0.000004421036) - 599503359036)
+ 6.409924512036) - 1.6825514036)

20.869979 + 021956403) - 0004216036) + 0000030821036) . 0000000105036)
+ 1576549510036) 4075521514036)

21.939104 + 009763103) - 0002692036) + 0.000027439036) - 0000000137036)
+ 3.303809510036) -3.13183E-l3(D‘)

20.578665 + 013604003) - 0003016036) + 0000028524036)
+ 3141009510036) . 283706513036)

21.836948 + 21.83694803) - 0001985036) + 0000014767036) - 5.36100658036)
+ 8.428101511036) - 390564514036)

21.306508 + 023509903) - 0005102036) + 0000048994036)
+ 5.754831510036) - 5.28509513036)

- 0000000136036)

- 0000000241036)

PARITYZ

31.749282 + 013843003) - 0003495(D6) + 0000028190 036) - 0000000117036) +
2387195510036) . 1.89162513036)

28.780355 + 0.288612(D) - 0007235036) + 0000064922 036) - 0000000285036)

+ 6003695510036) . 4.83283B-l3(D6)

29.653278 + 015828903) . 0005086036) + 0000053593036) . 0000000278036) +

6.965777510036) - 676923513036)

26.962741 + 020537703) - 0005462036) + 0000053788036) - 0000000260036)+

6047019510036) - 537239513036)

29.909067 + 003332003) - 0001108036) + 0000005790036) - 2.19820859036) +
6.62357511036) 4352005513036)

30.203679 + 026093703) - 0007177036) + 0000073567036) - 0000000374036) +

9170771510036) - 8.6724513036)

PARI'I'Y 3+

33.355291 + 018019503) - 0004551036) + 0000039300036) — 0000000178036) +
4092341510036) - 3.73547513036)

31.636575 + 026864003) - 0006649036) + 0000056770036) - 0000000236036) +
4.62487510036) - 335336513036)

31.804189 + 011293903) - 0003564032) + 0000033631033) - 0000000161036)
+ 3.760605510036) - 3.43528513036)

29.265988 + 013592503) - 0.003265(D2) + 0000025970036) - 0000000102036) +
1858697510036) - 118834513036)

31.230555 + 015022003) - 0003773036) + 0000030782(D6) - 0000000124036)
+ 2354011510036) 1.6851513036)

33.157787 + 0 22872903) 0006236036) + 0 000060718036) - 0 000000297036)
+ 70352865 10036) 6.45467513036)

JAN -F EB
MAR-APR
MAY-JUNE
JUL-AUG
SEP-OCT

NOV-DEC

JAN -FEB
MAR-APR
MAY-JUNE
J UL-AUG
SEP-OCT

NOV-DEC

JAN -FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

128
FAT % : HERD MEAVG < 17000 188

PARI'I'Yl

4.784496 - 005550903) + 0001034036) - 0000009586036) + 4554140558036)
- 04835510036) + 9.277578514036)

4.502008 - 004265103) + 0000741036) - 0000006887036) + 355942958036) -
9.23435511036) + 929375514036)

4.317131 - 0032555(D) + 0000399032) - 0000001800036) + 292680359036) .
6.149101513036) + 4.0475515(D6)

4.288202 . 003983203) + 0000804036) - 0000007243036) + 3363068258036) -
783487511036) + 7234014514036)

4.481086 - 003616403) + 0000658036) - 0000005766036) + 2.675900158036)
- 635356511036) + 6081416514036)

4.608210 -0.036717 (13) + 0000568036) -0000004271036) +

1641195758036) - 3.11611511(D6) + 2383076514036)

PARITYZ

4.813068 - 004286203) + 0000728036) - 0000006510036) +
- 70106511036) + 6.184371514(D6)

4.697708 . 005021103) + 0000947(D6) - 0000009585036) + 5.265206558036) -
143253510036) + 1.503961513(D6)

4.409835 - 0032147(D) + 0000408036) - 0000001924036) + 2952750559036) -
2.982046E -12036) + 9.17493515(D6)

5.330250 - 003910403) + 0000781036) - 0000006843036) + 3023255158036)
- 6.59472511(D6) + 5.636696El4(D°)

4.680708 - 004346903) + 0000815(D6) - 0000007357036) + 3.4788688E-8(D‘) -
834476511036) + 8.019642514(D6)

4.816938 - 0041601(D) + 0.000678(D6) - 0000005522(D6) + 233094458036) -
4.9039511(D6) + 4133813514036)

3059296558036)

PARITY 3+

5.026725 - 005187303) + 0000828036) - 0000006765036) + 2.835069958(D6) -
563272511036) + 4094646514036)

4.912596 - 0.052036(D) + 0000919036) - 0000009007036) + 4.878429258036) -
132045510036) + 138406513036)

4.570462 . 003335103) + 0000356(D6) - 0000001014(D6) + 290802159036) -
1951924511036) + 263086514036)

4.601333 - 005015903) + 0000994(D6) - 0000009010036) + 4175190758036) -
963258511036) + 8.765212514036)

4.733951 - 003976403) + 0000712036) - 0000006386036) + 3.006775358(D6) -
715439511036) + 6.799363514036)

4.950589 - 004578403) + 0000745036) - 0000006223036) + 2.729498958036) -
602727511036) + 5.346951514(D6)

JAN -FEB
MAR-APR
MAY-JUNE
J UL-AUG
SEP-OCT

NOV-DEC

J AN -F EB
MAR-APR
MAY-JUNE
J UL-AUG
SEP-OCT

N OV-DEC

J AN-F EB
MAR-APR
MAY-JUNE
J UL-AUG
SEP-OCT

NOV-DEC

129

PROTEIN % : HERD MEAVG < 17000 lbs
PARI'I'Y 1

3.774972 - 003999703) + 0.000814036) - 0000007698036) + 3.707609258036)
- 873484511036) 4» 801896514036)

3.667156 - 003579203) + 0000702036) - 0000006492036) + 3172341658036)
- 7.71211511036) + 7304939514036)

3.628918 - 003617903) + 0000717036) - 0000006492036) + 3183416658036)
- 806405511036) + 8185511514036)

3.658257 - 003597003) 4» 0000726036) - 0.000006089036) + 2541481558036)
- 525126511036) + 4305274514036)

3.771255 - 004291203) + 0000971036) - 0000009618036) + 4.772775558036) -

116649510036) + 1120757513036)

3.866311 - 004321303) + 0000886036) -0000008334036) + 3972198658036)
- 933081511036) + 8624617514036)

PARITYZ

3.826484 - 004178003) + 0000843036) - 0000007924036) + 3.7753091E-8(D‘) -
8.73349511036) + 7808622514036)

3.812229 - 004555503) + 0000971036) - 0000009868036) + 5217901158036) -
135517510036) + 1361626513036)

3.702129 - 003680303) + 0000703036) - 0000006153036) + 2925028358036) -
721558511036) + 7161339514036)

3.730167 - 004125203) + 0000844036) - 0000007325036) + 3.18403958036) -
6.84506511036) + 5809646514036)

3.927049 - 005075603) + 0001173036) - 0000011815036) + 5903452658036) -
144026510036) + 1372719513036)

3.991473 - 004742603) + 0000971(D6) - 0000009222036) + 4.454032758(D6) -
106108510036) + 9958419514036)

PARITY3+

3.849888 - 004503003) + 0000904036) - 0000008496036) + 4057359158036)
- 9.43379511036) + 8.498215514036)

3.790675 - 004592103) + 0000933036) - 000000903036) + 4562412258036) -
113527510036) + 1094378513036)

3.737808 - 004253303) + 0000812036) - 0000007105036) + 3345835858036) -
813045511036) + 7942724514036)

3.808120 - 004819803) + 0000993036) - 0000008753036) + 3877725458036) —
852576511036) + 7.429068514036)

3.944287 - 0054921(o) + 0001265036) - 0000012824036) + 6.476884558036) -
160038510036) + 1545867513036)

3.995065 - 005116803) + 0001054036) - 0000010057036) + 4871605758036) -
116248510036) + 109039513036)

JAN-FEB:

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

JAN ~FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

J AN-FEB

MAR-APR

MAY-JUNE

J UL—AUG

SEP-OCT

NOV-DEC

130
MILK (kg): HERD MEAVG 17000-21000 lbs.

PARITYl

19.570864 + 045057703) - 0007895(D6) + 0000066832036) - 0000000309036) +
7302981510036) - 6.91163513(D6)

18.778936 047583003) - 0008179036) + 0000064390036) - 0000000269036) +
5.719319510036) + 5.719319510036)

19.687441 + 041782703) - 0007634036) + 0000063429036) . 0000000278036)
+ 6219799510036) - 55889513036)

19.042971+ 040374803) . 0007742036) + 0000068342036) - 0000000313036) +
7.131615510(D6) - 6.43836513036)

19.142833 + 040907403) - 0007500036) + 0000065416036) - 0000000302036)
+ 7017259510036) - 653759513036)

18.925611+ 047769103) 0008625036) + 0000074139036) - 0000000336036) +
7594587510036) - 6.77215513(D6)

PARITY2

29.608509 + 061342603) - 0012519036) + 0000112(D6) + 0000000519036) +
1201653759036) - 109708512036)

27.875609 + 0.61342603) - 0.012519036) + 0000112036) - 0000000519036) +
1.201653759036) - 1.09708512036)

27.508181 + 055721703) - 0012090036) + 0000111033) - 0000000531034) +
1270287359035) - 120118512036)

25.603216 + 052180403) - 0011116036) + 0000101036) - 0000000469036) +
1083015459036) - 983891513036)

26.779859 + 050498003) - 0010762036) + 0000098220036) - 0000000462036) +
1.079234359(D6) - 99734513036)

26.139598 + 068536303) - 0014624(D6) + 0000136036) - 0000000649036) +
1526419859036) - 1.40865512(D6)

PARI'I'Y 3+

29.107826 + 058881903) -0011060036) + 0000090951036) -0000000396036)
+ 8633663510036) - 7.42822513(D6)

26.748951 + 071378703) - 0013943036) + 0000119036) - 0000000534036) +
119717859 036) - 10561512036)

28.152215 + 049187503) - 0009019036) + 0000069662036) - 0000000285036) +
5937944510036) - 494134513036)

25.768233 + 055658903) - 0010716036) + 0000088702036) - 0000000382036) +
8262542510036) - 707023513036)

26.682172 + 061544503) - 0012252036) + 0000106036) - 0000000479036) +
1074833359036) - 955233513036)

26.055479 + 0.469600(D) - 0010392036) + 0000097264036) - 0000000465036)
+ 109165659(D6) -10003512(D6)

JAN -FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

J AN -FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

JAN-FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

131

ECM(kg): HERD MEAVG 17000-21000 lbs.
PARITY 1

24.368318 + 026498003) . 0004822036) + 0000041142036) . 0000000196036)
+ 4893202510036) - 493094513036)

23.044177 + 027225503) - 0.004427036) + 0.000029041036) . 881076958036) +
1066412510036) -1.9894E-14(D‘)

22.944299 + 027560903) - 0005665036) + 0000051847036) - 0000000243036)
+ 5639921510036) - 516291513036)

22.476565 + 022620803) - 0004279036) + 0000038470036) - 0000000181036)
+ 420192510036) - 3.84745513(D6)

23.254221 + 023083403) . 0003909036) . 0.003909036) - 0000000136036) +
299993510036) - 267745513036)

23.737637 + 030744303) - 0005840036) + 0000051519036) - 0000000240036)
+ 5561407510036) - 505068513036)

PARITYZ

36.649567 + 034607103) - 0008074036) + 0000073312036) - 0000000344036) 4-
8050983510036) - 7.46363513036)

35.007667 + 0.34607103) - 0.008074036) + 0000073312(D6) - 0000000344036) +
8.050983510036) - 7.46363513036)

32.397490 + 036621103) - 0.009535036) + 0000097395036) - 0000000499036) +
1251052559036) - 122084512036)

30.809021 + 025704303) - 0005747036) + 0000051692(D6) - 0000000239036) +
5.458405510036) - 485765513(D6)

33.078773 + 025031703) - 0005679036) + 0000049772036) - 0000000225036)
+ 503196510036) - 445235513036)

33.859664 + 039375403) - 0009415036) + 0000089466036) - 0000000431036) +
1018052159036) - 937552513036)

PARITY 3+

37.344581 + 029159703) . 000624403) + 0000050187036) - 0000000211036) +
4.460289510036) - 3.73083513036)

34.432751 + 041036203) - 0008816036) + 0000072977036) - 0000000303036)
+ 6061931510036) - 458365513036)

34.440378 + 024375903) - 0.005462036) + 0000046818036) - 0000000210036)
+ 4.705644510036) - 412732513036)

31.793790 + 026849903) - 0005166036) + 0000039866036) - 0000000163036)
+ 0000000163036) - 266805513036)

34.110845 + 033099803) - 0006918(D6) + 0000057513036) - 0000000247036)
+ 5255278510036) - 4.38899513(D6)

33.157787 + 022872903) - 0006236036) + 0000060718036) - 0000000297036)
+ 7035286510036) - 045467513036)

J AN -F EB
MAR-APR
MAY-JUNE
J UL-AUG
SEP-OCT

NOV-DEC

JAN -FEB
MAR-APR
MAY-JUNE
J UL-AUG
SEP-OCT

NOV-DEC

J AN -F EB
MAR-APR
MAY-JUNE
J UL-AUG
SEP-OCT

NOV-DEC

132

FAT %: HERD MEAVG 17000-21000 lbs.
PARITY 1

4.865069 - 005450203) + 0000919036) - 0000007790036) + 3.421014858036) -
7.27908511(D6) + 5906713514036)

4.688932 . 005610603) + 0001049036) - 0000010165036) + 5.30920158(D6) -
138205510036) + 1399669513036)

4.358283 - 003485303) + 0000441036) - 0000002252036) + 5.141191459(D6) -
408351512036) - 649727516036)

4.433903 - 004692403) 4» 0000913036) - 0000008126036) + 3.739374758036) -
8.61623511(D6) + 785637514036)

4.629036 . 004648503) + 0000875036) - 0000008075036) + 3.936668458(D6) -
970948511036) + 9535162514036)

4.810550 - 004744903) + 0000756036) - 0000005984036) + 2.480844358036)
- 517695511036) - 5.17695511036)

PARITYZ

4.848686 - 005342803) + 0000885036) - 0000007509036) +
- 711653511036) + 5824799514036)

4.905476 - 0.05342803) + 0000885036) — 0000007509036) + 3316857258036) -
7.11653511(D6) + 5.824799514036)

4.403694 - 003072103) + 0000315036) - 0000000616036) + 5.38952259(D6) -
2800368511036) + 2800368511036)

4.544226 - 005209103) + 0001051036) - 0000009757036) + 4662950158036) -
11127510036) + 1048623513036)

4.751836 - 004751403) + 0000875036) - 0000007912036) + 3.759950958036)
- 90256511036) + 8635875514036)

5.016570 - 005786303) + 0001013036) - 0000008875036) + 4072863958036) -
940255511036) + 8679679514036)

3316857258036)

PARITY 3+

5.129514 - 005893503) + 0000960036) - 0000008079036) + 3.573506858036) -
7.77436511(D6) + 6542564514036)

5.060528 - 005937703) + 0001017036) - 0.000009409036) + 4811201358036) -
1.24633E-10(D’) + 1267446513036)

4.706764 - 004111303) + 0000496036) - 0000002298036) + 2875427659036) .
7367225512036) + 169265514036)

4.737814 — 005541903) + 0001048036) - 0000009326036) + 4299414358036) -
993091511036) + 90874514036)

5.000339 - 005335403) + 0000912036) - 0000007837036) + 3583751258036) -
83669511036) + 7856924514036)

4.950589 - 0.04578403) + 0000745036) - 0000006223036) + 2.729498958036) -
6.02727511(D6) + 5.346951514(D6) '

J AN -FEB
MAR-APR
MAY-JUNE
J UL-AUG
SEP-OCT

NOV-DEC

J AN-FEB
MAR-APR
MAY-J UN E
J UL-AUG
SEP-OCT

NOV-DEC

J AN-F EB
MAR-APR
MAY-JUNE
J UL-AUG
SEP-OCT

NOV-DEC

133

PROTEIN Q3: HERD MEAVG 17000-21000 lbs
PARITY 1

3.697221 - 003569403) + 0000708036) - 0000006522036) + 3086334858036)
- 720023511036) + 658618514036)

3.633067 - 003666203) + 0000756036) - 0000007191036) + 3.556250158(D6)

- 868749511036) + 8.249526514036)

3.574368 - 003335503) + 0000673036) - 0000006179036) + 3046408158036) -
7.71046511036) + 7.788858514036)

3.626643 - 0.03569403) + 0000713036) - 0000005921036) + 2.451877158036) -
504122511036) + 4.126954514(D6)

3.755259 - 004430903) + 0001024036) - 0000010199036) + 5036383958036) -
121759510036) - 1.21759510036)

3.879384 - 004324803) + 0000896036) - 0000008576036) + 4171488458036) -
100137510036) + 9.457497514(D6)

PARIY'I‘Z

3.681860 - 004247603) - 0042476036) - 0000008020036) 4» 3850805558036)

- 904778511036) + 8275931514036)

3.736440 - 0.04247603) + 0000853036) - 0000008020036) + 3850805558036) -
9.04778511036) + 8.275931514036)

3.643926 - 003531703) + 0000678036) - 0000005950036) + 2833470258036) -
700354511036) + 6969587514036)

3.769015 - 004420203) + 0000913036) - 0000008046036) + 3573940458036) -
791489511036) + 6975244514036)

3.840897 - 004818503) + 0001130032) - 0000011468033) + 5.765316458(D6) -
1.41543510035) + 1358236513036)

3.961791 - 004882903) + 000103303) - 0000010077036) + 4979586658036) -

121001510036) + 1153619513036)

PARITY 3+

3.805760 - 004259903) + 0000836036) - 0000007685036) + 3604263258036)
- 82537511036) + 7.338162514036)

3.783588 - 004743403) + 0000974036) - 0000009436036) + 4.754629658034) -
1.18156510(D5) + 1140423513036)

3.699887 - 004090703) + 0000780036) - 0000006807036) + 3199198858036) -
7.76842511036) + 7588073514036)

3.791871 - 0047954(D) + 0000982(D6) - 0000008602036) + 3.794944758036) -
834002511036) + 7294862514036)

3.928558 - 005546303) + 0001275036) -0.000012834(D3) + 6422833358036)
- 157193510036) + 1504522513036)

3.995065 - 0.05116803) + 0.001054036) - 0000010057036) + 4.871605758036) -
1.16248510036) + 1.09039513036) '

JAN-FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

J AN -FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

JAN-FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

134

MILK (kg): HERD MEAVG > 21000 lbs.
PARI'I'Y l

20.891444 + 0550796(D) - 0009002(D6) + 0000072003 036) - 0000000316036)
+ 7114211510036) -6.4471E-l3(D‘)

20.096926 + 0.579507(D) - 0009521036) + 0000073851036) - 0000000307036)
+ 6541044510036) - 55963513 (136)

19.964633 + 058988403) - 0010657036) + 0000091094036) .
0000000413036)+ 9523384510036) - 8.77709513036)

19.391712 + 052256403) - 0009081036) + 0000075194036) - 0000000328036)
+ 7227282510036) - 635738513036)

20.546637 + 0509218(D) - 0008689036) + 0000072230036) - 0000000319 (D6)
+7.118654510036) - 634228513036)

20.208420 + 058062503) - 0010198036) + 0000087644036) - 0000000401036)
+ 9216724510036) - 8.38377513513036)

PARITYZ

30.123020 + 075266603) - 0014650036) + 0000128036) - 0000000589036) +
1359752559036) - 123986512036)

30.699820 + 0752666036) - 0.014650036) + 0000128(D6) - 0000000589036) +
1.359752559036) - 123986512036)

29.374789 + 071925303) - 0014470036) + 0000129036) - 0000000602036) +
1.408811759036) - 129956512036)

28.315268 + 066360703) - 0012935036) + 0000112036) - 0000000508036) +
1158277159036) . 104837512036)

28.600983 + 0.7414503) - 0015026036) + 0000136036) - 0000000641036) +
1509112959036) -1.40639512(D6)

29.051251 + 080692103) - 0016444036) + 0000149036) - 0000000702036) +
1636848559036) - 149943512036)

PARITY 3+

30.395120 + 0.75266603) - 0014650036) + 0000128036) - 0000000589036) +
1.359752559036) - 1.23986512(D6)

29.655188 + 085839203) - 0016048036) + 0000134036) - 0000000596036) +
1324458659036) -1.1601E-12(D‘)

28.820848 + 075873203) - 0013831036) + 0000115036) . 0000000513036) +
1175084459036) - 107907512036)

28.285681 + 070008903) - 0012384036) + 0000096632036) - 0000000396036) +
8108496510036) - 653259513036)

27.231419 + 081599603) - 0015149036) + 0000127036) - 0000000556036)+
1228383259036) -1.07962512(D6)

30.163300 + 087427903) -0016558036) + 0000142036) - 0000000635036) +
1.419166459036) - 125222512036)

JAN -FEB

MAR-APR

MAY-JUNE

J ULoAUG

SEP-OCT

NOV-DEC

J AN -FEB
MAR-APR
MAY-JUNE
J UL-AUG
SEP-OCT

NOV-D EC

JAN -FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEEP-OCT

NOV—DEC

135

ECM(kg): HERD MEAVG > 21000 lbs.
PARI'I'Y 1

26.411556 + 032202303) - 0005190036) + 0000039782036) - 0000000172036)
+ 3983705510036) . 3.80856513(D6)

24.745699 + 035167703) - 0005331036) + 0000033975036) - 0000000101036)
+ 1180932510036) — 1799514036)

24.074561 + 040049603) - 0007740036) - 0.007740036) - 0000000325036) +
750956510036) - 684651513036)

23.429072 + 0.322281(D) - 0005475036) + 0000045917036) - 0000000205036) +
4630985510036) - 415997513036)

25.831184 + 0.270486(D) - 0004080036) + 0000029800036) - 0000000117(D6) +
2321344510036) - 183353513036)

26.225464 + 0338744(D) - 0006027(D6) + 0000051653036) - 0000000237036)
+ 5.473163510036) . 497381513036)

PARITYZ

39.134899 + 038485903) - 0008270036) + 0000071772036) - 0000000328( 136)
+ 755173913 -10036) - 692746513036)

39.504099 + 0384859(D) - 0.008270036) + 0000071772036) - 0000000328036)
+ 7551739510036) 6.92746513(D6)

35.643039 + 042698103) - 0009839036) + 0000094589036) - 0000000464036)
+ 1.116482459(D6) - 104168512036)

34.266410 + 035119903) - 0006752036) + 0.000056336036) - 0000000252036)
+ 5.723355510036) - 5145513036)

36.252342 + 041808403) - 0008869036) + 0000079302036) - 0000000370036) +
8647921510036) -798219513(D6)

38.291747 + 042143203) - 0009401036) + 0000085067036)
+ 8955862510036) - 794357513036)

- 0000000394036)

PARITY 3+

38.965899 + 0.38485903) - 0.008270036) + 0000071772036) . 0000000328036) +
7.551739510036) - 6.92746513036)

37.821224 + 052177103) - 0010640036) + 0000088128036) - 0000000371036) +
7613819510036) - 597131513036)

36.298880 + 043206803) - 0008884036) + 0000079436036) - 0000000379036) +
9085786510036) - 857625513036)

35.001319 + 036805603) - 0006051036) + 0000040885036) - 0000000143036) +
2380641510036) - 136593513036)

36.416400 + 046913803) - 0008927036) + 0000071718036) - 0000000303036)
+ 6424692510036) - 539581513036)

40.302362 + 046084903) - 0009411036) + 0000079160036)- 0000000347036) +
7574721510036) - 649208513036)

JAN -FEB

MAR-APR

MAY-JUNE

JUL-AUG

SEP-OCT

NOV-DEC

JAN-FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

JAN ~FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

136

FAT % : HERD MEAVG > 21000 lbs.

PARITYl

5.048945 -0.067368(D) + 0001179036) - 0000010363036) + 4.726432958 036)
-1.05468E-10 (136) + 9.100925514036)

4.746303 - 006039403) + 0001136036) - 0000011111036) + 5830615758036)
- 152009510 036)+ 1539698513 036)

4.602926 - 004926703) + 0000781036) - 0000006103036) + 2688889758036)
63316511036) 6139711514 (136)

4.565005 - 005089203) + 0000933036) - 0000008085036) + 3673443358036)
- 8.42399511036) + 7690035514036)

4.900238 - 006075703) + 0.001109 036) - 0000009966036) + 4.705588358 (D6)
- 111824510 036) + 1055021513036)

5.057261 - 006396103) + 0.001105036) - 0000009622036) +
- 10323510036) + 9609434514036)

4434571658036)

PARITYZ

5.183988 - 007050903) + 0001256036) - 0000011261036) + 5248490658036) -
120317510036) - 1.20317510036)

5.162458 - 007050903) + 0.001256036) - 0000011261036) + 5248490658036) -
120317510036) + 1072484513036)

3.622237 - 003741003) + 0000746(D6) - 0000006876036) + 3399920958036) -
859603511036) + 8649698514036)

4.580025 - 005553803) + 0001110036) - 0000010357036) + 4978968358036)
- 119289510036) 112721513036)

4.911130 . 005603203) + 0000987036) - 0000008633036) + 3994643158034)
- 937468511035) + 8804132514036)

5.147496 - 006897903) + 0001258032) - 0000011559033) + 5599920158036)
- 136547510036) + 1324887513(D6)

PARITY 3+

5.050068 - 0.07050903) + 0.001256036) - 0000011261(D6) 5.248490658036) -
1.20317510036) + 1.072484513036)

5.003657 - 006041303) + 0001010036) - 0000009137036) + 4605371258036) -
118552510036) + 1205131513036)

4.963884 - 0.060390 03) + 0000910036) - 0000006558036) + 2521975858036)
-5. 02575511036) + 410649514 (136)

4.775133 - 005895503) + 0001118036) - 0000010127036) + 4.768693358036) -
112529510036) + 1051363513036)

5.300176 + -0.062925(D) + 0001061036) - 0000008991036) + 4048569558036)
- 928613511036) + 8559221514036)

5.279307 - 007596803) + 0001311036) - 0000011440036) + 5258451558036) -
121606510036) + 1.119567E - 13036) ‘

J AN-FEB

MAR-APR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

JAN-FEB

MAR-APR

MAY-J UN E

J UL-AUG

SEP-OCT

NOV-DEC

J AN-FEB

MARoAPR

MAY-JUNE

J UL-AUG

SEP-OCT

NOV-DEC

137

PROTEIN %: HERD MEAVG > 21000 lbs.
PARITY 1

3.649535 . 0.034359 (D) + 0.000660 (D6) . 0000005902036) + 2.723126258036)
- 621586511036) + 5574643514036)

3.593252 - 003496103) + 0000707036) - 0000006549036) + 3148549658036)
- 748975511036) + 6941994514036)

3.551865 - 003344403) + 0000678036) - 0000006238(D6) + 3065388358036)
— 7.70039511(D6) + 770981514036)

3.609378 - 003538403) + 0000693036) - 0000005741036) + 24041958036) .
505605511036) + 4273525514036)

3.730886 — 004439703) + 0001022036) - 0000010212036) + 5072587858036)
- 123419510036) + 1176079513036)

3.858075 -0.045363(D) + 0000952036) -0000009197036) + 4514917658036)
- 109212510036) + 1036456513036)

PARITY 2

3.782083 - 004101203) + 0000800036) - 0000007319036) 4» 3433718558036) -
789735511036) + 7069964514036)

3.669063 - 0.04101203) + 0000800036) - 00000073190366 + 3.433718558(D6) -

7.89735511036) + 7.069964514036)

3.622237 - 0.03741003) + 0000746036) - 000000687036) + 3399920958 (D6) -
859603511036) + 8649698514036)

3.690833 - 004024103) + 0000807036) - 0000006903036) + 2986111858036) -

64751511036) + 5629547514036)

3.894535 - 005399203) + 0001236036) - 0000012413036) + 6197259358036) -
151244510036) + 1442741513036)

3.960364 - 005106403) + 0001065(D6) - 0000010295036) + 5061057258036) -

122588510036) + 1165573513036)

PARITY 3+

3.675863 - 0.04101203) + 0000800036) - 0000007319036) + 3433718558036)
- 789735511(D6) + 7069964514036)

3.735807 - 004479703) + 0000895036) - 0000008416036) + 4121622358036) -
997323511036) + 9.381195514(D6)

3.638324 - 003945503) + 0000759036) - 0000006791036) + 3274298858036) -
8.12292511036) + 806713514036)

3.807478 - 004883703) + 0000992036) - 0000008749036) + 3921757258036) -
880461511036) + 78901514036)

4.037144 - 005725103) + 0001285036) - 0000012752036) + 6316863458036) -
153349510036) + 1457874513036)

3.859189 - 005243803) + 0001095(D6) . 0000010621036) + 5.219204658(D6)
- 126054510036) + 1193026513 (D6)

138

 

 

 

APPENDIX 11.
Table II. 1. Number of records, cows, sires and dams, Mean and
SD for test-day milk yield by herd production level.
HERD PRODUCTION LEVEL
LOW MEDIUM HIGH
Number of herds 200 200 200
Number of records 20,420 58,760 92,742
Number of cows 4,866 12,494 19,921
Number of Sires 635 1,159 1,298
Number of Dams 1,841 4,674 7,960
Mean TD milk (kg) 21.29 25.01 28.94
SD TD milk (kg) 5.34 5.69 6.26

 

 

 

 

 

Table II. 2. Age at calving solutions (SOL) and SE for test-day milk production
of first lactation cows by herd production level
HERD PRODUCTION LEVEL
LOW MEDIUM HIGH
AGE SOL. SE SOL. SE SOL. SE
(months)
18-20 .000 .000 .000 .000 .000 .00
21-22 -1.74 2.81 1.17 1.15 1.917 .66
23-24 -.590 2.81 1.658 1.12 2.543 .63
25-26 -.617 2.80 2.195 1.13 2.912 .63
27-28 .288 2.80 2.439 1.13 3.362 .63
29-30 .320 2.80 2.807 1.13 3.553 .62
31-32 1.00 2.81 2.926 1.13 3.961 .66
32-34 1.33 2.82 3.057 1.15 4.360 .66
35-36 .77 2.82 3.560 1.16 3.849 .68

 

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