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This is to certify that the

dissertation entitled

DETERMINING PARAMETERS OF
ENERGY UTILIZATION IN
DAIRY CATTLE USING DATA
FROM PRODUCTION HERDS

presented by

John P . Walter

has been accepted towards fulfillment
of the requirements for

 

 

Ph.D. degree in Animal Science

7W

 

Major professor

43%»? 7, meg

M5 U i: an Affirmative Action/Equal Opportunity Institution 0- 12771

 

 

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DETERMINING PARAMETERS OF ENERGY UTILIZATION
' IN DAIRY CATTLE
USING DATA FROM PRODUCTION HERDS

'by

John P. Walter

A DISSERTATION

‘ Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Animal Science

1986

ABSTRACT
DETERMINING PARAMETERS OF ENERGY UTILIZATION

IN DAIRY CATTLE
USING DATA FROM PRODUCTION HERDS

by

John P. Walter

Data from 354 Holstein cows in 7 herds, on 4 rations based on production
level, and in various parities were used to estimate the efficiency of
energy conversion for maintenance, lactation, body weight change and
pregnancy. In an attempt to reduce the need for expensive balance
trials and scarce energy chambers, lactating cows from herds in
production were studied, and various indicators of energy efficiency
compared to published reports from animals in energy chambers. For each
cow, the fractions of energy apportioned to various products were
computed over the entire lactation and during periods of positive and
negative energy balance. Over 90% of energy required during a lactation
was for maintenance or lactation. Proportions of net energy and
metabolizable energy intake used for milk production were higher during
negative balance than positive, while expenditures for maintenance were
comparable. Data were adjusted to account for the delay in energy
absorption from feed intake, the amount of residual milk at each
milking, and the infrequency of body weights, and eighteen regression
models were applied. Among the models fitted were ordinary and two-
stage multiple regression models, and models accounting for

autocorrelated residuals. Results indicated that efficiencies during

positive energy balance were more easily and accurately estimated than
efficiencies during negative balance. Multiple regression models were
consistently found to overestimate maintenance and underestimate
lactation requirements. A two-stage model provided estimates closest to
those reported in the literature which were obtained from animals in
energy chambers. Models considering autocorrelation of residuals were
found to better fit daily variations in energy intake, but overall were
not an improvement over the two-stage model. Factors influencing
variation among animals of estimates for four models were examined.
Herd-season effect was determined to be most significant in affecting
coefficients of energy efficiency. Ration, parity, and linear and
quadratic covariates of total milk production over the lactation were

generally not significant.

ACKNOWLEDGMENTS

I'd like to thank my committee for their guidance and support
during my graduate program: Dr. Ivan Mao, Dr. Ted Ferris, Dr. Roy Emery
and Dr. Roy Black. Throughout my program Dr. Mao has been a patient and
wise advisor, but just as much a friend, confidante and sports teammate.
His entire family has been as my own from the moment I arrived, and I'll
always remember their kindness.

So many good friends have encouraged me over the past four years...
in particular, Dennis Banks, Ted Ferris, John Gill, Clyde Anderson,
William Enright and Denis Petitclerc have all made me listen, made me
think, and made me smile. My experience has certainly been richer for
their friendship.

My family, Mom and Dad, and Mary Pat, Mary Jo, Michelle, Chuck,
Tom, Chris, Polli, Carrie and Matt, Lib and Lou, and Paul and Tom have
shown more patience than I could have imagined possible. There is much
of them in everything I do.

Luca Buttazzoni has made numerous suggestions concerning this re-
search. To him for his thoughtful advice, and to the Eli Lilly company
for supplying the data which made this investigation possible, I offer
heartfelt thanks.

And finally, thank you Diane, for the warmth of your love and
understanding, and for the smile that brought a little sunshine to every
day.

A.M.G.D.

ii

TABLE OF CONTENTS

 

I. INTRODUCTION

II. REVIEW OF LITERATURE .

1. Introduction

2. Efficiency of feed conversion

3. Partitioning to useful product

3.

3.2.

W

w

p

1. Energy utilization for maintenance
3.
3
3

1.1. Sources of variation

.1. 2. Estimation of maintenance requirements
.1. 3. Efficiency of maintenance

Energy utilization for pregnancy

. Energy utilization for growth and liveweight change
.3. 1. Energy utilization for growth . . .
.3. 2. Energy utiliZation for weight change in support of

lactation

Energy utilization for lactation

.1. Environmental and genetic factors affecting

energy utilization for milk

3.4.1.1. Quantity of ration

3.4.1.2. Quality of ration

3.4.1.3. Frequency of feeding .

3.4.1. 4. Realized and potential milk yield .

3.4.1.5. Other sources of variation

.4.2. Rev view of endocrine pathways

3.4.2.1. Insulin

3.4.2. 2. Growth hormone

3.4.2.3. Prolactin .

3.4.2.4. Thyroxin

.4.3. Summary of reported efficiencies for lactation

4. Review of models and modeling in ruminant energetics

4.1.

4.2
a
4

Statistical models

Systems models

.2. 1. Systems modeling of feed. intake in cattle
2.

2. Systems modeling of energy exchange and
growth in cattle

iii

10
10
13
14

l6

18
19

23

26

27
27
28
29
3O
31
32
32
32
33
33
34

34

36

38

. 4O

. 42

III.

4.

METHODS OF ANALYSIS

. Description of data
. Partitioning of energy intake into forms of output

. Regression procedures

3.1. Procedures for data manipulation within regression
3.L l. Adjustment of milk weights to approximate
milk synthesis rates . . .
3.1.2. Distributed delay for estimating energy
availability
3.1.3. Estimation of continuous body weight curve
from discrete weights .
3.2 Multiple regressions to analyze energy utilization  by
various products . . . . . .
3.3. Two- -stage regressions using net energy as a measure
of enery intake.

3.4. Regressions considering autocorrelation among residuals

Analyses of variance on estimated coefficients from
selected models

IV. RESULTS AND DISCUSSION .

l.

2.

Partitioning energy intake into forms of output -
Effect of half-life of energy absorption and percentage of
daily residual milk on energy utilization

. Determination of predicted coefficient values from
literature

. Results from regression analyses
4.1. Multiple regression models .

. Two- stage multiple regression models

. Autoregressive models . .
Summary of estimates of partial efficiencies

J-‘l-‘D
DUI-IN

. Analyses of variance from selected models

iv

.‘45

. 45

. 47

. 49
. 49

50

S3

54

57

62

63

64

66

66

68

69

73
75
82
84
89

91

V. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Appendix I. Tabulation of data . . . . . . . . . . . . . . . . . . 99
Appendix II. Descriptions of algorithms used to modify data . . . . 102
Appendix III. Single pass algorithm of Cochrane-Orcutt procedure for
analyzing regression models containing autocorrelated
residuals . . . . . . . . . . . . . . . . . . . . . . 105
Appendix IV. Analyses of variance on coefficients from selected

models . . . . . . . . . . . . . . . . . . . . . . . . 109

LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . 113

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

II.l

II.2

II.3

II.4

II.5

III.1

IV.l

IV.2

IV.3

IV.4

LIST OF TABLES

 

Proportion of metabolizable energy and net energy
intake present in various forms of output

Efficiency of utilization of metabolizable energy
for maintenance (k ): values predicted from the
metabolizability o? the gross energy of the diet
(qm) . . . . . . . . . . . . . . .

Comparison of theoretical and realized net
efficiencies of growth expressed as percentage of
available metabolizable energy .

Regression of liveweight change on milk yield for
heifers at various stages of lactation (Broster et
a1, 1975).

Summary of reported partial efficiencies of
Metabolizable Energy utilization for lactation in
cattle

Summary of multiple regression models fit (model

number in parentheses) and relationships among them.

Percentage of net energy intake used for various
purposes, during periods of negative and positive
energy balance and over the entire lactation .

Percentage of metabolizable energy intake used for
various purposes, during periods of negative and
positive energy balance and over the entire
lactation

Correlations between estimated net energy available
in bloodstream an daily solids-corrected milk
synthesis for various half-lives of energy
absorption and various percentages of daily
residual milk

Comparison of mean estimated regression
coefficients using various half-lives of energy
absorption and various percentages of daily
residual solids-corrected milk .

vi

10

15

22

25

35

59

67

67

7O

70

Table IV.5

Table IV.6

Table IV.7

Table IV.8

Table IV.9

Table IV.1O

Table IV.11

Table IV.12

Mean regression coefficients in models with

dependent variable measured as Net Energy, over

periods of negative energy balance, positive energy
balance, and over entire lactation. Corresponding
standard deviations are parenthesized . . . . . . . . 77

Mean regression coefficients for models adjusted to a
per—unit-metabolic body weight basis, with dependent
variable measured as net energy intake per unit
metabolic body weight over periods of negative energy
balance, positive energy balance, and over entire
lactation. Corresponding standard deviations of means

in parentheses . . . . . . . . . . . . . . . . . . . . 78

Mean regression coefficients in models with

dependent variable measured as metabolic energy,

over periods of negative energy balance, positive

energy balance, and over entire lactation.

Corresponding standard deviations are parenthesized. . 80

Mean regression coefficients in models adjusted to
per-unit-metabolic body weight basis, with

dependent variable measured as metabolic energy per

unit metabolic body weight, over periods of negative
energy balance, positive energy balance, and over

entire lactation. Corresponding standard deviations

are parenthesized. . . . . . . . . . . . . . . . . . . 81

Mean regression coefficients in two-stage models

with dependent variable measured as net energy,

over periods of negative energy balance, positive

energy balance, and over entire lactation.

Corresponding standard deviations are parenthesized. . 83

Mean regression coefficients from models with and
without autocorrelation coefficient, adjusted on a
per-unit-metabolic body weight basis with dependent
variable measured as net energy, over periods of
negative energy balance, positive energy balance,

and over entire lactation. Corresponding standard
deviations are parenthesized . . . . . . . . . . . . . 86

Mean regression coefficients from models assuming
autocorrelation of residual terms adjusted to per-
unit—metabolic body weight basis with dependent

variable measured as ME, over periods of negative

energy balance, positive energy balance, and over

entire lactation. Corresponding standard

deviations are parenthesized . . . . . . . . . . . . . 86

Effect of eliminating cows having extreme
autocorrelation coefficients on means and standard
deviations of means for b0 and autocorrelation
coefficient obtained over entire lactation . . . . . . 89

vii

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

IV.13

IV.14

A.I.1

A.IV.2

Summary table of estimates of partial efficiencies of
lactation (kg) and maintenance (km)

Summary of significance of various factors on
regression coefficients from selected models .

Distribution
weights

Distribution
Distribution

Distribution
averages

Distribution
lactation

Distribution
Actaplanin .

Distribution

of

of

of

of

of

of

of

COWS

COWS

COWS

COWS

COWS

COWS

COWS

Distribution of cows

Analyses
complete

Analyses
complete

Analyses

of variance on
lactation from

of variance on
lactation from

of variance on

two-stage model (14)

among

among

among

among

among

among

among

among

numbers of recorded milk

parities
calving groups

daily milk production

months of initiation of

treatments with

herds

milk levels

estimates obtained over the
model (7)

estimates obtained over the
model (10)

estimates obtained from

Analyses of variance on estimates including
autocorrelation coefficient obtained over the
complete lactation from model (16)

viii

90

92

99

99

99

100

100

100

100

101

109

110

111

112

Figure

Figure

Figure

Figure

Figure

Figure

Figure

II.1

II.2

II.3

II.4

III.1

IV.l

IV.2

LIST OF FIGURES

Representation of the measurement of feed energy
value by Kellner and Armsby (Blaxter, 1962). Note
that to the left of the vertical dotted line
animals are losing body weight. The efficiency of
maintenance (km) is the slope. . . . . . .

Steps involved in the modeling process (Brown et
al, 1981)

Block diagram of cow model (from Forbes, 1983)

Block diagram of energy metabolism in a lactating
dairy cow (Smith et a1, 1979)

Determination of periods of positive and negative
energy balance by weight change throughout
lactation

Predicted vs actual metabolizable energy intake
in models without an autocorrelation coefficient .

Predicted vs actual metabolizable energy intake
in models with an autocorrelation coefficient

ix

14

39

. 41

. 43

61

88

88

I. INTRODUCTION

 

For the past several decades, there has been increasing interest in
the study of animal energetics. Among many possible reasons for the

increase, two are primary:

(1) Rapid advances in the fields of physiology, nutrition, microbiology
and systems science, among others, have enabled scientists to focus
as never before on cellular and tissue function within the animal;

and

(2) Economic pressures have forced the animal industries to consider
efficiency of production as an important factor influencing profit

and to seek ways to improve that efficiency.

However, despite these developments, the study of energetic efficiency
is not without its difficulties. When energy chambers are used to
monitor all energy transactions in domestic livestock, the high cost per
animal prevents a large number from being studied at once. Also, be-
cause the field is still rather young and because there is still an
incomplete understanding of the pathways and mechanics of energy meta-
bolism, many plausible models have been advanced through the literature.
In the case of dairy cattle, there exist at least three economically
important production functions: growth, reproduction and lactation. The
latter function is compounded by milk component percentages (eSpecially
butterfat and protein) which have economic significance. Many different

models to explain the relationship among these systems have been

published, making the choice of an appropriate model for study a .
difficult one. Finally, the interactions of physiology, nutrition,
genetics and other areas within many models can require cooperation
among researchers with expertise in diverse fields. Such teamwork may
be difficult to motivate and maintain.

This study has been a first step in developing methods by which .
geneticists and other scientists wishing to study efficiency can analyze
large bodies of energetics data. As such, it has proceeded in an ex-
ploratory manner and early results exerted an influence on later de-
cisions. The main objective during this research was to investigate
various statistical models relating energy input to output in lactating
dairy cows. These models were applied to data which was not collected
from animals in energy chambers, but from cows kept under field condi-‘
tions at several locations throughout the country.

The purpose of this research was to develop and examine a variety
of potential models for estimating efficiencies of energy utilization
from data collected on a farm rather than from energy chambers. Guiding
the judgement of the relative value of various models we tested were

these concerns:

(1) The model should suggest a meaningful biological interpretation. It
should consider those characteristics which have been shown to
influence energy utilization, rather than utilize complex statisti-
cal procedures whose relationship to energy metabolism pathways is

unclear.

(2) The model should produce results which agree reasonably well with

published results from the same model using data obtained from

energy chamber data.

(3) A model should be equally applicable over an entire lactation. A
cow's energy balance, defined as the rate of energy consumed as
feed less the rate of energy spent for supporting body functions,
will normally vary on both sides of zero throughout her lactation.
The ideal model will apply as well to periods of positive energy

balance as to those of negative energy balance.

It would be difficult to meet each of these criteria with the same
model. Instead they were applied both during model construction and
interpretation of results to decide which ones were superior for use
with field-collected data.

Potential application of this research can be seen along three
broad avenues. For researchers, the ability to monitor the energy
balance and partial efficiencies of research animals without requiring
expensive energy chambers would stimulate more extensive research into
energy utilization. For dairy geneticists, large data sets may now be
collected from many commercial operations having extensive breeding
records. This could facilitate important work concerning genetic para-
meters of efficiency for milk production, weight gain, or pregnancy.
Eventually, the opportunity to develop sire rankings based on efficiency
of production, and ultimately a true economic ranking (considering both
outputs and inputs) may be developed. Finally, for the dairyman, re-
search into the sources of environmental variation for efficiency can
lead to the farmer maximizing his own net profit by tailoring his herd

environment to produce milk, meat and calves most efficiently.

II. REVIEW OF LITERATURE

 

1. Introduction

 

With the help of research conducted by animal scientists, dairy
farming has evolved over the years into a specialized system for pro-
ducing as much milk per production unit (the cow) as possible. While in
the past this method has been sufficient to ensure adequate return to
the farmer, today's economic conditions necessitate consideration of the
efficiency, rather than solely the magnitude, of production. It has
long been presumed that economics of scale exist in milk production, and
therefore that, milk components being equal, a cow producing more milk
is economically superior to a cow producing less. While this belief may
be justified in some instances, clearly there exists the possibility of
increased efficiency of an animal offsetting its lower production, and
therefore yielding a higher net return.

The term 'efficiency' has been defined many ways in the literature.
Fundamental to any definition are the concepts of inputs and outputs.
For economic purposes, these would be weighted by costs and prices,
respectively.. In the context of energetics, inputs and outputs are
measured in units of energy. While it may be conceivable to measure
efficiency as the difference between outputs and inputs measured in
common units, for this study we will adopt the definition of productive
efficiency put forth by Bauman et al (1985b) as the yield obtained of a
product in ratio to the nutritional costs associated with that produc-

tion.

It is clear that, to understand the concept of efficiency, we must
understand the various forms of input and ouput of the animal, and the
relationships among inputs and outputs. This review will summarize much
of the completed research concerning inputs, outputs, and their inter-
action as it applies to ruminants in general, and dairy cattle in parti-
cular.

Because so many physiological functions contribute to the efficien-
cy of bovine metabolism, a complete review of all related published
research could fill many volumes. In the following summary, the litera-
ture will be presented as it relates to three major areas affecting
efficiency research: the efficiency of feed conversion, the partitioning
of energy into useful product, and mathematical and statistical models

useful for investigating energy efficiency.

2. Efficiency of feed conversion

Consideration of inputs to ruminants can be divided into two sec-
tions: the method of evaluation of energy content of feeds or rations,
and the value (in energy terms) of particular feeds, either alone or
associated with other feeds. In the literature, however, these two
sections are closely tied. Therefore this review will consider both the
method and the result of evaluation of feedstuffs for their energy
content.

The relationship among several measures of energy in a feed, based

on its productive value to a cow, is shown in the following equation:

Gross energy
- energy lost in feces -
Digestible energy
- energy lost in urine and methane -
Metabolizable energy
- energy lost as heat increment -

Net energy

It is important to note that each estimates a different utilization of
energy, and they have a heirarchical nature.

DeBrabander et a1 (1982) evaluated six energy evaluation systems
for their ability to predict actual energy available to dairy cows. The
systems they investigated included four which are or were commonly used
in Europe. Also considered were the net energy (NE) system (NRC, 1978),
in use in the United States, and metabolizable energy (ME) system de-
scribed by the Ministry of Agriculture, Food and Fisheries (1975) and
used in Great Britain and Ireland. The ME system used in the United
States is closely related to the latter system. The accuracy of each
system was assessed by regressing the recorded performance of 992 in-
dividuals on the energy intake as computed by each method. They found
that NE tended to overestimate the energy in roughages compared to
concentrates, while also overestimating maintenance requirements. These
faults were not found in the ME system. Part of this difference,
though, may be due to associative effects between specific feeds in the
rations. Sundst¢l et a1 (1980), using sheep to determine the utiliza-
tion of ME for maintenance, found an associative effect between roughage
and concentrate; that is, the actual ME available in a roughage depended

on the content of the entire diet and not solely on its own quality.

This agreed with the findings of van Es and Nijkamp (1969). Research by
Lingvall et a1 (1978), reported in Sundst¢l et al (1980) showed similar
results with lactating dairy cattle: when two groups of cows were fed
identical amounts of ME as grass silage or hay, the group fed grass
silage produced 5-15% more milk. Van der Honing and Steg (1980), in
contrast to findings reported above, reported NE to be readily cal-
culable from ME values, with a coefficient of variation for the estimate
of about 2.5%. Using diets of barley and corn to feed steers, Wainman
et al (1980) found the ME values of the two feedstuffs to be additive
with no evidence of any associative effects.

One difficulty with using ME as a measure of energy intake is the
finding that the efficiency of extracting ME from a feedstuff decreases
as intake increases (Blaxter and Graham 1955). It has been speculated
that this is a result of two separate phenomena:

1. As intake increases, digestibility of a feed decreaSes significant-
ly. Estimates of this decrease range from 2-4% per unit of intake
equivalent to maintenance requirement, (Moe et al 1965, Tyrrell et
a1 1966, Brown 1966); and

2. As intake increases, urine and heat losses, which are associated
with the conversion of DE to ME, are proportionally less (van Es
and Nijkamp 1969).

These two effects tend to offset each other, resulting in decreased
efficiency at high intake levels.

Vermorel et al (1980) reported that the efficiency of utilizing ME
for growth and maintenance was not affected by feeding level, in an
experiment with young calves. Theriez et a1 (1980) duplicated these

results with young sheep. These findings may indicate that ME as a

measure of energy in feed remains accurate over different levels of
feeding. In a discussion paper, van Es (1980) acknowledges the lack of
information on high-producing animals with regard to the effect of
feeding level on ME utilization, but asserts that for rations which
contain less than one-third roughage, the effect of feeding level on ME
content is variable.

Other factors exist which can cause variation in the efficiency of
conversion of gross energy intake into metabolizable energy or net
energy. Nutritionists have not been able to agree on the contribution
of associative effects of feedstuffs to a ration's digestibility. Sup-
porting the results of Wainman et a1 (1980) presented above, Blaxter
(1974) and Garrett (1980) found little deviation from additivity for
rations having wide ranges of forage/grain’ratio and ME content, re-
spectively. However, several studies have found that corn grain fed
with corn silage produces a depression in digestibility greater than
would be expected by considering either separately (Peterson et a1,
1973; Joanning et a1, 1981). Feed additives have been investigated to
increase metabolizability of a ration, especially by reducing the amount
of wasted methane produced as a by-product to microbial fermentation.
Chief among these is monensin, which can reduce methane production by 15
to 31% (Garrett and Johnson, 1983), although its effects on diet diges-
tibility are not clear, ranging from slightly negative to slightly
positive.

There appears to be little disagreement that among-cow variation in
conversion of feed to metabolizable energy is small (Bauman et al,
1985b). The relationship between milk production and efficiency of

energy conversion has also been found to be negligible by several

researchers (Davey et a1, 1983; Trigg and Parr, 1981; Grieve et a1, 1976).
Thus, it seems as though the main source of variation in synthesis of
useful product occurs during the process of partitioning available

energy after it has been absorbed into the bloodstream.

3. Partitioning to useful product

 

In lactating dairy animals, there are typically four major uses of
metabolizable energy which researchers have categorized: maintenance
including heat increment, lactation, pregnancy and weight change. We
will examine the efficiency of producing each of these forms of output.

Flatt et a1 (1970) detailed their research into partitioning of
gross energy intake among various outputs, including feces, urine,
methane, heat, milk and body tissue. From their results, ME intake
(MEI) and NE intake (NEI) were partitioned into various outputs. These
figures for the 12 cows used in their research are shown in Table 11.1.
In this work, NEI and MEI are computed from the animals' gross energy
intakes, taking into account the energy lost through feces, urine and
methane, and in the case of MEI, the additional energy lost in heat
production. For this reason, the totals of output percentages from both

MEI and NET always sum to 100%.

10

 

Table 11.1 Proportion of metabolizable energy (ME) and net energy (NE)
intake present in various forms of output.

 

 

Cow %NE intake as output in %ME intake as output in
Milk Tissue Maint Milk Tissue Maint Heat
Bethel 38.7 16.4 44.9 22.2 9.4 25.7 42.7
Ruby 54.1 2.1 43.8 31.2 1.2 25.3 42.3
Lorna 66.2 1.8 32.0 39.6 1.1 19.2 40.2
Vertis 68.9 -15.8 46.8 39.3 -9.0 26.7 43.0
Doris 53.3 13.1 33.6 29.8 7.3 18.8 44.0
Diana 59.5 6.2 34.3 36.1 3.8 20.8 39.3
Muzzy 67.3 -0.9 33.5 41.4 -0.5 20.6 38.6
Helene 59.3 7.3 33.4 36.3 4.5 20.5 38.8
Martha 55.8 -7.5 51.7 31.8 -4.3 29.5 43.0
June 68.1 -28.0 59.9 38.1 —15.7 33.5 44.1
Shirley 73.4 -28.0 54.6 38.9 -l4.8 29.0 47.0
Bessie 64.0 -8.7 44.7 36.2 -4.9 25.3 43.4

 

3.1 Energy utilization for maintenance

Maintenance requirements, as we will consider them here, consist of
the energy necessary to maintain the basal metabolism, conduct voluntary
body activity, and generate the heat necessary to maintain body temper-
ature (Kromann 1973, taken from National Research Council 1966). Main-
tenance does not take into account excess heat produced by the animal,

nor any form of production.
3.1.1. Sources of variation

Many factors have been examined for their effect on maintenance
requirements. Some of the earliest studies noted a close relationship
to functions of body weight. Rubner (1883) and Meeh (1879) both recog-
nized that using actual body weight to estimate maintenance needs tended
to overestimate requirements, and reported that the ratio of surface

area to maintenance requirements was fairly constant for many common

ll

mammals. Their work was refined by Brody (1945), who determined that
the best statistical fit of basal heat production by body weight fol-
lowed the function

Heat production - a * Body weightb,
where b is .7 to .75, heat production is measured in Real and body
weight in kg. In 1965, the European Association of Animal Production
agreed to use an exponent of .75 to convert body weight to metabolic
body weight. They stressed that their decision was an arbitrary one,
and hoped it would facilitate comparisons among many results of energy
balance studies. It was also noted that the determination of the proper
exponent was an empirical, rather than theoretical, consideration.
Along the same line, Thonney et a1 (1976) and Geers and Michels (1982)
reported that there were preferable exponents than .75 on an intra-
special basis, but that across species .75 fit well. Baldwin and
Bywater (1984) asserted that this exponent tends to overpredict main-
tenanCe requirements for larger animals and underpredict for relatively
smaller ones.

Colovos et a1 (1970) reported that physical activity of cattle
influenced maintenance requirements, and presented correction factors to
adjust heat production for the amount of time for which the animal was
standing. These adjustments were computed from their finding that a
double-change in body position, that is, one arising and one reclining,
requires 46 kcal of energy for a 600 kg cow. In previous work, Brody
(1932) found the same change to use 15 kcal of energy, although his
calculations were based solely on oxygen consumption during short inter-
vals of less than 12 minutes. The results of Colovos et al (1970) were

from analyzing oxygen, carbon dioxide and methane concentrations over

12

ten hour durations.

The effect of level of production on maintenance was addressed by
Brody (1945) who reported that maintenance requirements increased with
increased production. However, this finding has been argued among
nutritionists. In fact, the question is more one of semantics than one
of substance. Brody (1945) attributed increased requirements to the
metabolic and physiological needs of the productive process, while
others, notably Baldwin and Bywater (1984) preferred to consider main-
tenance a constant. Their justifications were both for convenience of
estimation, and because they believed the requirement differences to be
a cost of production and hence attributable to lactation, rather than
maintenance.

Taylor et al (1981) have addressed the role of genetics in influ-
encing the efficiency of meeting maintenance requirements. They used 11
pairs of twin Ayrshire cattle in their experiments, in which each trial
lasted nearly two years. Little effect of age on maintenance require-
ments per kg metabolic body weight was found, nor were there any dif-
ferences in efficiency of meeting maintenence needs due to age. They
found significant differences between animals in equilibrium maintenance
efficiency, and reported a within-animal repeatability of .7, even when
animals were allowed to reestablish equilibrium at higher levels of
feeding. They computed a coefficient of variation for efficiency, due
to genetics, of 6.4%.

Garrett and Johnson (1983) demonstrated the importance of diet and
physiological state on maintenance requirements. Because of the close
relationship between diet, physiological state, and energy balance, one

might expect the latter to affect maintenance requirements as well.

13

However, research by Patle and Mudgal (1977) indicated that the effect
of energy balance on energy expenditure for maintenance was small.

Baldwin and Bywater (1984) reviewed differences in maintenance
requirements due to differences in relative organ weights among animals.
For example, Webster (1981) reported that energy expenditures in gut
organs such as the liver and alimentary tract may contribute nearly a
third of basal heat production. They speculated that differences in
organ weights, especially those involved in mammary and alimentary
processes, may account for half of the apparent increase in maintenance
requirements in lactating ruminants.

Bauman et a1 (1985) report that van Es (1961) adjusted maintenance
requirements from his own and 237 additional energy balance trials to
constant body weight and obtained an estimate of among-cow coefficient
of variation of 4-10%. There appears to be little genetic correlation
between potential for milk production and maintenance requirements,

according to research published by Davey et a1 (1983).
3.1.2. Estimation of maintenance requirements

Estimation of the requirements of growing or lactating animals for
maintenance has been a source of disagreement since the early part of
this century. Armsby and Kellner reported different values of feed-
stuffs for meeting the requirement based on differing ways their esti-
mates were obtained (Garrett and Johnson, 1983): Armsby made his compu-
tations from the energy lost by fasting animals, deciding that their
true maintenance needs would be supplied by metabolizing body reserves;
Kellner preferred to feed livestock just enough to maintain their body

weight, with no extra energy for lactation, growth or pregnancy. Figure

14

11.1, from Blaxter (1962), illustrates their positions. In light of
more recent findings which indicate that maintenance requirements would
decrease when energy intake is limited (reviewed by Graham, 1980), it is
not surprising that the estimates of Armsby and Kellner differed from
each other. Webster et al (1974a) questioned the validity of using
fasting metabolic level as the basis for estimating maintenance require-
ments in growing steers, and favored instead the extrapolation of energy
intake down to a level of zero gain as a measure of maintenance needs.
An analogous process was used by Moe et al (1970) in estimating energy
used for maintenance of lactating dairy cows. They estimated energy per
unit of metabolic body weight (kg'75) for maintenance, along with ef-

ficiencies for lactation and growth, by multiple regression.

 

Kellner
Armsby

Energy
retained

 

 

0

 

 

Energy or feed intake

Figure 11.1 Representation of the measurement of feed energy value
by Kellner and Armsby (Blaxter, 1962). Note that to the
left of the vertical dotted line animals are losing body
weight. The efficiency of maintenance (km) is the slope.

 

3.1.3. Efficiency of maintenance

The variable km is used to denote the efficiency with which
nutrients replace body fat and protein as a sOurce of energy for main-

tenance. For example, if fasting animals lose 10 Meal/day of body

15

tissue but when fed require intake of 15 Mcal ME/day to maintain body
weight, the efficiency of maintenance (km) is 0.67. Blaxter and
Wainmann (1964) found that km was not constant, but tended to increase
with feed quality as determined by metabolizability of the ration.
Using digestibility of the ration as an indicator of feed quality, van
Es and Nijkamp (1969) obtained similar results. 'They determined that
feeding level affected digestibility considerably more than it affected
metabolizability. They reported an efficiency of ME for maintenance of
78%. Although the values for km reported in the literature vary widely,
this estimate is slightly higher than most. In general, km has been
found to be affected by types of feed as well as metabolizability of
feed, as shown in Table 11.2 published by the Agricultural Research
Council (ARC) in 1980. The figures were obtained from the research of

Blaxter and Boyne (1978).

 

Table 11.2. Efficiency of utilization of metabolizable energy for
maintenance (km): values predicted from the .
metabolizability of the gross energy of the diet (qm).

Values predicted when qm is:

 

Class of feed .40 .50 .60 .70

Pelleted 0.653 0.673 0.695 0.715
Forages 0.642 0.663 0.683 0.704
Mixed diets * 0.728 0.749 0.769
All diets 0.643 0.678 0.714 0.750

* - not available

 

16
3.2 Energy utilization for pregnancy

The efficiency of supporting a pregnancy in the ruminant has not
been widely researched. In general, more emphasis has been placed on
the study of efficiencies of growth and lactation for economic reasons,
although the importance of pregnancy in commencing the latter two pro-
cesses cannot be overlooked.

One of the most widely referenced studies of the efficiency of
energy utilization during pregnancy was completed by Jakobsen et a1
(1957). They used 17 calf fetuses, fetal membranes, and dam uteri to
obtain a function describing tissue deposition during cattle pregnancy.
They determined that the function

v - 0.4162 * e0-0174t
adequately described this process, where V denoted the energy content in
Mcal of the tissue due to pregnancy, and t was the number of days after
conception. The derivative of this function yields the instantaneous
change in energy content of the fetal tissues, and is expressed as

v _ 7.24 * e0.0174t

where v is the rate of energy deposition (in kcal/day) on day t. It
should be noted that no corrections were presented for birthweight of
the fetus, although it seems reasonable to expect that more energy would
be deposited in a larger fetus than into a relatively smaller one.

Jakobsen et al (1957) did not estimate the efficiency of main-
taining a pregnancy, but they did determine that support of pregnancy
increased heat production in the dam between 2 and 2.5 times, or 30
kcal/kg increased weight due to fetal and placental tissues. Bauman and
Currie (1980) reported that out of 88 kcal/kg per day required by the

pregnancy, 63% was heat, or 55 kcal/kg. Their report summarized the

17

known biochemical and endocrinological pathways for maternal-fetal pro-
cesses during pregnancy. They also stated that fetal growth and de-
velopment were energetically comparable in efficiency to other produc-
tive processes, and that nutrient requirements at the end of pregnancy
were 75% higher than for a non-pregnant animal of the same weight.
Langlands and Sutherland (1968), in a study of pregnancy in Merino
sheep, found a requirement of 200 kcal/kg fetus per day, or more than
double that reported for cattle above. This may be due in part to the
small fetal size and in part to the shorter gestation length of sheep
compared to cattle.

Moe and Tyrrell (1972) reasserted that the efficiency of use of ME
for pregnancy was low (<25%), as they had determined earlier (Moe et a1,
1970). In the latter study, they estimated requirements to maintain
pregnancy in dairy cattle at 60 to 65 6.0174t kcal on day t of lacta-
tion, corresponding to an efficiency of 11%. Rattray et a1 (1974)
estimated that efficiency was between 12 and 14%, depending on the
statistical model used. They speculated that the reason for this low
efficiency was that maintenance costs to the fetus and supporting mater-
nal tissues were ignored. Sykes and Field (1972) computed the efficien-
cy of ME for pregnancy to be 12-14% in Scottish blackface ewes. Tissier
et a1 (1980) computed body composition from measurements of deuterium
uptake rather than indirect calorimetry or successive slaughter to
measure body composition. They obtained efficiencies for pregnancy
between 13% and 16% in cattle. One reason for their choice of this
method was to account for maternal tissue mobilization, which, as Heaney
and Lodge (1974) reported, may be a normal feature of late pregnancy

that cannot be prevented by ad libitum feeding, even if it were

18

desirable to do so.

The ARC (1980) cautions that efficiency measures ignore the growth
of mammary gland, or any increase in maternal energy or protein stores.
Other factors have been investigated for their effect on efficiency of
pregnancy support. Iwasaki et al (1980) reported that maintenance needs
may increase with increasing state of pregnancy, but this may have been
due solely to increased maintenance requirements of the fetus. They
found that ME intake was not affected by the advancing of late stages of
pregnancy, which may lend additional support to the theory of maternal
tissue mobilization for pregnancy support. Rattray et a1 (1980) deter-
mined that body condition of the ewe, as determined by feeding level in
mid-pregnancy, can influence nutrient partitioning during later stages.
Heavy ewes supported fetuses from maternal reserves, while thinner ewes

tended to replenish depleted tissues at the expense of the fetus.

3.3 Energy utilization for growth and liveweight change

The physiology of growth in ruminants has been investigated in
depth by researchers since the nineteenth century, since all ruminant
species, breeds, and sexes undergo some pattern of development which has
economic value. In contrast, lactation studies have been primarily
focused upon dairy breeds, and both lactation and pregnancy are sex-
limited traits expressed only in females.

In this review, the energetics of growth will be discussed in two
rather arbitrary divisions: energy requirements for growth and the
energy required for weight change in support of lactation. The term
growth will be used to denote maturation of the animal (i.e., deposition

of protein, fat, and other tissue) as contrasted to catabolism and

l9

deposition of tissue, primarily fat, for use by the cow as energy for

lactation.
3.3.1 Energy Utilization for Growth

Both National Research Council (NRC,1978) in the United States and
ARC (1980) in Great Britain have published energy requirements for
growth in beef and dairy cattle. Although published requirements differ
between breeds, much of the difference can be attributed to differing
body compositions among breeds of cattle. Garrett (1980), using a
comparative slaughter technique to study 708 steers and 341 heifers,
reported that the energy value of weight gain in British-bred steers was
17% lower than in comparable heifers, but 35% higher than the average
value of a small sample of Charolais steers. Although he did not study
the composition of the gain, it seems likely that the Charolais breed
contained a higher proportion of protein, which is produced with less
efficiency than fat in growing ruminants. Similarly, Vercoe and Frisch
(1974), using three Australian breeds, found significant differences in
efficiency of growth. They cautioned, however, that in their study
changes in feedstuff or environmental conditions may have affected
computed efficiencies.

In another breed comparison study, Byers and Rompala (1980)
evaluated the efficiencies of eight Charolais (C) and eight Angus-
Simmental cross (A x S) steers. They computed a 62% efficiency of ME
utilization for growth in A x S, with only a 45% efficiency in C steers.
They proposed that the higher proportion of fat produced in the A x S
animals, compared to C which is higher in protein, accounted for the

increased efficiency in the former. Their hypothesis was supported by

20

Reid et a1 (1980), who inferred from their work with unpublished data
that fat can be gained more efficiently than protein. They agreed that
animals measured as more efficient would tend to have a higher ratio of
fat to protein than those less efficient, assuming the animals were of
similar breed, sex, age, and other characteristics. However, Vermorel
et a1 (1982) contradicted these findings. Studying 24 each of Charolais
and Holstein growing bulls, they found no significant differences be-
tween the breeds in efficiency of ME use for growth. Neither were there
differences due to feeding level or liveweight of the bulls. Despite
the Charolais having a higher percentage of energy retained as protein,
they reported no significant effect of body composition on efficiency of
growth.

There have been numerous other sources of variation in efficiency
of growth reported. Geay et a1 (1980) pointed out that the efficiency
with which ME is utilized for fat deposition declines when crude fiber
content of the diet increases or when metabolizability of the diet
increases. Menke (1980) proposed a curvilinear function to describe the
relationship between ME intake and protein retention. He included such
factors as body weight, proteinzenergy ratio and amino acid pattern of
the feed as independent variables to predict maximum energy retention as
protein and efficiency of protein deposition. Tyrrell and Moe (1980)
performed 59 measurements involving energy balance on 8 fattening Here-
ford heifers over a 55-week period. They reported that partial efficien-
cy of ME use for tissue deposition was unaffected by diet. Meissner
(1982) concluded that genotype by diet interaction did not affect effi-
ciency, but did affect total intake and total gain. He used 34 bull

calves of three breeds, Afrikaaner, Hereford, and Simmental, on two

21

divergent diets in reaching his conclusion.

When measuring characteristics of growth in ruminants, accurate
measurement of maintenance metabolism is essential. Efficiency measures
of growth may be strongly affected if fasting metabolism is considered
to be maintenance metabolism. Webster et al (1974b) advised that thus
using fasting metabolism would bias growth efficiency estimates upward
in animals over 200 kg and downward in animals under 200 kg. They
recommended that basal metabolic rate be used instead to estimate main-
tenance. Graham (1982) postulated that short-term calorimetric experi-
ments yield higher values of energetic efficiency than do longer trials
with growing animals. He stated that the discrepancy occurs due to an
appreciable energy expenditure associated with physiological state, and
which responds rather slowly to feed intake. Roux (1982) warned that
estimates of efficiency produced simultaneously for both fat and protein
deposition must be interpreted with great caution, for nearly colinear
independent variables tend to produce estimates which have rather larger
standard errors.

Many researchers have determined efficiencies of growth (kf) in
experimental animals. Tyrrell et a1 (1974) found that 6 Hereford hei-
fers required an average of 1.95 Mcal ME to deposit 1 Meal of tissue for
growth. This corresponds.to an efficiency for growth of 51%. They noted
that, for each additional 1 Meal in daily rate of growth, 95% of it was
retained as fat, while only 5% was in the form of protein. There is a
large variation in the reported values of kf depending on the quality of
ration. For rations containing little fiber, kf has been estimated at
0.7-0.75, while with high fiber rations the values are closer to 0.4

(ARC, 1980). Baldwin et al (1980), compared real net efficiencies of

22

growth to maximum theoretical efficiencies derived from biochemical
paths. Their results are summarized in Table 11.3. They noted that,
because there are more than one metabolic pathway for fat or milk syn-
thesis, an opportunity exists to selectively use more efficient paths.

They posed two questions as motivation for continuing energy efficiency

work:

(1) Can we learn to identify animals which are capable of attaining

maximum efficiency of production?

(2) If we knew exactly what the less efficient animals were doing,
could we manipulate their metabolisms so that their efficiencies

would approach those of the more efficient animals?

 

Table 11.3 Comparison of theoretical and realized net efficiencies of
growth expressed as percentage of available metabolizable

 

energy

Animal Theoretical Realized
rat 75% to 85% 30% to 70%
ruminant 70% to 80% 30% to 60%

(adapted from Baldwin and Smith 1974)

 

Webster et al (1976) studied the efficiencies of growth in eight
British Friesan x Hereford steers. They obtained an average percent
efficiency of about 62%. Earlier, Webster et al (1974a) had performed
similar experiments with fattening sheep and computed a percent effi-

ciency of fattening in that species of 61%.

23
3.3.2 Energy utilization for weight change in.support of lactation

The metabolism and catabolism of tissue in support of lactation is
quite different from growth, for it involves primarily fatty tissue,
with little or no protein in many circumstances. This distinction was
borne out by work of Reid and Robb (1971), who reported an average
overall rate of change of 4.38 Mcal per kg body weight in 53 mature
dairy cows of assorted breeds. The value of body tissue gain and loss
during lactation, however, was somewhat higher. They found that the
energy value of 1 kg of body tissue gained ranged from 4.8 to 9.4 Mcal,
while body tissue loss contained 6.3 to 7.9 Meal/kg. This would indi-
cate a difference in composition between tissues composing empty body
weight and tissues gained and lost throughout lactation, with the latter
probably being somewhat higher in proportion of fat.

Mobilization of body tissue reserves occurs in most cows during
peak periods of lactation. Some cows are capable of utilizing remark-
able quantities of tissue for lactation during such periods of negative
energy balance, when energy outputs such as milk and maintenance exceed
energy intake. Flatt et al (1970) described a cow, Lorna, "who lost 10
to 20 Mcal body tissue daily while producing 27 to 35 Mcal (85 to 110
lbs) milk daily...In late lactation, Lorna deposited an exceptionally
large amount of body tissue (15.2 to 18.8 Mcal) daily while still lacta-
ting 4.7 to 7.1 Mcal (15 to 22 lbs) milk daily." The same trend, but to
a lesser extent, of mobilizing body tissue early in lactation for re-
placement later in lactation was noted in 21 of 24 cows between 6 and 10
weeks post-calving. Flatt et al (1970) estimated that the net efficien-
cy of milk produced by either mobilization of body reserves or directly

from feed intake was approximately the same. Brown et al (1981) pro-

24

posed that quantitative measures of body fat might increase the accuracy
of estimating feed intake, due to increased accuracy of estimating the
amount of tissue mobilized for production. However, Neilson et a1
(1983) found no changes in backfat area, measured ultrasonically, among
cows in three production levels during early lactation. Their tests
took place during the early part of lactation. One might account for
these results by speculating that'the source of tissue metabolized
during negative energy balance is primarily the body cavity and not over
the back. Dairymen would question this possibility, as the improvement
in dairy character (general sharpness and angularity) of a cow in early
lactation is well known.

Bauman and Currie (1980) reported that cows took approximately 16
weeks post partum to consume enough energy each day to meet daily re-
quirements for milk production, by which time yield had fallen to less
than 80% of peak production. They calculated that, over the first month
of lactation, typically about one-third of the energy in milk is from
metabolization of body reserves. Flatt et a1 (1970) quantified this
process; cows in their study showed an average body tissue loss of 6.9
Meal/day in early lactation (8 weeks post partum), and average gains of
1.2 Meal/day in mid-lactation (24 weeks) and 4.9 Meal/day in late lacta-
tion (41 weeks). They found the effect of stage of lactation on amount
of body tissue mobilized or stored was highly significant. In fact,
when they reduced feed early in lactation they caused a drop in milk
production rather than an increase in tissue mobilization, which might
indicate that lactating cows preferentially use body tissue to produce
milk in early lactation.

Flatt and Moe (1971) observed little fall in liveweight in a cow

25

producing 100 lbs milk/day, while eating only enough feed (about 25
Meal/day) for about half that yield. The deficit in energy intake was
made up by catabolizing about 4.5 lbs fat/day. Moe et a1 (1971) there-
fore cautioned that liveweight change alone may not provide an accurate
indication of a lactating cow's energy balance. Broster et a1 (1975)
performed a regression of liveweight change on milk yield (kg/day) for
heifers on fixed rations at various stages of lactation. Their results

are summarized in Table 11.4.

 

Table 11.4 Regression of liveweight change on milk yield for heifers at
various stages of lactation (Broster et a1, 1975)

Weeks of Regression coefficient Residual
lactation and standard error degrees of freedom
1- 6 -0.122:.019 53
7-12 -0.042:.011 65
11-16 -0.062:.016 51
15-20 -0.052:.015 52
19-24 -0.040:.013 78

 

Note that the regression coefficient for weeks 1-6 is significantly
different from all other regression coefficients. Thus, the first six
weeks appear to be most important for tissue utilization toward milk
production.

The net efficiency of producing milk from body tissue reserves can
be thought of as two distinct processes: storage of feed energy in the
form of primarily fatty tissue, and metabolization of body tissue to
produce milk. Many researchers have considered both processes.

Patle and Mudgal (1977) worked with 24 Brown Swiss x Sahiwal cross-

bred cows to obtain an efficiency of 65-68% for utilization of ME as

26

tissue gain during lactation. Moe et a1 (1970) estimated the efficiency
of ME use for body gain at 75% in balance trials with 350 lactating
dairy cattle. Milk production from tissue loss was performed with an
efficiency of 82% in the same study, which agrees well with results of
Moe and Flatt (1969). In trials with 215 lactating, non-pregnant dairy
cows in negative energy balance, the calculated the average efficiency
of converting body tissue reserves to milk was 85-86%. These efficien-
cies were estimated by regressing ME intake on milk produced and body
tissue change, and a regression of milk produced on body tissue change
and ME intake. A value of 83% was used by Forbes (1977) in his simula-
tion work, but his source for this value was not referenced.

Moe et al (1970) computed the overall efficiency of producing milk
through the intermediary of body tissue as the product of the efficien-
cies of going to and from tissue. Their result was 75% x 82%, or a net
efficiency of 62%, compared with efficiency of milk production directly
from ME intake of 64%. Van Es (1976) estimated that the overall effi-
ciency of tissue deposition in late lactation then withdrawal in the

early part of the following lactation was 50%.
3.4 Energy utilization for lactation

Lactation, along with growth and weight gain, has been the form of
production most investigated by researchers of production efficiency.
Although the broad subject of energy efficiency during lactation encom-
passes the efficiencies of digestion and milk production as well as
endocrine effects, this section of the review will primarily deal with
production efficiency of milk. Endocrine pathways and influence will be

discussed rather briefly.

27

Moe et al (1970) asserted that the amount of energy required by a
lactating cow depends upon the genetic potential of the cow and the
level of production desired. This is not, they stated, because cows
vary in metabolic efficiency, since the metabolized energy obtained from
a sample of feed is approximately the same across cows. Rather, they
believed that cows vary widely in their response to additional energy
input.

The identification by Moe et al (1970) of genetic potential and
production level as the main two sources of variation is a broad simpli-
fication, however. Many more sources of variation have been examined.
3.4.1 Environmental and genetic factors affecting

energy utilization for milk
3.4.1.1 Quantity of ration. Using four groups of twenty Holstein hei-
fers in either the first or second two months of lactation, and fed at
either high or low levels of energy, Broster et a1 (1969) reported that
the group fed at low level early in lactation had the highest efficiency
of conversion of energy intake into milk. Although these more efficient
heifers produced less milk than their better-fed counterparts, both
groups mobilized similar amounts of body tissue, which made the former
group appear more efficient. These findings correspond well to the work
of Flatt et al (1970), who found that cows in early lactation had a
tendency to mobilize a maximum amount of body tissue for lactation.
Decreasing feed intake reduced milk output, but did not affect the
amount of tissue mobilized for lactation. In contrast, Grieve et a1
(1977), studying 49 first lactation Holsteins, determined that energy

efficiency for lactation increased with feed intake. Trigg et a1 (1980)

28

experimented with eight sets of monozygous twins to determine the effect
of underfeeding early in lactation. As expected, underfed cows produced
less milk, but they concluded that this was due to differences in energy
partitioning. Underfed cows were found to mobilize less fat for milk
than adequately fed animals. The underfed animals recovered to produce

at near normal levels when an adequate feeding regimen was resumed.

3.4.1.2 Quality of ration. As Coppock et a1 (1964) decreased the ratio
of hay to grain in the diets of six mature, lactating, non-pregnant
cows, the efficiency of milk production decreased from 65% down to 54%.
However, Hashizume et a1 (1965) reported greater energetic efficiency
for lactation in cows fed high levels of concentrates than those fed
low. They used six cows in a crossover design experiment, i.e., each
cow was fed in a Hi-Lo-Hi or Lo-Hi-Lo concentrate scheme, with each
level lasting 26 days. Flatt et a1 (1970) found that of ME% of ration
had no effect on the partitioning of nutrients toward lactation or
weight change. Because concentrate is higher than roughage in ME con-
tent, and because the primary differences in energy efficiency for
lactation are due to partitioning differences, their findings tend to
indicate an effect of concentrate level on lactation efficiency inter-
mediate to the former two studies. Similarly, Schneider et a1 (1979)
found little effect of ration metabolizability on efficiency for milk
production, although in their study all diets had rather high metaboliz-
ability. They drew their conclusions from respiration experiments con-
ducted on 40 lactating cows.

Other components of a ration have been examined for their effect on
energy efficiency for lactation. Tyrrell et al (1982b) fed different

levels of protein to lactating dairy cows and concluded that ration

29

protein had no effect on ME utilization for milk production. Kronfeld
et a1 (1980) observed increases in calculated efficiency of ME utiliza-
tion for milk when a higher percentage of fat was fed. Highly saturated
tallow was used as their source of fat in the diet. They speculated
that the energy cost to transport absorbed fatty acids was less than
that to synthesize them, and accounted for the increased efficiency.
Similarly, van Es and Nijkamp (1969) found that percentage of crude
protein in the diet had no effect on lactation efficiency, nor did crude
fiber percentage. They examined 41 cows on balance trial to reach their

conclusion.

3.4.1.3 Frequency of feeding. Though they admitted that their results
were not conclusive, Sutton et al (1982) found indications that frequent
feeding may increase the partitioning of energy to milk. Sixteen
Friesian cows were used in that study. These findings were reinforced
by work of Kirchgessner et a1 (1982), who also found that efficiency of
ME utilization for milk production increased slightly as frequency of
concentrate feeding increased. In their experiment, concentrates were
fed in two frequencies, twice and six times per day. The computed gain
in efficiency was 3%, from 61% to 64%. In contrast to both of the
previous studies, Van der Honing et a1 (1976) found no differences in
efficiency resulting from increasing frequency of feeding concentrates
from twice to eight times daily. In summary, the effect of increased

number of feedings is likely to be small, if it exists at all.

30

3.4.1.4 Realized and potential milk production. It has been hypothe-

 

sized that animals which produce more milk may be more efficient than
their less productive counterparts. The relationship between milk pro-
duction and efficiency has been the subject of several publications.
Hooven et a1 (1968) studied 661 lactations of 318 daughters from 17
sires. They defined efficiency as the ratio of fat-corrected milk to
net energy intake. Because milk production requires the majority of net
energy intake, the correlation between efficiency and production might
be expected to be rather high, though probably less than unity. In
fact, they reported a genetic correlation estimate of 0.92. They also
computed a heritability of 0.46 for efficiency. Whether their sample of
animals was representative of the population of dairy cows is question-
able, however. The heritability for fat-corrected milk (FCM) production
which they computed was 0.62, about twice that reported by most other
sources. Neilson et a1 (1983) also found gross efficiency strongly
affected by milk yield. A factorial design having three levels each of
milk yield and average backfat with an average of eight animals per
subcell was used. Custodio et al (1983) likewise found that increased
fat-corrected milk production corresponds with increased efficiency for
FCM, with a highly significant residual correlation of 0.75 between the
two traits. Additionally, correlations between daughter efficiency for
FCM production and sire Predicted Difference for Milk or dam Cow Index
were approximately 0.40.

The magnitude of any relationship between efficiency and milk
production is dependent on the definition of efficiency used. Workers
in New Zealand have considered efficiency as the proportion of ME par-

titioned to the udder which is secreted as milk. Using this definition,

31

Trigg and Parr (1981) compared Jersey lines of different genetic merit
for milk production, and were unable to detect any association between
predicted genetic merit and partial efficiency of ME conversion to milk
or ME conversion to body tissue. It has been reported by Bryant and
Trigg (1981) and Davey at al (1983) that animals of high genetic merit
for milk partition energy differently than animals of low genetic merit.
Apparently the differences between animals of different genetic merit
for milk production are primarily in the partitioning of energy within
the body, and not in efficiencies of energy utilization by productive

functions.

3.4.1.5 Other sources of variation. Flatt et al (1970) found stage of
lactation effects highly significant in effecting ME utilization for
lactation in Holsteins. Broster et a1 (1969) also saw indications of a
stage of lactation effect, although its magnitude was somewhat masked by
an interaction with ration in the design of their trial. Body weight
changes have been known for a long time to be related to stage of
lactation. Hooven et al (1968) found body weight changes to be signifi-
cant in affecting efficiency. They computed a genetic correlation of -
0.17 between body weight and efficiency of lactation. It must be remem-
bered that this is a between animal correlation, and doesn't indicate

the effect of weight change within a lactation on efficiency.

32
3.4.2 Review of endocrine pathways

The hormonal actions and interactions which influence energy parti-
tioning and efficiency of energy utilization are exceedingly complex.
Many of these hormonal effects remain unclear and are being researched.
However, some of the effects of several key hormones have been
determined and will be briefly discussed here, focusing upon their

influence on lactation.

3.4.2.1 Insulin. Insulin concentration in the serum of cows has been
observed in numerous studies to have an inverse relationship to milk
production during a lactation (Hart et a1, 1978). Perplexingly, how-
ever, insulin concentrations are generally lower in low milk producers
than in high producers. The insulin concentration has also been found
to be low in animals experiencing energy deficit (Hove, 1974; Schwalm
and Schultz, 1976). Level of feeding has not been found to influence
insulin levels. Two primary known effects of insulin in cows are to
inhibit gluconeogenesis and to facilitate increased glucose uptake and

utilization (Kipnis, 1973).

3.4.2.2 Growth Hormone. Growth hormone (GH) concentrations in serum are
higher in high producing than in low producing cows. (Johnson et a1,
1976; Hart et a1, 1978). Exogenous GH has been shown to increase milk
yield in cattle (Eppard et al, 1985; Bauman et al, 1985b) indicating
that increased yield is attributable at least partly to high serum
concentrations of GH, rather than merely a coincidental genetic correla-
tion. Efficiency of milk production, measured as production per unit of
feed intake, is also improved when exogenous OH is administered

(Machlin, 1973{ Peel et al, 1981), although Tyrrell et al (1982a) have

33

shown that this increase does not correspond to an increase in the
partial efficiency of ME utilization for milk production. It has been
theorized that GH plays a central role in the control of metabolites,
especially glucose and non-esterified fatty acids which are precursors
to lactation. It also has been speculated that in energy deficient
ruminants, CH may increase the rate of fat mobilization from adipose
tissue, which makes it an important factor in improving efficiency and
level of production during early lactation. Furthermore, GH has been
implicated in a mechanism which preferentially partitions energy toward

the mammary gland (Davis et al, 1983).

3.4.2.3 Prolactin. Once a lactation has been initiated, prolactin ap-
pears to have little effect on level of milk production in ruminants
(Hart et a1, 1978). After parturition, prolactin concentrations can be
markedly reduced without affecting milk production (Karg et al, 1972;
Hart 1973). Further, no differences have been found between high- and
low-producing cattle in their serum prolactin concentrations, either
during lactation or dry period (Hart, 1978). Season, however, has been
found to have significant effect on prolactin concentrations (Schams,
1972; Koprowski and Tucker, 1973). Suckling stimulus also causes a
temporary increase in serum prolactin (Tucker 1981). The effect of
prolactin on the efficiency of milk production has not yet been deter-

mined.

3.4.2.4 Thyroxin. The effect of thyroxin on level of milk production is
still unclear. There have been several studies which failed to find
significant differences in serum thyroxin concentrations between levels

of high- and low-producing cows (Bodoh et al, 1972; Hart et a1 1978).

34

However, other studies have shown that thyroxin concentrations are
higher in lactating than non-lactating cows, and that concentration is
inversely related to level of milk production (Heitzmann and Mallinson,
1972; Vanjonack and Johnson, 1975). Exogenous administration of thy-
roxin has been shown to cause increased milk production (Blaxter et al,
1949), but a corresponding increase in efficiency does not occur, as

more energy intake is required (Thomas, 1953).

The above discussion of four key hormones involved in lactation
serves only as an introduction to the vast area of research concerning
endocrine control of lactation in the ruminant. The field is far too
extensive to be adequately discussed here. An abundance of excellent
review articles have appeared in recent years, such as Hart et al
(1978), Tucker (1979,1981), Baldwin et a1 (1980), Bauman and Currie

(1980), Bauman and Elliot (1983), Hart (1983), Collier et a1 (1984), and

Bauman et al (1985a).
3.4.3 Summary of reported efficiencies for lactation

Many researchers have published their evaluations of the partial
efficiency of ME utilization for lactation. Although they use many
different methods to deriving their figures, the results are remarkably

consistent, as illustrated in Table 11.5.
4. Review of models and modelingjin ruminant energetics

A model is the backbone upon which statistical inferences for both
quantitative and qualitative relationships are supported. As such,

correct specification of a model is paramount to adequately evaluate

_35

Table 11.5. Summary of reported partial efficiencies of Metabolizable
Energy utilization for lactation in cattle.

 

Source Number of animals Efficiency
Coppock (1964) 103 75%
Coppock et a1 (1964) 6 54% - 65%
Flatt et al (1970) * 67%
Kirchgessner et a1 (1982) * 61% - 64%
Moe et a1 (1970) 350 63% - 65%
Moe et a1 (1972) * 61% - 64%
Reid (1962) 59 70%

Tyrell et al (1982a) * 61% - 62%
van Es and Nijkamp (1969) 41 54% - 58%

 

*Not available

 

research data and form useful conclusions. Many models have been pro-
posed to explain the relationships between inputs and outputs in
ruminant energetics. These can be divided into two functional types:
(1) statistical models, which are often used to determine the existence
or magnitude of various relationships among independent and dependent
variables, based on experimental data; and (2) systems models, which can
be used to describe the interrelationships between measured rates of
inputs and outputs in a system working through a time period. This
section will review several published models of each type which have

been used in the study of ruminant energetics.

36

4.1 Statistical models

 

The statistical method used most frequently to analyze ruminant
energetics has been multiple regression using linear models. Descrip-
tions of previously undefined terms in the models to be reviewed are

listed below.

MEI - Daily metabolizable energy intake

MBW - Daily metabolic body weight (generally BW‘7S)
Emilk - Energy contained in milk produced daily

Milk - Daily milk production

E+wt chg - Energy required for daily body weight gain

E Energy produced during daily body weight loss

-wt chg

Moe and Flatt (1969) used the models

MEI/MBW - b0 + b1(Milk/MBW) + b2(E-wt chg/MBW) (1)
- -137 + 1.468( " ) + 1.262( " )
and
Milk/MBW - bO + b1(MEI/MBW) + b2(E_wt chg/MBW) (2)
- -79.7 + 0.632( " ) - 0.840( " )

to examine the use of body tissue reserves for milk production during
periods of negative energy balance in dairy cows. Their solutions for
each regression coefficient are shown. Model (1) considers required '
energy input to the animal as a function of output, while model (2) uses
energy output from the udder as dependent on sources of energy to the
udder. The results from the second model are easier to interpret, as
the regression coefficients are the partial efficiencies of conversion
of ME to milk and body tissue to milk.

Note that each of the terms in both models, with the exception of

37

the intercept, are on a per-unit-MBW basis. Constructing the models in
this way provided two benefits, one statistical and one conceptual. ’The
statistical advantage stems from maintenance being considered a function
of MBW. A model could be written without an intercept and including
major metabolic functions requiring energy:

MEI - b1(MBW) + b2(Milk) + b3(E:_wt Chg)
While correct biologically, such a model would be difficult to analyze
statistically because of the absence of an intercept term. If each
variable in the model is divided by MBW, however, we can regain the
intercept. We must assume that MBW is constant throughout lactation if
the models are to be exactly identical. Because MBW tends to vary about
i 10% throughout lactation, it is hoped that the consequences of vio-
lating this assumption are small. Conceptually, comparing the results

from such a model across cows of different sizes is made easier, since

all variables, and hence solutions, are reported per unit of MBW.

Moe et al (1970) developed another set of multiple regression
models to study the requirements of maintenance and partial efficiencies
of production. Using lactating and dry cows in positive and negative

energy balance, their models and solutions for regression coefficients

were:
- -2.889 + 0.153(" ) + 1.512(" ) + 1.270( " )
- -1.889 + 0.135(" ) + 1.576(" ) + 1.378( " )

38

I
ax
\J
on
H

+ 0.050(" ) + 0.990( " )

1.401 + 0.089(" ) + 1.703( " )

Equations (3) and (4) were applied to lactating cows in negative and
positive energy balance, respectively, while (5) and (6) were for dry
cows in negative and positive balance respectively. Because the units
for the regression coefficients are energy input per unit output, the
partial energy efficiencies of production can be found by inverting the
respective regression coefficients. For example, model (3) resulted in
a partial energy efficiency for milk production of 1/1.512 or 66%.

The above 6 models were applied to data from 350 animals in energy
chambers at Beltsville. There has not been a large-scale study which
addresses the question of efficiency using animals maintained in normal

herd conditions due to the requirements of MEI and body weight measures.

4.2 Systems models

Using statistical methods, a researcher determines the magnitude
and significance of sources of variation. Systems analysis permits
modeling the behavior of system outputs in response to measurable in-
puts. The primary tools in this technique are modeling and simulation.
The process of modeling develops a set of mathematical equations to
predict changes in the real world, while simulation is the use of model-
ing to study the dynamics of a system (Mertens, 1977). A sequence of
steps has evolved which traces the modeling process (Brown et a1, 1981),
‘as depicted in Figure 11.2.

There are many more reports of statistical analyses than systems

39

 

Define Problem
or
Objectives

 

 

 

 

 

Observe System

 

 

 

 

 

Develop Block Diagram
to Describe System

 

 

 

 

 

Collect and Analyze

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Data
l
Additional
data
Formulate Mathematical
Model
Improve
model
1 Verify and Validate Reject
Model model

 

 

 

 

 

 

 

 

 

 

Accept Model

 

 

 

 

 

Simulate Results

 

 

 

 

 

Evaluate and Apply Results
to Original
Objectives

 

 

 

 

 

Publish Results

 

 

 

Figure 11.2 Steps involved in the modeling process (Brown et al, 1981)

40

analyses in ruminant energetics. Application of systems analysis in
this area involves complex computerized modeling of the ruminant diges-
tive and endocrine systems. Two applications will be discussed to
illustrate the ability of systems modeling to simulate actual biological
events and predict response of a process to certain stimuli. The first
is the modeling of feed intake in cattle, and the second is the simula-

tion of energy exchange and growth.

4.2.1 Systems modeling of feed intake in cattle

One of the earliest efforts to develop a model for predicting feed
intake in cattle was by Monteiro (1972). He used changes in milk pro-
duction and body weight throughout a lactation to predict the daily
voluntary feed intake by a cow. He relied on a statistical model to
obtain his prediction equation. The static nature of the relationships
among variables in his equation, however, could not account for the
observed slow increase in intake during early lactation. 'To better fit
his observations, Monteiro added a lag parameter which made his model
cow produce less milk early in lactation than was observed in experimen-
tal cows. Forbes (1977) used the data from Monteiro (1972) and form-
ulated a dynamic model of feed intake in which metabolically controlled
intake (MI) was compared with physically controlled intake (PI), and the
smaller amount considered to be the animal's intake. This approach is
considered dynamic because a change in M1 at a given time t led to
increased intake at time t which in turn resulted in a change in P1 and
M1 at time t+l. Forbes later (1983) extended his model to predict
feeding frequency, producing in effect a minute-by-minute model of the
factors which are thought to control feed intake. A block diagram of

his cow model is shown in Figure 11.3.

41

 

 

l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

total amount;
reduced if ME

 

requirements

 

L not met

 

 

 

 

ME REQUIREMENTS Which is PHYSICAL LIMIT
ii T71 the smaller? ]I1 to intake
MILK YIELD FOOD INTAKE
from data or Cow eats enough DIGESTIBILITY
idealized lactation i—1 to supply ME and
curve. Depressed requirements ME CONCENTRATION
if ME requirements unless prevented of food
i not met from doing so by
[physical restriction
J
FAT DEPOTS
MAINTENANCE 0.5 kg/day GUT CAPACITY
deposited; no depressed by
a(BW)0'75 set maximum to increasing

abdominal fat

 

 

 

Figure 11.3. Block diagram of cow model (from Forbes, 1983)

 

Bywater (1984) extended the performance of feed intake models by in-

cluding rumen function in his simulation.

This addition considers

digestion rate, fluid turnover, and particle breakdown rate for their

influence on MI.

Bywater claims that his model determines the lag in

the effect of metabolizable energy status on feed intake more effective-

ly than prior published models.

However, he admitted that there was a

systematic error in predicting intake, especially early in lactation,

thought to be attributed to inadequacies of the lag function he used.

In fact, all models put forth to date share this difficulty of accurate-

1y predicting feed intake during the early part of lactation. It is

42

apparent that for feed intake models, the delay function plays an impor-
tant role in maintaining accurate correspondence between requirements

and intake.
4.2.2 Systems modeling of energy exchange and growth in cattle

Unlike the models discussed above, modeling of energy exchange in
cattle might be termed 'micromodeling', because it deals with events
which occur along biochemical pathways within the digestive and endo-
crine systems. As such, to fully understand such models, a working
knowledge of biochemistry is required. However, a simplified presenta-
tion of research conducted in this area will be instructive in showing a
representation of digestion which is frequently ignored in higher-level
models of ruminant energetics.

Smith et a1 (1980) discussed the stages involved in developing a
model of metabolism in the ruminant. They began by specifying, in block
diagram form, the main pathways of energy transformation (Figure 11.4).
Note that they combined four subsystems (liver, adipose, mammary and I
peripheral tissues) which together with the blood as transport mechanism
and gut as input source made up the complete system for study. After
evaluating the behavior of this model, however, they decided that the
adipose subsystem did not adequately reflect existing concepts or ex-
plain available data. As a result, they developed a complex series of
chemical kinetic equations which represented the transformation of
sugars and acetate into carbon dioxide, fatty acids, and glyceride
glycerol.

The modeling of adipose tissue metabolism is a complicated task,

whose results must be continuously compared to existing data to ensure

43

an accurate simulation. Schulz (1980) proposed a system of energy
accounting as glucose is continually cenverted into fatty acids or
oxidized. .Although his method appeared to accurately determine energy
contents of feeds over a wide range of intakes, no mechanism was in-
cluded to monitor the rates of reaction, and hence it would be difficult
to incorporate his model into a system which required delays in this

process.

 

 

 

I2 6 .._.. AA
-o AC . K3 Blond Adipose
LO . 16
5 L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\ fi— 3 G 2- ese 1 36?-
‘37 9 _" 0 6 18 5 -' 63
(\ LlVCf 2 5 02 m
I
Prop. m-Gluc ‘ co; 55‘; L 9
I 16
TO 2 0 2 ’9 T5
2.0 I I. 9
FA I 7 LPL 0 18 FA
I5 _ ‘l / '
. . 3
3.2 J10 e I l—_'1// z \ 0ch l L___J,
L AC -1 . NEFA L ‘/”169
J
J
F f . Mammary 1
Peripheral tussws J._ J 1 _;_§_ _. Ml“!

 

 

 

 

‘AC'KB {TI—'lot

1

 

 

H
I
l
Ll

Oxidation and

blosymhesm ‘- — G i Loci
\ / CC:

9 0
L .j G r. Pro: 4

Figure IIg4 Block diagram of energy metabolism in a lactating dairy cow
(Smith et a1, 1979)

 

 

 

 

 

 

 

 

 

 

 

 

 

Reichl (1980) described a computer program of his design which
required as inputs measured intakes of digestible protein, digestible
fat and digestible carbohydrates and the desired retentions of proteins
and fat. The output from the program includes heat production, ATP

balance, oxygen consumption, carbon dioxide, methane and urea produc-

44

tion, yield of microbes in the rumen tract and a series of efficiencies
of digestion. The system which his program simulated was composed of
six submodels on three different levels. These submodels were (1)
general outputs and (2) metabolic pathways on the whole animal level,

(3) flux rates and (4) pool sizes on the individual tissue level, and
(5) redox states and (6) membranes on the level of subcellular frac-
tions. The purpose of his model was to examine the characteristics of a
steady state resulting from given inputs rather than simulate the effect
of a sequence of inputs through time on rate of nutrient and energy

transfer.

In summary, then, both statistical analysis and systems modeling
have been used to study the metabolism of dairy cows. Statistical
methods are best applied to answer questions about linear relationships
among the data, while systems analysis is better able to describe intri-
cate interactions among the rates of change of variables through time.
A second difference between the two methods is that statistical proce-
dures are better equipped to directly estimate the probabilities of
hypotheses, while systems science system requires that any hypotheses be
tested only by examining the performance of a complete systems model.
The determination of which means of analysis to use in a study is one
which should be made by the researcher, considering the availability of
data, his knowledge of the both qualitative and quantitative relation-

ships among the data, and the questions he wishes to investigate.

III. METHODS OF ANALYSIS

1. Description of data

Data were supplied by the Lilly Research Laboratory of Eli Lilly
and Co. of Greenfield, Indiana. Several variables were measured
throughout one lactation for each of 405 cows of various ages. The cows
were distributed in seven herds: two commercial dairies in California
and Pennsylvania and five institutional herds: the Lilly Research farm
in Greenfield, and herds at Michigan State University, Southern Illinois
University, Western Kentucky University and a penitentiary in North
Carolina. The data had been collected to test the efficacy of an exper-
imental compound, Actaplanin, on production and feed intake. One of
four dosages of the drug was administered to each cow throughout a
lactation. The influence of the drug was not a central concern to this
study, therefore it was treated as a nuisance variable.

Four rations were formulated to meet the requirements of high-
producing, medium-producing and low-producing cows, and heifers. All
heifers, regardless of production, were fed identically composed Heifer
rations. To determine the appropriate ration to be fed each of the
remaining cows, Lilly considered average milk production during the
first three weeks. Cows which produced less than 62 lb per day over the
first three weeks were classified Low, between 62 and 75 lb/day Medium,
and those over 75 were considered High producers.

To facilitate blocking of animals for the Actaplanin trial, a

calving group was also recorded for each cow. The number of groups

45

46

varied among herds, and was based on the cows' calving order within a
herd. A calving group variable was not considered in the present study.
Production data were recorded at regular intervals and included

daily milk weights in 1b and biweekly percentages of milkfat, protein,
lactose, and solids-not-fat. Milk data were corrected for solids to an
energy value of 340 kcal per lb using a formula published by Tyrrell and
Reid (1965):

SCM - 12.3 * Fat + 6.56 * SNF - 0.0752 * Milk (1)
where SCM is daily solids-corrected milk yield, Fat is daily fat produc-
tion, SNF is daily production of solids-not-fat and Milk is milk yield.
All quantities are in units of weight, e.g. lb or kg. The weights of
Fat and SNF needed for this equation were computed from linear interpo-
lations between biweekly measurements of fat and SNF percentages, and
daily milk yield data.

Feed intake was measured daily: dry matter intake (DMI) in lb and
net energy intake (NEI) in Mcal. Net energy of a ration was determined
using tables published by the National Research Council (NRC, 1978).
Additionally, body weights were taken according to the following proto-
col: four measurements the first month, one measurement every two months
for the next eight, and one on each of days 300 and 301 of lactation.
The dates of all of the above observations were also recorded.

Breeding dates throughout the lactation were available, as was some
calving information, such as weight, sex and condition of the calf, for
many but not all cows. Dates of calving both before and after the
recorded lactation were reported for many cows. When available, the
date of calving after the lactation was used to create a variable,

Pregi, consisting of the estimated weight of the fetus and placental

47

tissue in kg on day i. A formula published by Jakobsen (1957) was used
for computing Preg:
Pregi _ e.Ol74*i
Dam and sire identification were not included on the supplied magnetic
tape, but were available in printed form from Lilly. Neither identifi—
cation was required for this research.

Before proceeding with statistical analysis, a preliminary tabula-
tion was performed. A summary of this tabulation is presented in Appen-

dix I. The data were then reformatted to eliminate redundant and err-

oneous information, which reduced the number of cows from 405 to 391.

4

2. Partitioning of energy intake into forms of output

During a lactation, a cow may partition energy into several forms
of production: maintenance (including heat production), lactation, sup-
port of pregnancy and fetal growth, and tissue metabolism.and cata-
bolism. If the quantity of energy partitioned into a certain product is
only a small fraction of the total energy consumed, then differences
between animals in the efficiency of creating that product will not
affect overall efficiency greatly. To understand the relative energy
requirements of various forms of production, energy intake was parti-
tioned according to the amount of gross energy output by each product
over several time periods. The time periods chosen were the whole
lactation, and durations of positive and negative energy balance.

Two methods of measuring energy intake are net energy for lactation
(NE) and metabolizable energy (ME). Empirical observation of feeding
tables published by the NRC (1978) reveals that the relationship between

ME and NE concentrations (Meal/kg DM) in a feed is

48

NE - (ME + 0.2473) / 1.8315

for many common feeds. Applying this equation to estimate daily meta-
bolizable energy intake (MEI) from daily net energy intake for lactation

yields
MEI - NEI * 1.8315 - 0.2473 * DMI (2)

where DMI is measured in lb and all energy measures are in Mcal. Equa-
tion (2) was used throughout this research to estimate MEI. The differ—
ence between the NE and ME content of feeds is that ME includes energy
which is converted to heat during the production process in addition to
the energy required for milk, maintenance and body tissue production,
while NE does not include energy spent as heat. It must be remembered
that by using equation (2) to convert NEI and DM1 into MEI, the varia-
tion among cows in efficiency of conversion of feed to energy is re-
duced. There was little alternative, however, since true MEI can only
be measured on an animal within an energy chamber or wearing respiration
apparatus which can monitor body heat.

For each cow, the fraction of energy apportioned to the various
products was computed. The process was repeated using MEI and NEI as
energy sources, and over all three time periods. Products considered
from MEI were solids-corrected-milk, body tissue, maintenance and heat
of production. NEI accounted for solidsacorrected-milk, maintenance

requirements and body tissue gain or loss.

I?“

pl

01:

he

ILL.)

49
3. Regression procedures

To examine the relationship between feed energy and energy of
products during a lactation, a series of regressions of energy intake on
output was performed. Many models were considered, each postulated to
have a meaningful biological interpretation. The coefficient solutions
from each model were compared to corresponding published estimates from
data collected on animals in energy chambers. Before these models are
described, however, several procedures common to most or all of them
will be explained. The following techniques used within each model
adjusted the data to more accurately reflect the underlying biological

functions of lactation, digestion and weight change.
3.1. Procedures for data manipulation within regression

Several variables in the data set required adjustment to make them
more useful in the regressions. One example, the formula for estimating
MEI, has already been presented. Three more techniques were used to
modify the data before regression. These were:

(1) adjustment of milk secretion data to estimate rates of milk
synthesis;

(2) a distributed delay to estimate the continuum of energy in the
bloodstream of a cow from discrete intake measures; and

(3) producing a continuous curve for estimating body weight from a
small number of measurements taken at intervals throughout
lactation.

Appendix 11 describes the algorithms used to perform the above adjust-

ments, along with segments of FORTRAN Code implementing the algorithms.

 

In

50
3.1.1. Adjustment of milk weights to approximate milk synthesis rates

Milking an animal until all milk is removed is not economical per
unit of milking time and can cause health problems. Current management
practices recommend removing about 75%-85% of milk in the udder at each
milking (Bath et al, 1978). The residual milk is retained by the udder
until the subsequent letdown, when most of it is secreted. The amount
of energy required daily for milk production is a function of daily milk
synthesized within the udder rather than daily milk yield. Because not
all of the milk synthesized by the udder is secreted at each milking, we
must distinguish between these two quantities. Also, milk synthesis is
a continuous process while daily milk yields are discrete measures which
may vary considerably in magnitude from day to day. Adjusting daily
milk records to a basis of milk produced daily in the udder can elim-
inate some of the large differences between consecutive days which may
have been caused by inconsistent milking practices. For example, the
judgment of different milkers with respect to proper duration for leav-
ing milking apparatus attached to the udder may vary, depending also on
the milking rates of other cows in a parlor at the time.

The following algorithm was used to obtain estimates of daily rates
of milk synthesis from production data. All cows in the study were
milked twice daily, and for simplification each of the two milk yields

was considered exactly half the day's production.

51

Let: dm- - milk yield on day i

mi 1 - milk yield at first milking on day i
’ -O.S*dmi

mi 2 - milk yield at second milking on day i
, -O.S*dmi

ds. - milk synthesized on day i

s. - milk synthesized during one-half of day i

f - fraction of total udder capacity yielded at one milking
fd - fraction of milk synthesized and secreted per day
Now, for the first day, if we assume f - 0.83,

m1,1 ‘ f*51

m1,2 f*Sl + f*<1‘f)*sl

dmi ' m1,1 + m1,2

[0.83 * 31 + 0.83 * 31 + 0.83 * 0.17 * 51] / 2
- 1.8 *Sl-O.9 *dsl

Therefore, fd - 0.9, indicating that if residual milk is 17% of the
udder capacity at each milking, daily residual milk is 10%. In other
words, 90% of the milk synthesized on day i is secreted on the same day.
In general, for any day i of lactation,
This study required the computation of daily milk synthesized (dsi) for
each day i. Notice that, for day i-l,

dmi-l - 0.9 * dsi-l + 0.09 * dsi-Z + 0.009 * dsi-3 + ... (4)
Now if we multiply equation (3) by 10 and subtract from it equation (4),

10 * dmi - dmi-l - 9 * dsi

with all other terms dropping out. Then, to obtain the quantity of milk
synthesized on day i,

asi - [10 * ami - dmi_1] / 9 (5)

52

Equation (5) was applied to all milk yield data except for the first
day. On day 1, the amount of milk synthesized was set to 110% of the
yield. To examine the effect on efficiency estimates of this adjust-
ment, two preliminary analyses were run in which the daily proportion of
residual milk was varied between 0% and 25%.

The first procedure was to compute simple phenotypic correlations
between daily milk synthesized and daily energy available in the blood-
stream. One correlation was computed for each cow, and the mean of the
resulting 391 correlations determined. As this parameter was increased
from 0% to 15% and then to 25%, the correlation to daily available
energy decreased slightly.

The second analysis fit the model

NEI - b0 + b1(SCM) + b2(WtChg) + e
where NEI is the daily energy available in the bloodstream (Mcal),
discussed in III.3.1.2, and WtChg is the daily weight gain or loss (lb)
computed as described in III.3.1.3. SCM is the solids-corrected milk
synthesized daily in the udder (1b), and varied depending on the frac-
tion of residual milk used in the model. This parameter took each of
three values: 0%, 13% and 25%. Data from a single cow were fit, and
regression coefficients obtained. Little difference was observed among
resulting efficiencies, regardless of the percentage used to compute
residual milk. Following this trial, a 10% residual milk weighting was

used for all further regressions.

53
3.1.2. Distributed delay for estimating energy availability

The data included daily DM1 and NEI, which were estimated from
measures of feed disappearance. These data provide discrete measures of
energy available for production. However, the measure of energy re-
quired in this study is the daily energy available for production,
rather than daily energy consumed. The two are related through time, as
energy consumed is gradually digested and made available to the metabo-
lism. Using NEI and MEI without correcting for this delay in avail-

ability would require several assumptions:

(1) that feed disappearance correctly predicts the cow's internal
energy status,

(2) that the cow consumed her daily energy at a single point in time
each day, and

(3) that the energy was instantly available for use in production or

maintenance.

In fact, these assumptions in general can not be supported. Variations
in daily feed disappearance weighings may be due to factors other than
daily consumption, such as wastage or human error. A cow may consume
feed at several times throughout the day. Finally, it takes some time
for the energy in the feed to become available to the cow in the blood-
stream.

A delay function was used to simulate the ongoing process of diges-
tion. In addition, this function could reduce the effect of large
differences in intake on consecutive days. The resulting rates of
energy available in the bloodstream would be more continuous, i.e., not

as subject to large daily variation. The input to the process was daily

54

energy intake, and its output was the daily energy available in the
bloodstream. The most critical parameter used by a delay function is
the half-life of the process. In this study, the half-life is the time
it takes for half the feed energy ingested by a cow over the course of a
day to reach the bloodstream. This parameter must consider that feed is
consumed over a 24 hour period and is constantly being digested. Re-
search has indicated that the half-life is related to the quality of
feed consumed, with high quality corresponding to a shorter half-life
(Bath et al, 1978). Typical values for the parameter ranged from 8 to
20 hr (Colucci et a1, 1981).

Choosing a reasonable half-life for this analysis involved a com-
promise. Reported estimates of the half-lives for many typical rations
were about 12 hr (Colucci et a1, 1981). On the other hand longer
delays, on the order of 24 hr, improved the ability of the function to
produce a smoother output. A value of 18 hr was chosen as.a reasonable
compromise. Two analyses described in III.3.1.1 were performed to
determine the effect of varying the half-life on resulting efficiency
estimates and on correlations between daily milk synthesis and energy
availability. The parameter was varied among 0, 18, 24 and 36 hr in
both procedures. For both analyses, the differences among results from
using different half-lives were negligible. For the remainder of the

research, 18 hr was used as the half-life.
3.1.3. Estimation of continuous body weight curve from discrete weights

A serious shortcoming of the data was the paucity of body weight
measures. Animals recorded for a complete lactation were weighed only

10 times, and the distribution was such that weights were taken only

55

every two months from day 22 through day 299 of lactation. Body weight
is an important indicator of whether a cow is adding to or mobilizing
body tissue, which is a requirement for or source.of energy, respective-
ly. Without adequate body weight information, the additional energy
supplied by the cow in negative energy balance can not be considered,
nor can the additional requirement for weight gain later in lactation
during pregnancy.

Several methods were available which would generate estimates for
body weights during periods between existing measurements:

(1) linear interpolation between data points;

(2) fitting a spline curve to the data; or

(3) computing a least-squares polynomial equation to fit the data.
The former two methods would produce curves which exactly include exist-
ing data points. This is undesirable, for it was not uncommon in the
data to find a difference of 50 lb between body weights taken on consec-
utive days. Much of this difference was likely to be caused by differ-
ing gut fill rather than change in empty liveweight. Because splining
causes the resulting weight curve to be continuously differentiable,
when applied to weights recorded on consecutive days it could cause
unrealistically large rates of change for several days before and after
the consecutive measures. Interpolation has the disadvantage that it
results in identical rates of daily weight change for up to 60 consecu-
tive days. The method would create ten different rates of weight change
throughout the lactation from the ten different body weights per animal.

None of these disadvantages are shared by polynomial regression,
provided that an appropriate polynomial is chosen. The choice of which

degree of polynomial to use is a difficult one. Polynomials of higher

56

degree result in better fit of the curve to data, but there is a danger
of error due to insufficient precision on most computers when the degree
exceeds about six. Within this limitation the degree should be chosen
as high as possible without fitting random variation, or noise. This
decision is frequently subjective.

Regressions were performed using polynomials of varying degree on
body weight measurements from several representative cows. Visual exam-
ination of the fits indicated that a 4th degree polynomial was adequate
to reflect major inflections in the weight curve throughout lactation
without fitting the noise associated with measures on consecutive days
described above. Therefore, for all cows with lactation lengths of at
least 250 days, daily body weights were estimated by a 4th degree poly-
nomial fit to actual weights. Care was taken to ensure that cows in-
cluded were weighed at least seven times before applying the polynomial
regression to their body weight data. If the degree of a polynomial
approaches the number of observations being fit, wild fluctuations may
occur in its curve which can make it unsuitable for estimating weights
between observations. Although the regression line would continue to
fit the data with minimum residual variance, predictions of weights at
times between weighings may have a much larger error component than if
the analysis had more degrees of freedom for error.

Polynomial regressions were performed on the body weight records
from 244 cows having a lactation length of at least 250 days. From the
solutions for each cow, daily body weights were estimated for each day
of lactation. Daily metabolic body weights (MBW) were computed by
raising daily weight estimates to the 0.75 power as recommended by the

NRC (1978). A WtChg variable was also obtained from estimated daily

57

body weights. On day i, WtChgi was computed as the difference between

body weights on day i and i-l. WtChgl was set to zero.

For the remainder of this study, the terms NEI and MEI will refer
to daily energy available within the bloodstream, i.e. after the delay
has been applied to the energy intake data. Similarly, SCM will refer
to the amount of solids-corrected milk synthesized daily, rather than

amount of SCM secreted per day.

3.2 Multiple regressions to analyze energy utilization by various
products

One of the assumptions required by multiple regression is that
independent variables are measured without error. Although it is sel-
dom, if ever, completely satisfied when observing biological systems,
several variables in this study may be in serious violation of this
assumption. These variables, and the effects of their errors in
measurement, merit further discussion.

All recorded independent variables in the models to follow con-
tained a degree of uncertainty. For example, daily solids-corrected
milk records were not found by analyzing and correcting every unit of
milk for its energy content, but by applying equations from Tyrrell and
Reid (1965) involving milk and components yield. However two indepen-
dent variables, WtChg and Preg, were subject to much larger measurement
error than SCM or NET. The source of error in WtChg was the fourth
degree polynomial approximation of body weight as a function of day of
lactation. Though in general the polynomial fit body weight rather well
over the length of lactation, the 56 day interval between measures

during middle and late lactation prevented accurate estimation of day-

58

by-day changes. The variable Preg, weight of fetal and maternal support
tissues, was also subject to error. The formula of Jakobsen et a1
(1957) generalized the fetal growth curve, although fit of the curve was
not as precise during the second half of gestation as during the first
half. It appeared that the fit of the curve was within about 20% of
most measured fetal and tissue weights during the second half of gesta-
tion for the investigation of Jakobsen et a1 (1957). With varying sizes
of dam and weights of fetuses, it is reasonable to expect that similar
inaccuracies occurred in the data for this study.

In a simple regression, the estimated regression coefficient is the
ratio of covariance between independent and dependent variables and
variance of independent variable. The presence of measurement error in
an independent variable, such as WtChg and Preg, could increase the
variance of the variable. If we assume that on average the covariance
between each variable and NEI is unaffected, then in the case of simple
regression the estimated regression coefficient would be smaller than
the true parameter. A similar effect may arise in multiple regression
models. Therefore any assertions of the significance of a regression

estimate are likely to be on the conservative side.

Twelve multiple regression models were examined which involved
either NEI or MEI as the measure of energy intake. Table 111.1 illus-

trates the terms in each model and the relationships among models.

59

 

Table 111.1. Summary of multiple regression models fit (model number in
parentheses) and relationships among them

dependent variable

 

 

Net energy Metabolizable energy
independent per per
variables linear unit MBW linear unit MBW
MBW,SCM (l) (4) (7) (10)
MBW,SCM,WtChg (2) (5) (8) (ll)
MBW,SCM,WtChg,Preg (3) (6) (9) (12)

 

A more specific description of each model, identified by number in
Table 111.1, is shown below. The subscript 1 indicates measurements on

day i, where i is from 1 through the final day of milk production.

(1) NEIi - b0 + blSCMi + ei

(3) NEIi - b0 + blSCMi + sztChgi + b3Pregi + ei

(A) NEIi/MBwi - b0 + bl(SCMl/MBW1) + 81

(6) NEIi/Mswi - b0 + bl(SCMi/MBWi) + b2(WtChgi/MBWi) + b3(Pregi/MBWi) + ei

(7) MEIi - b0 + blNESCM,i + 91

(8) “Eli ' bo + blNESCM,i + bZNEWtChg,i + ei

(9) MEIi ' b0 + blNESCM,i + bZNEWtChg,i + b3NEPreg,i + 91

(10) MEIi/MBWi - b0 + bl(NESCM’i/MBW1) + ei

(11) MEIi/MBWi - b0 + b1(NESCM,i/MBW1) + b2(NEWtChg’i/MBW1) + ei

(12) MEIi/MBWi - b0 +b1(NESCM’i/MBW1) +b2(NEwtChg,i/MBW1) +b3(Pregi/MBWi) +ei

Because each model is independent from the others, b0, bl’ b2, b3 and ei

60

were different from model to model. The random residual term, e1, was
assumed to be normally distributed with mean 0 and homogeneous variance
in all models. No covariances were assumed among observations. These
assumptions have been applied in most published studies of energy util-
ization by regression. However, the sequential nature of the data
through time suggests that autocorrelated errors may occur. Section
111.3.3.4 will describe the techniques used to examine the effects of
autocorrelation.

Models (3) through (6) and (10) through (12) are transformations of
models without intercepts, with each variable measured on a per-unit-MBW
basis. This can be seen through multiplication by MBWi. A transforma-
tion consisting of dividing each daily variable by MBWi was performed
because of the statistical difficulties of interpreting a model when no
intercept term is included. As an indication of the problem, R2 values
can assume any real values when no intercept is in the model, compared
with theoretical bounds of 0 and 1 when an intercept is fit. After a
model without intercept is transformed, R2 values could be directly
compared with those from models having an intercept. However, residual
variances could not be compared because the transformation changed the
scale of the dependent variable. The preferable estimator of residual
variance would untransform the data and compute a residual sum of
squares. This would have a substantial computational cost, but an
economical approximation was calculated by estimating the residual var-
iance of the transformed model and multiplying by the square of the mean
divisor of the transformation. For example, if data were transformed by
dividing by MBW, then the resulting residual variance was computed by

multiplying residual variance from the transformed model by the square

61

of mean MBW.

Each regression model was fit to 357 cows having a lactation length
of at least 250 days. Each model was fit for each cow over the entire
lactation, over the period of positive energy balance, and over the
period of negative energy balance. The energy balance of an animal
during a lactation was determined by daily body weight change. When the
change was positive, she was considered to be in positive energy bal-
ance, while negative balance was indicated by a daily weight loss (Fig-
ure 111.1). Because of the polynomial regression technique used to
estimate body weights throughout lactation, this method of energy bal-
ance determination was more free of day-to-day errors due to degree of
gut fill, body water content or mismeasurement. It was also highly

unlikely to produce a daily body weight change of exactly zero.

 

Body
weight

negative| positive

 

 

Day of lactation

Figure 111.1. Determination of periods of positive and negative
energy balance by weight change throughout lactation

 

62

3.3. Two-stage regressions using net energy as a measure of

energy intake

A two-stage regression procedure was developed to produce more
biologically reasonable solutions for coefficients of variables requir-

ing the majority of energy expenditure. The technique used was:

Stage 1: The quantity of energy required by all except one independent
variable, as estimated using parameters published by NRC
(1978), was collectively considered as a new independent var-
iable whose coefficient had expectation 1.0. A multiple
linear regression of NEI on the remaining variable and the new
composite variable was then performed.

Stage 2: Energy required by the fitted variable was computed using the
regression coefficient estimated in stage 1. This energy was
subtracted from the original NEI and a multiple regression

performed of the difference on the remaining variables.

The two-stage models used are listed below. For each model, an analysis
was performed over periods of positive and negative energy balance, as
well as over the entire lactation, for each of the 357 cows having a

lactation length of at least 250 days.

(13) Stage 1: NEIi/MBWi - be + bl(Reqt for SCMi+ WtChgi)/MBWi + ei

Stage 2: (NEIi-bOMBWi)/SCMi - b5 + bthChgi/SCMi + 8i

(14) Stage 1: NEIi/SCMi - b0 + bl(Reqt for MBWi+ WtChgi)/SCMi + ei

Stage 2: (NEIi-bOSCMi)/MBWi a b6 + bthChgi/MBWi + ei

Note that both (13) and (14) are per-unit-MBW models as described in

III.3.2. Also, performing the regressions in two stages produces co-

63

efficient estimates which are not best in the sense of minimizing resid-
ual variance. The sole justification for using this method is that it

could produce coefficients within biologically reasonable bounds.

3.4. Regressions considering autocorrelation among residuals

Because the data for each cow are sequential through time, it is
likely that residuals are autocorrelated" Four models were used to
examine the effects of including an autoregression term on coefficient

estimates. These models are described below.

(15) (NEIi - NE Reqt for MBWi+ WtChgi)/SCMi - bO + ei ,
where ei-(0,02)
(l6) (NEIi - NE Reqt for MBW1+ WtChgi)/SCMi - bO + ei ,

where ei - p*ei_l + u., u ~ (0,03)
(17) (MEIi - ME Reqt for MBWi+ WtChgi)/SCMi - b0 + ei
where ei-(0,02)

(l8) (MEIi - ME Reqt for MBWi+ WtChgi)/SCMi - b0 + e.

where ei - p*ei_1 + u-, u ~(0.0,21)

Models (15) through.(l8).are simple per-unitxMBW models to facilitate
comparisons among solutions for b0 and among estimates of p, the auto-
correlation coefficient. An algorithm was developed which enabled effi-
cient iteration for computing p. A complete description of the al-
gorithm with a FORTRAN implementation is presented in Appendix III.

This algorithm did not guarantee estimates of p within the parameter
space of (-l,1), but in application fewer than ten of 357 estimates from
each model were out of the parameter space.

Autoregression models were applied to 357 cows with at least 250

64

day lactations, over three durations: the entire lactation, and periods

of positive and negative energy balance.

4. Analyses of variance on estimated coefficients from selected models

Four models, (7), (10), (14) and (16) were selected and their
coefficients used in analyses of variance to determine the contribution
of various factors to the variance of regression coefficients. The
models were representative of those examined in this study: one was a
two-stage model, one included an autocorrelation coefficient, and the
remaining two were multiple regression models. The coefficients used
were from the period of the entire lactation rather than positive or
negative energy balance. .Analyses of variance were performed on a total
of nine coefficients from the four models.

The analysis of variance (ANOVA) model is Shown on the next page:

65

. . 2

where: '
degrees of
freedom
yijklm - regression coefficient
for a cow
p - constant 1
H81 - effect of 1th Herd-Season 24
RJ - effect of jth Ration 3
Tk - effect of kth Treatment 3
A1 - effect of 1th Parity group 2
Milkijklm - covariate of Milk production 1
from entire lactation
Milkijklm - covariate of squared milk 1
production
eijklm - random residual ~(0,02) 322

357 observations

Only main effects were included in the ANOVA, along with covariates of
milk and milk squared. The covariates were considered to examine the
belief that much variation in efficiency can be accounted for by differ-
ences in production. Four seasons were obtained by month of initiation
of lactation, with January through March denoted season 1, and so forth
in three month groupings. Several herds had no cows initiating lacta-
tions in one or more seasons, hence the herd-season effect has only 24,
rather than 28, degrees of freedom. Parity was considered as first,
second, third, and all later parities. Confounding between the heifer
ration and first parity reduced the number of degrees of freedom for

Parity to 2.

IV. RESULTS AND DISCUSSION

 

l. Partitioning energy intake into forms of output

The results of partitioning energy input into useful product are

shown in Tables IV.l and IV.2. Table IV.1 displays the utilization of

NE intake while ME intake is considered in Table IV.2. Requirements for

the various outputs were obtained from the National Research Council

(NRC, 1978) recommendations.

(1)

(2)

(3)

Several observations apply to both tables:

The proportion of energy required by milk production is higher
during periods of negative energy balance than positive energy
balance. This was expected, because during negative energy balance
the energy available from feed is supplemented by energy gained
from metabolized body tissue.

There are negligible differences in energy used for maintenance
between negative and positive energy balance.

The energy required for pregnancy support at any time during the
lactation is very small in comparison to that required for other
purposes. This is an indication that the influence of pregnancy on

our efficiency studies may be small.

66

67

Table IV.1. Percentage of net energy intake used for various
purposes, during periods of negative and positive
energy balance and over the entire lactation

 

 

Weight
Period Maint Milk Change Pregnancy Other
Negative 30.98 67.46 -8.54 0.08 10.02
energy balance
Positive 29.70 58.99 9.19 0.14 1.97
energy balance
Overall 29.94 60.58 5.88 0.13 3.48

lactation

 

Table IV.2. Percentage of metabolizable energy intake used
for various purposes, during periods of negative and
positive energy balance and over the entire lactation

 

 

_ Weight Heat
Period Maint Milk Change Pregnancy Increment
Negative 20.81 45.31 -5.74 0.05 39.56
energy balance
Positive 19.95 39.68 6.18 0.09 34.09
energy balance
Overall 20.11 40.73 3.95 0.09 35.12

lactation

68

The category Qghgp in Table IV.1 contains excess NE intake which
cannot be accounted for by the four production functions. One could
speculate that the NRC (1978) recommendation of constant maintenance
requirements throughout lactation with respect to metabolic body weight
may underestimate maintenance needs during negative balance. Another
part of its large value of 10.02% in negative energy balance may be
caused by an overestimation of energy metabolized by weight loss. There
are only about three body weight measurements during negative balance,
and that variable may therefore be more subject to error than either
milk or maintenance.

Table IV.2 indicates that the energy gained from the difference in
WtChg between negative and positive balance is divided rather evenly
between heat increment and milk production. Because the relative
amounts of energy expended on milk production and heat increment are
about the same, the even partitioning of extra energy from tissue might
be expected. 1

For all periods it is clear that milk production and maintenance
are the productive functions which require the most energy throughout
the lactation. Heat increment, though not a productive function,
accounts for a large percentage of ME throughout lactation, while the
energy needs for body weight change and pregnancy are relatively small.
2. Effect of half-life of energy absorption and percentage of

dailygresidual milk on energyputilization

Two different methods were used to examine the effect of varying
the rate of energy absorption through digestion, as well as the daily
amount of residual milk. Table IV.3 shows the correlations between NE

available in the bloodstream and daily solids-corrected milk synthesized

69

by the udder, when various half-lives are applied to energy intake and
several percentages of daily residual milk are assumed for milk
production. Table IV.4 presents results of several analyses, each using
the same model, for which only the percentage of residual milk and
half-life of energy availability were varied. Not all combinations of
energy half-lives and residual percentages were examined, but only those

most likely to show contrast.

Both Tables IV.3 and IV.4 indicate little effect of varying either
the half-life of energy or the percentage of residual milk on the
relationship between energy input and energy utilization. Note that the
values in Table IV.4 are mean coefficients computed from only seven
cows. However, the most extreme differences in parameters (between
half-life-O, residual-100% and half-life-l.5, residual-75%) produced
changes in coefficients of less than 10% in each of the seven cows and
three coefficients. For reasons described in 111.3.1.2 and 111.3.l.3,
ensuing regressions used a half-life for energy absorption of 0.75 days

and a 10% value for daily residual milk.
3. Determination of predicted coefficient values from literature

One of the objectives of this research was to develop models which
would use field-collected data to produce estimates comparable to those
from energy-chamber data. However, most of the models used in this
study have not been applied to energy-chamber data. Therefore, some
published coefficient estimates required adjustments to enable their

comparison to the solutions obtained in this study.

70

Table IV.3. Correlations between estimated NE available in bloodstream
and daily SCM synthesis for various half-lives of energy
absorption and various percentages of daily residual milk

Percentage of daily residual milk
Half-life of energy

 

 

absorption in days 0% 15% 25% 50%
0 .44 .43 .40 .40
0.75 .44 .43 .39 .39
1.0 .44 .43 .39 .39
1.5 .43 .42 .39 .39

 

Table IV.4. Comparison of mean estimated regression coefficients*
using various half-lives of energy absorption and
various percentages of daily residual SCM

 

 

 

 

Half-life of Percentage of daily residual milk

energy absorption

in days 0% 13% 25%

b0 bl b2 b0 b1 b2 b0 b1 b2

0 19.7 .152 .266 - 19.3 .159 .278
0.75 19.7 .152 .265 19.5 .157 .271 19.3 .160 .276
1.0 - - 19.3 .160 .274
1.5 ~ - 19.3 .160 .272

* model: NEI - bO + bISCM + sztChg + e

71

Four uses of energy were considered in this study: maintenance, SCM
production, pregnancy and body weight change. Published reports have
assumed that the amounts of energy required by these functions are
additive, as will this investigation. That is, the amount of energy
required by a cow is simply the sum of requirements for each of the four
functions. The computation of predicted values for each of the four
functions will be described. The average relationship between NE and ME
in this data set was

NE - .6717 * ME,
which is dependent on the energy concentration (NE per kg dry matter) of
the ration as inferred by equation (2) in section 111.2. This
relationship was used to adjust all NE requirements to ME requirements.
The following four sections will describe the computation of predicted
estimates of coefficients. All weights in the equations have units of

kg, and all energy measurements are in Mcal.

Maintenance. The NRC (1978) estimated NE requirements for maintenance
(NEMaint) by
NEMaint - 0.073 * MBW,
where MBW is metabolic body weight, or body weight to the three-fourths
power, as described in section 111.3.1.3. Predicted metabolic energy
requirements for maintenance (MEMaint) were computed by
MEMaint - NEMaint / 0'6717
- 0.109 * MBW .
Models which have an intercept obtain mean total daily maintenance

requirements, rather than requirements per unit MBW, as the estimate for

b0.

72

The mean MBW (MBW) for all cows was 121.7 kg'75. Therefore predicted
value for this coefficient is

NE - o. 073 * M——BW
”an": - o. 073 * 121. 7 - 8. 89 Mcal

ME . - 0.109 * MBW
C
mam - 0.109 * 121.7 - 13.27 Mcal

Solids-corrected milk production. NE requirement for SCM production
(NESCM) is

NESCM - 0.340 * SCM,
since milk production has been solids-corrected to 340 kcal/lb (NRC,
1978; Flatt and Reid, 1965). ME requirement for SCM production (MESCM)
is

MESCM - NESCM / 0.6717

- 0.506 * SCM .

The relationship between ME intake used for milk and net energy produced

as milk is the reciprocal of efficiency, or 1.0 / 0.65.

Pregnancy. As described in section 111.1, the variable Pregt represents

the weight of fetal tissues (e'0174t

) on day t of pregnancy. Moe et a1
(1970) computed NE requirements for pregnancy (NEPreg) of

NEPreg - 0.065 * Preg.
The predicted ME requirements (MEPreg) are

- 0.097 * Preg.

Bod

the

9%

“4

f0:

‘9

5118

4.\

73

Body weight change. NRC (1978) estimates the NE requirements for weight
gain (NE+WtChg) and weight loss (NE-WtChg) during lactation as:

NE+WtChg - 5.12 * WtChg , and

NE-WtChg - 4.92 * WtChg,
respectively. These correspond to ME requirements (ME+WtChg and
ME-WtChg) 0f

ME+WtChg - 7.62 * WtChg , and

ME-WtChg - 7.32 * WtChg .
The relationship between NE used for tissue gain or loss and the energy
in that tissue can be expressed in two ways: for tissue gain, the ratio
of tissue energy deposited per unit NE input; for tissue loss, NE
produced per unit of tissue energy metabolized. Because the ratio is in
the form of output per unit input, it can be interpreted as an
efficiency. For weight gain, this efficiency is 0.75, while for tissue
mobilization it is 0.82 (Moe et al, 1970). Thus, the net efficiency of
the complete process of tissue deposition and metabolization is 0.75 x
0.82 - 62%. The same efficiencies were used to compute ME utilization
for weight change, since the average relationship between ME and NE was

the constant multiple 0.6717.
4. Results from regression analyses

Eighteen regression models were examined, and their coefficient
estimates will be presented in tables grouping similar models together.

Three types of comparisons can be made within each table:

1) Estimates for each coefficient can be compared to those for other

coefficients. For example, b1 can be contrasted with b2, and so

forth.

74

2) Corresponding coefficients from different models can be compared.
If independent variables were completely uncorrelated, the expected
value of be, for example, remains the same regardless of model

used.

3) Estimates obtained from the same period of lactation may be compared.
For example, estimates obtained from data recorded during negative energy
balance may be contrasted to those from the entire lactation, or positive

balance.

The index numbers (1) through (18) will be used to refer to each of
the 18 models presented in section III. The number of animals included
in regressions depended on which period was being analyzed. For a cow
to be considered in a period of either positive or negative energy
balance, she was required to have at least 50 days gaining or losing
weight, repectively. This criterion was adopted to prevent cows only
marginally gaining or losing weight from unduly influencing mean
estimates. 1t eliminated 181 cows from being considered for negative
energy balance, although none were restricted from positive balance.
The number of cows included in a regression for any period were:

negative energy balance: n - 176;
positive energy balance: n - 357; and

entire lactation : n - 357.

Few cows were reported pregnant during negative energy balance. For
this reason, no coefficient estimates are listed for models including a

pregnancy term for periods of negative energy balance.

75

4.1. Multiple regression models

 

Tables IV.5 through IV.8 present mean coefficient estimates for
models (1) through (12), which are shown below. The subscript i
indicates day of observation. 4
(l) NEIi - b0 + bISCMi + e1
(2) NEIi - b0 + b1$CMi + b2WtChgi + e1

(3) NEIL - b0 + bISCMi + b2WtChgi + b3Pregi + 61

(4) Nari/nevi - b0 + b1(SCM1/MBW1) + e1

(5) NEIi/MBWi - b0 + b1(SCMi/MBW1) + b2(WtChgi/MBW1) + e1

(6) NEIi/MBWi - b0 + b1(SCMi/MBWi) + b2(WtChgi/MBWi) + b3(Pregi/MBWi) + ei

(3) M511 ‘ bo + biNEscu,1 + bZNEWtChg,i + 31

(9) "Eli ' bo + blNEscu,1 + bZNEWtChg,i + b3NEPreg,i + ei
(11) MEIi/MBWi - b0 + b1(NESCM’i/MBW1) + b2(NEwtChg,i/MBW1) + e.

l

(12)'MEIi/MBWi - b0 +b1(NESCM’i/MBW1) +b2(NEwtChg’i/MBW1) +b3(Pregi/MBWi) +ei

Models are grouped by method of energy intake measurement (ME or NE) and
whether they are adjusted per unit MBW. Before considering each
separately, some observations can be made which apply to all four
tables.

Within each table, for all combinations of models and periods, the
estimates of intercept were higher than predicted. Mean coefficients
for b1, corresponding to SCM, were low compared to values reported in
the literature. Estimates of coefficients for WtChg, b2, were variable
but mostly positive, with larger coefficients of variation than b0 or

bi. Finally, b3, the coefficient for Preg, is generally negative. The

311.

76

negative coefficient implies that supporting pregnancy generates rather
than requires energy, which is not biologically reasonable. The
standard deviation of mean coefficients tends to be largest when
estimates are made during negative energy balance, smaller for positive
energy balance, and smallest over the entire lactation. This is
attributable to the greater numbers of observations on each cow in the

latter two periods, compared to negative energy balance.

Table IV.5 contains results of regressions using models (1) through
(3). Comparing results among models, there appears to be little change
in b1 or b0 when the WtChg term is added to the model. Adding a
pregnancy term causes slightly greater changes in the coefficients.
Changes in coefficients estimated from different periods are not great
for either b0 or b1. Differences between periods are larger for the
coefficients of WtChg and Preg (b2 and b3), accompanied by larger

coefficients of variation than either b0 or b1.

Table IV.6 presents coefficients from models (4) through (6), whose
variables have been adjusted to a per-unit-MBW basis. If metabolic
weight were constant throughout lactation, estimates of the intercept
would be expected to differ from estimates using models (1) through (3),
while other coefficients would be identical. In practice, MBW was not
constant within animals, although its coefficient of variation was the
smallest among the four independent variables considered. Therefore the

coefficients for b1 through b3 all differ slightly from the first three

models.

In contrast to the first six models, models (7) to (12) measured

77

 

 

 

 

 

 

 

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78

 

soc. m_.m No.2 3m. meo.o emetoeem

 

 

 

 

 

 

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acmccwdou new: .mummn 3mzluwcslcmd m o» nmumsnem maoeoe Lou mucmwofiuuooo :oflmmmtwwt :mo: o.>H manna

79

independent variables in units of energy required for production, rather
than quantity of production. The reciprocal of any regression coeffi-
cient except for the intercept indicated the efficiency of conversion of

metabolizable energy into an output.

Results from using models (7) through (9) are shown in Table IVJL
Coefficients pertaining to milk production (b1) were less than unity,
‘which implies greater than 100% efficiency; Therefore this model was
unacceptable for estimating efficiency of ME conversion to SCM.
Likewise, accurate estimation of the efficiency of energy conversion to
weight change and fetal growth was difficult. With the exception of
estimates from negative energy balance, b2 was computed as less than
unity. Estimates of b3, the energy required per Mcal increase in energy
content of fetal tissues, were all less than zero. Generally, when Preg
was included in the model, it adversely affected.both the accuracy and

the precision of the remainder of the coefficients.

Table 1V28 contains mean coefficient estimates and standard
deviations of means from models (10) through (12). These models are
similar to models (7) through (9), but have been adjusted to a per-unit-
MBW basis. Regression coefficients for SCM and WtChg in models (7)
through (12) are expressed as ME intake per unit NE used for maintenance
or products. Reciprocals of these regression coefficients, that is, NE
output per unit ME intake, were interpreted as the partial efficiencies
of meeting the requirements of independent variables. Because a valid
efficiency cannot exceed 100%, coefficients producing efficiencies
greater than 100% were not regarded as biologically reasonable.

Coefficients for maintenance were about twice what has been

80

 

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cow. Pas. cow. Fmo.om mpo.om mom.mm Aw.

 

 

 

 

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81

 

 

 

 

 

 

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w.>H magma

82

reported, increasing with the number of terms in the model. Estimates
of intercepts were closer to predicted for periods having more
observations, such as over the whole lactation, than for those having
few observations, as during negative energy balance. The coefficients
for SCM (b2) also grew progressively worse as more variables were
included in the model and when fewer observations were used to obtain
estimates. Mean estimates of coefficients for WtChg (b3) and Preg (b4)
are also given in Table IVJL Although when computed from periods of
negative energy balance they approach estimates reported in the
literature, on the whole these estimates are less than unity, and often
less than zero. Coupled with the adverse effects of including WtChg and
especially Preg variables on intercept and SCM coefficients, there is

little benefit to including these two variables in the model.

4.2. Two-stage multiple regression analyses

Two-stage models used in this research are shown below.

(13) Stage 1: NEIi/MBWi - b0 + bl(NESCM,i + NEWtChg,i)/MBwi + ei
Stage 2: (NEIi-bOMBWi)/SCM1 - b6 + bthChgi/SCMi + ei
(14) Stage 1: NEIi/SCMi - b0 + bl(NEMaint,i + NEWtChg,i)/SCM1 + ei

Stage 2: (NEIi-bOSCMi)/MBWi - b5 + bthChgi/MBWi + 63

The results from two-stage regression are shown in Table IV.9, which
follows the same format as the previous four tables of this section.
Although the method of analysis differed from that of previous models,
the expectations of coefficients from literature reports, made under the
same assumption of independence among independent variables are

identical to models (4) through (6).

83

 

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aconcmamu new: maouoe emanates» CH mucowowmumoo :memwcmmt :mmz o.>H manna

84

Model (13), as was found with each of the previous models,
overestimated requirements for maintenance and underestimated those for
SCM. Mean coefficient estimate of WtChg varied greatly with the stage
of lactation, but had much higher standard deviations than those for
either maintenance or SCM coefficients, whose standard deviations were
in fact rather small.

Model (14) produced results closer to reported than any of the
other models examined to this point. The coefficient for maintenance,
though still 40% higher than reported values, differs by less than any
other difference produced from previous models. Part of this smaller
difference may be accounted for by some correlation between MBW and
WtChg, as the coefficient for WtChg (b3) was smaller than expected.
Finally, the b2 coefficient mean estimate, corresponding to NE required
per pound of SCM produced, matched almost exactly previously reported
research results. It was further encouraging that the standard
deviation of the mean coefficients for MBW and SCM were rather small.
This indicated that not only were the mean estimates of these
coefficients reasonable, but the coefficients measured for most of the
individual cows were reasonable as well. This property, that solutions
for most cows be biologically meaningful, had not been satisfied by any
of the previous thirteen models, and is important if we wish to estimate

biological efficiency for animals without requiring energy chambers.
4.3 Consideration of serial autocorrelation of residuals

The last type of model considered was designed to compare the
effects of an autoregressive residual term on estimates of energy

utilization for milk production. Models (15) through (18), used to

85

investigate the effect autocorrelated residuals, are listed below.

(15) (NEIi - NE Reqt for MBWi+ WtChgi)/SCMi - b0 + ei ,
where ei ~ (0,02) 4

(l6) (NEIi - NE Reqt for MBWi+ WtChgi)/SCM1 - b0 + ei ,
where ei - p*ei_1 + ui, u ~ (0,03)

(17) (MEIi - ME Reqt for MBW1+ WtChgi)/SCMi - b0 + ei ,

where e1 ~ (0,02)
(18) (MEIi - ME Reqt for MBWi+ WtChgi)/SCM1 - b0 + ei ,

Where e- '- p*ei-l + U. u ~ (0103)

1 i’

Two measures of energy intake were used, NE and ME. In each case,
requirements for maintenance and weight change were held constant over
all cows, so that only the coefficient for milk production was
estimated. Regression coefficients obtained with and without the
assumption of autocorrelation among residuals were compared.

Table IV.10 presents results from models using NE as the measure of
energy intake. The regression coefficient is larger than reported
regardless of whether the model is autoregressive, although b1 values
estimated without autocorrelation approached literature values more
closely. Table IV.11 shows results from models which used ME as the
measure of energy intake and held energy requirements for maintenance
and weight change constant. The reciprocal of b1 was taken as a measure
of efficiency of conversion of ME to SCM. As before, regression
coefficients were slightly higher than expected, resulting in computed
efficiencies of 55% to 60%. Again, though, inclusion of an
autoregressive residual term had more effect on the standard deviations

of coefficient means than on the means themselves.

86

 

 

 

 

 

 

 

 

 

Table IV.10 Mean regression coefficients from models with and without
autocorrelation coefficient, adjusted on a per-unit-MBW
basis with dependent variable measured as NE, over periods
of negative energy balance (-), positive energy balance
(+), and over entire lactation (A). Corresponding standard
deviations are parenthesized.

b1 [SCM] autoregression coefficient (p)
Model - + A - + A
(15) .424 .363 .376
(.010) (.004) (.004)
(16) .500 .415 .392 .685 .751 .769
(.061) (.041) (.013) (.013) (.006) (.006)
Reported 0.34

Table IV.11 Mean regression coefficients from models assuming
autocorrelation of residual terms adjusted to per-unit-MBW
basis with dependent variable measured as ME, over periods
of negative energy balance (-), positive energy balance
(+), and over entire lactation (A). Corresponding standard
deviations are parenthesized.

b1 [NESCM] autoregression coefficient (p)
Model - + A - + A
(17) 1.838 1.665 1.704
(.040) (.016) (.016)
(18) 1.692 1.833 1.732 .629 .689 .713
(.168) (.161) (.022) (.014) (.006) (.006)

 

Reported

1.54 -

 

87

By fitting an autoregressive model, we would expect that the
variance of within lactation prediction error would decrease. Figures
IV.1 and IV.2 illustrate differences in daily predicted ME intake
throughout the lactation of a particular cow, from models with and
without autoregression terms to actual data. The autoregressive model
succeeds in reducing the correlations among consecutive residuals, and
better follows the curve of daily energy intake. However, these figures
also suggest the primary difficulty with applying results from using
this type of model. To accurately estimate the energy required on day t
requires measures of production such as SCM, WtChg, and MBW which are
available. The autoregressive model also needs the residual from day t-
1, which cannot be available until a lactation is completed and
coefficients for regression and autocorrelation are computed. This
dilemma might be at least partially resolved as data sets with more than
one lactation per cow become available. The repeatabilities of
autocorrelation and regression coefficients may be high enough to permit
their estimation by an earlier lactation and use within later ones.

The second shortcoming with the autoregression models as
implemented in this research concerns the inability of any iterative
algorithm, such as the modified Cochrane-Orcutt (1949) algorithm used in
this study, to guarantee globally best estimates of the autocorrelation
coefficient or even ensure estimates within the parameter space (-1,l).
When autoregression parameters greater than unity are estimated,
regression coefficients frequently are so large or small in magnitude as
to be rendered useless. .As a result, population estimates can be
greatly affected by the number of individuals whose autocorrelation

coefficients are greater than unity. For example, Table IV 12 indicates

88

 

BO

70 4 Aatual

 

50 -‘ Predicted
5o .1
4o 4 , A ‘

. 1 l ,5
so -1‘ l i

20‘

 

ME Intake (Meal)
1 1W

 

10-1

 

 

l
1
I
l
I
o I I T I I 7 j I j j—fi j j

I I
O 40 80 120 160 200 240 280
Day of lactation

Figure IV.1 Predicted vs actual metabolizable energy intake in models
without an autocorrelation coefficient ,

 

BO
70 -‘ Actual
BO -' Predicted

_ AWHA.‘

 

  

 

l‘ . " ,
‘i'.“\ . a
. .1...

ME Intake (Meal)

 

 

 

 

i . . x ..
i '1 ‘ l '
20 '-
10 '1
o F I T I I 1 I 1 l f j 1 1 I
O 40 BO 120 1 60 200 240 280

Day of lactation

Figure IV.2 Predicted vs actual metabolizable energy intake in models
with an autocorrelation coefficient

89

the changes in population estimates for coefficients when cows having
extreme p's are progressively eliminated from the data set. Clearly,
the biggest change in estimates is obtained when cows with p greater
than unity are eliminated. Limitations of p < .95 or p < .90 have
comparatively small effects thereafter. Especially apparent is the
large reduction in the standard deviation of the mean estimates, due to

eliminating extreme animals, when those with p > 1.0 are deleted.

Table IV.12 Effect of eliminating cows having extreme autocorrelation
coefficients on means and standard deviations of means for
b0 and autocorrelation coefficient obtained over entire

 

 

lactation

Model (16)

Cows eliminated Mean p Mean b1

None .769:.006 .392:.013
p > 1.0 .768:.006 .379:.004
p > .95 .767:.005 .380:.004
p > .90 .754:.005 .376:.004

Model (18)

Cows eliminated Mean 2 Mean bl

None .713:.006 l.732:.022
p > 1.0 .712:.006 1.718:.018
p > .95 .7lli.006 l.715:.017
p > .90 .7OS:.OO6 1.706:.Ol6

 

4.4 Summary of estimates of partial efficiencies

Table IV.13 summarizes mean estimates of the partial energy
efficiencies of maintenance and lactation obtained from each of
the 18 models, All estimates were computed over the period of
the entire lactation. The efficiency of converting ME to milk or

maintenance is nearly the same, and reported as 65% by NRC

90

(1978). Only model (14) produced reasonable estimates of partial
efficiencies of both maintenance and lactation. Models (15) through
(18), while not designed to estimate partial efficiency for maintenance,
produced reasonable estimates of efficiency of lactation. Values
greater than unity, produced by models (1) through (13), are not
reasonable as true efficiency estimates. Their relative value may still
be useful to rank cows for partial efficiency of lactation, although

this question was not further investigated.

 

Table IV.13 Summary table of estimates of partial efficiencies
of lactation (k2) and maintenance (km)

Multiple regression models Two-stage models

 

 

 

I
|
km k1 : km kg
(1) .271 1.52 | (13) .325 1.18
(2) .292 1.35 | (14) .578 .649
(3) .259 1.75 |
I .
(4) .318 1.15 | Autocorrelation models
(5) .334 1.08 |
(6) .277 1.51 | k2
|
(7) .287 1.47 | (15) .601
(8) .309 1.32 | (16) .581
(9) .272 1.69 | (17) .588
I (18) .578
(10) .325 1.14 |
(11) .342 1.06 |
(12) .280 1.49 |

Reported value - 0.65

91

5. Analyses of variance on regression coefficients from
selected models

 

The results from eighteen regression models have been presented and
discussed. From them, four models were selected and used in analyses of
variance (ANOVA) to determine the effects of various factors present in
the data on coefficients for individual cows. The models were chosen to
be representative of the various combinations of independent and
dependent variables; one was a two-stage model, one included
autocorrelated residuals, and the remaining two were simultaneous

multiple regression models. The models chosen are listed below:

(7) ME - b0 + b1 ESCM + e

(10) ME - b1 EMBW+ b2 ESCM + e

(14) Stage 1: NE - b2 SCM + b' EMBW+WtChg + e
Stage 2: NE - b2 SCM - b1 MBW + b3 WtChg + e

(16) NEt ' NEMaint,t ' NEWtChg,t ' b1 SCM: + at

where et - p et_1 + ut , ut ~ (0.03)

The coefficients used were computed over the entire lactation rather
than only during positive or negative energy balance, to best reflect
the cows' overall efficiencies.

Factors in the ANOVA model were described in section 111.4. They
were herd-season, ration, treatment with Actaplanin, parity, and
covariates of total milk over the lactation and total milk squared. No
two-way or higher interactions were included.

Complete tabular results from the analyses of variance are included
in Appendix IV. A summary of these tables is presented in Table IV.14,

which allows the comparison of factors of significance across models.

92

Most evident from Table 1V213 is the importance of herd-season on nearly
all coefficients. Many possible reasons for influence of herd-season
exist, ranging from different qualities of feedstuffs throughout the
year and across herds, to temperature variation (possibly affecting
maintenance requirements), and varying care in measuring or recording

data among herds.

Table IV.13 Summary of significance of various factors on regression
coefficients from selected models

Model (7) | Model (10) | Model (14) | Model (16)

b0 b1 : b1 b2 : b1 b2 ‘b3 : rho b0
ms...” 1;; 1;: : 1:; 1;: : 1:41:11; : 1;; 1;;
Ration ns ns : ns * : ns * ns : ** *
Treatment ns ns : * ns : ns ns ns : ns ns
Parity ns ns : ns ns : ns ns ns : ns ns
Milk & Milk2 ns ns : * ns : ns **, ns : ns ns

** : a <.01
* : a <.05
ns : a >.05 (not significant)

93

The ration factor, which acts to partially block cows by production
level, significantly affects coefficients in four of nine analyses.
Although from this table it appears that the relationship between
coefficients and milk production is not strong enough to warrant
covariate terms, perhaps a simple blocking of production level into low,
medium, or high groups would be effective in explaining variance.

Finally, neither treatment with Actaplanin nor parity appeared to
have much effect on coefficients. We would expect the consequences of
ignoring these two factors to be small when studying differences in

coefficients among cows.

V. CONCEUSIONS

Data from Lilly Research laboratories was examined by 18 regression
models. The data consisted of measurements on milk production,
component percentages, body weights and intake through complete
lactations of 405 cows. Cows were distributed in seven herds, and fed
one of four rations by determined by production level and parity. A
nuisance treatment, dosage of the pharmaceutical Actaplanin, was also
recorded. Models were investigated for their ability to yield energy
utilization coefficients approaching those obtained using data from
animals in energy chambers.

Tabulation of the data revealed that an average of over 90% of net
energy during lactation goes into meeting requirements of milk
production and maintenance. Of all metabolic needs for energy during
lactation, pregnancy support was found to require the least amount of
energy, less than 1% in nearly all cases. The energy requirements for
gain or energy yield from loss of body tissue were also smaller than
those for either milk production or maintenance, generally in the range
of i 15% of net energy intake.

Multiple linear regression models were used to compute coefficient
estimates describing energy conversion into useful product. Compared to
previously published results, this method produced consistently higher
efficiencies for satisfying maintenance requirements, and lbwer for
meeting the needs of milk production. The efficiencies computed for

pregnancy and weight change were more widely variable across cows than

94

95

those computed for milk production and maintenance. Adjustment of
variables to a per-unit-MBW basis did not improve estimates compared to
those predicted from energy chamber work. Likewise, considering energy
as Net Energy versus Metabolizable Energy had only a modest effect on
the relative magnitudes of partial efficiencies for milk production and
maintenance. Finally, increasing the number of output products
considered as a function of energy inputs in a model adversely affected
the correspondence of resulting coefficients to published values from
energy chamber research.

A two-stage multiple regression procedure which fit milk alone in
the first stage, followed by maintenance and weight change in the
second, was superior to all other models in the comparison of computed
regression coefficients to published values. Further, the estimates of
partial efficiencies for the various forms of production were
biologically reasonable for nearly all cows. However, when maintenance
was fit first followed by milk and weight change, the fit was no better
. than for the multiple regression described in the previous paragraph.

Finally, the effect of assuming autocorrelated residuals was
examined. The main advantage to using an autoregressive model appeared
to be in its accuracy of predicting daily feed intakes from previous
days' productions and intakes. However, estimates for energy
efficiencies were somewhat poorer than from models without
autoregression, compared to reported values. A second difficulty was
the periodic occurence of autocorrelation coefficients outside the
parameter space, specifically greater than unity. This problem affected

a small number of cows, and could be overcome using more elaborate

computational techniques.

96

Analyses of variance were performed on resultant coefficients from
several models to ascertain common significant sources of variation.
Herd-season was found to be highly significant for one or more
coefficients from every model. Several coefficients were moderately to
highly affected by Ration, but not to the degree of Herd-season. The
nuisance variable of Treatment, as well as Parity and covariates of Milk
and Milk2 were, in general, not found to be significant sources of

variation.

This research has shown that estimating parameters of production
efficiency from data collected on-farm has the potential to supplement
expensive, limited energy chamber studies. Before widespread
application of these findings, however, several further questions must

be addressed:

1. The results and comparisons reported in this study deal only with
mean parameter estimates. Research must be conducted to show that
estimates for individual animals obtained from data collected on-
farm correspond to those from data collected on the same cows in
energy chambers. Examination of this question might require
gathering data for analysis from a small number of animals in
energy chambers, and using a subset of that data to emulate an on-
farm collection scheme. This subset would be analyzed as 1 have

described in this paper.

2. One of the shortcomings of the data set was the infrequency of body
weights on individuals. The effect of more frequent weighings

should be examined, and a weighing schedule developed which would

97

specify the number and days of weight measurements that optimize
estimation of a body weight curve. In this way, measurement error
for body weight change would be reduced, and daily energy balance

could be more accurately estimated.

3. The data for this research did not include observations from
subsequent lactations, nor from dry periods. Observations from
more than one lactation would enable the computation of
repeatabilities, while data from the dry periods could yield better
estimates of energy utilization for pregnancy, weight change, and

maintenance without the simultaneous influence of milk production.

Application of this research may be seen to benefit many facets of
the dairy industry. As automated feeding and data-collection systems
become more common on commercial dairy farms, a body of data could be
developed which would enable scientists to compute genetic parameters of
partial efficiencies. As the quantity of data grows, sire evaluation
for efficiency measures would become feasible. At the same time, the
genetic relationship between efficiency and milk production or
conformation could be computed.

To estimate coefficients of energy conversion into products on a
routine basis at the commercial dairy level, certain data must be
collected regularly. Minimally these include energy intake, milk
production, butterfat test, and body weight. The minimum necessary
frequency of data collection has not been addressed by this research and
may vary depending on the variable observed. The importance of frequent

body weighings, for use in computing rate of tissue gain or loss, should

be emphasized.

98

The application of efficiency data collected on a commercial herd
may produce immediate benefits to the herd itself. Because of the
logistics and expense of putting a commercial herd through an energy
chamber to collect data, little research has'been reported concerning
the effects of differences in efficiency on animal health. Also, the
effects of additives (such as growth hormone or antibiotics) or
management techniques (such as three- or four-times-per-day milking)
have not been studied within commercial herds. If these findings make
such research possible, tomorrow's dairy farmer may be able to tailor
his management of individual cows to maximize the profitability of each
one, and obtain the most profit, rather than simply the most milk, that

his herd can produce.

APPENDICES

Table 1.1.

Appendix I.

 

Tabulation of data

Distribution of cows among numbers of recorded milk weights

number of recorded milk weights

<200 201-225 226-250 251-275 276-300

301-325 >325

 

 

 

 

N of cows 36 4 12 52 233 68 0
Table 1.2. Distribution of cows among parities
parity

_1_ _2_ 3 _4_ 5 _§_ 7 8 other
N of cows 106 147 68 26 18 9 4 6 21
Table 1.3. Distribution of cows among calving groups

calving group

_1_ ._2 a a _s_ ....6. -7. . _§__ othe. r.

N of cows 107 97 81 45 28 20 10 3 14

99

100

Table 1.4. Distribution of cows among daily milk production averages
average milk production (lbs/day)
<35 35-40 40-45 45-50 50-55 55-60'60-65 65-70 70-75 75-80 289

N of cows 11 21 50 58 94 80 45 19 10 8 9

 

Table 1.5. Distribution of cows among months of initiation of lactation
month

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

 

N of cows 31 38 24 12 8 11 35 38 50 69 50 39

 

Table 1.6. Distribution of cows among treatments with Actaplanin

dosage code
BN CN DN EN error

N of cows 96 99 99 97 14

 

Table 1.7. Distribution of cows among herds

 

Herd location N of cows
Greenfield, IN 71
Western Kentucky 44
Pennsylvania 62
Southern Illinois 44
California 61
Michigan 64

North Carolina 59

101

Table 1.8. Distribution of cows among milk levels
milk level
Heifer Low Medium High error

N of cows 105 65 143 78 14

Appendix II.
Descriptions of algorithms used to modify variables
A. Adjustment of milk weights for actual daily milk produced

This adjustment must be used when the cow secretes on day 1 some
fraction p of the milk that she actually produces on day i. The actual
algorithm for adjusting milk secreted to milk produced on day i is:

301‘1
Milk producedi - 2 pi(Milk secretedi)
i-l

for example, when p-0.75, the milk produced on day 10 would be computed
by:

O.75(mi1k10) + 0.752(mi1k11) + 0.753(milk12)

where milki - milk secreted on day 1. However, this method is rather

expensive to use computationally. A numerical approximation used in
this research was

i .
Milk producedi - E p1(Mi1k secretedi)
i=1

Because of the relatively small daily change in milk producing ability
and the comparatively large distortion in milk produced caused by
residuals, this technique will approximate the first method quite well.
Its advantage is in computational simplifications, where daily milk
produced can be computed using the algorithm:

MILKP-MILK(1)
DO 1 I-l,NDAYS
MILKP - P*MILK(I) + (l.-P)*MILKP

l CONTINUE

where the first MILKP is milk produced on the current day, the second is
the previous day's milk produced, MILK(I) is milk secreted on current

day, and P is the fraction of milk produced on one day which is secreted
the same day.

102

103

B. Distributed delay for estimating energy availability

A delay routine is used to account for feed intake not being
instantaneously converted to energy, but rather gradually digested and
absorbed. Llewelllyn (1965) provided a source for a subroutine which
simulates such a delay.

SUBROUTINE DELDT(RINR,ROUTR,CROUTR,DEL,IDT,DT,K)
DIMENSION CROUTR(K)

definition of variables:
RINR - input rate
ROUTR - output rate
CROUTR - array holding intermediate rates
DEL - delay half-life; i.e. time for 1/2 input to be output
IDT - # of internal "micro-delays" to produce smoother output
DT - distance between inputs (i.e. 1 day)
K - length of CROUTR

0000000000

DELI-DEL*FLOAT(IDT)/(FLOAT(K)*DT)
ROUTRFO.
DO 2 J-l,IDT
RIN-RINR/FLOAT(IDT)
D0 1 I-l,K
ABC-CROUTR(I)
CROUTR(I)-ABC+(RIN-ABC)/DEL1
RIN-ABC
l CONTINUE
ROUTR-ROUTR+CROUTR(K)
2 CONTINUE
RETURN
END

To use such a routine, CROUTR is initialized to the first input rate,
and the subroutine is then called at regular intervals, with RINR as
input, and ROUTR as desired output.

C. Estimation of body weight curve from discrete weights

For purposes of this research, a fourth-degree polynomial was fit, but
the procedure is applicable to polynomials of any degree. There is a
danger, when using too high a degree, of obtaining a nearly singular
incidence matrix which introduces inaccuracies into the solutions. In
our case, the 60-bit single precision of a CDC Cyber series mainframe
computer combined with no more than quartic equations produced reliable
results for estimating weights to more than 5 digits. This was
sufficient for our purposes.

000000

104

SUBROUTINE WTCURV(WEIGHT,N,B)
DIMENSION WEIGHT(N),B(5)

description of variables:
WEIGHT - array of weighing days in col 1 and weights in col 2
B - solutions to 4th degree equation (output)
N - # of observations in WEIGHT

...initialize X'X and X’y to 0...(not shown)

X(l)-1.
DO 1 I-l,N

T-WEIGHT(I,1)

DO 2 I-2,S
X(K)-T*X(K-l)
CONTINUE

Y-WEIGHT(I,2)

...add X and y to X'X and X'y equations...(not shown)

CONTINUE

...solve equation X'Xb - X'y...(not shown)

RETURN
END

Appendix III.

 

Single pass algorithm of Cochrane-Orcutt procedure
for analyzing regression models
containing autocorrelated residuals

Ordinary multiple regression has the form

 

 

 

 

 

 

 

 

 

r i r
y1 X1,1 x1,2 x1,3 x1,4 xl,m b0
Y2 x2,1 x2,2 x2,3 x2,4 x2,m b1
y3 x3,1 x3,2 x3,3 x3,a x3,m b2
Y4 x4,1 X4,2 “4,3 X4,4 x4,m b3
b4
ynJ xn,1 Yn,2 xn,3 xn,4 xn,m bm
. .
r w
x1 e1
x2 e2
x3' + e3
xa' ea
’31' en
. .
y X b + e

105

 

 

e1
e2

e3

 

106

However, when residuals are autocorrelated, the error structure is

et - pet-1 + ut, where u~N(0,02uI)

 

 

and
r \
V(e) - 1 p p2 p3 p4
p 1 p 92 p3
p2 p 1 p p2
93 p2 p l p
p4 p3 p2 p l
L J
At time t,
yt - xt'b + et - xt'b + pet-1 + ut (l)
and at time t-l,
yt'l - xlt_1b + et_1 . (2)

Multiplying (2) by p and subtracting from (1) yields

yt ’ yt-l ' (Kt ' pr-l) b + ”t

107

which can be expanded

 

r w r 1
Y2 ‘ PYl Xé ' Pxi
Y3 ‘ PY2 Xé ‘ Pxé
Y4 ' PY3 ' Xé ' Pxé
y5 - py4 x5 - pr b + u
Yn ' PYn-l xfi ‘ ”Kn—l
r 1 L 1

 

 

 

or
y* - X? b + u .
Setting up the normal equations and solving,

b - (xi'x*)'1x*'y* .

Terms on the right hand side of this equation can be expressed as

n
*1?
X 'x ' {aij} a 2 (in ‘ PXk-l i)(xkj ' ka-l j)
k=2 ’ i
n n n 2n
- x .x . - p 2 x -x . - p E x .x . + p Z x .x - (3)
k k k k-l, k-l, k k-l, k-l,
k=2 1 J k=2 1 J k=2 1 J k=2 1 J
and
n
*, *
X y ' {Ci} = Z (in ' ka_1 17(Yk ' Pyk-l)
=2 '
n n n 2n
-Ex. - 2x . - 2x. + 2X - . (4)
k Yk P k-l, Yk P k yk-l P k-l, yk-l
k-2 1 k-2 l k=2 1 k=2 1

Note that each summation in (3) and (4) is constant with respect to p
and so needs only to be computed once and recalled for each iteration
when converging on p. Thus, b and p can be computed iteratively while

 

108
requiring only one pass through the data.

On each iteration, p is computed using the relationship between
consecutive residuals:

A A

et ' P et-l + ut

 

and
e - y - Xb
Therefore
n A A
2 e e
t-l t
A k-2
p .. . (S)
n A
2 e3
k-2

Numerator and denominator in (5) are computed by

nA A n A A
E e e - 2 (y - x b)(y - x b)
t-l t k—l k-l k k
k=2 k=2
n m A n m A n
= Z yk_1yk - 2 b. ( 2 xk-l .yk) - 2 b. ( Z xk'yk-l)
k=2 i=0 1 k-2 ’1 i=0 1 k=2 J
m m A A n
+ 2 E b b. ( E x .x .) (6)
i k-l, k
i-O j-O J k-2 l J
and
“A2 n A A
2 et - Z (yk - xkb)(yk - xkb)
k=2 k=2
n m A n m m A A n
= 2 ykyk - 2 2 bi ( E inyk) + 2 E bibj ( E inxkj) (7)
-2 i=0 k=2 i=0 j-O k=2

respectively.A NoteAthat each inner summation over n in (6) and (7) is

invariant to b and p, which enables computation on one pass through the
data.

Appendix IV.

 

Analyses of variance on coefficients from selected models

Table A.IV.1 Analyses of variance on estimates obtained over the
complete lactation from model (7):

(a) ANOVA for be

Factor df Partial SSQ MS F test
Herd-Season 24 8870.3098 369.5962 4.7060 **
Ration 3 369.6157 123.2052 1.5687
Treatment 3 401.6214 133.8738 1.7046
Age 2 59.8698 29.9349 0.3812
Milk + Milk2 2 277.5130 138.7565 1.7668
Residual 322 25289.1151 78.5376

Total 356 37999.6875

(b) ANOVA for b1

Factor ' df Partial SSQ MS F test
Herd-Season 24 51.0875 2.1286 7.7611 4*
Ration 3 1.5732 0.5244 1.9120
Treatment 3 0.5695 0.1898 0.6921
Age 2 0.0546 0.0273 0.0995
Milk + Milk2 2 0.1237 0.0619 0.2255
Residual 322 88.3154 0.2743

Total 356 147.5734

a -.05 a -.01-

Critical values: F24,322 - 1.55 1.83
F3’322 3 2.62 3.84 .
F2’322 = 3.02 4.66

109

110

Table A.IV.2 Analyses of variance on
complete lactation from

(3) ANOVA for b1

(b)

Critical values: F24,322 -

Factor

Herd-Season
Ration
Treatment
Age

Milk + Milk2
Residual

Total

ANOVA for b2
Factor

Herd-Season
Ration
Treatment
Age

Milk + Milk2
Residual

Total

ME/MBW - b0 +

df Partial SSQ MS
24 0.5660 0.0236
3 0.0034 0.0011
3 0.0394 0.0131
2 0.0008 0.0004
2 0.0319 0.0160
322 1.3870 0.0043
356 2.2018
df Partial SSQ MS
24 52.1432 2.1726
3 2.1370 0.7123
3 0.8797 0.2932
2 0.0815 0.0408
2 1.0528 0.5264
322 77.0205 0.2392
356 145.6503
a -.05 a -.01
1.55 1.83
F3,322 - 2.62 3.84
F2’322 - 3.02 4.66

estimates obtained over the

model (10)

b1 NESCM/MBW + e

uj

uac>uac>U1

test

.4752
.2592
.0468
.0963
.7077

test

.0831
.9781
.2259
.1704
.2007

*3!

**

111
Table A.IV.3 Analyses of variance on estimates obtained from
two-stage model (14)
Stage 1: NE/SCM - b1 + b' (NEMBW+NEWtChg)/SCM + e
Stage 2: (NE - b1 SCM)/MBW -.b0 + b2 WtChg/MBW + e

(a) ANOVA for b0

Factor df Partial SSQ MS F test
Herd-Season 24 0.1891 0.0079 2.6277 **
Ration 3 0.0136 0.0045 1.5071
Treatment 3 0.0056 0.0019 0.6257
Age 2 0.0008 0.0004 0.1250
Milk + Milk2 2 0.0113 0.0057 1.8839
Residual 322 0.9657 0.0030
Total 356

(b) ANOVA for b1
Factor df Partial SSQ MS F test
Herd-Season 24 2.1084 0.0879 4.4247 **
Ration 3 0.1823 0.0608 3.0606 *
Treatment 3 0.0273 0.0091 0.4583
Age 2 0.0278 0.0139 0.7001
Milk + Milk2 2 0.3265 0.1633 ‘8.2223 **
Residual 322 6.3931 0.0199
Total 356 9.2522

(c) ANOVA for b2
Factor df Partial SSQ MS F test
Herd-Season 24 499.5187 20.8133 0.5165
Ration 3 46.6595 15.5532 0.3860
Treatment 3 200.4571 66.8190 1.6581
Age 2 64.5340 32.2670 0.8007
Milk + Milk2 2 139.7847 69.8924 1.7344
Residual 322 12976.0263 40.2982
Total 356 14118.7647

a -.05 a =.Ol

Critical values: F24’322 - 1.55 1.83
F3’322 a 2.62 3.84

F2,322 . 3.02 4.66

112

Table A.IV.4 Analyses of variance on estimates including
autocorrelation coefficient obtained over the complete
lactation from model (16):

(NE: ' NEMaint,t ‘ NEWtChg,t)/SCM ' b0 + at
where et - p et_1 + ut ’iut ~ N(0.03)

(a) ANOVA for p

Factor df Partial SSQ MS F test
Herd-Season 24 0.7110 0.0296 3.2602 **
Ration 3 0.1174 0.0391 4.3049 **
Treatment 3 0.0381 0.0127 1.3975
Age 2 0.0040 0.0020 0.2190
Milk + Milk2 2 0.0214 0.0107 1.1786
Residual 322 2.9261 0.0091
Total 356 3.9029

(b) ANOVA for bO
Factor df Partial SSQ MS F test
Herd-Season 24 0.8773 0.0366 0.6149
Ration 3 0.6687 0.2229 3.7495 *
Treatment 3 0.1728 0.0576 0.9691
Age 2 0.2668 0.1334 2.2439
Milk + Milk2 2 0.3211 0.1605 2.7002
Residual . 322 19.1432 0.0595
Total 356 21.2083

(2 -.05 a -.01
Critical values: F24,322 - 1.55 1.83
F - 2.62 3.84
3,322
F2’322 = 3.02 4.66

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4A”

B C. 5

E nut a

DLlE

B D. an

6

Data

Du

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