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thesis entitled
Evaluating Reproductive Management

Changes in a Dairy Herd:
Effects of Lactation Curve Specification

presented by

Corey Catherine Risch

has been accepted towards fulfillment
of the requirements for

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6/01 c:/ClRC/DaIeDue.p65-p.15

EVALUATING REPRODUCTIVE MANAGEMENT CHANGES
IN A DAIRY HERD: EFFECTS OF LACTATION CURVE SPECIFICATION

By

Corey Catherine Risch

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Agricultural Economics

2002

ABSTRACT

EVALUATING REPRODUCTIVE MANAGEMENT CHANGES
IN A DAIRY HERD: EFFECTS OF LACTATION CURVE SPECIFICATION

BY

Corey Catherine Risch

An economic model was developed to evaluate reproductive management decisions for a
dairy farm. The model includes opportunity costs of management labor, capital, and
changes in herd structure associated with reproductive performance improvements. The
reproductive analysis was conducted using alternative lactation curve specifications to
examine the influence of lactation curve specification on reproductive management
decisions. Four common lactation curve models were fitted to daily milk yield data from
a dairy herd, pooled by parity and season of calving. Nonlinear models showed higher R2
and lower root mean square error than the Wood models, particularly for cow lactations.
Despite fit differences, all lactation curve models showed identical reproductive
management decision results. Scenario values assessed using the Wood models were
consistently lower than both the nonlinear models. Changes in labor and replacement
costs were larger than the changes in milk income over feed costs for all lactation curve

models.

Copyright by
COREY CATHERINE RISCH
2002

ACKNOWLEDGEMENTS

This thesis could not have been accomplished without the guidance and support of many
people. I would first like to thank my major professor, Dr. Christopher Wolf for his
guidance — and patience — down the long winding road that led to this thesis. I would also
like to thank my guidance committee, Dr. J. Roy Black and Dr. Jim Lloyd, for their
constructive feedback. As well, thank you to Joe Domecq and Gregg Hadley for their
personal and professional guidance throughout my graduate school experience. I would
also like to express heartfelt gratitude to my friends and family for their friendship and
support throughout this project. Your listening ears and much needed advice, as well as
all the fun stuff, was worth more than words can express. And finally, I would like to

thank my cats for sticking around through the whole thing.

iv

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

CHAPTER 1. INTRODUCTION
1.1 Reproductive performance
1.1.] What is reproductive performance?
1.1.2 Reproductive performance is important to profitability
1.1.3 Reproductive performance is on the decline
1.2 Herd reproductive management decisions
1.2.1 Evaluating reproductive management decisions
1.2.2 Opportunity costs of reproductive management decisions
1.3 Projecting milk yields for reproductive analysis
1.4 Objectives and overview
1 .4.1 Objectives
1.4.2 Overview
CHAPTER 2. EVALUATING CHANGES TO THE HERD REPRODUCTIVE
MANAGEMENT SYSTEM
2.1 Reproductive analysis methods in the literature
2.1.1 The optimal calving interval conundrum
2.1.2 Extended calving intervals with bST use
2.1.3 Herd reproductive decision analysis

2.1.4 Herd analysis methods

10

10

10

14

15

15

17

18

19

2.2 Reproductive management as an investment
2.3 Conceptual model
2.3.1 Step one: Determining the present value of lactation
2.3.2 Step two: Calculating the annuity equivalent
2.3.3 Step three: Incorporating the change in the herd structure
2.3.4 Step four: Comparing alternative reproductive management scenarios
2.4 Reproductive management groups
2.4.1 Parity and season of calving as management groups
2.4.2 Management groups in reproductive analysis
2.5 Empirical model
2.5.1 Step one: Determining the present value of the lactation
2.5.2 Step two: Calculating annuity equivalents
2.5.3 Step three: Incorporating changes in herd structure
2.5.4 Step four: Comparing alternative scenarios

2.6 Summary and Conclusions

CHAPTER 3. USING LACTATION CURVE MODELS TO EXTEND LACTATION IN
HERD REPRODUCTIVE ANALYSIS

3.1 Lactation curve models for herd reproductive analysis
3.1.1 Lactation curve functional forms
3.1.2 Persistency: Modeling milk yield decline
3.1.3 Modeling the pregnancy effect

3.2 Preliminary analysis: Individual lactation curves

3.2.1 Empirical lactation curve model

vi

21

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25

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49

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56

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58

58

3.2.2 Persistency measurements

3.2.3 Data and statistical methods

3.2.4 Preliminary analysis results and discussion
3.3 Pooling by management group

3.3.1 Empirical lactation curve models

3.3.2 Data and statistical methods

3.3.3 Results and discussion

3.4 Summary and conclusions

CHAPTER 4. EFFECTS OF LACTATION CURVE MODEL SPECIFICATION ON
REPRODUCTIVE MANAGEMENT DEDISIONS

4.1 Farm characteristics
4.1.1 Financial characteristics
4.1.2 Production characteristics and market prices

4.2 Herd reproductive management system: Current system and change
scenarios

4.2.1 Current herd reproductive management system.

4.2.2 Allocating additional labor to visual estrus detection.

4.2.3 Substitution of a timed breeding protocol for visual estrus detection.
4.3 Results and discussion

4.3.1 Annuity equivalents by management group

4.3.2 Decision results by lactation curve model

4.3.3 Sensitivity analysis

4.4 Summary and conclusions

vii

6O
62
65
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72
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108
109
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114
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122

CHAPTER 5. SUMMARY AND CONCLUSIONS 135

5.1 Summary of methods and results 135
5.2 Conclusions: Selecting an empirical lactation curve model 137
5.3 Avenues for further research of reproductive decisions 138

BIBLIOGRAPHY 142

viii

LIST OF TABLES

Table 2.1. Calving intervals examined in the empirical analysis.

Table 3.1. Comparison of fit across lactation curve models, from Vargas
et al. (2000). '

Table 3.2. Modifications to the Lactation Persistency Model.
Table 3.3. Persistency measures for the modified LPM.
Table 3.4. General description of the data set.

Table 3.5. Summary of regression results from individual lactation analysis.

Table 3.6. Persistency measurements for first lactation heifers by season of calving.

Table 3.7. Persistency measurements for mature cows by season of calving.

Table 3.8. General description of the data set used in group analysis by
management group.

Table 3.9. R-squared (R2) and root mean square error (RMSE) for heifers
by season of calving and stage of lactation.

Table 3.10. R-squared (R2) and root mean square error (RMSE) for mature cows
by season of calving and stage of lactation.

Table 3.11. Selected persistency results for group lactation curve analysis for
heifer lactations by season of calving and lactation curve model.

Table 3.12. Selected persistency results for group lactation curve analysis for
cow lactations by season of calving and lactation curve model.

Table 3.13. Differences in milk yield associated with various calving intervals
for heifer lactations by season of calving and lactation curve model.

Table 3.14. Differences in milk yield associated with various calving intervals
for cow lactations by season of calving and lactation curve model.

Table 4.1. Farm data used in reproductive management decision analysis.

Table 4.2. Comparison of price and herd characteristics across reproductive
management change scenarios.

ix

46

81

82

83

84

85

87

88

89

90

91

92

93

94

125

126

Table 4.3. Annuity equivalent values for heifer lactations by calving interval
and season of calving.

Table 4.4. Annuity equivalent values for cow lactations by calving interval
and season of calving.

Table 4.5. Comparison of the expected change in annualized net income for
four alternative reproductive management scenarios.

Table 4.6. Components of the expected change in annualized net income for
four alternative reproductive management scenatios: Labor,
replacement, IOFC, and other cash flows.

Table 4.7. Data used in sensitivity analysis for reproductive management decisions.

Table 4.8. Comparison of the expected change in annualized net farm income
with various scenario characteristics.

Table 4.9. Comparison of the expected change in annualized net farm income
with various farm financial characteristics.

Table 4.10. Comparison of the expected change in annualized net farm income
with various farm production characteristics.

Table 4.11. Comparison of the expected change in annualized net farm income
at various milking herd sizes.

127

128

129

129

130

131

132

133

134

LIST OF FIGURES

Figure 2.1. Evaluation model for changes to a herd reproductive management system. 47
Figure 2.2. Cows move through management groups in the herd in defined patterns. 48

Figure 3.1. Milk yield effect of pregnancyand extended calving interval
(delayed pregnancy) 95

Figure 3.2. Depiction of lactation by Wood, Morant, Diphasic, and LPM models. 96
Figure 3.3. Lactation persistency model and the four-know LPM used in this study. 97

Figure 3.4. Comparison of Wood lactation curve regression results with and
without correction for first degree serial correlation. 98

Figure 3.5. Lactation curve affected by seasonal milk yield depression. 99
Figure 3.6. Projected milk yields for first lactation heifers calving in the winter. 100
Figure 3.7. Projected milk yields for first lactation heifers calving in the spring. 101

Figure 3.8. Projected milk yields for first lactation heifers calving in the summer. 102

Figure 3.9. Projected milk yields for first lactation heifers calving in the fall. 103
Figure 3.10. Projected milk yields for cows calving in the winter. 104
Figure 3.11. Projected milk yields for cows calving in the spring. 105
Figure 3.12. Projected milk yields for cows calving in the summer. 106
Figure 3.13. Projected milk yields for cows calving in the fall. 107

xi

Chapter 1
INTRODUCTION

1.1 Reproductive performance

1.1.1 What is reproductive performance?

Reproduction is essential to milk production. All cows must maintain a continuous
reproductive cycle to keep producing milk at an economically viable level. Continuity of
the reproductive cycle is maintained by establishing and sustaining a pregnancy during
lactation; calving begins a subsequent lactation. Reproductive performance is the degree
of success in accomplishing pregnancy rapidly after each calving. Reproductive
performance can be measured with average pregnancy rate, the proportion of
nonpregnant cows that become pregnant in each estrous cycle. Pregnancy is
accomplished in two steps—estrusl must be detected and a successful breeding must take
place. The estrus detection rate (EDR) is the proportion of nonpregnant cows that are
correctly determined to be in estrus (and bred) in each estrous cyclez. The conception
rate (CR) is the proportion of cows bred in each estrous cycle that become pregnant. The

pregnancy rate is the multiplicative product of the success rates of these two steps.

 

l Estrus is the period of sexual receptivity that occurs at the beginning of each estrous cycle. Estrus
typically occurs every 18-24 days and last 12-24 hours. Ovulation occurs during estrus and is the only time
during the estrous cycle when conception can result from a breeding (Senger, 1997).

2 In this thesis, the estrus detection rate applies only to cows eligible for breeding by meeting any
requirement for minimum days to first service. Further, all cows detected in estrus are assumed to be bred.
Thus, the estrus detection rate is identical to the breeding rate.

The pregnancy rate(s) in the herd defines the calving interval distribution across cows in
the herd. The calving interval is the length of time between a cow’s successive calvings.
Higher levels of reproductive performance result in shorter calving intervals. The calving
interval can be voluntarily extended by delaying the first breeding. The biological
minimum calving interval in most herds is 12 months. Calving intervals of 18 months or

more can be considered relative reproductive failure.

1.1.2 Reproductive performance Is Important to profitability

Improving reproductive performance influences herd profitability by increasing the
frequency of calving (inversely, the calving interval), affecting both net income and labor
allocation. Shorter calving intervals are associated with additional calves born each year,
increased milk yield, and a decrease in cows culled and replaced due to reproductive
failure. Thus, revenues for milk and calves and feed, labor, and veterinary expenses are
all increased and culling revenues and replacement costs decreased by reproductive
performance improvements. The change in labor requirements for estrus detection,
breeding, and herd health is also a significant economic consideration. Estrus detection,
breeding, and herd health all require management and (or) skilled labor, which are

typically limited on farms and thus have high opportunity costs.

The dairy science literature has traditionally indicated that that short calving intervals
(~13 months) are higher in value than their longer counterparts because cows spend a
larger proportion of their lifetime in peak production (I-Iolmann et al., 1984; Schmidt,

1989). Estimated losses associated with low reproductive performance are significant.

Estrus detection failure was estimated to cost the dairy industry $300 million annually in
1994 (Senger). Plazier et a1. (1997) valued a one percent improvement in estrus detection
rate at $22.50 per cow. Using a partial budget model, Hady et a1. (1994) reported that
comprehensive improvements in reproductive performance for a 300 cow Michigan dairy
herd could increase net income up to $18,485. Schmidt (1989) estimated that reducing
the calving interval from 14 months to 13 months would increase income over feed and

variable costs by up to $21.50 per cow.

1.1.3 Reproductive performance is on the decline

Statistics indicate that calving intervals have been, on average, increasing. Calving
intervals in the mid-19803 averaged 13.5 months but now approach 15 months (Lucy,
2001). A combination of reasons has been suggested for these findings. In the dairy
science literature, the most common explanation is decline in fertility associated with

high levels of milk production (Lucy, 2001; Stevenson, 2001).

Management choices due to economic considerations, too, likely play a part in this
phenomenon. One critical decision is the allocation of Scarce farm resources to
reproductive management activities. Reproductive management requires significant
amounts of labor and capital, both of which are increasingly scarce resources for a farm.
Allocation of these resources to reproductive activities is intricately tied to reproductive
performance. Thus, allocating these resources to other enterprises on the farm and (or)
activities in the dairy enterprise is limiting to reproductive performance. Some producers

voluntarily reduce their allocation of labor to reproductive activities in order to reduce the

labor requirements of the dairy herd. Recent popular press articles indicate that the cost
of voluntarily extending the calving interval may be reduced in herds using bST, due to

high milk yield persistency (Galton, 1997; Roenfeldt, 1996).

1.2 Herd reproductive management decisions

The methods that a dairy farm currently employs to accomplish pregnancy define the
herd “reproductive management system.” A specific reproductive management system
can be associated with a particular level of reproductive performance. The managerial
decision is whether or not to change the current herd reproductive system. The decision
involves an assessment of the benefits of improving reproductive performance and the

costs of implementing the change.

The most common decision is whether to change estrus detection to improve reproductive
performance and (or) reduce labor requirements. Daily allocation of skilled labor is
important to successful estrus detection (F ogwell, 1998). Thus, management labor is
often allocated for its accomplishment. Visual estrus detection by management labor can
be replaced with hired labor. Because the skill level of hired labor is often lower than
management, hired labor usually accomplishes a much lower success rate than

management with the same allocation of time.

The labor required to improve reproductive performance, especially estrus detection, can

be partially replaced with capital. Technology options to improve reproductive

performance and save labor have proliferated (N ebel and Jobst, 1998; Senger, 1994;
Stevenson, 2001). Timed breeding protocols (e.g., Ovsynch) synchronize estrus such that
successful breeding can be accomplished without visual observation. Mechanical estrus
detection systems (e.g., HeatWatch) replace visual observation with pressure sensors

mounted on the cow to detect signs of estrus.

1.2.1 Evaluating reproductive management decisions

Because wide variation exists among estimates of the value of improving reproductive
performance, it is critical that individual farms evaluate their specific reproductive
management decisions using the farm’s data. Simulation studies have found the “value
of a day open”3 to be $0.10 per cow to $3.00 per cow (Holmann et al., 1984; Plaizier et
al., 1998; Schmidt, 1989). Some recent studies have indicated the possibility of positive
values to extending the calving interval for some cows — reducing reproductive
performance (Jones, 2000; Van Amburgh et al., 1997; Van Arendonk and Dijkhuizen,
1985). Jones (2000) concluded that this scenario was unlikely to be profitable for cows
with normal milk yield patterns. Reproductive simulation analyses indicate that the value
of improving reproductive performance varies with herd factors, including replacement
costs, feeding systems, and seasonal variation in milk production (James and Esslemont,

1979; Schmidt, 1989; Van Arendonk and Dijkhuizen, 1985).

 

3 The “value of a day open”, a common concept in the dairy science literature, can be defined as the
additional value to be gained when the calving interval is shortened by one day.

The manager’s decision to implement a reproductive technology depends upon the
benefits of the improvement in reproductive performance relative to the costs of the new
management system. Benefits of improved reproductive performance include increased
milk production and calf sales, combined with decreased forced replacement and
breeding needs. Costs include the labor and supplies (e.g., pharmaceuticals) required to
attain the improvement, as well as increased fresh cow costs associated with more

frequent calving and feed costs to support additional milk production.

1.2.2 Opportunity costs of reproductive management decisions

In addition to these changes in income and costs, reproductive management decision
analysis presents additional challenges in assessing the opportunity costs. Opportunity
costs are created when use of a resource in one activity precludes its use for another.
Reproductive management decisions involve traditional opportunity costs of labor and
capital. In addition, changes in reproductive performance across a herd create

opportunity costs in changing the herd structure.

The opportunity cost of capital is a key economic factor in reproductive decisions.
Changing reproductive performance shifts capital use over time. Shortening or extending
a calving interval represents a delay in the beginning of the next lactation, the return
associated with reproduction in this lactation. Calving intervals of different lengths
represent delays of varying lengths. In addition, the returns associated with reproductive
management investments implemented today occur over the subsequent years.

Incorporating the farm’s opportunity cost of capital allows comparison of reproductive

investments that change reproductive performance (calving interval lengths) to different

degrees with different reinvestment requirements.

The opportunity cost of the management labor, too, is important to reproductive
decisions. The cost to other farm enterprises of the using scarce management labor for
reproductive activities is difficult to estimate on an individual farm. Incorporation of this
value is critical to a reproductive analysis to reflect the value (costs) of an investment that

spares (uses) scarce management labor.

Finally, opportunity costs created when reproductive performance of one herd
management group is changed at the expense of another must also be considered. For
example, if a heifer’s calving interval is extended, then her higher-yielding cow lactation
is delayed. At the herd level, this means that the herd would become a higher proportion

of heifers if heifer calving intervals were systematically extended.

1.3 Projecting milk yields for reproductive analysis

Accurately projecting the milk yield effect of changes in reproductive performance is
difficult but may be critical for management decisions that appropriately reflect the
economic costs. Changing the length of lactation requires predicting milk yield for a
hypothetical situation. Reducing calving interval means that the appropriate portion of
the lactation must be removed, and lengthening the calving interval requires that an

additional period of lactation be added.

Milk yield ascends rapidly after calving, peaking at 40-70 days after calving. Peak yields
may be fleeting or continue on for months, as is common in first lactation. Alter peak,
milk yield declines slowly and progressively through the remainder of lactation. Late
lactation milk yield is a key opportunity cost of the decision to reduce the calving interval
— it is replaced with early lactation milk yield in the next lactation. Conversely, the
opportunity cost of the decision to extend the calving interval is the early lactation milk
yield that is replaced by the milk yield at the end of the lengthened lactation.
Underpredicting the milk yield in the extended portion of the lactation would overvalue
an investment that improves reproductive performance (shortens calving interval). If the
farm implemented the investment, it would fail to realize the projected increase in net

income for the dairy enterprise.

Across individual cows, persistency of milk yield4 is key to the value of shortening the
calving interval (Jones, 2000; Van Arendonk and Dijkhuizen, 1985). Low persistency of
milk yield (rapid decline in yield after peak) is associated with a high value to shortening
the calving interval. Highly persistent milk yields can result in a positive value to
extending the calving interval (Van Arendonk, 1985; Jones, 2000). These findings have
critical implications for the importance of the milk yield characterization in determining
the value of changing the calving interval. However, persistency is not specifically

defined such that findings can be applied in dairy herds.

 

4 Persistency of milk yield refers to the rate of milk yield decline after peak yield. The milk yield of a cow
with a highly persistent milk yield declines very slowly.

Lactation curve models used in reproductive simulation studies vary significantly in their
depiction of milk yield decline as well. The most common lactation curve model, used
reproductive analyses by Hady (1994) and Jones (2000), is the incomplete gamma
firnction proposed by Wood, which assumes proportional decline in milk yield over
lactation. In contrast, Van Arendonk (1985) and Olds (1979) use models that assume a
linear decline. Each of these shapes lead to a different value of the milk yield change that

results from extending or shortening lactation.

An empirical lactation curve can be fit to herd milk yield data for individual farms,
especially those with daily milk yield data. The lactation curve model provides structure
for assessing the change in milk yield that reflects the unique lactation curve shape of the
herd. The Wood model is desirable for this purpose because it has a simple mathematical
form that can be estimated using linear regression methods. However, evaluation studies
generally indicate that the Wood model is not as accurate as more complicated altemative
firnctions in modeling milk yield over lactation. These studies show the Wood model to
result in low r-squared (R2) values, as well as serially correlated error terms because the
the functional form is inconsistent with the actual shape of lactation (Congleton and

Everett, 1980; Vargas et al., 2000).

A number of nonlinear models have been recently proposed as alternatives to the Wood
model. These models show higher R2 values and less serial correlation of residuals than
the Wood model. However, these models have more complicated mathematical forms

that require more sophisticated methods to fit farm data.

1.4 Objectives and overview

1.4.1 Objectives

The objective of this thesis is to develop an evaluation method for herd reproductive
management decisions using a feasible lactation curve model suitable for farm analysis.

Specifically, this research seeks to accomplish the following objectives:

0 develop an evaluation model for herd reproductive management decisions that
compares the values of alternative reproductive investments using appropriate
economic methods and utilizes input information available in herd production and

financial records;

0 examine the impact of empirical lactation curve model selection on the results of
reproductive management decision analysis by comparing the analytical results using

various common lactation curve models; and

0 demonstrate the economic and lactation curve model applied to a case farm,

evaluating alternative reproductive technologies.

1.4.2 Overview

In this thesis, an economic model is developed to evaluate herd reproductive management

decisions using methods that account for opportunity costs of capital and labor. Present

10

values for each lactation, converted to annuity equivalents, place all calving intervals on
the basis of annualized returns. The annuity equivalents are then weighted by the herd’s
calving interval composition to determine the total value of the herd. Comparison of the
values for the current herd against the value of alternatives determines the most profitable

reproductive management decision.

Four empirical lactation curve models are fitted to the daily milk yield data for a dairy
farm — two variations of the Wood model and two nonlinear models. The reproductive
analysis is conducted using the results from each lactation curve. Four reproductive
management alternatives are considered — two that allocate additional labor to

reproduction and two that substitute technology for labor.

Despite differences in estimates of the milk yield effects of the changes in reproductive
performance, all lactation curve models yield the same reproductive management
decision. Changes in labor and replacement costs exceed the changes in milk income
over feed costs for all lactation curve models. Thus, the simpler Wood model is an
appropriate choice of empirical lactation curve model for reproductive management

decision analysis.

11

Congleton, W. R., Jr., and R. W. Everett. "Error and bias in using the incomplete gamma
function to describe lactation curves in dairy cattle." Journal of dairy science 63,
no. 1 (1980): 101-108.Galton, D. M. "Extended calving intervals, BST may be
profitable." F eedstufifs (1997).

Hady, P. J ., J. W. Lloyd, J. B. Kaneene, and A. L. Skidmore. "Partial budget model for
reproductive programs of dairy farm businesses." Journal of dairy science 77, no.
2 (1994): 482-491.

Holrnann, F. J ., C. R. Shumway, R. W. Blake, R. B. Schwart, and E. M. Sudweeks.
"Economic value of days open for Holstein cows of alternative milk yields with
varying calving intervals." Journal of dairy science 67 (1984):636-643.

James, A. D., and R. J. Esslemont. "The economics of calving intervals." Animal
production 29(1979): 157-162.

Jones, B. L. "Economic consequences of extending the calving intervals of dairy cows
treated with recombinant bovine somatotropin." University of Wisconsin Center
for Dairy Profitability (Working Paper) (2000).

Lucy, M. C. "Reproductive loss in high-producing dairy cattle: where will it end?"
Journal of dairy science 84, no. 6 (2001): 1277-1293.

Nebel, R. L., and S. M. J obst. "Evaluation of systematic breeding programs for lactating
dairy cows: a review." Journal of dairy science 81, no. 4 (1998): 1 169-1 174.

Olds, D., T. Cooper, and F. A. Thrift. "Effect of days open on economic aspects of
current lactation." Journal of dairy science 62 (1979): 1167-1170.

Plaizier, J. C. B., G. J. King, J. C. M. Dekkers, and K. Lissemore. "Estimation of
economic values of indices for reproductive performance in dairy herds using
computer simulation." Journal of dairy science 80, no. 11 (1997): 2775-2783.

Plaizier, J. C. B., G. J. King, J. C. M. Dekkers, and K. Lissemore. "Modeling the
relationship between reproductive performance and net-revenue in dairy herds."
Agricultural systems 56, no. 3 (1998): 305-322.

Roenfeldt, S. "BST -- Extended calving intervals pay." Dairy Herd Management, April
1996, 36-38.

Schmidt, G. H. "Effect of length of calving intervals on income over feed and variable
costs." Journal of dairy science 72, no. 6 (1989): 1605-1611.

Senger, P. L. "The estrus detection problem: new concepts, technologies, and
possibilities." Journal of dairy science 77, no. 9(1994): 2745-2753.

Senger, P. L. Pathways to pregnancy and parturition. lst ed. ed. Pullman, WA:: Current
Conceptions, 1997.

12

Stevenson, J. S. "Reproductive management of dairy cows in high milk-producing
herds." Journal of dairy science 84, no. E. Suppl. (2001): E128-E143.

Van Amburgh, M. E., D. M. Galton, D. E. Bauman, and R. W. Everett. "Management
and economics of extended calving intervals with use of bovine somatotropin."
Livestock production science 50 (1997): 15-28.

Van Arendonk, J. A. M. "Studies on the replacement policies in dairy cattle. II. Optimum
policy and influence of changes in production and prices." Livestock production
science 13, no. 2 (1985): 101-121.

Van Arendonk, J. A. M., and A. A. Dijkhuizen. "Studies on the replacement policies in
dairy cattle. III. Influence of variation in reproduction and production." Livestock
production science 13, no. 4 (1985): 333-349.

Vargas, B., W. J. Koops, M. Herrera, and J. A. M. v. Arendonk. "Modeling extended
lactations of dairy cows." Journal of dairy science 83, no. 6 (2000): 1371-1380.

13

Chapter 2
EVALUATING CHANGES TO THE HERD REPRODUCTIVE

MANAGEMENT SYSTEM

Comparing lactation curve models in proper context requires a reproductive management
decision analysis framework. That is, to determine whether the choice of lactation curve
model affects analysis results. An appropriate framework for a herd manager evaluating
a reproductive management decision compares the values of reproductive performance
under the current system and with the proposed change by considering its costs and
benefits for the herd, including the opportunity costs of labor and capital of changes in
reproductive management. Further, the evaluation must standardize calving interval
alternatives in comparable units. Finally, to facilitate farm use, the model must use input

information easily derived from common herd records.

This chapter outlines a conceptual and empirical model for evaluating the expected
change in herd value associated with specific management change scenarios. In Chapter
4, use of this model is demonstrated on a case herd. The analysis is run using alternative
lactation curve specifications in order to evaluate the effect of lactation curve

specification on reproductive decision results.
In this model, reproductive management is treated like an investment, with changes in the

management system and reproductive performance shifting capital investment and

returns over time. The first step in establishing the value of a reproductive management

14

change is determination of the present value and annuity equivalent values for lactations
with different calving intervals. Associating a calving interval distribution with the
expected level of reproductive performance allows these values to be summed to the total
herd value. The reproductive management decision is evaluated by comparing the values

of alternative management scenarios against the value of the current herd management.

2.1 Reproductive analysis methods in the literature

2.1.1 The optimal calving interval conundrum

Many studies in the dairy science literature have sought to establish a rule of thumb for
the “optimal calving interval”. Although studies have established that shorter calving
intervals are generally associated with higher income, they provide limited insight into
reproductive management decisions. The values in these studies reflect average income
over feed and selected variable costs (IOFVC) for individual cows — not the investments
and management changes in the herd that must be made to improve the herd reproductive

performance.

Louca and Legates (1968) found that 13 month calving interval for heifers and a 12
month calving interval for mature cows5 maximized milk yield using regression analysis
of DHIA data. Follow-up studies reported that income over feed and selected variable

costs is also maximized with 12 to 13 month calving intervals. Olds (1979) found that

 

5 In this document, “heifer” refers to a milk-producing cow in her first lactation. Similarly, “mature cow”
refers to a milk-producing cow in her second or greater lactation.

15

income over feed costs was reduced when calving intervals exceeded 12 months, by
$1.18 per cow per day for mature cows and $0.71 per cow per day for first lactation
heifers. Holrnann et al. (1984) found that 13 month calving intervals would result in
$0.21 to $0.40 per cow per day more income over feed costs than 15 month calving
intervals in simulated Texas herds. Schmidt (1989) incorporated variable costs for
bedding, marketing, and replacement, finding that calving intervals exceeding 13 months
are associated with decreases in income over feed and variable costs of $0.10 to $0.71 per
cow per day open. No changes were reported in the Optimal calving interval at evaluated

milk prices, feed costs, and milk yield levels (Holmann et al., 1984; Schmidt, 1989).

Van Arendonk and Dijkhuizen (1985) questioned the assumption that there exists an
optimal calving interval for all cows. The results from their stochastic dynamic
simulation model of insemination and replacement decisions indicated different optimal
calving intervals for cows classes based upon parity", days open, and season of calving.
Optimal calving intervals ranged from 12 to 18 months across these cow classes. Cow
classes associated with greater persistency of milk yield in late lactation had longer
optimal calving intervals, indicating that milk yield patterns through lactation were
shown to influence the optimal calving interval. Limiting calving intervals for all cows

in the herd to less than 16 months was associated with reduced net income.

 

6 Lactation number, e.g., if parity equals one, the cow is in her first lactation.

16

2.1.2 Extended calving intervals with bST use

After the introduction of bST, a debate emerged about whether bST-related increases in
persistency of milk yield lead to longer optimal calving intervals. Although results from
field trials have suggested that bST use makes extended calving intervals profitable,
methodological problems in theses studies lend question to whether this conclusion

should be widely accepted.

Van Amburgh et a1. (1997) conducted a field trial to evaluate extended calving intervals
on “real farms.” Their conclusion that the delayed breeding group was more profitable
than their short calving interval counterparts is questionable, due to significant
methodological difficulties. The study randomly assigned cows in nine herds to 13.2 and
16.5 month calving interval groups, setting the minimum days to first service of 60 and
150 days, respectively. However, many cows in the trial did not become pregnant
consistent with this planned schedule. As a result, milk yields at the end of lactation for

these cows were projected using “standard adjustment factors” rather than actual data.

Arbel et a1. (2001) conducted a similar study on high-producing Israeli herds with similar
lactation curves to the Van Amburgh study. These investigators, too, concluded that the
delayed breeding group was more profitable than the control group. In this study,
however, the economic value of the groups was calculated on a per-day basis from the
beginning of lactation through the first 150 days of the next lactation. Since the dry
period is more diluted for cows with a longer initial lactation, values are biased toward

longer calving intervals.

17

Jones (2000) evaluated these recommendations in a simulation using net present value
(NPV) analysis to compare annualized returns across calving intervals with milk yield
patterns consistent with bST use. Annualized returns were not improved with extended
calving intervals; rather, retums were maximized with a 13 month calving interval. Jones
concluded that extended calving intervals, up to 15 months, would be optimal only for
lactations with unrealistically high persistency (<6% decline per month). These results

were not sensitive to milk price, peak milk production, or opportunity costs of capital.

2.1.3 Herd reproductive decision analysis

The optimal calving interval question does not fully represent the reproductive
management decisions made by a dairy farm manager. The managerial decision to
change the current herd reproductive management system requires consideration of the
benefits and costs of the decision. Improvements in reproductive performance may
increase IOFVC but also require an investment in additional labor, training, or

technology to improve estrus detection and / or breeding success.

The marginal change in net revenue associated with increasing reproductive performance,
both EDR and CR, is highly related to previous reproductive performance (Pecsok et al.,
1994). Reproductive performance improvements face diminishing marginal returns.
Oltenacu et a1. (1981) evaluated the profitability of improved reproductive efficiency
with a dynamic simulation model that reflected the higher success rates and increased

costs of more intensive reproductive efforts. The scenarios with highest profitability

18

were at the middle values of reproductive performance (55% estrus detection rate and
50% conception rate). Diminishing returns on investment of time and money into
breeding program were apparent above these levels.

Reproductive management decisions depend upon the methods and expected
performance improvement associated with the change scenario under consideration.
Hady et a1. (1994) evaluated the decision to hire additional labor to improve reproductive
performance on a Michigan dairy farm using a partial budget model. If the reproductive
performance improved such that days to first service decreased from 80 to 60 days, EDR
and CR increased from 50% to 60% and 35% to 50%, respectively, the total increase in
net income was expected to exceed $18,000. However, if only CR was improved (to
40%), then the net income was expected to increase by $1,226. The net income change,
as well as the decision to hire additional labor, were affected by milk price and

replacement costs.

2.1.4 Herd analysis methods

A partial budget model, such as the one used by Hady et a1. (1994), quantifies the total
changes in the revenue and cost effects of the management change, holding all other
aspects of the farm constant. The model isolates changes in net income that result from
reproductive management changes. However, comparing the total change in net income
across alternative management system changes requires that the alternatives have the
same investment life. Also, opportunity cost of capital is not recognized using this
method. Because the model is based upon changes in the average days open, it assumes

that calving intervals within the heifer and mature cow groups are normally distributed.

l9

Jones’s (2000) net present value model views a cow’s reproductive life as an investment
- beginning with her purchase, continuing with cash flows through each lactation, and
ending with a salvage value. The optimal calving interval is the one that maximizes
annualized net income. This straightforward investment model accounts for opportunity
costs and compares calving interval alternatives in standardized units. However, the
model also requires a fixed number of lactations in a cow’s productive lifetime, an

unreasonable assumption on farms where culling is tied to reproductive performance.

The dynamic programming model developed by Van Arendonk and Dijkhuizen (1985)
evaluates decisions to inseminate and (or) cull at each estrus throughout lactation,
considering both the opportunity costs and the inherent risk and uncertainty in the
decisions. The model was designed, however, to evaluate decisions within a reproductive
management system, not potential changes to the system. Additionally, this complex
model was not intended for on-farm use but rather for development of management

guides for herd management decisions.

To evaluate reproductive management decisions, a herd needs a framework that:

0 compares the values of reproductive performance under the current system with the
proposed change by considering the marginal costs and benefits for the herd;

o incorporates opportunity costs of labor and capital in reproductive management
changes;

0 evaluates the calving interval alternatives in comparable units; and

20

0 uses input information easily derived from common herd records.

2.2 Reproductive management as an investment

Reproductive management is an investment because it involves capital use that affects
returns over time. A farm manager invests capital and other resources to accomplish
pregnancy for cows in the breeding herd. The continuing investment into the
reproductive system and the resulting reproductive performance influences returns to the
dairy enterprise over the following years. Reproductive management and performance

changes alter these herd returns in months and years after the change is implemented.

The herd reproductive investment can be subdivided into the investment in each cow-
space in the herd. Each cow-space continuously contains a lactation; these lactations
vary in calving interval. In a herd maintaining a constant size, each space in the herd is
continuously occupied. Each lactation that is completed - by beginning a new lactation
or exiting the herd — is “replaced’ with another lactation. This replacement is equivalent
to reinvestment in another lactation. The calving interval is thus the length of the
investment in a lactation and, as such, its length defines the frequency of reinvestment. A
lactation that included a pregnancy is replaced with a cow lactation, while a nonpregnant
lactation ends with culling and is replaced with the lactation of a replacement heifer.

The dairy farm manager’s decision to modify the current herd reproductive management

system involves changes to both the lactation investments and the distributions of calving

21

intervals (investments) across the herd. The additional investment in estrus detection and
breeding involved in accomplishing a change in performance alters the cash flows of the
individual lactations. Changes in herd reproductive performance alter the distribution of
the calving intervals in the herd. An improvement in performance leads to a higher
proportion of lactations with short calving intervals — with more frequent reinvestment.
With consistent performance, the herd will ultimately reach a new steady state

distribution that can be evaluated against the old one.

Decisions regarding reproductive management changes can be evaluated using
investment analysis tools. Net present value examines changes in cash flow over time,
reflecting the inherent lag between investment and return associated with the capital
investment. To evaluate a potential reproductive management change, we quantify the
changes to the value of the calving interval distribution — both the changes in the lactation
investments and the change in the frequency of reinvestment. We can then compare the
total herd value across all considered reproductive management scenarios and selecting

the scenario with the highest value.

2.3 Conceptual model

A present value simulation model was developed to evaluate potential changes to a
reproductive management system. The conceptual model, depicted in Figure 2.1, is
adapted from J ones’s (2000) calving interval analysis for use with herd reproductive

management decisions. The model is not intended to determine the optimal calving

22

interval, but rather it allows comparison of the values of alternative reproductive
management changes. This model evaluates only the difference between the value of the
“original” herd and the same herd after the management change once steady state has
been reached. The adjustment time required for implementation is not accounted for in

this analysis.

The goal of the analysis is to determine the expected change in herd value if the proposed
reproductive management change were adopted. A proposed change should only be
adopted if the expected value of the herd with the proposed change exceeds the herd’s
value under the current reproductive management system. These values can be
determined by evaluating the reproductive management investments in each lactation and
the calving interval distributions under the current and proposed reproductive

management systems.

Determining the values of the current and proposed reproductive management systems is
a four-step process. First, the cash flows in lactations of different calving interval
scenarios are quantified and standardized to their value at the beginning of lactation using
present value analysis. Then, annuity equivalent values of each of these lactations can be
determined and the annualized values compared. The herd value is the weighted sum of
the annuity equivalent values according to the distribution of calving intervals. Finally,

the values of alternative management change scenarios can be compared.

23

2.3.1 Step one: Determining the present value of lactation

The first step is to determine the value of each calving interval’s lactation standardized to
the same point in time — the beginning of the lactation, at calving — for each management
change scenario. The present value of lactation is calculated by using the farm’s
opportunity cost of capital to discount the cash flows in each period of lactation to the
first period. The farm’s opportunity cost of capital is the return that one could earn from
the best alternative use of capital. The sum of the discounted cash flows represents the

present value of the lactation:

(l) PVij = [CFnj * PVIFk,n] , and

:iibdz

l

(2) PVIFM = _1_
(1+k)n ,
where PVij = present value of lactation with calving interval j in scenario i,
CFnj = incremental after tax cash flow for calving interval j in period n,
N = total number of periods, and
PVI Fk, n = present value interest factor with discount rate k for period n,

k = farm’s opportunity cost of capital (discount rate).

All cash flow changes affected by calving interval are included in the present value
calculation. This includes cash flows that vary in magnitude and (or) timing across
calving intervals (e. g., milk income, feed costs). Those cash flows associated with
specific stages of lactation (e.g., fresh cow, breeding, and dry cow costs) must also be

incorporated, since the effects of reinvestment frequency changes will be reflected in the

24

annuity calculation. These cash flow changes may be comprised of the changes in

revenues and expenses after taxes, the depreciation tax shield, and net working capital.

2.3.2 Step two: Calculating the annuity equivalent

Because the present values of each lactation represent investments of different lengths
they must be converted to a repeating annualized value for any comparison to take place.
The calving intervals can be compared on the basis of annualized expected return by
converting the present value of the lactation to their annuity equivalent value. The
annuity equivalent is the perpetual stream of income that a lactation with the particular
calving interval would generate each year given an infinite constant scale replacement of
the calving interval at the opportunity cost of capital. Constant scale replacement implies
that, within the herd, each lactation with a 15 month calving interval is replaced with
another lactation with the same calving interval and an identical cash flow stream (i.e.,

milk revenues). The replacement lactation is not necessarily fiom the same cow.

The annuity equivalent value for each calving interval for each lactation is the present

value of the lactation adjusted by an annuity factor based upon the investrnent’s length,

 

(3) A3,, = pvij ,
PVIFAkJ,
1 - 1
(4) pVIFAm = (1+k)“ ,
k

where AEj = annual equivalent value of calving interval j in scenario i, and

PVij = present value of lactation for calving interval j in scenario i,

25

PVI FAj = present value annuity factor for calving interval j,
k = monthly discount factor, and

n = total number of periods (months) in the calving interval.

2.3.3 Step three: Incorporating the change in the herd structure

The annualized values for the current and the proposed management scenario account for
the change in the value of each of the calving interval investments. The distribution of
these calving intervals in the herd will also change. With a consistent pregnancy rate
culling rates for both reproductive and nonreproductive culls, the herd will eventually
settle into a steady state calving interval distribution. That is, the number of lactations in
the herd with each calving interval will be stable over time. Once this steady state
distribution is determined, the value of a scenario can be calculated as the weighted sum
of the annualized values of the calving intervals by the scenario’s steady state

distribution:

E

5

II
“lib/Jar

H

where Vi = value of scenario i to the herd,

p (CIj) = number of cows in the herd with calving interval j under scenario i.

2.3.4 Step tour: Comparing alternative management scenarios

If the scenario value of the proposed change exceeds the current scenario value, then the
investment adds value to the herd and should be undertaken. If not, then the current

reproductive management system should be maintained. A scenario with a lower value

26

than the current herd is expected to decrease the value of the herd and should not be
implemented. If multiple changes are under consideration, then the value of each
scenario should be compared to the current herd value. If the changes are mutually

exclusive, then the highest positive value change should be implemented.

2.4 Reproductive management groups

The identical constant scale replacement assumption implies uniformity in reproductive
management decisions, pregnancy rates resulting the same management system, and all
analytical components (e.g., milk yield patterns over the course of lactation) across all
cows in the analysis. While this may not be valid for an entire herd, many herds are
subdivided into groups of cows with similar characteristics in order to improve
management efficiency. Cows are treated uniformly within these management groups,

managed for the best interests of the group rather than an individual cow.

2.4.1 Parity and season of calving as management groups

Season of calving and parity are common bases for management groups in many herds.
First lactation heifers have different physiological needs than mature cows, since they
have not reached full maturity at the time of calving. In some herds, cows are physically
separated into these parity groups to better meet the nutritional and social needs of first
lactation heifers. Season of calving groups are separated by time, and differences in

management across $838011 vary across farm.

27

Milk yield patterns

Both parity and season groups influence milk yield patterns over the course of lactation. -
Factors such as nutrition, health, and climate may influence peak yield and (or) the rate of
milk yield decline itself, depending upon the stage of lactation and nature of the effect.
Heifer milk yields peak lower, at a later lactation stage (days in milk), and decline at a
slower rate (pounds of milk yield loss per day) (Friggens et al., 1999). Heifers are also
less subject to the accelerated milk yield decline in late stages of pregnancy - that is, they
show a smaller pregnancy effect (Oltenacu et al., 1980). Also, total milk yields of heifers

are consistently lower than that of their mature counterparts.

Season of calving impacts the shape and scale of the lactation curve, with particular
effects on persistency (Danell, 1982a). Seasonal patterns tend to occur similarly each
year within a particular herd, although the nature of these patterns are unique to each herd
(Rowlands et al., 1982). The season of calving effect in most herds consists of seasonal
heat stress and feed changes, which are common in the spring and summer (Garcia and
Holmes, 2001). These seasonal milk yield effects interact significantly with stage of

lactation (N gwerume, 1994).

As a result, the lactation curves of cows calving in various seasons reflect these effects
differently. Garcia and Holmes (2001) found that spring calving cows in New Zealand
show more persistent milk yields than their winter calving counterparts. Cows calving in

summer show consistently lower but more persistent production than their fall and winter

28

calving herdrnates (N gwerume, 1994). Oltenacu (1980) found that cows calving July

through September showed the largest pregnancy effect.

2.4.2 Management groups in reproductive analysis

Because of differences in management and milk yield patterns, parity and season of
calving are key determinants of the value of reproductive performance improvement. In
particular, first lactation heifers are expected to have smaller production and profit losses
than mature cows due to their more persistent milk yields (Olds et al., 1979). Modeling
seasonal differences in milk production, both James and Esslemont (1979) and Delorenzo
et a1. (1992) found notable differences in the optimal calving interval across cows calving
in different seasons. These differences are evident across annuity equivalent values

calculated for each management group.

Reproductive decisions for management groups cannot be accurately analyzed separately
because management groups are not independently affected by herd reproductive
management changes. When pregnancy rates and the resulting calving interval
distributions are different across groups of cows, the relative sizes of management groups
may change. For example, if pregnancy rate of cows calving in the summer decreases (or
improves less than) winter calving cows, winter calving cows will comprise a greater
proportion of the herd at steady state. When relative management group sizes shift due to
reproductive performance changes, the tradeoff of one group for another creates an

opportunity cost.

29

In addition, the relative sizes of management groups are heavily influenced by culling
assumptions in the reproductive analysis. If culling is assumed to occur consistently after
a constant number of lactations or months in the herd, then relative management group
sizes do not change. In most herds, however, a fixed number of cows are culled each
year for reasons not related to reproductive performance, such as low production, injury,
or illness. In addition, cows are culled if they fail to conceive by a particular stage of
lactation, i.e., the calving interval becomes too long. Under these culling guidelines,
unequal reproductive performance across groups leads to unequal culling (and
replacement), which results in unequal management group sizes. For example, a
disproportionate improvement in heifer reproductive performance would lead to relative
increases in the culling of mature cows, resulting in a greater proportion of first lactation

heifers comprising the herd.

Analysis of herd reproductive management changes can incorporate the differences in
annuity equivalent values across management groups. The annuity equivalents and
calving interval distributions are weighted by management group sizes in Step three to
account for the relative change. Steady state management group sizes are determined
using the pregnancy rates and culling rates for each management groups to quantify the
movement between each group. Figure 2.2 depicts the defined paths of cows in the herd
across four management groups -- parity (heifer and cow) and two seasons. In steady
state, group sizes are stable -- no net movement occurs between groups, and movement in
equals movement out of each group. Movement between groups is quantified and used to

determine the number of cows in each steady state management group.

30

2.5 Empirical model

The simulation model was developed to quantify the value of alternative reproductive
management scenarios related to changes to the estrus detection system. Such changes
could include allocating additional labor to visual observation or replacing visual
observation with a number of technology alternatives in order to increase the estrus
detection success rate. Because of the number of management alternatives available,
estrus detection usually offers more potential to improve reproductive performance than

other aspects of reproductive management (Stevenson, 2001 ).

Cows were pooled into eight management groups, defined by parity and season of
calving. Two parity groups were defined as heifers (first lactation) and cows (second and
later lactations). Four season of calving management groups were defined, each
representing three calendar months of the year. A uniform distribution of calving over

the months within each season of calving management groups was assumed.

As shown in Table 2.1, ten calving intervals were examined at three week intervals (the
length of one estrus cycle) from 11.5 months to 17.75 months. The lengths of pregnancy
(gestation) and the dry period were fixed at 40 weeks (280 days) and 8 weeks (56 days),
respectively. Lactations that would remain nonpregant beyond 264 days in milk,
consistent with the 17.75 month calving interval, are considered cull lactations. This
criterion is consistent with the longest optimal calving intervals found in Van Arendonk

and Dijkhuizen (1985).

31

An additional lactation was developed to represent lactations that terminate with culling
for reproductive reasons. Reproductive cull lactations continue for 12 months, at which
time the lactation is simultaneously terminated via culling and replaced with a new heifer
lactation. In this model, culling occurs at 365 days in milk (or earlier if milk yield falls
below 50 pounds per day). Replacement occurs at the end of the 365 day lactation,
regardless of the “date” of culling. Thus, all cull cow and heifer lactations are replaced

with a heifer lactation in the same season of calving.

The conceptual model outlined in Section 2.3 can be applied more generally than the
model proposed here. The model can be modified to accommodate any change in herd
reproductive performance, such as new breeding techniques or a change in the time of
first breeding. The model could be also modified for use with other management groups,
calving intervals, and culling assumptions. This discussion is beyond the scope of this

research.

2.5.1 Step one: Determining the present value of the lactation

Establishing cash flow vectors

The columns of each matrix represent the calving intervals in the management group,
with the net cash flow in each period (3 weeks) through the lactation represented in each
row. Because the longest calving interval has 26 periods, all cash flow matrices have 26
rows. The matrices of expected net cash flows for calving intervals in each management

group are created from individual cash inflow and outflow matrices of elements affected

32

by a change in reproductive management. The net cash flow matrix is calculated by

combining the cash inflow and outflow matrices:

P o
(6) (=ij = Z Iijn - 2 OUTlmn
p=l q=l
where Cij = a j x n matrix representing the net cash flows in each period n for

a lactation with calving interval j in management group m,

Iij = a j x n matrix representing cash inflows in each period n
associated with cash inflow activity p and calving interval j in
management group m,and

OU'I‘ltun = a j x n vector representing cash outflows in each period n
associated with cash outflow activity q and calving interval j in

management group m.

All changes in after-tax revenues and expenses, depreciation, and net working capital that
vary in magnitude or timing across calving intervals, in addition to those associated with
specific stages of lactation must be included in the analysis. Relevant cash inflows
include milk, calf, and culling revenues. Relevant cash outflows consist of feed,
veterinary, breeding, labor, dry cow, and replacement expenses. Matrices were
developed based upon cash flows grouped for similar production structures. The
elements of each matrix (e.g., milk, feed) were derived from a matrix of the expected
physical units of each cash flow event in each period over the lactation multiplied by a

scalar unit price.

33

Labor and tax expenses. Because of their intricate relationship with specific events and
cash flows throughout lactation, changes in labor and tax expenses are incorporated into
the cash flow matrix for the activity in which it is used. The tax structure in this analysis
reflects a sole proprietorship or partnership farm operation. All revenues and expenses in

this analysis are considered taxable at the ordinary income tax rate, except as noted.

Labor costs associated with the change in calving interval consist of the wages paid for
hired labor and the opportunity cost of management labor. Hired labor costs are
considered variable to the dairy enterprise at an hourly rate consisting of all wages and
benefits provided. Management labor on a dairy farm is often a scarce resource; as such,
allocating it to reproduction requires that it be removed from another farm activity. Thus,
management labor use for reproductive management represents an opportunity cost to the
remainder of the farm operation. Since such opportunity costs represent lost income,

they are considered tax deductible at the ordinary income tax rate.

Milk revenues and feed expenses. Milk revenues are affected by both the change in
lactation length and frequency with which a new lactation begins. Shorter calving
intervals are inherently associated with a shorter lactation, but the high yield stages early
in lactation occur more frequency. Milk revenues are calculated for each period of
lactation (excluding the dry period) using an empirical lactation curve fitted to herd milk
yields. Alternative lactation curve specifications and the applicable empirical methods

will be examined in Chapters 3 and 4.

34

Feed expenses are closely associated with milk production, as additional feed intake is
required to support the additional milk production. One additional pound of feed on a dry
matter basis is required for every 2.0 pounds increase in milk production (Council, 1988).
Feed expenses are deducted at the ordinary income tax rate (1999). The formulation of
the ration would remain constant, since the milk production change results from truncated
lactation length and more frequent calving. Feed expenses are directly associated with

milk production and assessed in the same period.

Fresh cow revenues and expenses. Calf revenues, veterinary expenses, and herd health
labor costs that occur in the first month of lactation are realized more fi'equently with
shorter calving intervals. All calves are considered to be sold by the dairy herd
enterprise. Bull calves are typically sold in the weeks following birth, and heifer calves
are sold or transferred to the replacement heifer enterprise. Mastitis and metabolic
disorders are most prevalent in the first few weeks of lactation. Cows afflicted with these
disorders require veterinary care and additional labor for their treatment. Cows and
calves require special care during the first weeks of lactation, requiring allocation of

additional labor.

Breeding apenses. Breeding expenses vary with calving interval when the estrus
detection rate is changed. A voluntary waiting period of 60 days was used for this
analysis. All cows were considered eligible for estrus detection, and if detected,
breeding. Anestrus and other factors delaying days to first service were not modeled. All

cows detected in estrus are serviced. The breeding and associated labor costs for one

35

breeding are associated with the last breeding for each calving interval. An expected
number of breedings equal to the estrus detection rate would apply to all prior periods
after 60 days in milk. Breeding and associated labor expenses are taxable at the ordinary

income tax rate.

Culling and replacement. Only cull cow sales associated with reproduction are
considered in this analysis, as other culling strategies are assumed unaffected by
reproductive performance. Culling revenues and replacement costs are assessed in the
last period of a cull lactation. Replacement expenses consist of the expenses associated
with obtaining the replacement animal. Income from the sale of cull cows is taxed at the
capital gains tax rate. To facilitate analysis, heifer calves are considered sold and
replacements purchased. Replacement purchases result in a non-deductible change in
cash flow that alter the farm’s depreciation over the 5-year MACRS investment life. The

purchase of replacement heifers increases the farm’s depreciation tax shield.

Variable dry period expenses. Unlike feed for the milking herd, feed expenses for dry
cows are not tied to milk production. Rather, dry cow feed expenses are assessed on a
daily basis. A constant dry period of eight weeks was considered for all lactations. Dry
cow costs were realized in the last three periods of the lactation. Although the amount of
dry period expense does not vary across calving intervals, the calving interval does
determine the frequency with which this expense is realized. Shorter calving intervals are

associated with a greater proportion of time spent in the dry period.

36

Present value of lactation

The net cash flows by period can be discounted back to determine the present value of
each lactation in management group m. The present value represents the value of the
lactation at the beginning of that lactation. The values across calving interval represent
different lengths of time. The present value of the lactation is determined from the
product of a present value interest factor matrix and the net cash flow matrix for each

management group:
(7) Pm = PVIFk'n * Cij,

where P... is a 1 x j column vector containing the present values of lactation for
calving interval j in management group m,
PVI Pk, n is a n x 1 row vector containing the present value interest factor
for each period n (since calving) in a lactation, based upon the herd’s
discount rate k, and
Can is the net cash flow matrix representing the cash flow in each period

n for lactations with calving interval j in management group m.

2.5.2 Step two: Calculating annuity equivalents

The column vectors Pm that contain the present value of lactation for calving intervals
within each management group can be combined into a single 11 x 8 matrix for the herd,
with each element [m,j] representing the present value for a lactation in management
group m with calving interval j. The A matrix, which contains the annuity equivalent

values for calving intervals in each management group, is derived by multiplying the P

37

matrix by a square matrix, the diagonal elements of which contain annuity factors with

the respective k and n values. That is,

(8) Ajm = ij * PVIFAkm

where Ajm is a j x m matrix containing the annuity equivalent values for lactations
in each management group m with calving interval j,
ij is the m x j matrix containing the present value of lactation by calving
interval and management group, and
1311117711.,n is a square j x j matrix containing the present value interest
factor for annuities with reinvestment in the nth period, based upon the

herd’s discount rate k.

2.5.3 Step three: Incorporating changes in herd structure

Determining calving interval distributions for each management group

The A matrix contains annualized values for each of the calving intervals in each
management group. In determining the total herd value, expected calving interval
distribution must be calculated for each management group. These calving interval
distributions can be calculated from the pregnancy rates for each management group,
since the pregnancy rate indicates the expected proportion of nonpregnant cows
conceiving in each estrus period. Let C be a m x j matrix such that

(9) c[mrj] = PRm * NPm,j-il

38

where

C [m, j ] is element [m,j] in matrix C, the proportion of the management
group m with calving interval j,

PRm = the pregnancy rate for management group m, and

NPm, j - 1 = the proportion of the management group not pregnant after

estrous cycle associated with calving interval j.

Calculating management group sizes

The steady state distribution of cows across management groups can be derived from a

transition matrix '1‘ and a herd size matrix M. Each element mm; in T represents

movement from group m; to group m2 and can be derived fiom equations defining each

management group by the composition of that movement. One row must be modified to

reflect the total herd size as the sum of the groups. The result is

(10) Tx

where

H.

'r is a square m x m matrix, representing the steady state movement
amongst management groups m,

X is a 1 x m row vector of variables identifying the number of cows in
each management group where the cows originated, and

H is an m x 1 matrix identifying the net result of the movement amongst
management groups. All elements are zero except in the row modified to
represent the sum of the groups totaling the herd size, where the element

contains the size of the milking herd.

39

Rearranging equation (9), the steady state management group sizes — contained in the x

matrix — can be solved as

(11) x = HT“;

where 'I"1 = inverse of matrix T.

Determining herd structure

The 8 matrix represents the steady state distribution of the herd by management group
and calving interval. Combining the management group sizes -- the diagonal elements of
matrix X -- with the with calving interval distribution for each management group —
matrix C -- the number of cows with each calving interval in each management group can

be calculated as

(12) s = c * diag(X),

where S is a j x m matrix identifying the number of cows with calving interval j
in each management group m,
C is a j x m matrix of the calving interval distribution for each
management group, where each element [j,m] is the proportion of each
management group m having the calving interval j, and
diag (X) is a m x 1 vector containing the diagonal values from matrix x,

the groups sizes of each management group m.

40

Total herd values for each reproductive management scenario
The value of reproductive management alternative i, Vi, is the sum of the diagonal
elements of a matrix created from the product of the new herd distribution and the

annuity equivalent value matrices:

(13) Vi = Z} diag[AS]i - Ii,

where X diag [AS] 1 is the sum of the elements in a m x 1 vector of the

diagonal elements fi'om the product 115,,

A is the m x j matrix containing the annuity equivalent values for calving
intervals in each management group -- element [m, j ] is the annuity
equivalent value for a lactation in management group m with calving
interval j,

S is a j x m matrix identifying the number of cows with calving interval j
in each management group, and

I; is a scalar value of the annuity equivalent value of any residual

implementation costs for scenario i.

2.5.4 Step tour: Comparing alternative scenarios

The value of each alternative management change scenario, V1 is compared to the value
of the current management system, V0, to determine if the management change is
undertaken. If V1 > V0, then the investment is expected to add value to the herd and

should be implemented. If not, then the current reproductive management system should

41

be maintained, since implementation is expected to decrease the value of the herd and
should not be implemented. For multiple projects, each V1 should be compared, and the

highest value scenario selected.

2.6 Summary and Conclusions

A reproductive management decision analysis model was developed to evaluate expected
changes in herd value associated with specific alternative management change scenarios.
Changes in the management system and reproductive performance were evaluated by
calculating present value and annuity equivalent values for lactations with different
calving intervals. To determine the total herd value under the proposed management
system, the annualized values were associated with the calving interval distribution based
on the expected reproductive performance of the proposed system. Change scenarios can
be evaluated by comparison to the value of the current management system and amongst
alternatives. This model examines only the current management scenario against
alternative management change scenarios once they reach steady state. The model does

not account for herd values while the herd is in transition.

This model utilizes herd information that can be derived from common herd management
and financial records. Most input information can be calculated from herd prices,
statistics, and characteristics. Like other model inputs, information for milk yield
projections is available in the production records of most records. Herd managers

wishing to fit an empirical lactation curve model to their herd’s data to assist in milk

42

yield projections have a number of options. However, the tradeoff between effort and

accuracy is not clear from past research.

The remainder of this thesis evaluates the use of empirical lactation curves for milk yield
projection for reproductive management decision analysis. In Chapter 3, milk yield data
for a herd is analyzed using commonly recommended empirical lactation curves fi'om the
literature. The milk yield projections resulting from these lactation curve models are
used in a reproductive analysis for the herd in Chapter four to determine if the choice of

lactation curve model influences reproductive analysis results.

43

Arbel, R., Y. Bigun, E. Ezra, H. Stunnan, and D. Hojman. "The effect of extended
calving intervals in high-yielding lactating cows on milk production and
profitability." Journal of dairy science 84, no. 3 (2001): 600-608.

Danell, B. "Studies on lactation yield and individual test-day yields of Swedish dairy
cows. 1. Environmental influence and development of adjustment factors." Acta
agriculturae scandinavica 32 (1982).

DeLorenzo, M. A., T. H. Spreen, G. R. Bryan, D. K. Beede, and J. A. M. v. Arendonk.
"Optirrrizing model: insemination, replacement, seasonal production, and cash
flow." Journal of dairy science 75, no. 3 (1992): 885-896.

Friggens, N. C., G. C. Emmans, and R. F. Veerkamp. "On the use of simple ratios
between lactation curve coefficients to describe parity effects on milk
production." Livestock production science 62, no 1 (1999): 1-13.

Garcia, S. C., and C. W. Holmes. "Lactation curves of autumn and spring calved cows in
pasture-based dairy systems." Livestock production science 68 (2001): 189-203.

Hady, P. J ., J. W. Lloyd, J. B. Kaneene, and A. L. Skidmore. "Partial budget model for
reproductive programs of dairy farm businesses." Journal of dairy science 77, no.
2 (1994): 482-491.

Holrnann, F. J ., C. R. Shumway, R. W. Blake, R. B. Schwart, and E. M. Sudweeks.
"Economic value of days open for Holstein cows of alternative milk yields with
varying calving intervals." Journal of dairy science 67 (1984): 636-643.

James, A. D., and R. J. Esslemont. "The economics of calving intervals." Animal
production 29 (1979): 157-162.

Jones, B. L. "Economic consequences of extending the calving intervals of dairy cows
treated with recombinant bovine somatotropin." University of Wisconsin Center
for Dairy Profitability (Working Paper) (2000).

Louca, A., and J. E. Legates. "Production losses in dairy cattle due to days open." Journal
of dairy science 51 (1968): 573.

National Research Council. Nutrient Requirements of Dairy Cattle. Washington DC:
National Academy Press, 1988.

Ngwerume, F. "Application of a multi-trait animal model to predict next test-day milk
production." Michigan State University, 1994.

Olds, D., T. Cooper, and F. A. Thrift. "Effect of days open on economic aspects of
current lactation." Journal of dairy science 62 (1979): 1 167-1170.

Oltenacu, P. A., T. R. Rounsaville, R. A. Milligan, and R. H. Foote. "Systems analysis
for designing reproductive management programs to increase production and
profit in dairy herds." Journal of dairy science 64, no.10 (1981): 2096-2104.

Oltenacu, P. A., T. R. Rounsaville, R. A. Milligan, and R. L. Hintz. "Relationship
between days open and cumulative milk yield at various intervals from parturition
for high and low producing cows." Journal of dairy science 63(1980): 1317.

Pecsok, S. R., M. L. McGilliard, and R. L. Nebel. "Conception rates. 1. Derivation and
estimates for effects of estrus detection on cow profitability." Journal of dairy
science 77, no. 10 (1994): 3008-3015.

Rowlands, G. J ., S. Lucey, and A. M. Russell. "A comparison of different models of the
lactation curve in dairy cattle." Animal production 35 (1982): 135-144.

Schmidt, G. H. "Effect of length of calving intervals on income over feed and variable
costs." Journal of dairy science 72, no. 6 (1989): 1605-1611.

Stevenson, J. S. "Reproductive management of dairy cows in high milk-producing
herds." Journal of dairy science 84, no. E. Suppl .(2001): E128-E143.

Van Amburgh, M. E., D. M. Galton, D. E. Bauman, and R. W. Everett. "Management
and economics of extended calving intervals with use of bovine somatotropin."
Livestock production science 50 (1997): 15-28.

Van Arendonk, J. A. M. "Studies on the replacement policies in dairy cattle. H. Optimum
policy and influence of changes in production and prices." Livestock production
science 13, no. 2 (1985): 101-121.

Van Arendonk, J. A. M., and A. A. Dijkhuizen. "Studies on the replacement policies in
dairy cattle. III. Influence of variation in reproduction and production." Livestock
production science 13, no. 4 (1985): 333-349.

US Department of Treasury, Internal Revenue Service. "Farmers Tax Guide."2001.

45

Table 2.1 Calving intervals examined in the empirical analysis.

 

 

Lacating and Lactating and
Calving interval Lactation length Open Pregnant

wks mos wks days wks days wks days
50 1 1.54 42 294 10 70 32 224
53 12.23 45 315 13 91 32 224
56 12.92 48 336 16 112 32 224
59 13.62 51 357 19 133 32 224
62 14.31 54 378 22 154 32 224
65 15.00 57 399 25 175 32 224
68 15.69 60 420 28 196 32 224
71 16.38 63 441 31 217 32 224
74 17.08 66 462 34 238 32 224
77 17.77 69 483 37 259 32 224

 

 

46

Figure 2.1. Evaluation model for changes to a herd reproductive management

system.

I’ ..........

Step four

 

Expected change in
net income for

 

 

 

I

 

 

the scenario 5
Less value for current herd system :

 

 

 

Step two

 

 

 

Cows in MG x CI

 

AE by MG‘CI

 

 

 

 

 

 

 

 

 

 

 

Number of cows .

 

 

. % of each MG

<—-‘ PVIFA by C1

 

 

 

 

 

 

 

 

 

 

 

 

t---—------

matures ............. /v

m each MG With each CI Total PV by C1
T for each MG
Td—t PVIF by period
Culling Herd PR5
patterns size by MG Net Cash Flow
by period
for each MG x CI

Abbreviations:

MG = management group
CI = calving interval

PR = pregnancy rate

PV = present value

AB = annuity equivalent

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Other Revenues & Milk Revenues
Expenses by period by period
for each MG x CI for each MG x CI

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Herd production Lactation curve
and financial Model and
characteristics Milk yield data

Step one

47

Figure 2.2. Cows move through management groups in the herd in defined
patterns.

V .- :31
Replacement .’ CULL
[purchased in] -—> 8:22:11 892:; 1 ". - --->.| [sold in]

Season 1 V \, I-’ Season 1
\ .
It
.I .\
Replacement . A ,I \ CULL
[purchased in] —> 8:21;: 2 882:; 2 ‘- - - - g [sold in]
Season 2 , Season 2
4) "'~--.-._._._.-._.-._.......--7!
i ______________________________________ -3
I First lactation heifers and mature cows enter a cow lactation at

calving. (Season depends on calving interval.)

— ..... p Heifers and cows culled at the end of lactation.

Replacement heifers enter the herd at calving,
in the same season as the cull.

' ' " ' ‘ " Cull cows and heifers are replaced with a replacement
heifer, purchased in the same season as the cull.

48

Chapter 3
USING LACTATION CURVE MODELS TO EXTEND LACTATION IN

HERD REPRODUCTIVE ANALYSIS

Reproductive decision analysis for a farm hinges upon an accurate projection of the
expected change in milk yield associated with the reproductive performance change.
Reproductive performance influences milk yield by changing the length of calving
intervals of cows in the herd. The opportunity cost of extending the calving interval is
the early lactation milk yield that the additional segment of milk yield replaces.
Similarly, this late lactation milk yield is the opportunity cost of reducing the calving
interval — this segment is replaced with early lactation milk yield when lactation is

shortened.

An accurate projection of the change in milk yield associated with a change in calving
interval requires capturing the rate and shape of the milk yield decline. This change is
based upon an extension or truncation of the mathematical model used to characterize the
lactation curve. Reproductive simulation models often project changes in milk yield with
standard adjustment factors based uponilarge sets of regional data with variables that
systematically influence milk yields, such as climate or parity. While these projections
are representative of a uniform set of herds with similar characteristics to the data set,
they do not provide appropriate guidance for the individual farm looking to conduct their

reproductive management decision analysis with their own lactation curve data.

49

Lactation curves for an individual herd can be more accurately characterized using
individual herd milk yield data, particularly with daily milk weights. However,
accurately calculating the expected change in herd milk yield from their data requires a
functional form for the lactation curve model that adequately characterizes the lactation
curve shape (persistency) of the herd and its management groups. Most simulation
reproductive analyses are based upon the Wood model due to its simplicity (Hady et al.,
1994; Jones, 2000; Wolf, 1999). However, other studies indicate systematic problems

with the Wood model’s fit, and nonlinear models have been proposed.

In this chapter, the first objective is to determine if there is sufficient variation in lactation
curve shape within a herd to question the accuracy of the Wood model for reproductive
analysis. This is accomplished by examining the variation in lactation curve shapes of
cows in a herd. A lactation curve model was developed to measure the decline rate and
possible changes in that rate and fitted to individual lactations. Results indicate that
indeed decline rate and the change in the decline rate does vary across cows, potentially
by management group. Common lactation curve models were then fit to pooled daily
milk yield data for each management group and the differences in the characterizations of
lactation curve shape examined. The results from these lactation curve models are
incorporated into a reproductive management decision model in Chapter 4 to determine

the degree to which choice of lactation curve model influences analytical results.

50

3.1 Lactation curve models for herd reproductive analysis

For reproductive analysis, we are projecting the milk yield change associated with
changing the length of lactation and the onset of pregnancy. Lactation typically ends
two months prior to the next calving to allow sufficient physical preparation for the next
lactation. A shorter calving interval has an earlier onset of pregnancy and, thus, fewer
days in lactation. In contrast, a longer calving interval has more days before pregnancy

begins and so lactation continues longer.

Ascent and peak yields are not affected by the calving interval. Delaying pregnancy
alters the stage of lactation (days in milk) in which the milk yield depression associated
with late gestation begins This “pregnancy effect” begins earlier in lactation with shorter
calving intervals than for longer calving intervals. The total effect of changing lactation
length is the accumulated change in milk yield over the course of a lactation resulting
from the delayed pregnancy effect. Thus, the portion of the lactation curve that is
extended when pregnancy is delayed is the milk yield decline pattern before the

pregnancy effect begins, as demonstrated in Figure 3.1.

Empirical lactation curve models are commonly used to project lactation milk yields for
hypothetical differences in the calving interval. The prediction for the change in milk
yield at the end of lactation is affected by the way the model depicts peak yield,
persistency, and the pregnancy effect. Parametric lactation curve models provide
structure to extension that allows prediction outside of the data set. Accurate projection

of the milk yield change requires that the model accurately characterize the trend in milk

51

yield decline as well as the onset and magnitude of the pregnancy effect. This allows
accurate prediction of the change in milk yield due to lactation extension or truncation
and shifting of the pregnancy effect when simulating changes in the calving interval

length.

3.1.1 Lactation curve functional forms

Many fimctional forms for the lactation curve have been proposed in the dairy science
literature. Most involve a tradeoff between the quality and consistency of fit, based
partially upon the flexibility of the lactation curve shape, and the complexity of the
mathematical form and statistical methods required to fit the curve. Table 3.1 shows the
results of a evaluation study from Vargas et al. (2000), comparing the quality of fit of

these models.

1. Wood model

The lactation curve model proposed by Wood (1967) is the functional form most
commonly used in analyses that require fitting milk yield data. The Wood model, or
parts of it, have been used in reproductive analyses (Hady et al., 1994; Jones, 2000; Wolf,
1999), as well as other applications that involve fitting data (Freeze and Richards, 1992;
Schaeffer and J amrozik, 1996). Its popularity is due in large part to its simple

mathematical form:

(14) Y. = a tb e‘“,

where Yt = milk yield on day t of lactation, and

t = days in milk on lactation day t.

52

The equation usually estimated using linear regression techniques is its logarithmic form,

(15) lnYt=lna+blnt—ct.

Despite its convenience, extensive evaluation of the Wood model indicates systematic
lack of fit, causing autocorrelated residuals and biased predictions of completed lactations
(Congleton and Everett, 1980; Olori et al., 1999; Vargas et al., 2000). In particular, the
Wood model is inadequate in describing the time and yield of peak, leaving high positive
residuals in early lactation (weeks 5 to 10) and negative residuals in mid lactation (weeks
10 to 25) (Olori et al., 1999). Its depiction of milk yield decline as proportional rate of

change overestimates late lactation milk yields (Vargas et al., 2000).

2. Morant model
Morant and Gnanasakthy (1989) expanded upon Wood’s incomplete gamma model to

provide a more flexible form for persistency,

(16) In yt = a — blt’z/Z + bz/t + c(1+t'/2)t').

where t’ = (t — 21.4)/100.

Unlike the Wood model, the relative rate of change in this model does not necessarily fall
to constant value in mid and late lactation. Rather, the second derivative is a horizontal
asymptote. As a result, this model fits extended lactations far better than the Wood
model, showing higher R2 values and less autocorrelation among residuals. Indeed, the

Morant model fit was the only linear model recommended for use in fitting lactation milk

53

yields across evaluation studies (Morant and Gnanasakthy, 1989; Perochon etal., 1996;

Vargas et al., 2000)

3. Diphasic model
The diphasic model takes the form:

(17) Yt = albl tanhz [b1(tY-C1)] + azbz tanhz [b2(t-C2)],

where a1 = ‘/2 asymptotic total yield in phase 1,
bl = rate of yield relative to al per day in phase 1,
c1 = day of peak yield in phase 1,
y = power transformation of time,
a; = '/2 asymptotic total yield in phase 2,
b2 = rate of yield relative to a; per day in phase 2, and

c2 = day of peak yield in phase 2.

Vargas et a1. (2000) describes the diphasic model, proposed by Grossman and Koops
(1986), as the best fitting empirical mathematical model for both standard and extended
lactations. As a result of the fit, this model has been increasingly used in lactation curve
applications, although it has not yet been included in a reproductive analysis. The
primary limitations of the diphasic model include unintuitive parameters and large data
requirements (i.e., degree of fi'eedom problems do not allow estimation from monthly
milk data), as well as a common failure to satisfy convergence criteria when analyzing .

daily milk yield data from individual cows.

54

4. Lactation persistency model

The lactation persistency model (LPM), a linear spline model with two knots, represents

milk yield through lactation as three connected linear segments -- a linear ascent, a flat

peak, and a linear descent, smoothed with exponential terms. The empirical form,

proposed by Grossman et al (1999), is:

(18) Yr:

where t: 1

Y?

P

131

r2

YP + 131 (t‘tri

_ rlbl 1n [et/r1+et1/r1] + r2b3 1n [et/r2+e(t1+P)/r2] '
[l + eti/ri] [l + eit1+pllr21

 

 

days in milk at start of constant peak yield,
constant peak yield,

duration of constant yield,

slope of yield ascent,

slope of yield descent,

duration of transition 1 (ascent -) peak), and

duration of transition 2 (peak -) decline).

Vargas (2000) found the LPM model nearly comparable in fit to the diphasic model, but

like the diphasic model, it frequently failed to converge with daily milk yield data. Its

primary advantage is the intuitiveness of its parameters - each parameter measures a

distinct aspect of lactation curve shape.

55

3.1.2 Persistency: Modeling milk yield decline

Persistency is generally defined as the degree to which milk yield is maintained at peak
level — the milk yield pattern in the declining phase of lactation (i.e., after peak).
Important properties of persistency are the rate of change in milk yield in the decline
phase of lactation and the change in the rate of decline. Empirically, persistency can be
defined as the lactation equation’s first derivative of milk yield, and the change in

persistency, as the second derivative in the decline phase of lactation — after peak yield.

These four lactation curve models depict milk yield decline (persistency) very differently,
as depicted in Figure 3.2. The Wood model shows milk yield decline that converges to a
constant proportional rate of change. The LPM model, in contrast, depicts a linear
decline. The Morant model allows a more flexible shape for decline, as does the

Diphasic model with multiple decline phases.

A significant literature is available regarding most appropriate functional form. Despite
the abundance of persistency measures in the literature, little light has been shed upon the
true shape of milk yield decline. Although lactation curve model comparisons typically
indicate that functional forms allowing variation in milk yield decline shape show the
best fit, the cited reason is often early lactation fit (Olori et al., 1999; Vargas et al., 2000).
The Wood model, in particular, has been shown to have poor fit in late lactation and has
thus been deemed not suitable for modeling extended lactations (Rowlands et al., 1982;

Vargas et al., 2000).

56

3.1.3 Modeling the pregnancy effect

The other important component of modeling milk yield for reproductive analysis is the
pregnancy effect, as its onset is shifted when the calving interval is changed. Danell
(1982b) reports that the pregnancy effect consists of an average milk yield losses of 3 to 5
kilograms per day beginning at approximately 100 days pregnant. Oltenacu et a1. (1980)

firrther reported that the additional milk yield decline is an additive effect.

The pregnancy effect can be incorporated using values fi’om the literature, or it can be
measured from the milk yield data. Hady (1994) incorporated the results of Oltenacu‘s
(1980) examination of the negative relationship between partial lactation yields and days
open to arrive at parameters for the lactation curves in his partial budget model. Van
Arendonk (1985) used adjustment factors based upon Danell (1982b) for his insemination

and replacement model.

For individual herds, measuring the pregnancy effect when fitting their milk yield data
may be more accurate, since the magnitude of the pregnancy effect may not be constant
across herds. When using linear lactation curve models, investigators commonly
represent the pregnancy effect with an additional parameter for days pregnant. For
nonlinear models, Coulon et a1. (1998) proposed the following additive modification to

account for the pregnancy effect:

(19) PE; = a (wp - 18) em,

57

where PEt = milk yield reduction on day t of lactation attributable to the effects of
pregnancy, and

Wp = weeks pregnant.

For example, Perochon et al. (1996) incorporated Coulon’s pregnancy effect and a similar
season effect into the Morant model, creating a comprehensive model that he

recommended for capturing individual variability in lactation curves.

3.2 Preliminary analysis: Individual lactation curves

The most commonly used lactation curve model, the Wood model, may not adequately
capture the rate and shape of milk yield decline across herds and their management
groups. The goal of the preliminary analysis is to determine if there is reason to believe
that a flexible shape model would more accurately characterize the change in milk yield

for a herd considering a reproductive management change.

3.2.1 Empirical lactation curve model

The LPM, from Grossman et a1. (1999), was modified for use in this preliminary analysis.
The LPM is a linear spline model that represents milk yield through lactation as three
connected linear segments -- a linear ascent, a flat peak, and a linear descent. The
modified model can capture two distinct segments of declining milk yield and an

additional segment for additional decline in late stages of pregnancy. Modifications to

58

the LPM for this analysis, summarized in Table 3.2 and depicted graphically in Figure

3.3, include:

0 Adding a third knot (and corresponding fourth segment) to allow two phases of milk
yield decline. This allows the model to represent a change in the rate of mid-lactation
milk yield decline. Vargas (2000) used a similar three-knot version of the LPM in his
evaluation study — the model fit ranked second in R2, RSD, DW, and MAD against

other common lactation curve models.

0 Incorporating an additional knot for lactations that involve pregnancy — the last
segment of the model, its timing based upon days pregnant rather than days in milk,
allows a different rate of decline in late stages of pregnancy. Since nonpregnant cows

have zero days pregnant throughout lactation, they will not display a fifth segment.

0 Fixing the length of transition between segments (r1, r2, r3, r4) to one day. Forcing
sharp transitions ensures clearly defined transitions between production phases. This

restriction does not significantly reduce model fit (Grossman et al., 1999).

The resulting empirical model is of the form:

(20) Yr = Yp '1' b1 * (DIMt_t1)" b1 * lnIIGDIMt-tetll/(l'teull
+ b3 * ln((eDmt+et2)/(1+et2))
+ (bi-b3) * 1n( (eDmt+et3) / (1+e‘3))
+(b5—b4) * ln((eDPt+e“)/(1+e“))
where yt = milk yield (lbs.) on day t since calving,
yp=peakyield,

bj = slope of segment j, j = 1 to 5 (b2 = O), and

59

tj = day t since calving of transition from segment j to j +1
DIMt = days t since calving, and

DP: = days pregnant on day t since calving.

As shown in Figure 3.3, the parameters of the model identify the rate of change of milk
yield of each segment and the days in milk at which the rate of change changes. The b
parameter represents the milk yield change (pounds per day) of the corresponding
segment. The t parameters can be interpreted as the days in milk at the transition to the

next segment.

3.2.2 Persistency measurements

Milk yield decline

Important properties of persistency are the rate of decline and the change in the decline
rate — the first and second derivatives of the empirical lactation curve model. The
modified LPM used in this analysis allows direct measurement of these characteristics to
from model parameters, as shown in Table 3.3. Persistency, both before and after the
effects of pregnancy begin, can be quantified using the slopes and transitions in the

lactation curve identified by the modified LPM.

The modified LPM model used in this analysis depicts two decline rates (b3 and b.;) that
are constant in pounds per day. Both these b values are negative, as they represent the
rates of milk yield change in pounds per day for their respective decline segments. The

difference between the slopes of the decline segments (b3-b4) is the only change in

60

decline rate that can be represented by this model. A positive value indicates that decline
in later stages of lactation is faster than in earlier stages; vice versa for negative values.
Thus, the rate of decline can be classified as:

0 Decreasing, if b3 is negative and b3 > b4,

0 Increasing, if both b3 and b4 are negative and b3 < b4, or

o Constant, if the model failed to use the knot allowed for the segments prior to the

pregnancy effect, thus depicting one segment of decline.

Pregnancy effect

Since the model allows an additional knot in pregnant cows, an additional decline rate

can be represented for advancing stages of pregnancy. In pregnant cows, the difference

between the slopes of the second decline segment (b4) and final segment (b5) represents

the additional decline associated with advancing pregnancy, or the “pregnancy effect”.

Since non-pregnant cows are limited to a three knot model (days pregnant is zero for the

entire lactation), only pregnant cows can display this additional change in decline rate.

Both onset and magnitude of the pregnancy effect were measured for pregnant cows:

0 Onset -- days pregnant at t4, if b4 < b5 and the cow is pregnant greater than 100 days
at 14.

- Magnitud -- the difference in slope between the final segment (b5) and the previous

segment: b5 — by, if constant decline, b5 — b4 otherwise.

Lactations in which the slope of the final segment (b5) was less steep than the prior

decline segment and (or) the accelerated decline began before 100 days pregnant were

61

classified as not displaying a pregnancy effect. Rather, the final segment was considered
an extension of the prior segment. The slope for the combined segment was then

calculated as the weighted average of the two segments.

Peak yield

Although not a part of persistency, peak production defines the starting point for milk
yield decline. It characterizes the tradeoff of early lactation milk production and late
lactation when calving interval is changed and the starting point for milk yield decline.
Peak yield, onset, and duration can be simply calculated from parameters of the modified
LPM:

- Peak yield — defined as the parameter yp.

o Onset of peak yield — defined as the days in milk at the beginning of peak yield, t].

0 Duration of peak yield —number of days between onset of peak yield (t1) and the

beginning of milk yield decline (t2), or the value of t; — t1.

3.2.3 Data and statistical methods

This study used historical daily milk yield data from Michigan State University Teaching
and Research Farm, a Holstein dairy farm in central Michigan, milking approximately
150 cows. The study included lactations that began after January 1, 1995 and ended
before March 15, 1998. Milk yield at this facility averaged approximately 25,000
lbs/year over the period of the study. Although tie stall and free stall housing systems are
used in this facility, no explicit feeding or production groups were defined (i.e., first

lactation heifers were not separated from mature cows).

62

Because the results are ultimately intended for use in herd reproductive management

analysis, cows in lactations that would likely be managed separately fiom the normal

population were removed from the data set. Lactations with the following characteristics,

each of which occurred in less than five percent of the herd, were excluded from the

study:

lactation length less than 200 days — these cows would not likely be part of the
breeding herd, nor would they demonstrate lactation curve shape features examined
here;

spontaneous abortion after 100 days pregnant - termination of pregnancy once it has
begun to depress milk yield would interfere with the milk yield decline patterns
measured in the study;

dry period of less than 45 days — extremely short dry periods do not provide sufficient
time for normal mammary development prior to lactation;

mastitis after 100 days in milk — since mastitis interferes with milk production during
and after infection, the milk yield decline pattern for cows experiencing mid and late
lactation mastitis does not reflect herd production; and

recorded incidence of lameness and (or) miscellaneous diagnoses — these disorders
interfere with milk production processes such that the lactation curve would be

markedly different than the rest of the herd.

Each lactation is a time series of daily milk yields beginning on the day of calving (1

DIM) and continuing through the end of lactation. No differentiation was made between

63

lactations terminated at dry off, for culling, or by death. The data set consisted of 362
lactations - 132 from first lactation heifers, and 230 from mature cows. Table 3.4
summarizes the descriptive statistics for this data set. Lactation length varied from 201 to

613 days.

The modified LPM model described in Section 3.4 was fitted to the daily milk yield in
each lactation using nonlinear least squares methods in the STATA statistical package,
version 6.0. Convergence was determined based on the change in relative change in
residual sums of squares between iteration i and iteration i-l. The convergence criterion
is met when the relative difference is less than 1045. If a maximum of 1000 iterations
were exceeded, then the lactation failed to converge. Of the initial 362 lactations, 8
heifer lactations and 17 cow lactations failed to meet the convergence criteria, leaving

338 lactations (124 heifer and 214 cow) for the lactation curve shape analysis.

Although serial correlation of residuals is expected (Vargas, 2001) in the resulting
lactation curve model, it was not corrected in the nonlinear models due to computational
limitations. Comparison of regression results for the Wood model before and after
correction for first-order serial correlation indicates that the parameters before and after
correction are very similar for all management groups. Figure 3.4 illustrates the
predicted lactation curve for heifers in the data set with and without correction for serial
correlation. The cumulative difference between the two sets of parameters to 365 days in
milk is 46.5 pounds, or 0.20% of the total lactation production. The difference between

the models at 365 days in milk is 0.41 lbs or 0.89% of milk yield on day 365. Thus,

64

failure to correct for first order serial correlation in the nonlinear regressions models is
not expected to affect milk yield estimates based upon the results. The remaining serial

correlation does, however, prevent reliable formal hypothesis testing.

Lactation curve shape measures were calculated for each lactation from regression
results. For most lactations, this involved the simple calculations fi'om

parameters described in Section 3.2.1. In lactations where one or more knots (segments)
was not used by the model in the course of regression, other model parameters from the
regression results did not reflect the conceptual definitions in Section 3.2.2 (e. g., positive
b value for a downward sloped segment). However, milk yield values predicted by the
model were consistent with the typical lactation curve shape. As such, the lactation curve
shape parameters described in Section 3.2.2 were calculated from predicted milk yields

rather than the regression results.

3.2.4 Preliminary analysis results and discussion

Herd results

The modified LPM captured between 45 and 97% of variation in daily milk yields over
individual lactations that converged. The average R2 value was 0.80 (SD = .11). All cow
lactation curve results demonstrated the expected right skewed pattern with clear ascent,
peak, and decline. Table 3.5 summarizes the mean regression results across all lactations

in the herd.

65

Persistency values showed a high degree of variation across the herd, with large standard
deviations relative to the mean. The largest part of the herd (39.6%) showed a decrease
in decline rate (i.e., the second decline segment was flatter than the first). Slightly fewer
(31.4%) demonstrated a single segment decline (constant decline rate). Only 29.0%
showed an increasing rate of decline, with milk yield declining faster at the end of
lactation. Those with a decreasing rate of decline had a larger average change (a
reduction of 0.65 lbs decline per day) than those showing an increasing rate of decline (an

additional 0.28 lbs decline per day).

The average peak yield was 96.2 pounds, continuing from 32 to 94 days in milk. About
half (55.5%) of the lactations in which a pregnancy occurred showed an accelerated
decline in milk yield in late pregnancy. Across these lactations, decline in the second
segment after peak was 0.47 pounds per day faster than in the segment following peak
yield. The onset of the observed pregnancy effect was often later than found in previous
studies (100-125 days pregnant) with the mean value of 156 days pregnant. Timing
values (days in milk) for both peak production and the pregnancy effect had large
standard deviations relative to their means. The standard deviations for peak yield and

the size of pregnancy effect were much smaller.

Results by management group
Results indicate apparent differences in persistency, as well as characteristics of peak
yield and the pregnancy effect, across management groups. Tables 3.6 and 3.7 show the

persistency measures for heifers and cows, respectively, by season of calving.

66

Heifer vs. Cow

Heifers typically demonstrated later, lower, and longer peak yields than cows. Indeed,
some heifer lactation curves did not demonstrate a distinct peak in production, but rather
remained flat through most of lactation and declined only at the end of lactation. Where
the average heifer peak yield was 78 pounds per day beginning at 33 days in milk and
continuing for 81 days, the average cow peak yield was 107 lbs / day beginning at 27
days in milk and lasting only 51 days. More heifers than cows (69% vs. 48%) displayed
an accelerated milk yield decline in late stages of gestation. The mean acceleration for
heifers (an additional 0.41 lbs of daily milk yield loss) was slightly smaller than for cows

(an additional 0.51 lbs per day), although the cow values varied more widely.

Season of calving

Season of calving influences persistency as well as peak production. Differences in peak
and persistency reflect the different lactation stages at which the season of calving groups
experience summer heat stress and the resulting depression in milk yield. Mean peak
yields for heifers calving in the summer and fall are smaller and later in lactation than
winter and spring-calving heifers. Cows calving in summer and fall would experience
summer heat stress in early lactation. Decreasing decline rates are significantly more I
prevalent in cows calving in the fall and heifers calving in winter. Summer milk yield
depression affects these cows in mid lactation, allowing recovery to follow in late
lactation. In these cases, it is likely that the first decline segment represents the

depression, the second depicts reduced decline associated with recovery.

67

Regression results from this empirical model may not be as accurate in projecting the
extension of lactation for reproductive analysis when the lactation is affected by seasonal
milk yield depression. Like the decline segments, observed pregnancy effects for some
cows appear to be confounded with milk yield depression occurring in the summer
months. The high “pregnancy effect” observed for winter calving heifers and cows may
also reflect the response to summer heat stress, as late gestation occurs in the summer

months.

Seasonal milk yield depression is also linked to cases such as that shown in Figure 3.5
This winter-calving heifer shows a sharp decline in mid lactation consistent with milk
yield depression resulting from summer heat stress. The positively sloped second
segment of decline likely represents the milk yield recovery afterward. This pattern was
common in winter and spring calving cows and heifers. If this increasing segment were
extended to represent longer lactations associated with an extended calving interval, an
artificially high projection of the milk yield change results. In reality, once recovery
from the summer milk yield depression is complete, milk yield would resume its natural
decline. Whether this new rate of decline is greater or less than the original decline rate

(prior to summer heat stress), however, is not known.

Results of the preliminary analysis are consistent with the hypothesis that variation in
lactation curve shape across management groups is more adequately reflected with a
flexible functional form. Further analysis is required to examine the degree to which

lactation curve models reflect herd management group milk yields and the implications of

68

lactation curve model selection on reproductive management decision analysis. The

following analysis looks at the results of fitting other lactation curves to this data.

3.3 Pooling by management group -

An accurate projection of the milk yield change associated with a change in reproductive
performance is a critical component in reproductive management decision analysis. A
manager can fit the herd milk yield data with a lactation curve to quantify the expected
change associated with the delay in pregnancy and subsequent lengthening of lactation.
(Note: The effects of the change in lactation frequency are determined in the reproductive
model.) When considering herd reproductive management in groups, a lactation curve

assessment for each management group is required.

Eight management groups established for this analysis by parity and season of calving.
Because of their fixed shapes, lactation curves commonly used may not adequately
represent the differences in the lactation curve across these management groups in a herd.
The goal of this section is to establish a lactation curve for each management group using
various lactation curve models from the literature. The lactation curve model results can
then be incorporated into the herd reproductive management decision analysis to
determine whether more complicated nonlinear models provide different results than the

more commonly used Wood model.

69

3.3.1 Empirical lactation curve models

Four lactation curve models were selected for the functional form of the relationship
between days in milk and milk yield by management group — the Wood model, the LPM
(spline) model from the preliminary analysis, a three-knot LPM model from Vargas et a1.
(2001), and the diphasic model. The Wood model is the most commonly used fitted
lactation curve. The extended LPM and diphasic models were recommended by Vargas
(2001) as the empirical lactation curve models with best fit for milk yield through
lactation. The hyperbolic tangent function in the diphasic model was converted to the

mathematically equivalent exponential form to facilitate statistical analysis.

A pregnancy effect term was added to each lactation curve model to allow the differences
in the onset of pregnancy associated with each calving interval to be represented in the
reproductive analysis. The Wood model was included both with and without a pregnancy
effect term, since both have been used in reproductive models. The pregnancy effect for
the Wood model, in logarithmic form, is represented an additional parameter that results
in a multiplicative effect on milk yield, as in Hady et a1. (1994). In the spline models, the
pregnancy effect is represented with an extra segment in the model. Coulon’s (1998)
proposed pregnancy effect, shown in equation (19), is used with the diphasic model. The
onset of the pregnancy effects for the Wood and diphasic models were fixed at 125 days

pregnant, consistent with Danell (1982b) and Coulon (1998).

The resulting empirical lactation curve models were:

(21) WOOd: Ln Y: = a + b 1n DIM: + C DIMt,’

70

(22) Wood (PE): Ln yt = a + b 1n DIMt + c DIM: + dDPt;

(23) LPMS: yt = yp + b1 * (DIMt-tl)

b1*ln( (exp (DIMt) +exp (t1) / (1+exp (t1))
b3*ln( (exp (DIMt) +exp (t2) / (1+exp (t2))
b4*1n( (exp (DIMt) +exp (t3) / (1+exp (1:3))
b5*ln( (exp(DPt) +exp (t4) / (1+exp (t4) );

+++i

(24) LPM4: Yt: = Yp + b1*(DIMt-'t1)
-b1*ln( (exp (DIMt) +exp (t1) / (1+exp (C1))
+b3*ln( (exp (DIMt) +exp (t2) / (1+exp (t2))
+b5*ln( (exp(DPt) +exp (t4) / (1+exp(t4) ); and
(25) Diphasic:
Y1: = arbr" [1‘ ( (exp(2b1(DIMt-C1) '1) / (exp(2b1(DIMt-C1) +1) I

+ azbz“ [1‘ I (EXP (2b2 (DIMt'Czi '1) / (EXP (2b2 (DIMt'Cri +1) I
+ apt: (opt-125) *exp(-bp*AdePt) .

For all models,
yt = daily milk yield for cow i in lactation day t,
DIM: = days since calving on day t of lactation
DP: = days since conception on day t,
Adj DPt = DPt — 1 2 5, days after the expected pregnancy effect onset at 125
days pregnant, and

a, b, c, etc . = estimated parameters.

3.3.2 Data and statistical methods

The data set used in the individual lactation analysis, consisting of daily milk yield data
from the Michigan State University dairy herd, was also used in this analysis. To more

fully represent the entire herd, most lactations excluded fiom the preliminary analysis

71

were included here. However, incomplete lactations (<200 days) were not included in
this analysis. In addition, extremely long lactations (greater than 425 days) were
truncated to prevent undue influence of the late lactation milk yields from the few
extended lactations on the estimated lactation curve parameters. The data set consisted of
panel data, with days in milk as the time series variables and lactation as the cross-
sectional variable. The data set contained 334 lactations, ranging in length from 200 to

425 days in milk, as dictated by the exclusion criteria from the preliminary analysis.

Pooling of lactations by management groups

Using separate parameter sets to represent groups of cows with different characteristics is
a common method of representing management variables. This method is used primarily
effective for characteristics that affect multiple parameters of the lactation curve but not
the underlying functional form. Indeed, heifer lactation curves are commonly estimated
separately from mature cows, such as in Vargas (2000) and Hady (1994). Following this
method, data sets were separated and lactation data pooled into eight management groups
— two parity groups each subdivided into four season of calving groups. Summary
statistics for each management group are summarized in Table 3.8. The following

criteria were used in pooling:

Parity:
o Heifers Parity = 1
0 Cows Parity = 2+

72

Season of calving:

0 Winter Calved between December 1 and February 28

0 Spring Calved between March 1 and May 31

0 Summer Calved between June 1 and August 31

a Fall Calved between September 1 and November 30

Pooling of observations across time

Within management group, daily milk yields (to 425 days in milk) for all lactations were
used in this analysis. A dummy variable for each lactation was incorporated into the
lactation curve models. Thus, individual lactations were differentiated with a scale
parameter, under the assumption that persistency for all lactations in each group come

from the same population.

The general form of the resulting lactation curve model was:

(26) Yit = f(DIMt) "I' 9(Dpt) ‘1' a1 COWIDi + nit,

where yit = milk yield for cow i in mgrnt group j on DIM t,
f (DIMt) = relationship of milk yield on DIM! to days in milk on day t,
g (DPt) = relationship of rrrilk yield on DIM, to days pregnant on day t,
ai = deviation of rrrilk yield for cow i from the group mean,
COWIDi = categorical variable representing cow i, and

uit = error term for cow i on day t.

73

Regression methods

Each lactation curve model was fitted using pooled group data in STATA version 6. For
each set of pooled milk yield data, milk yield was regressed on days in milk and days
pregnant using least squares methods for each of the lactation curve functional forms.
Regressions of the Wood models, which are linear in parameters, were corrected for first-
order autocorrelation using the Prais-Winsten transformed regression estimator,
performed for the value that minimized the sum of squares of the transformed equation.
The milk yield observations were assumed independent across lactations but not within,
and so the Huber/White estimator of variance was used. The nonlinear LPM and
diphasic models were regressed using nonlinear least squares methods, using the same
methods as the preliminary analysis. As discussed in Section 3.2.3, serial correlation was
not corrected in the nonlinear models, but the residual serial correlation is not expected to

affect the parameter results.

3.3.3 Results and discussion

All lactation curve regressions for all management groups converged. Evaluation of the
models was based upon the R2 statistic and RMSE, which varied across model,
management group, and stage of lactation. R2 and RMSE were calculated from the
predicted data for milk yield (pounds per day). For the entire lactation, R2 values ranged
from 0.43 to 0.74. Tables 3.9 and 3.10 show the R2 and RMSE of each lactation curve
model for each management group in the various stages of lactation for heifers and cows,

respectively. Stages of lactation were defined by days in milk, as in Vargas et al., (2000).

74

Fit was generally better in the middle stages of lactation than either the beginning or end.
In general, the nonlinear models fit better than the linear Wood models, but none of the
curves showed the best fit for all management groups in all stages of lactation. All LCMs
except LPMS had at least one stage of lactation for one management group with a

negative r-squared value.

Milk yield projections for each management group were calculated using the group mean
value for the dummy variable for lactation (COWIDi), combined with other regression
results from the pooled group data. Figures 3.6 to 3.13 depict the fitted curves for each
management group. Selected persistency measures for each lactation curve model are
shown in Table 3.11 (heifers) and 3.12 (cows). Values in these tables were calculated for
lactations with pregnancy beginning at 125 DIM. Although persistency is depicted
differently across lactation curve models, the models showed similar milk yields through
lactation. Differences in the rate of milk yield decline across lactation curve model are

most prominent at the end of lactation.

The Wood model fit heifer lactations more consistently with the nonlinear models than it
did cow lactations. The milk yields of heifer lactations were generally more persistent,
which is consistent with the Wood model’s depiction of milk yield decline. Compared to
the nonlinear models, the Wood model did not fit lactations with more rapid and
accelerating decline well. These characteristics were most common in cow lactations. In
particular, the Wood model did not accommodate the sharp decline in milk yield that

occurs in late lactation of winter and fall cows. When a pregnancy effect is incorporated,

75

the model showed better fit, but the pregnancy effect reflected the summer heat stress and
associated milk yield depression rather than milk yield reductions associated with
reproduction. Shifting the onset of the pregnancy effect for changes in calving interval is

not an accurate representation of the expected changes in milk yield for these cows.

Whether the improved fit of the nonlinear models is necessary for accurate reproductive
management decisions requires further analysis. Tables 3.13 and 3.14 show the expected
differences in cumulative lactation milk yields associated with different calving intervals.
In Chapter 4, these milk yield projections are incorporated into the reproductive decision
model from Chapter 2 and the results evaluated to determine if the differences in fit

would influence herd reproductive management decisions.

Although the five-segrnent LPM model captured the variety of milk yield decline shapes
apparent in the herd, its usefulness as the basis for lactation curve extension is
questionable. All lactation curve models except LPM5 showed larger cumulative milk
yields for longer calving intervals and declining differences between successively longer
calving intervals. The LPM5 model depicted ranges of increasing milk production for
some groups, which resulted in total milk yield projections that increase at an increasing
rate with lengthening calving interval. As a result, LPM5 results will be excluded from

the Chapter 4 analysis.

76

3.4 Summary and conclusions

The expected milk yield change associated with a change in reproductive performance is
critical to valuing the changes in reproductive performance. Accurately calculating the
expected change in milk yield requires a functional form for the lactation curve model.
Lactation curve models currently used in reproductive analyses often do not allow for
adequate variation in the shape of milk yield decline to describe a herd of cows —

especially when subdivided into management groups.

A generalized form of the Lactation Persistency Model, designed to measure multiple
milk yield decline rates, was fit to daily milk yields from individual lactations in a
Michigan dairy herd. Results indicated apparent differences in persistency, defined as the
rate(s) of decline and the change in decline rate, which support the possibility that
parametric models with a fixed shape may provide inaccurate projections of the milk

yield change associated with a change in the calving interval.

Milk yield data from the lactations used in the preliminary analysis were pooled into
parity and season of calving management groups. Common lactation curve models --
including the commonly used Wood model and recently proposed nonlinear models —
were fit to the pooled data. All lactation curve models showed differences in lactation
curve shape across management groups consistent with previous findings in the literature,
including slower milk yield decline and lower peak yields for first lactation heifers than

their mature counterparts and for summer versus winter calving heifers and cows.

77

Across management groups, the lactation curve models depicted persistency differently.
These differences were more pronounced across mature cow groups than heifer groups.
Extension predictions, too, appear different by lactation curve model. However, the
statistical significance of these observations is not tested in this analysis due to residual
autocorrelation in the nonlinear models. In Chapter 4, the effects of lactation curve

model selection on reproductive management decision analysis are examined.

78

Congleton, W. R., Jr., and R. W. Everett. "Error and bias in using the incomplete gamma
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Olori, V. E., S. Brotherstone, W. G. Hill, and B. J. McGuirk. "Fit of standard models of
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80

Table 3.1.. Comparison of fit across lactation curve models, from Vargas et al.

(2000).

 

General measures of fit over all lactation.

 

 

 

 

RSD DW Cases where
Mean SD Mean SD Mean SD DW > 0 [1]
Wood 0.957 0.03 0.870 0.22 0.56 0.27 23
Morant 0.973 0.02 0.660 0.17 0.86 0.42 16
Diphasic 0.987 0.01 0.480 0.13 1.74 0.44 1
LPM 0.985 0.03 0.420 0.26 1.79 0.60 2
Mean absolute deviation by stay of lactation [2]
1-100 DIM 101-200 DIM 201-305 DIM 306+ DIM
Mean SD Mean SD Mean SD Mean SD
Wood 45.8 14.9 42.7 15.0 80.7 41.0 115.9 56.8
Morant 58.2 12.3 38.1 16.1 53.3 31.8 84.1 47.2
Diphasic 46.1 27.5 17.7 8.2 26.8 17.0 43.2 28.2
LPM 36.1 30.5 18.3 21.8 22.6 16.5 50.4 59.4

 

[1] Number of runs (of 26) with significant positive autocorrelation

[2] Mean absolute deviation is defined as the sum of daily absolute deviations for the

period specified.

81

Table 3.2. Modifications to the Lactation Persistency Model.

 

 

Model LPM Reduced Three-knot Four-knot
LPM LPM LPM

Authors Grossman, 1999 Grossman, 1999 Vargas, 2000

Segments 3 3 4 5 if pregnant,

4 if not

Transition length r's not fixed r, = r2 = l r's not fixed All r’s = l

Ascent b1 not fixed bl = yp / t1 b1 not fixed b, not fixed

Peak b2 = 0 b2 = 0 b2 not fixed b2 = 0

 

82

Table 3.3. Persistency measures for the modified LPM.

 

 

Shape characteristic Measurement criteria

Persistency

First rate of decline b3 pounds / day

Second rate of decline b4 pounds / day

Decreasing decline rate ‘Yes’ if b3 < b.,

Increasing decline rate ‘Yes’ if b3 > b,

Constant decline rate ‘Yes’ if middle knot is not used

Pregnancy effect

Onset t4 days in milk (if t4>100 DCC. Ifnot, none)

Magnitude b5 — b4 (if t, = onset. If not, appropriate b
values.)

Peak

Peak yield yp pounds

Peak onset t1 days in milk

Peak duration t2 - t1 days

 

83

Table 3.4. General description of the dataset.

 

Herds l
Cows 179
Lactations 362

First lactation 132

Second or later lactation 230
Records 13 1,215
Records per lactation 315 +/- 59.4
Lactation length 321 +/- 61.0
Daily milk yield 75.0 +/- 11.9

 

84

Table 3.5. Summary of regression results from individual lactation curve analysis.

 

 

 

 

 

 

 

Frequency Mean StDev
Decline shape
Decreasing 1 34 3 9. 64%
lst slope (0.40) 0.472
2nd slope 0.41 1.003
Change (0.65) 0.937
Linear 106 3 l 36%
Slope (0.23) 0.185
Increasing 98 28.99%
lst slope (0.28) 0.450
2nd slope (0.56) 0.842
Change 0.28 0.657
Peak characteristics
Yield (lbs/day) 96.2 20.75
Duration (days) 62 56.9
Begn 32 31.2
End (beg'n decline) 94 58.0
Pregnancy effect
Total pregnant 281 83.1%
Occurrence 1 56 55.5%
Onset (DCC) 158 36.6
Acceleration (add’l lbs/day) 0.47 0.35

 

85

 

 

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87

Table 3.8. General description of the dataset used in group analysis by

management group.

 

 

 

 

 

HEIFERS Winter Spang Summer Fall
Cows 31 22 25 36
Lactations 31 , 22 25 36
Records 10,364 7,030 8,988 1 1,538
Records per lactation 334 +/- 51.7 320 +/- 48.8 360 +/- 55.3 321 +/- 48.7
Lactation length 335 +/- 51.9 321 +/- 48.2 364 +/- 59.6 323 +/- 47.6
COWS Winter Spring Summer Fall
Cows 72 35 38 77
Lactations 72 30 38 74
Records 22,454 1 1,587 1 1,682 22,809
Records per lactation 312 +/- 64.1 331 +/- 53.4 307 +/- 75.9 296 +/- 55.9
Lactation length 324 +/- 73.6 333 +/- 52.9 311 +/- 76.3 306 +/- 53.0

 

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Chapter 4
EFFECTS OF LACTATION CURVE MODEL SPECFICATION ON

REPRODUCTIVE MANAGEMENT DECISIONS

A reproductive management decision involves determining the value of the reproductive
performance improvement and the implementation costs associated with the proposed
management change. A reproductive management change should be implemented only if
the expected value of the new system (with the management change) exceeds that of the
current system. The decision analysis model outlined in Chapter 2 provides a framework
for evaluating the annualized net returns for alternative herd reproductive management

change scenarios.

In this reproductive model, the cash flows for lactations of different calving intervals are
first quantified and standardized to their value at the beginning of lactation using present
value analysis. Then, annuity equivalent values of each of these lactations and the
distribution of calving intervals and management groups are determined. The total herd
values of the current herd and the alternatives is the sum of the annuity equivalent values
for the herd distribution. The difference between the value of each alternative and the
current herd is the expected increase (or decrease) in annualized returns to the herd at
steady state herd management group proportions under the new reproductive

management system.

108

In this chapter, four potential reproductive management change scenarios are evaluated
using this framework. The goal of this analysis is to compare decision analysis results
across lactation curve models used to project the change in milk yield for a case herd.
Each scenario was evaluated using results from each of the empirical lactation curve
models discussed in Chapter 3. Only milk yield revenues and feed expenses varied with
the selected empirical lactation curve model. Although the values varied across lactation
curve model, all lactation curve models yielded identical rankings for the value of the

scenarios.

4.1 Farm characteristics

The financial and production characteristics of the case farm were based upon recent
farm summaries and other industry data (Nott, 2000; OSU Extension 1999). Market
prices and farm characteristics used in this analysis are shown in Table 4.1. The values
for the case farm represent a typical mid-size (i.e., 150-400 cows) Midwest dairy. The
case herd maintains 100 milking cows with constrained milking herd space but
unconstrained dry cow space, as would be the case when the milking herd is housed in a

freestall barn and dry cows in bedded pack or pasture.

Later in this chapter, the role of key values and characteristics are examined through
sensitivity analysis. Farm financial characteristics examined in the sensitivity analysis
include herd size, opportunity cost of capital, milk price, and feed costs. Farm production

characteristics include herd health, labor efficiency, and nonreproductive culling rates.

109

4.1.] Financial characteristics

Opportunity cost of capital

An opportunity cost of capital of 8%, equal to the farm’s weighted average cost of
capital, was used to derive all present value interest and annuity factors. An 8% annual
opportunity cost of capital reflects an average value for a moderately leveraged Michigan
dairy, consistent with Harsh et a1. (2001). All reproductive management investments
were considered to have the same financial risk as the farm, a standard implicit
assumption in present value analysis. Since the reproductive investments are relatively
small, they were assumed to have the same debt-equity mix as the farm. The investments
were considered too small relative to the size of the farm to influence farm liquidity or

solvency.

The opportunity cost of capital, rather than the incremental cash flows and present value
of lactations, was adjusted for inflation to simplify the calculations. The discount rate
used in the analysis was 5%. The average inflation value considered was 3%, which is
generally consistent with expected inflation values. Milk production is commonly
expected to increase 2% annually. Agricultural statistics indicate that labor wage can be
expected to grow at 3.7% annually, while expected rise in other production costs is 2.5%

per year (USDA, 2000).

Taxes and depreciation
The marginal tax rate on ordinary income for the case farm totals 34.9%, consisting of
28% federal tax, 4% state tax, and 2.9% Medicare tax. The farm is not subject to

additional social security tax. Capital gains are taxed at 20% (IRS, 2001). Replacement

llO

heifers are depreciated using the five year modified accelerated capital recovery system

(MACRS).

4.1.2 Production characteristics and market prices

Milk revenues

Milk yield revenues were based on a unit milk price of $13.50 per hundredweight. Milk
yield continues until 60 days prior to the end of the calving interval, in order to allow a
dry period before the next lactation, unless production falls below 20 pounds per day. In
this case, milk yield was stopped and the dry period is begun early. Milk yields for each
alternative were projected using each of the four lactation curve models fiom Chapter 3,
adjusting the end of lactation and the onset of the pregnancy effect for the various calving

intervals.

Calf revenues
Heifer calves are sold at weaning (eight weeks) for $250 and bulls at one week of age for
$50. Calves are managed in groups by hier labor, with an average labor requirement of

20 minutes per head per week. Calf mortality rate prior to sale is 5%.

Culling revenues and replacement costs

Culling for non-reproductive reasons is 25% of each management group per year. This
value affects only the change in herd distribution, not the cash flows associated with
particular lactations. Cull cows are valued at $450 per head, while replacement heifers

are purchased for $1,400 per head.

lll

Feed expenses
Feed expenses were determined using a unit price of $0.06 per pound of dry matter. Feed
requirements were directly related to milk yield, with a conversion rate of 0.5 pounds of

dry matter per pound of additional milk.

Breeding expenses
Breeding expenses for semen and supplies total $22.00 for each breeding. A timed
breeding using Ovsynch adds an additional $18 to the cost of each breeding for the

hormone injections and related supplies.

Labor expenses
Hired labor is valued at $12 per hour, which would consist of all wage, benefits, and
applicable taxes. The opportunity cost of labor to reproduction was assessed at $25 per

hour to representing the value of the farmer’s labor in alternative activities on the farm.

Herd health expenses

Herd health disorders associated with the beginning of lactation, including metabolic
disorders and some types of severe mastitis, occur in 15% of cows calving. Veterinary
expenses, consistinf of veterinary service fees and the costs of treatment products,
associated with treatment of herd health disorders total $100 per case. Managing the care

of a cow with a health disorder requires four hours of management labor per case.

112

4.2 Herd reproductive management: Current system and
change scenarios

4.2.1 Current herd reproductive management system

Under the current herd reproductive management system, labor use for estrus detection
and breeding requires a management labor input of one hour per day visually detecting
estrus and one-quarter hour per breeding throughout the year. All cows meeting the
minimum days to first service and detected in estrus are bred. Breeding begins at 70 days

in milk for all management groups.

The level of reproductive performance (pregnancy rate) that results from this
management system varies across management groups. Pregnancy rates in winter and
spring months far exceed those in summer and fall months7. Estrus detection success is
severely impaired in summer months, since cows under heat stress often fail to show
signs of estrus. Since heat stress also impairs follicular development, conception rates
are depressed in the months that follow. Pregnancy rates for first lactation heifers are

generally higher than mature cows and less affected by season (Lucy, 2001).

Reproductive performance in a herd can be increased by improving the current visual
estrus detection system and (or) by implementing a new estrus detection system. Table
4.2 compares the labor use, breeding costs, and reproductive performance in the current

herd reproductive management system to that associated with each scenario. Four

 

7 It is important to note that the effects of season on reproduction express themselves in cows that calved
one to two seasons earlier, since breeding occurs between 70 and 250 days in milk.

113

alternative reproductive management change scenarios were evaluated in this analysis -
two involving additional labor to observe estrus and two that incorporate the Ovsynch
hormonal synchronization protocol into the reproductive management system. The
Ovsynch protocol — a series of three injections followed by timed breeding — eliminates

the need for estrus detection in that estrous cycle (Pursley et al., 1997).

4.2.2 Allocating additional labor to visual estrus detection.

Additional labor for estrus detection provided by management labor can improve estrus
detection rate significantly (Stevenson, 2001). In the first alternative (LBRl), an
additional hour of management labor is allocated each day to estrus detection. Thus, the
farm manager spends two hours each day actively observing cows for signs of estrus.
The estrus detection rates in each management group are expected to improve under each

scenario, since observation time is a key determinant of estrus detection success.

The second alternative (LBR2) involves substituting hired labor for all management labor
in estrus detection. Under this scenario, the hired labor spends 2 hours each day
observing the herd for cows in estrus. Since observer skill level is also critical to the
EDR (F ogwell, 1998), the expected EDR improvement is greater for the management
labor scenario (LBRl) than the hired labor scenario (LBR2). The relative differences
across management groups remain because they result from physiological differences
across cows. Because the breeding system is unchanged, the CR in all management

groups is equal to the current system.

114

4.2.3 Substitution of a timed breeding protocol for visual estrus detection.

The Ovsynch protocol has been promoted as a labor saving replacement for the
traditional visual detection of estrus. The Ovsynch protocol is associated with an average
40% pregnancy rate each time it is conducted, higher than most visual estrus detection
systems (Pursley et al., 1997). Ovsynch pregnancy rates are affected by parity and
season in the same patterns as traditional reproductive methods, although the effects are
less dramatic (Tenhagen et al., 2001). For all management groups in this analysis,
pregnancy rates associated with an Ovsynch breeding exceed those for breedings
accomplished with traditional methods. Perfect application of the protocol was assumed

for both scenarios.

Because the three-inj ection protocol allows timed breeding, observation of estrus is not
needed. Applied to the entire herd, the herd’s estrus detection system can be eliminated.
The Ovsynch system can also be used to partially replace the current estrus detection
system. In this analysis, both full implementation (OVSl) and a supplemental use in

conjunction with a modest reduction in visual estrus detection (OVSZ) were considered.

Full replacement of visual estrus detection with Ovsynch

In OVS 1 , the hormonal synchronization protocol is conducted on all cows in the breeding
herd beginning at 70 days in milk and continuing until they are pregnant or culled. Full
replacement of current reproductive management system with the Ovsynch protocol
eliminates the need for estrus detection in the herd. However, nonpregnant cows are only
bred on alternating estrous cycles. Without visual estrus detection, nonpregnant cows are

not identified at the following estrus. Rather, they are diagnosed by palpation at 40 days

115

after breeding (the approximate equivalent of two estrous cycles), at which time the

Ovsynch protocol can be conducted again.

Partial replacement of visual estrus detection with Ovsynch

A partial replacement scenario (OVSZ) that captures the increased PR of the Ovsynch
system, as well as the reduced turnaround time of a visual estrus detection system, was
also examined. Under the OVSZ scenario, the Ovsynch protocol is applied to all cows for
their first breeding at 70 days in milk, after which cows return to the regular breeding
herd. In their next cycle, cows are observed for signs of estrus and bred if detected.
Thus, the first service pregnancy rate is 40%, while EDR and CR for future cycles remain

at the original herd values.

Since Ovsynch is not conducted regularly on all cows, the visual estrus detection system
for the herd must remain in place. However, visual estrus detection need only occur
during one week of every three-week cycle. Applying the Ovsynch protocol “partially”
to the entire herd results in synchronization of the estrous cycles of all cows at the first
service. Nonpregnant cows continue their cycle such that subsequent estrus periods
occur at approximately the same time. Like the current system, management labor

conducts all estrus detection.

116

4.3 Results and discussion

4.3.1 Annuity equivalents by management group

Table 4.3 and 4.4 contain the annuity equivalent values for heifers and cows for each
calving interval in each season of calving by lactation curve model. These values
represent the armualized gross margin for the lactation of a given calving interval in the
management group with constant replication -- that is, when the number of cows in each
calving interval management group is continuously maintained. As a result, differences
in annualized values across calving intervals, management groups, and lactation curves
represent only the contribution of the group to the herd value. The value of changing the
calving interval cannot be inferred without adjusting for the changes in herd structure

associated with specific reproductive performance changes.

Calving interval

Within management group, annuity equivalent values were generally higher for shorter
calving intervals. Values decreased at an increasing rate as calving intervals became
longer. While annual differences between the shortest two calving intervals were
approximately $1.00 to $1.50 for heifers and $2.00 to $2.50 for cows, the difference
between the longest two calving intervals was nearer to $2.00 for heifers and $3.00 to
$5.00 for cows. Cull lactations represent failure to conceive -- i.e., not pregnant after 254
days in milk. The value of these lactations was lower than other calving intervals

because it reflects the cost of the resulting replacement.

117

Management groups

Cow lactations generated more annualized net income than heifer lactations within
season of calving. This pattern held across season of calving, except that summer cow
lactations were less valuable than winter heifer lactations. Lactations of heifers and cows
calving in the fall winter were generally more valuable than those calving in other
seasons. Summer lactations were the least valuable for both heifers and cows, likely

reflecting the lasting influence of heat stress on milk yields over lactation.

Patterns across lactation curve models

The patterns in calving intervals and management groups discussed above were similar
across lactation curve functional form. One notable exception was the ranking of calving
intervals for spring-calving heifers by the WoodPE model, which showed the highest
value for a 62 week calving interval. Differences between lactation curve models for
same calving interval and management group ranged from $1.00 to $5.00 for heifers and
$10.00 to $20.00 for cows. Cull lactations varied the most, caused by differences across
lactation curve model in the modeling of the pregnancy effect (and its removal). The
value of cull lactations of the same calving interval and management group exceeded $10

for heifers and $25 for cows.

4.3.2 Decision results by lactation curve model

The analytical results for the reproductive management change scenarios, shown in Table
4.5, indicated that decision results were consistent across all lactation curve models. The
rankings of the alternatives were identical across lactation curve model, despite variation

in the expected change in annualized retums of the alternative change scenarios by $50 to

118

$150. The full implementation of Ovsynch (OVSl) had the highest value for this herd
across all lactation curve models. Using the Wood model, annualized net farm income
was expected to be $1,176 higher than the current system once the OVSl was
implemented and steady state was reached. The analogous values under the LPM and

diphasic models were $1,292 and $1,342, respectively.

OVSZ is associated with significant improvement in reproductive performance as well as
reducing management labor use. Although increasing estrus detection by management
labor (LBR2) provides a similar improvement in reproductive performance,
implementing this change is expected to decrease net farm income by $330 to $600 per
year, depending upon the selected lactation curve model. LBR2 increases management
labor requirements. Replacing the current visual estrus detection system by hiring
additional labor (LBRl) or partially with Ovsynch (OVSl) would also increase net farm
income, but to a lesser degree. These scenarios captured lesser amounts of reproductive

performance improvement and reduction in management labor needs.

The expected change in milk revenues made up a relatively small portion of the total
expected change associated with these scenarios. In Table 4.6, the expected change in
annualized returns for each of the change scenarios is partitioned into four categories —
milk revenue over feed costs (IOFC), change in labor costs, change in the net cost of
replacement, and all other cash flow changes. Of these, only the IOFC category was

affected by the lactation curve model selection.

119

IOF C values for the nonlinear models were closer to each other than either of the Wood
models. Values from the Wood models were lower than the nonlinear models.
Differences in IOFC between across lactation curve models were large relative to IOF C
, values but did not affect the decision. The Wood models predicted a slight decrease in
IOFC while the nonlinear models predicted increases for the labor scenarios. The Wood
PE model also predicted a decrease in IOFC for the Ovsynch scenarios. The increase
projected by the basic Wood model was only a fraction of the projection by both
nonlinear models. Since the annuity equivalent values in the Wood model decreased
progressively with increasing calving intervals, these sign differences are not related to
the Wood model’s ability to predict lactation extension. Rather, differences from the
nonlinear models result from differences in characterizing lactation curve shape across
management groups. The shift in herd structure toward management groups with lower
annualized values caused larger decreases in value by the Wood model than the nonlinear
models.

Differences across IOFC projections by lactation curve model were generally small
relative to other components of the scenario values. A large portion of the change
scenario’s value results from the change in labor costs. Whereas savings in labor costs
were $1,056 and $697 for OVSl and OVSZ, respectively, the largest estimated changes
in IOFC (diphasic model) were $175 for OVSl and $103 for OVSZ. Changes in
replacement and other cash flows, too, often exceeded the expected change in the IOFC

for all lactation curve models.

120

4.3.3 Sensitivity analysis

In order to examine the influence of key assumptions on the in results across the lactation
curve models, the analysis was run at high and low expected values for the market prices
and farm characteristics. Farm financial characteristics included herd size, opportunity
cost of capital, milk price, and feed costs. Farm production characteristics included herd
health, labor efficiency, and nonreproductive culling rates. Additionally, unit costs for
labor change scenarios and labor use for Ovsynch were examined. The values used in the

sensitivity analysis are summarized in Table 4.7.

Results for each of these analyses are shown in Tables 4.8 through 4.11. Despite the

differences in projected scenario values across lactation curve models, scenario rankings
were identical for all characteristics. OVSl resulted in the largest increase in annualized
returns, followed by OVS2 and LBR2. Most analyses indicated that LBRl would result

in decreased annualized returns.

The Wood models consistently reported lower values for each alternative than the
nonlinear (LPM4 and diphasic) models. Since each alternatives increased the proportion
of the herd with shorter calving intervals, this finding is consistent with previous findings
that the Wood model overestimates late lactation yields (Vargas et al., 2000). The effect
was much more pronounced for cows than for heifers. As such, the Wood models
provided more conservative estimates of the value of reproductive performance

improvements.

121

The value of incorporating a pregnancy effect into the Wood model, as in WoodPE, is
questionable. The WoodPE model did not always lead to analytical results closer to the
more accurate nonlinear models. Replacing the days pregnant variable (DPt) with an
adjusted days pregnant variable (Adj DPt), used with the diphasic model, may enhance

the model’s ability to capture the milk yield depression associated with late gestation.

4.4 Summary and conclusions

Four alternative reproductive management scenarios to improve reproductive
performance were evaluated using the reproductive decision analysis model developed in
Chapter 2. Analysis was conducted using milk yield projections from each of the
lactation curve models examined in Chapter 3. Two alternatives involved allocating
additional labor — hired or management - to improve estrus detection rates. The other
two substituted partially or fully the Ovsynch timed breeding protocol for estrus

detection. The case farm was designed to be representative of mid-size Midwest dairies.

Differences in annuity equivalent values for calving intervals within each management
group were consistent with previous findings. In general, annuity equivalents for shorter
calving intervals were more valuable than longer calving intervals. However, annuity
equivalents for cow lactations were higher than heifers, and winter and fall calving
lactations were greater than those calving in spring and summer. Thus, management
changes that result in a relative increase in cow and (or) winter lactations will have a

higher value than those that shift toward heifer and (or) summer lactations. Results

122

indicated that the full implementation of the Ovsynch protocol had the highest value for
the case farm under a range of market prices and farm characteristics for all lactation

CUI'VCS.

Lactation curve models consistently agreed on value rankings for annuity equivalents and
management decisions in this analysis, despite the differences in lactation curve shape
and milk yield predictions found in Chapter 3. Values projected using the Wood models
were lower than those from the nonlinear models. Thus, the Wood models may provide
a more conservative estimate of the change in milk revenues and feed costs resulting
from a change in reproductive performance. Nonlinear models may provide more
accurate results, since they show better fit throughout lactation. However, other factors
affecting the projected value of reproductive management changes may be more
important. Changes in labor and replacement costs were generally larger than the
changes in milk revenues over feed costs. As a result, use of the nonlinear models for

fann-level management decision analysis may not be worth the effort.

123

Coulon, J. B., L. Perochon, and F. Lescourret. "Modelling the effect of the stage of
pregnancy on dairy cows' milk yield." Animal science : an international journal
of fundamental and applied research 60, no.3 (1995): 401-408.

Fogwell, R. "Detect heat -- No bull." Michigan Dairy Review 3, no. 1(1998).

Harsh, S. B., C. A. Wolf, and E. Wittenberg. "Profitability and production efficiency of
the crop and livestock enterprises of Michigan dairy operations: 1998 summary
and analysis." Staff Paper. Michigan State University, Deparrnent of Agricultural
Economics, January 2001.

IRS. "US Master Tax Guide." US Department of Treasury, Internal Revenue Service.
2001

Lucy, M. C. "Reproductive loss in high-producing dairy cattle: where will it end?"
Journal of dairy science 84, no. 6 (2001): 1277-1293.

Nott, S. B. "1994 to 1998 FinPack Balance Sheets for 35 Michigan Dairies." Department
of Agricultural Economics, Michigan State University.

OSU_Extension (1999) Dairy cow and replacement budget: Large breed., 2000, The
Ohio State University Extension.

Pursley, J. R., M. C. Wiltbank, J. S. Stevenson, J. S. Ottobre, H. A. Garverick, and L. L.
Anderson. "Pregnancy rates per artificial insemination for cows and heifers
inseminated at a synchronized ovulation or synchronized estrus." Journal of dairy
science 80, no. 2 (1997): 295-300.

Stevenson, J. S. "Reproductive management of dairy cows in high milk-producing
herds." Journal of dairy science 84, no. E. Suppl. (2001): E128-E143.

Tenhagen, B. A., M. Drillich, and W. Heuwieser. "Analysis of cow factors influencing
conception rates after two timed breeding protocols." Theriogenology 56, no. 5
(2001): 831-838.

USDA. "Agricultural Statistics." National Agricultural Statistics Service.

Vargas, B., W. J. Koops, M. Herrero, and J. A. M. v. Arendonk. "Modeling extended
lactations of dairy cows." Journal of dairy science 83, no. 6 (2000): 1371-1380.

124

Table 4.1. Farm data used in reproductive management decision analysis.

 

 

 

 

Price data
Replacement cost $1,400.00 per head
Cull price $450.00 per head
Calf value

Heifer (at weaning) $250.00 per head

Bull (at 1 week) $75.00 per head
Milk price $13.50 per CWT
Feed cost $0.06 per lb DM
Dry cow cost $2.00 per day
Veterinary expense $100.00 per case
Breeding expense $22.00 per breeding
Hired labor wage $12.00 per hour
Opportunity cost of management labor $25.00 per hour
Opportunity cost of capital 8.00% per year
Inflation 3.00% per year
Marginal tax rate 35%
Capital gains tax rate 20%
Labor use data
Labor hours per calf (average) 1.5 hrs Hired
Labor hours per health disorder case 4 hrs MGT
Labor hours per breeding 0.5 hrs MGT

 

Other herd characteristics

Milking herd size 100 head
Health disorder incidence[1] 15%
Milk yield for early dry off 20 lbs

 

[1] Percent of cows that suffer from mastitis or metabolic disorders in a given lactation.
Each afllicted cow is also referred to as a case.

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128

Table 4.5. Comparison of the expected change in annualized net income for four
alternative reproductive managment scenarios.

 

 

 

LBRl LBR2 OVSl OVS2
Mgmt Hired Partial Full
Total:
Wood 5 (578.30) $ 166.82 $ 855.19 $ 1,175.65
WoodPE $ (591.44) $ 132.19 $ 775.70 $ 1,119.21
LPM4 $ (451.65) $ 217.71 S 904.98 $ 1,291.62
Diphasic $ (330.37) $ 267.97 S 909.52 $ 1,342.15
Per Cow (average):
Wood $ (5.78) $ 1.67 S 8.55 $ 11.76
WoodPE $ (5.91) $ 1.32 $ 7.76 $ 11.19
LPM4 $ (4.52) $ 2.18 $ 9.05 $ 12.92
Riphasic $ (3.30) $ 2.68 $ 9.10 $ 13.42

 

Table 4.6. Components of the expected change in annualized net income for four
alternative reproductive managment scenarios: Labor, replacement, IOFC, and
other cash flows .

 

 

LBRl LBR2 OVSl OVS2
Mgmt Hired Partial Full
Change in cash flows
Labor $ (1,141.84) $ 5.64 $ 696.97 $ 1,056.15
Replacement $ (303.62) $ (262.49) $ (174.33) $ (501.92)
Other 8 878.18 $ 456.27 $ 283.54 $ 613.38

Change in milk income over feed costs

Wood $ (11.03) 8 (32.60) 8 49.01 8 8.03
WoodPE 8 (24.17) 8 (67.23) 8 (30.48) $ (48.41)
LPM4 8 115.63 $ 18.29 8 98.80 8 124.00
Diphasic 8 236.91 8 68.55 8 103.33 8 174.53

 

129

Table 4.7. Data used in sensitivity analysis for reproductive management
decisions.

 

 

 

Scenario characteristics

Case Low High

Relative cost of scenarios [LaborzCapital]

 

 

 

 

Hired labor $ 12.00 $ 8.00 $ 18.00 per hour
Management labor $ 25.00 $ 15.00 $ 50.00 per hour
Ovsynch injections $ 18.00 $ 24.00 $ 12.00 per breeding
Ovsynch labor use 0.35 0.10 0.50 hrs per brdg
Farm financial characteristics
Case Low High
Milk vs. feed prices
Milk price $13.50 $11.00 $16.00 per CWT
Feed cost $0.06 $0.08 $0.04 per lb DM
Opportunity cost of capital 8% 6% 10%
Farm production characteristics
Case Low High
Culling rates (non-reproductive) 25% 15% 40%
Herd health costs
Health disorder incidence[1] 15% 7% 30%
Veterinary expense $ 100.00 $ 50.00 $ 200.00 per case
Labor efficiency
Labor hrs per fresh cow 1.50 2.00 1.00 hrs hired
Labor hrs per health disorder case 4.00 6.00 2.00 hrs mgmt
Labor hrs per breeding 0.25 0.50 0.10 hrs mgmt
Milking herd size 100 50 150 milking cows

 

[1] Percent of cows that suffer fi'om mastitis or metabolic disorders in a given lactation.
Each afflicted cow is also referred to as a case.

130

 

 

 

 

 

 

 

 

 

 

 

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134

Chapter 5

SUMMARY AND CONCLUSIONS

5.1 Summary of methods and results

An economic simulation model was developed to evaluate reproductive management
decisions for a dairy farm. Reproductive management was considered as an investment,
with changes in the reproductive management system altering the capital investment and
return structure for the herd. The model considers calving intervals on the basis of
annualized net returns to the dairy herd enterprise — first calculating the present value of
each lactation, then converting it to an annuity equivalent. The model implicitly deals
with management labor and capital constraints of dairy farms by including the related
opportunity costs. As well, the model considers the changes in herd structure associated

with reproductive performance improvements.

In order to evaluate the influence of lactation curve specification, the reproductive
analysis was run using milk yield projections from for common lactation curve
specifications — two variations on the Wood model, a modified LPM model, and the
diphasic model. Each lactation curve was fitted to 362 lactations of daily milk yield data
from a dairy herd (over three years). The lactations were pooled into eight management
groups defined by parity and season of calving. Differences in lactation curve shape
were evident across management groups, suggesting differential values for improving

reproductive performance. First lactation heifers, as well as all cows calving in summer,

135

showed lower but more persistent peak yields than their mature and (or) winter-calving

counterparts.

Analysis of the residuals of the lactation curve models across stage of lactation and
management group indicated that the fit of the nonlinear models (LPM and diphasic
models) is consistently better than the Wood models. Nonlinear models showed
consistently higher R2 and lower root mean square error (RMSE) than the Wood models
for most stages of lactation in all management groups. The Wood results were similar to
the nonlinear models for heifer lactations but relatively poor (lower R2 and higher

RMSE) for cow lactations.

Annuity equivalents for lactations of each calving interval and management group
differed across lactation curve models. Similar to results in previous studies, shorter
calving intervals had higher annuity equivalents than longer calving intervals. In general,
heifer lactations were lower in value than mature cow lactations, and winter lactations
were more valuable than spring and summer lactations. It is important to note that these
lactations must be considered in the context of the herd decision. Changes to the
reproductive performance of individual management groups affect the distribution of
management groups in the herd. The nonlinear models showed greater differences in

value across calving intervals and management groups.

Incorporated into the reproductive model, however, all lactation curve models agreed on

the rankings of the management change scenarios. The net scenario values assessed

136

using the Wood models were consistently lower than both the nonlinear models. No

consistent pattern in values was found between the Wood models with and without the
pregnancy modification. Changes in labor and replacement costs associated with each
investment scenario were larger than the changes in milk income over feed costs for all

lactation curve models.

5.2 Conclusions: Selecting an empirical lactation curve model

Lactation curve specification influences the annuity equivalent values, the weighted sum
of which compose the herd value. Changes in herd structure from a reproductive
management change affect the distributions of both management groups and calving
interval. The lactation curve functional form must capture differences in lactation curve
shape across both management groups as well as calving intervals. However, changes in
labor and replacement costs were consistently larger than the changes in milk income
over feed costs. Thus, accurate projections of all three components are critical to

accurate reproductive management analysis.

The simple mathematical form of the Wood model did not compromise the reproductive
decision results in this analysis despite its inability to reflect all lactation curve shape
differences across management groups. The rankings of alternative management change
scenarios were identical to nonlinear lactation curve models in all analyses. The Wood
model consistently provided the most conservative estimate of the impact of each

proposed reproductive management change. The greatest improvement in accuracy of

137

milk yield projection would likely be gained by using one of the nonlinear models for
cow lactations. Cow lactations are more likely to violate the standard Wood shape,

declining at an increasing rate.

The benefit of incorporating the pregnancy effect into the Wood model was not borne out
by this data. Although analysis of the milk yield regression results indicated that the
model with the pregnancy effect (WoodPE) had somewhat better fit, results of the
reproductive analysis were not always closer to the nonlinear models. Thus, the added
estimation requirements may not be justified. Additional study may indicate a more

accurate linear method of incorporating a pregnancy effect into the Wood model.

Additional study is also needed to determine the applicability of these lactation curve
models to herds using bST. The additive modification proposed by Wiegel (1992) can be
easily incorporated into the diphasic model, although farm-level analysis would then
require nonlinear regression methods. It is also possible that the Wood model may fit
bST-enhanced cow lactations more appropriately, given the slower rate of decline in

these lactations.

5.3 Avenues for further research of reproductive decisions

This reproductive model provides a more rigorous economic analysis of the value of herd
investments that improve reproductive performance. However, the analysis in this thesis

represents four reproductive management alternatives for a single herd. Augmentation of

138

the model may improve its usefulness. Additional scenario alternatives, as well as a
range of culling assumptions, could be incorporated into the empirical model. Although
such changes may require structural adjustment of the analytical model, the foundation is

provided in the conceptual model.

The reproductive management decision model currently reflects whole-farm capital and
management labor constraints by incorporating opportunity costs of scarce resources.
Linear programming could be utilized to apply the model to farms with explicit resource
constraints to the dairy herd. Alternative scenarios would be considered as individual

activities with the model projecting periodic resource use for each.

Incorporating the adjustment period values into the analysis would improve the accuracy
of the value projections. The model compares the value of current herd performance to
the alternative scenario’s value once the herd reaches steady state. Steady state is
reached when management group sizes become stable after the indefinite adjustment
period following a comprehensive reproductive change. Projecting management group
and calving interval distributions in each period during adjustment would allow the
associated annuity equivalents to be more accurately distributed, allowing the opportunity

cost of capital over time to be accounted.

Dairy science research continues to develop technologies that can improve reproductive

performance, providing herd managers with an increasing array of available management

alternatives. In response, managers must make a large set of associated implementation

139

decisions. Because of the inherent difficulties in projecting the effects of reproductive
management changes, decision models such as the one outlined here are critical for
assisting managers in making these decisions. Future research must continue to develop
a simple yet sound analytical framework for analyzing increasingly diverse set of herd

reproductive management decisions.

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140

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