SEJXSGNS 8F GAMING - .. AGE, MANAGEMENT, AND
GENETIC QIFFERENCES FOR MILK

‘s‘hesis for the Degree of Ph. D.
MiGHéGAE‘é STATE UNIVERSETY
WELLEAM WA‘YME WUNBER
1967

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thesis entitled

SEASONS OF CALVINGj-AGE, MANAGEMENT,
AND GENETIC DIFFERENCES FOR MILK

presented by

WILLIAM WAYNE WUNDER

has been accepted towards fulfillment
of the requirements for

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ABSTRACT

SEASONS OF CALVING--AGE, MANAGEMENT,
AND GENETIC DIFFERENCES FOR MILK

by William Wayne Wunder

Maximum likelihood was used to study the effects
of three ages Q32, 3,234 years), six seasons of calving
(January-February, March-April, etc.), and their interac-
tions on the 305 day-2x-ME milk of completed lactations
of Holstein cows in Michigan DHIA. Maximum likelihood
utilizes the probable producing ability of the cow and,
therefore, should remove genetic differences between sea-
sons from seasonal effects on lactational milk yield. Two
values of repeatability, 0.4 and 0.55, made little differ-
ence in the constants for age, season, and age x season
interaction-effects.

Data were 37,247 records in 198 herds on test con-
tinuously at least from 1958 to 1964, 4195 records in 51
drylot herds, and 3651 records in 51 pasture herds. The
drylot herds used no pasture during 1963-64 or 1962-64 and
were paired with 51 pasture herds which used at least 85
days of pasture during the same years and were from the
same counties. The drylot and pasture herds were matched

as closely as possible for years on test, herd size, and

William Wayne Wunder

registered or grade cows.

Yields were largest in the January-February season.
After this they declined steadily, were least in July-August,
and sharply improved again. Below average production ex-
isted from May until October. The best and worst seasons
differed by 776 lb milk. The magnitude of seasonal influ—
ence did not change from 1958-60 to 1962—64. Comparisons
were made between the pasture and drylot herds and between
quartiles of the 198 herds ranked on the DHIA herd average
of milk for 1960 to 1964. The drylot herds showed more
variation with season than did the pasture herds. For
1958-60 the greatest seasonal variation occurred in the
first quartile herds, whereas the least occurred in the
fourth. During 1962-64 seasonal variation was largest in
the first quartile herds, intermediate in the second, and
least in the third and fourth. Seasonal effects differed
some among the quartiles and between pasture and drylot
herds.

Interactions of age with season were present in
that the total change associated with season was about 250
lb less for two-year-olds than for three-year-olds, while
three-year-olds in turn varied 60 lb less than cows four
years or older.. July-August was much more detrimental to
yield of the two older groups than to two-year-olds, where-
as March-April calvings were distinctly more favorable to

the two older groups. Cows of all ages yielded least

William Wayne Wunder

following July-August calvings, while maximum yields were
associated with January-February calvings for the three-
year-olds and November-December calvings for the others.
Although the seasonal pattern was similar, age x season
interactions varied among the quartiles and between the
pasture and drylot herds, indicating herd x age x season
interactions may be an important source of variation. Age
x season interactions seemed to be largest in the lower
producing herds.

Age constants varied widely among the sets of herds.
For the 198 herds during 1958-64 the three-year-old constant
was largest and the four years or older constant smallest.

An analysis of variance within herd and year, with-
in sire-season groups, between sire groups within season,
between seasons within sire, and between different sires
in different seasons was unable to partition seasonal dif-
ferences into genetic and environmental components because
of excessive variation among paternal sisters within season.

Interactions of herds with age, season, and age x
season appeared large enough to be.a source of errors in

the ranking of bulls tested in a limited number of herds.

SEASONS or CALVING—-AGE, MANAGEMENT,

AND GENETIC DIFFERENCES FOR MILK

by

William Wayne Wunder

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Dairy

1967

ACKNOWLEDGMENTS

I wish to express my sincere appreciation to Dr.
Lon D. McGilliard for his consistently sound advice during
the formulation of the problem and the analysis of the data
and for his encouragement and helpful suggestions during
the writing of the thesis.

Dr. John L. Gill is gratefully acknowledged for
his superb teaching of statistics and for statistical help
during this study.

The encouragement and counsel of Dr. Clinton B.

Meadows during the period of graduate study was appreciated.

ii

ACKNOWLEDGMENTS . . .
LIST OF TABLES. . . .
LIST OF FIGURES . . .
INTRODUCTION. . .'. .

REVIEW OF LITERATURE.

TABLE

Variation Due to Season
No Seasonal Differences
Breed Differences in the Effects of Season.
Differences in Seasons Associated with Age.
Environmental Influences on

Lactations. .

Genetic Differences

Summary . . . . .
SOURCE OF DATA. . . .

METHODS O O O O O O 0

RESULTS AND DISCUSSION.

OF CONTENTS

Between

Constants for Seasons
Age by Season Interactions.
Effects of Management on Seasonal
Patterns of Seasonal Calving.

Effects of Age. .

Two-Year-Old

9

Seasons . . . .

Genetic Variation Between Seasons

Variation

CONCLUSIONS AND APPLICATIONS OF RESULTS . . . .

SUMMARY 0 O O O O O 0

LITERATURE CITED. . .

iii

0 O O 0 O O

Page

ii

10
10
ll
14
15
l7
19
22
35
37
43
50
SO
58
64
69

72

LIST OF TABLES

Table Page

1. Variance used in generating records of dummy
herds O O O O O O O O O O O O O O O O C O O O 21

2. Examples of best and poorest agreement between
ML estimates of years, ages, and seasons
plus age x season interactions when r = 0.4
and r = 0.55. . . . . . . . . . . . . . . . . 36

3. Number of cows of three ages calving in each
Season 0 O O O O O O O O O O O O O O O O O O O 51

4. Maximum likelihood estimates of age effects
(in lb ME milk) 0 O O O O O O O O O O O O O O 57

S. Constants (in 1b ME milk) for years 1958-64
from 198 herds. O O O O O O O O O O O I O O O 57

6. Variance components from genetic and environ-
mental season analysis of DHIA data . . . . . 59

7. Variance components from genetic and environ-

mental season analysis of dummy herd data . 6O

8. Ratios of variance components for sires,
season, and residual. . . . . . . . . . . . . 61

iv

LIST OF FIGURES
Figure Page
1. Season constants from 198 herds 1958-60,
1962-64, and 1958-64 0 o o o o o o o o o o o 38
2. Constants for season plus age x season inter-
action from 198 herds 1958-60, 1962—64, and
1958-640 0 o o o o o o o o o o o o o o o o o 40

3. Season constants for pasture and drylot herds. 44

4. Season plus age x season constants for pasture
and drylot herds . . . . . . . . . . . . . . 44

5. Season constants from herds in quartiles by
yield of milk 1958-60, each quartile fitted
separately . . . . . . . . . . . . . . . . . 45

6. Season plus age x season constants for herds
in quartiles by yield of milk 1958-60. . . . 47

7. Season constants from herds in quartiles by
Yield Of milk 1962-640 0 o o o o o o o o o o 48

8. Season plus age x season constants for herds
in quartiles by yield of milk 1962-64. . . . 49

INTRODUCTION

The low reproductive rate, high percentage of in-
voluntary losses, and long generation interval in dairy
cattle make genetic progress from female selection very
slow. Thus, almost all the genetic gain must come from
the selection of sires. The rapid growth and acceptance
of artificial insemination (AI) allows a greater selection
differential among dairy Sires than was possible with nat-
ural service and provides large enough breeding populations
that progeny testing and using proven sires Should provide
the most rapid genetic improvement.

Because much of the variation among lactational
records and progeny groups of Sires is environmental, de-
viations of daughter records from herdmate averages have
been widely used to remove the environmental effects of
herds, years, and calving seasons from the differences
between progeny groups. When sires have large numbers
of daughters scattered over many herds, the environmental
differences between sires usually are cancelled. However,
in sampling young sires in AI there is usually a practical
limit to how many matings should be made to young sires.
This means either that sires may not have enough daughters
to average out environmental differences between progeny

groups, or that too few bulls will be sampled, limiting

the selection differential. Thus, it is important to make
the progeny test as accurate as possible with a minimal
number of daughters, so that more Sires can be sampled.

Recent research has shown the effects of season
of calving may not be the same for two-year-olds as for
older cows. Selection pressure varied between seasons in
another study. Further research is needed to verify and
determine the magnitude of these differences. If they are
large enough, comparing cows with herdmates of the same
age may increase the accuracy of progeny tests.

The objectives of this study were to use an anal—
ysis taking into account the probable producing abilities
of the cows calving in each season to determine in what
manner and how much seasonal variation differs between two-
year-olds and older cows and what effect level of hard pro—
duction and certain management practices have on seasonal
variation. The final objective was to partition seasonal

differences into genetic and environmental components.

REVIEW OF LITERATURE

The milk record of a cow is the result of her geno-
type and environment acting together. For this reason it
is difficult to evaluate the genetic ability of a cow to
produce milk. The same problem is present in progeny test-
ing bulls since the average production of the daughters
represents the genetic contribution of the sire, a genetic
contribution from the dam, and an environmental influence
of unknown magnitude or Sign. Most sire proving work is
concerned with eliminating or reducing the environmental
contribution to daughter averages so that dairy sires may
be ranked on some measure that is correlated as closely
as possible with their genetic merit.

In one of the early studies of sources of varia-
tion among lactational fat records, Plum (1935) determined
that differences between herds contributed 33% of the total
variation. Van Vleck et al. (1961) reported herd differ-
ences accounted for 30% of the variation in lactational
milk and fat records and that interactions involving herds
contributed an additional 8 to 17% of the total variation.
A smaller component of variance for herds was calculated
by Sundaresan and Freeman (1961). They found herds con—
tributed 5 to 6% of the total variation whereas interac—

tions involving herds accounted for approximately 12% of

the total variation among lactational milk and fat records
from 12 state-owned herds in Iowa. Because herds and in-
teractions involving herds are major contributors to vari-
ation among lactational milk and fat records, the influence
of the herd should be considered in comparing the produc-
tion records of animals in different herds.

In current evaluation of sires and dams, removal
of herd and other environmental influences is attempted
by subtracting from the production of a cow the average
production of all other non-paternally related cows of the
same breed in the same herd that calved in the same month
as the cow being evaluated or in the previous or succeed-
ing two months (herdmates). In actual practice the herd-
mate average is adjusted for finite numbers, and only 0.9
of the difference between the average of the herdmates and
breed average is subtracted from the record of the cow be-
ing evaluated. However, the principal of using the average
of the herdmates to measure the environmental opportunity
afforded the cow in question is still present.

Identification and evaluation of sources of varia-
tion among lactational records within a herd give some in-
dication of what adjustments should be made on records and
what combinations of available records might yield the best
estimate of environmental opportunity.

Some of the identifiable sources of variation among

lactation records within a herd are the age of the cow,

frequency of milking, length of the lactation, year the
record was made, and the season in which initiated (season).
Conversion factors for standardizing records to a
mature age (ME) and a twice-a-day (2x) frequency of milk-
ing are widely used and accepted in the United States.
To standardize the length of lactation records, incomplete
lactations are either excluded or extended to a 305 day
equivalent while the production of only the first 305 days
is used for longer lactations. Lactations shorter than
305 days and terminated by a normal drying-off are not ex—
tended. Year to year fluctuations are circumvented by com-
paring cows that calved within the same year or some other
appropriately short time interval or are minimized by using
deviations from yearly herd averages or from herdmate aver-

ages.

Variation Due to Season

Many workers have observed variation in lactational
milk and fat yields due to the month or season of the year
in which the cow calved. Generally, in the United States,
Canada, and countries of Northern Europe, lactations initi~
ated in the fall and winter months have a higher average
yield than lactations begun at other times in the year.
Lactational milk and fat yields differ little in the effect
Iof season.
In one of the early investigations of the influence

of season on milk production, McDowell (1922) observed that

the cows freshening in the fall produced 6689 lb of milk,
while those freshening in the winter, summer, and spring
produced 6439, 5941, and 5842 lb, respectively.

Cows calving in November had the highest average
yield (about 6% above the mean for both milk and fat) in
a study by Cannon (1933) of 68,000 yearly records from Iowa
cow testing associations for the years 1925-1930. Lacta-
tions begun in the month of June had the lowest yearly milk
production while May, June, and July were equally low months
for yearly fat production. Cows freshening each month from
November to June were lower in yearly milk production than
the group freshening in the preceding month. From June
until November the cows freshening in each month averaged
more milk than those in the preceding month.

Cows calving in November through January produced
13.6% more fat than cows calving in May through July in
5860 yearly records made by Guernsey, Jersey, or Holstein
cows in Iowa between 1922 and 1932 (Plum, 1935).

Annis et al. (1959) reported cows calving in March
and April produced 5% more milk than cows calving in July
and August. The data were 35,000 lactations by Guernsey,
Holstein, and Jersey cows in Washington. Lactations were
adjusted to 305 day-Zx—ME. Breeds differed little.

Among 38,000 Holstein records from Iowa DHIA files,
cows calving in the late fall and winter months yielded

about 5% more milk than cows calving in the late spring

and summer months (Bereskin and Freeman, 1965). November
and December were equal for the calving month with highest
lactation production while cows calving in August had the
lowest lactational milk yield. Records were corrected to
305 day-2x—ME.

In southeastern United States, Fosgate and Welch
(1960) studied records from 15 Georgia DHIA herds of mixed
breeds. Regression analysis indicated that cows calving
in the spring (highest season) produced 990 lb more milk
than cows calving in the summer (lowest season). In an-
other study of Georgia DHIA cows of mixed breeds (Lee et
al., 1961), the rank of the seasons in descending order
was winter, spring, fall, and summer. Branton et al. (1958)
reported that season had a highly Significant effect on
722 lactations made by 283 Holstein cows in Louisiana.
Season had a Significant effect on the lactational milk
yield made by Jersey cows at the Florida Agricultural Ex—
periment Station (Wilcox et al., 1965).

Variations with season in lactational production
have been noted in northeast United States. Among 22,000
lactational records made by cows of mixed breeds in Connec-
ticut DHIA herds, cows calving in January through March
produced approximately 10% more than cows calving in June,
July, or August (Frick et al., 1947). In 4000 New York
state DHIA lactation milk records, September, October,

November, and December were the most favorable calving

months for high production while April, June, and July were
the most unfavorable (Hickman and Henderson, 1955). Cows
calving in December produced 17% more than cows calving

in July, based on 305 day-2x-ME milk lactation records of
4% made by 4000 cows of mixed breeds (Morrow et al., 1945).

In 49,000 Holstein HIR lactations from 35 states,
cows freshening in the favorable part of the year (October
through April) produced 5% more milk than cows freshening
in the unfavorable part of the year (Tucker and Legates,
1965). Cows calving in the most favorable month, January,
produced 8.7% more milk than those calving in July, the
least favorable month.

Woodward (1945) analyzed records of 15,000 cows
in 12 states and concluded that October and November were
the most favorable months for calving while July was the
least favorable.

Work in extending part records has shown that the
extension factors vary with seasons (Lamb and McGilliard,
1960, and Aulerich, 1965). In addition, Aulerich (1965)
found cows calving between August and March exhibited a
more consistent lactation curve.

Among Holstein ROP lactations in western Canada,
cows calving in November produced 9% more milk than cows
calving in July (Jarvis, 1960). Differences between the
average milk production of cows calving in each of the 12

months of the year or in each of three seasons were

significant (p (.01) .

Records of dairy cows in Great Britain are also
influenced by season. Hammond and Sanders (1923) reported
that among 1410 lactational milk yields by cows of mixed
breeds in four milk recording societies in England, cows
calving in October and November produced 978 1b more milk
per lactation than did cows calving in June and July. Later
with a much larger sample of cows Sanders (1927) determined
that cows calving in November through February produced
10% more milk per lactation than cows calving in May through
August. In Scotland cows of the Ayrshire breed calving in
winter produced about 10% more milk than those calving in
summer (Mahadevan, 1951).

Season of calving had pronounced influence on the
lactational yield of dairy cattle in Denmark and Sweden
with summer being the unfavorable season (Hofmeyr, 1955).
Among Norwegian Red-and—White cows season accounted for
4% of the within herd variation in milk yield (Syrstad,
1965). Season affected milk yield equally in high and low
level herds while its influence varied somewhat among three
districts. Autumn and early winter months were the most
favorable in all three districts.

Dairying is seasonal in New Zealand with most cows
calving in the spring months of July and August. Very few
cows calve later than October and all cows are dried off

in May. Season effects are due to weather, feed supplies,

10

and length of lactation. Among cows calving in August 93%
milked until the eighth month (March), while only 72% of
the cows calving in October milked until the eighth month

(May) according to Searle (1961).

No Seasonal Differences

Insignificant differences between the lactational
production of cows freshening in different months of the
year were reported by Oloufa and Jones (1948). The data
were first lactation, two-year-old records from 10 Willa-
mette Valley counties in Oregon, a region with a monthly
mean temperature range from 38°F to 68°F.

Differences in average lactational milk yield of
Jersey cows calving in the four seasons at the Florida
Agricultural Experiment Station were not significant (Arnold
and Becker, 1935).

In both of these studies, the authors felt that
the mild weather of the area was the reason for no signif-

icant variation due to season.

Breed Differences in the Effects of Season

Differences between breeds in response to season
were noted among New Hampshire Ayrshire, Guernsey, Holstein,
Jersey, and Milking Shorthorn cows (Morrow et al., 1945).
Jersey cows freshening in June, July, August, and Septem-
ber made above average lactational milk records while sum-

mer freshenings resulted in below average production for

11

cows of the other four breeds. Also, the range between
the highest and lowest month for lactational milk yield
was least for the Jerseys.

Wylie (1925) observed an atypical response to
season by Jersey cows. Among 2900 ROM records, those
lactations initiated in July had the highest average while
lactations begun in April through June and August and
September were the lowest.

The general patterns of the association of month
with lactational milk yield were similar for four breeds
(Frick et al., 1947). The data were actual lactational
records by 9000 Guernseys, 8000 Holsteins, 2000 Ayrshires,

and 2000 Jerseys in Connecticut.

Differences in Seasons Associated with Age

Sundaresan and Freeman (1961) observed a difference
in the percent of total variation caused by season for
first records as compared with all records. The data were
12,623 completed records made by 4487 Holstein cows in
12 state-owned Iowa herds. The records were adjusted to
305 day-2x-ME and were made during 1940 to 1956. The vari-
ance components for season are listed below as percentages

of the total variance.

 

 

Source All Records First Records
3 month season 1.5 0.2

6 month season 1.8 0.4

12

Variations in lactational milk yield due to month
were smaller for two and three-year-old cows than for cows
aged four to Six or over Six years among Guernsey, Holstein,
and Jersey cows in Washington state (Annis et al., 1959).
Of all four age groups three-year-olds showed the least
variation due to month. The most unfavorable month among
two—year-olds was June while for the three older groups
of cows it was August. When two-year-olds were compared
with all other cows, the younger cows showed less varia-
tion in lactational milk production due to season. To
study interactions between the influence of season and
the herd management level, the herds were assigned to a
high, medium, or low group according to the average fat
production of the herd. A11 cows over two years of age
were grouped together. With but two exceptions the influ-
ence of season on milk yield was consistent at the three
herd levels within ages. First, there was a slight reduc-
tion in seasonal variation for cows over two years of age
in the high herds. Second, among two-year-olds spring was
the least favorable season in high herds, whereas summer
was the least favorable for medium and low herds. For fat
production of two-year-olds a distinct reduction occurred
in the influence of season in high herds while the medium
herds exhibited greater seasonal variation than low herds.
The effect of season on lactational fat production of cows

over two years of age was not influenced by the level of

l3

herd production. No reasons were given to explain why,
among two—year-old cows, high producing herds would show
slightly greater variation in lactational milk production
due to season than medium and low producing herds, while
at the same time they show a sharply reduced variation in
lactational fat production in comparison with the medium
and low producing herds.

Using the actual lactational yield of milk, Frick
et al. (1947) noted that differences between the most favor-
able and least favorable month became relatively greater
as age increased. However, conVerting the records to a
ME basis might remove these seasonal differences between
the age groups.

The investigation by Jarvis (1960) indicated the
least favorable calving for two-year-old Holsteins in
western Canada was in May, June, and July while for older
cows it occurred most frequently in July and August.

Seasonal differences in ME age correction factors
were reported by McDaniel and Corley (1966) in 1,795,895
lactational milk and fat records of cows of all breeds and
all areas of the United States. Separate factors developed
for milk records by two-month seasons (January-February,
etc.) and breed Showed the age correction factors for milk
yield of two-year—old cows of all breeds were smallest for
July—August and September-October. These results would

indicate that calvings during July to October have a more

l4

favorable effect or a smaller unfavorable effect on the
lactational milk yield of two—year-olds than of mature cows.
Analysis of variance of the age correction factors for Hol-
steins and Guernseys indicated a significant effect of sea-
sons on age correction factors. The results of this study
represent the average condition over 14 years and may not
accurately describe present conditions.

Converse to the results of McDaniel and Corley
(1966), Gravir and Hickman (1966) found no seasonal dif-
ferences in the percentage increase in average level of
production from first lactation to maturity in an analysis
of 108,000 Holstein ROP lactational milk and fat records
in Canada. Seasonal divisions were September through Feb—
ruary and March through August and covered September, 1958,
through August, 1960. The increase from second or third
lactation to maturity was essentially the same for both
seasons. However, they did find a significant difference
in the slope of first-lactation yield-age regression curves

for the two seasons.

Environmental Influences on Two-Year-Old Lactations

That cows calving at less than 36 months of age
exhibit a more consistent lactation curve than do mature
cows is well known. If, as suggested by Dr. Lon D.
McGilliard, a more consistent lactation curve has greater
resistance to environmental influences, then the lactation-

al milk yield of two-year-old cows might be affected

15

differently or to a lesser degree by season than the milk
yield of older cows. The results of a study by Allaire
and Gaunt (1965) support this hypothesis. They found the
linear regression of first lactation records on first lac-
tation or all lactation contemporaries to be smaller than
when a record representing any parity was regressed on
contemporaries that included all lactations. The authors
suggested that these results might be interpreted to mean
that first lactation records are not as susceptible to
prevailing environmental conditions as are later lactation
records. This interpretation is strengthened by higher
heritabilities for first lactations (Barker and Robertson,
1966, Freeman, 1960, and Rendel et al., 1957) and smaller
variation among first lactations (Deaton and McGilliard,

1964).

Genetic Differences Between Seasons

In Michigan, as in many other states, certain
months of the year have been designated as a base build-
ing period for milk marketing purposes. During this time
it is economically important to ship a maximum amount of
milk to the processing plant. Consequently, it might be
that cows due to calve during the base building period
are subjected to less culling than cows due to calve dur-
ing the other months of the year. If a differential cull—
ing rate occurs throughout the year, inequalities may ex-

ist in the average genetic value of cows calving during

16

the various seasons of the year. As most heifers calve
in the fall in Michigan, culling occurs with each lacta—
tion, and the average calving interval is 13 months; cows
calving in the winter months may be a more selected group
than those calving in the fall. In addition, any special
effort by the dairyman to keep his better cows from calv-
ing in the months least favorable for high lactational pro-
duction might also result in genetic differences between
groups of cows calving in different months or seasons of
the year.

In Holstein cows in New York, Allaire and Henderson
(1966) found small differences in the percent of cows sur—
viving to start another lactation when the calvings were
divided into three seasons. For cows in the first through
the fourth lactations, 77% of those calving in August
through November, 73% of those calving in December through
March, anda72% of those calving in April through July were
saved. While these differences in culling are small, they
do not preclude the possibility of seasonal differences
in average genetic ability caused by an accumulation of
differential culling over time and selection of the calv-
ing season for cows of different producing abilities.

The methods used to eliminate environmental dif-
ferences between groups of offspring in progeny testing
vary among countries. A review of these methods is given

in Johansson (1961). The yield of daughters is compared

17

with that of their contemporaries in the same herd in Great
Britain and Finland; in Sweden and New Zealand the daughters'
average yield is compared with the yield at corresponding
ages of daughters of other bulls in herds on the same pro—
duction level; and New York and the USDA use herdmates calv-
ing in the same year and season or in the same S-month-moving
season as a basis of comparison. In Denmark, Sweden, Norway,
and Great Britain the progeny test is based on the first
lactation of the daughters and age correction factors are
avoided or are made to a standard age at first calving,
whereas in the United States and New Zealand the individual
records are corrected to a mature age. Season is ignored

in Holland, Great Britain, Sweden, and Finland and is cir-
cumvented by seasonal calving in New Zealand, Norway, and

the Danish progeny testing stations. Fixed year-seasons

are used by New York and rolling S-month-seasons are used

by the USDA to remove seasonal influences. Such diversity
in progeny testing methods implies that no one system is
entirely correct and that continued study of ways to remove

age, season, and other environmental influences is needed.

Summary
There is evidence in the literature that the lac-

tational yield of two-year-old and possibly three-year-old
cows is affected differently by season than is the lacta-
tional yield of older cows. However, no reports were found

of the effects of season on the lactational production of

18

cows of different ages taking into account possible differ-
ences in the producing ability of cows calving at different
times in the year.

Many writers have expressed the opinion that the
quantity and quality of feed available throughout the year
may be contributing to the influence of season of calving.
Estimates of seasonal effects for cows of different ages
from records made in recent years at different levels of
management should indicate the influence of management on
seasonal effects. Such results could be useful in deter—
mining what records to use as herdmates in evaluating rec-
ords.

To estimate genetic differences between the cows
calving in different seasons would be of interest. If such
differences exist, they need to be accounted for in eval-

uating dairy animals.

SOURCE OF DATA

Two sets of data were from Michigan DHIA Holstein
herds, while a third set was simulated data. For the first
set the Michigan DHIA annual herd summary sheets were used
to identify 51 herds that used no pasture during 1963 and
1964, and 1962 where possible. The 51 herds were located
in 20 counties and will be referred to as "drylot" herds.
For comparison with the drylot herds, 51 herds using at
least 85 days of pasture during each of the same two or
three years will be referred to as "pasture" herds. To
make the drylot and pasture herds as much alike as pos-
sible, the pasture herd chosen to pair with each drylot
herd was from the same county, covered the same years, and
was matched as closely as possible with respect to herd
Size, number of years on DHIA testing, and whether the herd
had registered or grade cows.

The second set consisted of 198 Holstein herds from
14 counties in Michigan. The 14 counties represented each
of four geographic areas of Michigan in the same ratio as
if the entire Michigan DHIA population had been used. Rec-
ords from herds in these counties that had been on test
from at least 1958 to 1964 were obtained. Nine of the dry—
lot herds and 10 of the pasture herds were also among the

198 herds.

l9

20

In both sets of data only records of 305 days or
those terminated by a dry date prior to the 305th day were
used. All records were adjusted to 2x-ME using factors
by Kendrick (1955). Each record was made by a Holstein
cow whose sire and dam were Holsteins.

The 4195 drylot records by 2719 cows averaged
14,921 lb milk, while 3566 pasture records by 2318 cows
averaged 14,175 lb milk. The 37,247 records in the 198
herds were from 15,507 cows and averaged 13,868 lb milk.

The third set of data, the Simulated data, was used
to evaluate the analysis of genetic differences between
cows calving in different seasons. The data had been de-
veloped in a problem of improving milk production through
breeding in an undergraduate course in dairy cattle breed-
ing at Michigan State University. The simulated data (dummy
herds) were generated with procedures and parameters devel-
oped from populations of real cows. The parameters used
in the dummy herds are listed in Table 1.

At each class meeting the student received the rec-
ords of his dummy herd for the current year and determined
his own matings and culls. The genetic value of the off-
spring was computed as the average genetic value of the
sire and dam plus a chance factor of about one-half the
genic variance. The chance factor served to restore genetic
variation and to simulate the random part of inheritance
contributed by segregation and recombination in Mendelian

inheritance.

21

Table l. Variance used in generating records of dummy herds

 

Standard
Source Variance‘ Deviation
Total 684

Between herds (environmental) 225 15
Within herds 459 21
Genic 121 11
Permanent environment 64 8
Between years 49 7
Residual 225 15

‘Variances are in (100 1b milk)2, standard deviations in
(100 1b milk)

A total of 8874 records representing 15 herds and 19 years

was available.

METHODS

If an estimate of the probable producing ability
of the cows (Lush, 1949) is not used in estimating effects
of season (influence of season of calving on lactational
yield) and the averages of the abilities of cows calving
in the different seasons differ, then confounding between
effects of season and differences in average ability will
result.

Analysis by least squares does not utilize esti-
mates of the ability of the cows. As Henderson (1949a)
has pointed out, the least squares method may yield seri-
ously biased estimates of some of the parameters because
of the effects of culling. In populations where selection
on the magnitude of performance has taken place, most of
the cows surviving to make an additional record had favor-
able environmental conditions for the earlier record. Since
the temporary environmental effects are random from lacta-
tion to lactation, the average of the temporary environ-
mental influences for a group of later records is apt to
be less favorable than for the earlier records and thus
bias the estimates of years and other environmental effects
downward.

Henderson (1949a) and Henderson et a1. (1959) have

shown that maximum likelihood techniques are appropriate

22

23

for estimation in situations where repeated observations
are used and selection based on the magnitude of previous
performance was practiced. The model employed in the pres-

ent analysis was

Yijklm = u + ti + a3 + 5k + (as)jk + hl + c1m + eijklm
where Yijklm is the 305 day-2x-ME record of the mth cow in
the 1th herd who calved at the jth age in year 1 during

the kth season,

u is the population mean of ME milk records,

ti is the amount the conditions peculiar to the 1th year

raise or lower its average production from the average

of all years,

aj is the amount records made by cows of the jth age group

differ from the average of all ages,

th

s is the amount effects peculiar to the k season raise

k
or lower its average production from the average of all
seasons,

(as)jk is an interaction which causes the production of cows

of age j calving in season k to differ from the sum of

the effects of the jth age group and the kth season,
hl is the amount conditions associated with the 1th herd
cause the average of the 1th herd to differ from the
average of all herds,
th - th
c1m is an amount the production of the l cow in the m

herd is above or below the average of all cows in the

mth herd, and

24

eijklm is a random deviation associated with the record
th th

of the m cow in the 1
th

herd, who calved in the ith

th

year at the j age in the k season.

The c are random variables normally and inde-

1m
pendently distributed about a particular hl with zero means
and variance C. The eijklm are normally and independently
distributed random variables with zero means and variance

E. The clm and eijklm are uncorrelated.

Maximum likelihood estimation (ML) involves find-
ing estimates which maximize the probability of obtaining
the samples at hand. The likelihood is defined as the joint
distribution of the sample and is written as

l 2

1 -
L = 'TT ~J2HE exp. 2E.(Yijklm-u-ti-aj-asjk-hl-clm)
ijklm

l-‘N

.TT 1 exp - c

1m \| ENC 56'9-

Estimates of the parameters in the ML model are
obtained in a manner similar to least squares. The loga-
rithm of the likelihood function is differentiated with
respect to each of the parameters and the resulting equa-
tions are set equal to zero. The ML equations obtained

are of this form:

2 " z A z A z:
n..... G+Ai n1....ti + jan...aj + kn..k..sk + jkn.jk..
z . /\ _
(a8)jk +ln. . .1. £1 +§Iznn. . .lmclm - Y. . . . C (l)

A A
n1....{} + ni""ti +§n1j°”aj + Eni. 'k’°sk +§Enijk”

A mAm
(a8)jk ‘l' l M11...l 1 +12%. {11...}. = Yiooooe (2)

25

and analogous equations for the other years (i);

A 2 A A A 22
n.j...u + inij"°ti + n.j...aj + En.jk..sk + jkn'jk°°
A A
(as)jk + {4131.91 +2l§n.j.lmclm = y.j... <3)

and analogous equations for the other ages (j);

n.. ..G + Zhi. k..t.i +§n.jk ..aj + n..k..Q

k jk..
A A
(as)j +§nukl +%Zn°°klmc 1m = Y..k.. (4)

and analogous equations for the other seasons (k);

Zn.
k * 3

A A
i nijko::: + nojk jkoosk jk k

+ §n°jkl +§Lzrhjklmc 1m = Y'jk” (5)

and analogous equations for the other age-seasons (j,k);

A
..u+ +n.

n Q+n
jk j

..(é§)j

A
éniHl'ti + En'jfl .aj +En'°kl°ls\k + Egn'jkf

A
+ nooolohl +2n-joolmé 1m = Yooolo (6)

A.
.u +

n...l

A
(as)jk

and analogous equations for the other herds (l);

A
u +

n...lm

in A A
i win]. + :n'j°lmaj +§nnklmsk +§Erhjklm

E A
(as)jk + :"'1mfil + (n...1m + C)c1m = Y...1m (7)

and analogous equations for the other cows (l,m).

th th

= 1 if the m cow in the l

i°'lm
in the ith year and = o if she did not make a record in

the 1th year. A dot in the subscript denotes summation

n herd made a record

over that particular subscript.
Two additional equations are obtained to be solved
simultaneously with the others;

a = 21?.32

n
‘§§ 1m

 

and

A A
§=2ii§§(yijklm- u - £1 - aj — sk - asjk - hl -

n.....
The equations for the variance components C and E cannot
be solved simultaneously with the other ML equations; how-
ever, estimates of C and E are available in the literature
and their use should allow valid estimates of the other
parameters.

The above set has an equation for each year, age,
season, age x season combination, herd, and cow. Among
the cow equations the coefficient for cows differs from
that used in least squares analysis by the quantity E/C.
This quantity is related to repeatability as defined by
Lush (1949). In terms of repeatability r a C/(C+E) the

coefficient for cows in the cow equation becomes n... +

lm
(l-r)/r.

Solving equations (7) for the c1m yields

no.- r
1m _ A A ./.\. .0.

6
1m ’

lm

A A
where t is the mean of the t associated with that partic—

i

ular cow, a is the mean of the 9 etc. The value of Q

j’ lm
is closely related to the probable producing ability of
the cow as defined by Lush (1949) illustrating that an ap-
proximation of the probable producing ability of the cow
is used in finding estimates for the other elements in the
model.

The original application of ML to dairy cattle prob—

lems was to estimate genetic and environmental changes.

27

Cows were nested in groups composed of animals born during
a specified time period or perhaps sired by the same bull.
These groups of cows served as fixed genetic points from
which to estimate genetic and environmental changes. In
the model used here cows belong to a herd which includes
all animals that made a record in a three- or seven-year
period. Consequently, there is no means of measuring gen-
etic change over time.

Herd effects must also be considered as fixed,
which is contrary to normal usage. The outcome on the
accuracy of the other estimates from using fixed herd ef-
fects is not known. Miller et al. (1966), using a maximum
likelihood model in which cows were nested in herds rather
than birth year or sire groups, obtained estimates of age
effects that were consistent with theoretical expectations.
Inclusion of birth year groups in a model with age and year
of record causes complications. As pointed out by Rendel
and Robertson (1950), Henderson et al. (1959), and Miller
et a1. (1966), if ages, year of birth, and year of record
are in the model, the last birth year will be confounded
with the youngest age and the last year of record and a
unique solution to the ML equations will not be possible.

Henderson et al. (1959) defined the repeatability
used in the ML equations as intra-group rather than intra-
herd since their model had cows nested within birth-year

groups. In the present model, cows are nested within herds;

28

therefore, intra-herd repeatability was indicated. The
appropriate value for intra-herd repeatability may range
from 0.4 to 0.55 depending on whether or not the effects

of year and season have been removed. The effect of errors
in the repeatability used is not clear. Henderson (1958)
reported on variation in environmental trends resulting
from using different values for repeatability in a model
estimating both yearly environmental and genetic trends.

He observed that estimates of yearly environment were
biased downward by 0.08 lb fat per cow per year for each
0.01 the value used for repeatability was above the true
value. The effects of errors in repeatability in models
where several parameters are being estimated is not appar-
ent. To get indications of the effects on the estimates
from different values for repeatability which might reason-
ably bracket closely the correct value, 0.4 and 0.55 were
used in the model.

The interactions not fitted in the model such as
herd x year, herd x season, year x age, year x season, and
the three-way and four-way interactions may cause biases
in the estimates of the parameters in the model.

Cows were not permitted to have two records in the
same year. When this occurred, the second of the two rec-
ords was removed if both records were classified as normal.
If unusual conditions such as abortion, etc., affected one

of the records, it was removed. When unusual conditions

29

were listed for both records, the record appearing most
nearly normal was retained.

Multiple records by a cow at two or three years
of age were prevented by assigning the record to the next
highest age classification if the cow had a previous rec-
ord at that age. Cows were permitted to have multiple
records in the four years and older age class. Cows less
than 24 months of age at calving were classified as two—
year-olds.

The parameters of interest in this model were the
jk’ l and c1m were nui-
sance parameters. To reduce the matrix to a manageable

ti’ aj, Sk’ and the as whereas the h
size, it was necessary to absorb the equations for cows
and restrict the number of herds to approximately 50.
Henderson (1949a, 1949b) explained and illustrated absorp—
tion of cow equations into the rest of the ML equations.

As shown above, equation (8), c can be expressed in terms

lm
of the other elements in the model, thus making it possible

to subtract this new expression for c from the u, ti’

lm

aj, sk, as. , and h equations and eliminate the cow rows

3k 1
and columns from the matrix (absorption). In his illustra-
tion Henderson constructed the full matrix, including all
cow equations, before starting absorption. Even with a
large computer, constructing the full matrix places an im-

practical limit on the number of cows that can be used in

the analysis or makes the absorption of the cow equations

30

a formidable task. The absorption procedure used in the
present study required a matrix only one row and column
larger than the absorbed matrix. To reduce the required
matrix size, the data were ordered so that all records of

a cow appeared consecutively in the data. Then the sequence
of steps used by Henderson for absorption was changed in
that as soon as all the information on a cow was in the
matrix, the cow equation was absorbed and set back to zero
before data on the next cow were added to the matrix. This
sequence of steps permits one row and column of the matrix
to be used repeatedly for all the cows in the analysis.
Since the cow equations are independent of each other the
resulting absorbed matrix is the same whether all cow equa-
tions are in the matrix before absorption begins or cow
equations are incorporated and absorbed one at a time.

This same procedure can be used to absorb herds and reduce
the number of herd rows and columns in the matrix to one

of each.

The months of the year were grouped into six con-
secutive two-month seasons to put more cows into each sea-
son and still retain several points at which to measure
seasonal change. Three ages (£2, 3, 29 years) were used
since age correction factors show most of the increase to
mature age production is reached by 48 months (Kendrick,
1955).

Standard errors of the ML constants were not

31

calculated. The error mean square obtained using the ML
constants is inflated compared to the least squares mean
square. Therefore, standard errors for the ML constants
should be calculated using the elements of the ML inverse
matrix and the error mean square from least squares anal-
ysis of the same data (Miller, 1967). Least squares anal-
ysis of these data with cows nested within herds was not
attempted because the herd equations disappear when the
cow equations are absorbed.

A second objective concerned estimating genetic
differences between the cows calving in different seasons
of the year. If selection pressure on cows differs with
the season in which they calved or are due to calve, then
variation may exist between seasons in the average genetic
value of the cows. Interpretation of the variance compo-
nents resulting from a statistical analysis of paternal
and non-paternal sisters calving in the same and different
seasons provided estimates of genetic and environmental
differences between seasons.

Analysis was within years within herds to avoid
analyzing variation from these sources. Maternal sisters
with records in the same year were withheld from the anal-
ysis along with any cow whose sire was unknown. In addi-
tion, all cows over 64 months of age were excluded to in—
crease the average number of daughters per sire. Three

seasonal divisions were used. The first was based on the

32

base milk period and compared January through June calvings
with July through December. The second division was sug-
gested by Michigan DHIA averages and compared October through
April calvings with those of May through September. The
final comparison was based on the maximum likelihood esti-
mates and contrasted November to April calvings with May
to October calvings.

In the first mathematical model the 305 day-Zx—ME

milk record of the kth th

daughter of the i sire calving
in the jth season is:

Yijk = u + Si + mj + eijk

where u is the yearly herd mean; 51 is the deviation of

th

the daughter average of the i sire from u; mj is the

average differences between u and cows calving in the jth

season; and eijk is the deviation of the record of the kth
daughter of sire i from the average of the daughters of

the ith

sire calving in the jth season. u is a fixed quan-
tity, the si, mj, and eijk are uncorrelated variables drawn
from populations with zero means and with variances, S, M,
and B, respectively.

This model was used to analyze differences among
daughters of the same sire in the same season, differences
between groups of daughters by different sires in the same
season, and differences between groups of daughters by dif-

ferent sires calving in different seasons. The expected

values of the mean squares obtained in these analyses are:

33

Within Sires Within Season B (1)
Among Sires Within Season 8 + le (II)
Among Sires in Different Seasons 8 + k S + k M (III)

2 3
The k's are the appropriate coefficients for the components
of variance.

One further analysis was made of differences among

groups of daughters by the same sire but calving in differ-

ent seasons. This analysis was according to a second model
th

in which the 305 day-2x-ME milk record of the k daughter
of the ith sire which calved in the jth season is:
Yijk = u + 51 + mij + eijk

where u is the yearly herd mean; 51 is the deviation of

the daughter average of the ith sire in the herd from u;

mij is the average difference between daughters in the ijth

sire-season group and the average of all the daughters of

th

the i sire in that herd and year; and eij is the devia-

th

k
daughter in the ijth sire-

tion of the record of the k
season group from the average of the ijth group. In this
model seasons are nested within sires. Again, u is a fixed
quantity and the Si’ mij, and eijk are uncorrelated vari-
ables drawn from populations with zero means and with the
variances, S, M', and B, respectively.
The expected value of the mean square from this

analysis is:

Between Seasons Within Sire E + k M' (IV)

4

Again k is the appropriate coefficient for the component

4
of variance.

34

M is a measure of the genetic variation between
seasons (GS)plus the environmental variation between sea-

sons (ES) while M' is a measure of iGS + ES. This can be

shown by letting mij = gsij + esij where gsij is the aver-

th

age genetic merit of the daughters of the i sire in the

jth

sire-season group. Then

season and esij is the environmental level of the ijth

mij - mi'j’ = (gsij - gsi'j')+ (esij - esi'j') and

E(M) = %E(mij - min.)2 = GS + as + 2Cov(GS)(ES)
where sirei l sirei’ and seasonj £ seasonj’.
The correlation between GS and BS is assumed to be zero
so E(M) = GS + 83. Since seasons are always compared with-
in sires in the second model, all comparisons are between
groups of cows who received half their genes from the same

I l
sire. In this case mij = Egsij - esij. Then

. . 1
mij - mij' = Elgsij - gsij') + (esij - esij:) and

a r 2 l
ij - mij’) = ZGS + ES + Cov(GS)(ES)

Once more the correlation between GS and BS is assumed to

be zero so that E(M') = iGS + ES.

Equating the expectations of the four mean squares

3(M’) = %£(m

to their actual results will yield estimates of E, S, ES,
and GS. ES and GS were of primary interest while B and S
were necessary to get solutions to the set of simultaneous

equations.

RESULTS AND DISCUSSION

Effects of season, age at calving, and their inter-
actions on ME lactational milk yield were estimated by max-
imum likelihood for six seasons of two months each (January-
February, March-April, etc.) and three ages (5?, 3,.24 years).
Because the exact repeatability of milk for these data was
not known, 0.4.and 0.55 were chosen to bracket the range
within which repeatability might fall. Examples of the
best and worst agreement between the estimates of the ef-
fects of season plus age x season interaction from using
the two values are in Table 2. Even in the most divergent
case the results for season plus age x season interaction
differed little.

Some of the changes in the constants for year and
age from varying repeatability also can be seen in Table 2.
Changing repeatability affected randomly the estimates for
ages but affected the estimates for years in a consistent
manner. When years were improving, 0.55 estimated a small-
er amount of improvement, whereas the decline for deterior-
ating yearly effects was larger than for 0.4. This is com-
patible with earlier work (Henderson, 1958) in which values
of repeatability larger than the true value produced a down—
ward bias in yearly environment. In the present investiga—

tion yearly effects were not partitioned into genetic and

35

36

Table 2. Examples of best and poorest agreement between
ML estimates of years, ages, and season plus age x
season interactions obtained using r a 0.4 and r = 0.55

 

 

2.3.512 Worst

(3rd Quartile 1962-4) (Pasture 1962-4)
r=0.4 r=0.55 r=0.4 r=0.55

1962 -306 -281 -338 -303
l963 125 121 98 93
1964 182 160 240 210
S 2 yrs. -l67 -l6l 23 12
3 yrs. 73 70 31 60
_>_ 4 yrs. 94 91 -54 -72
2 x 31 -120 -129 520 512
2 x 32 —681 -656 -85 -152
2 x S3 -159 —l7l -71 -89
2 x 34 —273 -274 -220 -222
2 x S5 -20 14 -72 ~101
2 x 56 251 250 66 124
3 x S1 198 187 -87 -6
3 x 52 492 491 188 259
3 x 33 -66 -63 379 477
3 x S4 -398 -397 -422 —415
3 x 35 6 0 285 254
3 x 36 206 202 -157 -209
4 x S1 276 293 296 268
4 x 52 534 503 320 334
4 x 53 3 -18 -191 -184
4 x 84 -610 -595 -714 -731
4 x S5 -46 -29 -69 -99
4 x 86 407 391 34 ~20

37

environmental components because of confounding between
year of birth and age. Since effects of herd, year, and
season were removed for estimating the producing ability
of the cows (see equation 8 in Methods) and the results
of using the two values differed little, only the results

from 0.55 will be shown and discussed.

Constants for Seasons

The ML estimates of seasonal effects on lactational
milk yield for cows in the 198 herds appear in Figure 1.
Highest yield occurred for calvings in January—February.
After this yield declined steadily through March-April,
drastically deteriorated during May-June and again in July-
August, and then sharply improved through December. Below
average production existed from May until October. These
results agree well with those of Tucker and Legates (1965).
Since the magnitude of seasonal influences did not change
from 1958-60 to 1962-64, changes in management of dairy
herds during this time had little effect on seasonal vari—
ation.

Total farm labor requirements are usually least
during the winter, and there is opportunity for dairymen
to provide better management for their dairy herds. This
period coincides with the most productive part of the lac-
tation for cows calving during late fall and winter. In
addition these same cows often get a boost in production

from pasture in spring during the latter part of their

38

acmmmm

 

 

 

.|.l $-33

IIIII vmlmmmd
l omlmmma

.oomu
.oomu
.ooeu
.oomu

qus
10.0

mg
.oom

.ooe

.. oom

.oom

 

 

uman>02nm .uuouammum [ms<uflswuv .csnnsmSum .ua<numsum .nmmucmnua
.emummma .omummma mcumr was some mucmpmcou commmm .H .mam

. vmlmmma can

39

lactation when they normally would be declining rapidly

in production. Pasture in late summer frequently does not
provide as much feed as spring pasture; this condition oc-
curs when the feed requirement of cows freshening in fall
and winter is at or near its least. Temperatures above
80-85° and high humidity accompanied by high temperatures
both depress the cow's feed intake and milk yield. Since
these conditions normally occur during the summer, cows
freshening in spring and summer would be affected most.
Other factors probably play important roles in causing

seasonal variation.

Age_byg$eason Interactions

The sums of the ML constants for season and age
x season interactions in the 198 herds are in Figure 2.
The total change associated with season for 1958-64 was
about 250 lb less for two-year-olds than for three-year-
olds, while the three-year-olds in turn exhibited 60 lb
less change with season than did four-year-olds. The sea-
sonal pattern was the same for all three ages, but there
were interactions. The yield of the two older groups was
much lower for calvings~in July-August than the yield of
two-year-olds. Cows three or older produced more milk than
two-year-olds when calvings were in March-April, while three-
year-olds produced the least among cows that calved in
November-December.

There were differences between 1958-60 and 1962-64

40

Figure 2. Constants for season plus age x season inter—
action from 198 herds 1958-60, 1962-64, and 1958-64

1958-60 1962-64

 

 

 

 

 

l l l l 1 I if I I I
l 2 3 4 . 5 6 l 2 3 4 5 6
Season . Season
_<_2 yrs.
3 yrs. """""
24 yrs. -----

1958-64

 

 

 

41

in that conditions for January to April were less favorable
to two-year-olds in 1962-64 and July-August was more unfavor-
able to cows four years or older during 1962-64. For 1958-
64 cows of all ages yielded least following July-August
calvings while maximum yields were associated with January-
February calvings for three-year-olds and November-December
for the other two ages.

The age-season relationships are similar to those
presented by McDaniel and Corley (1966) with remarkable
agreement for July-August calvings. Their figures, however,
indicate yields of two-year-olds were most and equally be-
low the yields of the older cows for January-February and
March-April and nearly as much below the yields of the older
cows in November-December. Differences between the results
of the present inquiry and those of McDaniel and Corley
may be due to age-season interactions and/or age-yield
relationships which are unique to Michigan but are not
typical of the entire United States.

The present results differ from those of Annis et
al. (1959) in which three-year-olds varied less with sea-
son than did the other ages and reached maximum yields when
they calved in November-December. The differences again
may be due to geographic location.

-The causes of age x season interactions could not
be determined by the ML analyses, but some possible causes

might be conjectured. Two-year-olds, because of the flatter

42

lactation curve, probably have more resistance to the causes
of seasonal variation. Cows of all ages freshening in all
seasons differ little in the amount of milk produced on the
ninth and tenth test days (Aulerich, 1965). As two—year-
olds start their lactations approximately 15 lb milk per day
lower than older cows (Aulerich, 1965), their potential for
variation in lactational yield is smaller. The relatively
larger records made by two-year-olds for lactations initi-
ated by July and August calvings may be due to both a flat-
ter lactation curve and inadequate feed during late summer
and early fall. If the average two—year—old Holstein weighs
1100 lb and milks 42 lb on the first two test days and the
average mature Holstein weighs 1350 lb and milks 57 lb on)
the first two test days, the TDN requirement for the older
cow is 4 lb per day larger (Morrison, 1956). If pasture
conditions and supplemental feeding practices from late

July through September provide insufficient TDN, the cows
with the largest requirements may decline most in produc-
tion. Likewise, if larger or older cows are affected more
quickly by increasing heat and humidity, the two-year-olds
should again perform relatively better for July and August
calvings than older cows. In many herds heifers may be
managed differently from cows prior to freshening, and

this could contribute to age x season interactions.

43

Effects of Management on Seasonal Variation

Comparisons were made between herds using pasture
and no pasture and between groups of herds at different
levels of production to evaluate the influence of differ-
ent management on seasonal variation. Fifty—one pairs of
drylot and pasture herds were compared. In addition, the
DHIA herd averages of milk for 1960 to 1964 were used to
order 198 herds from high to low. To avoid rewriting the
ML computer program for different numbers of herds used,
the 198 were assigned to four quartiles of 51 herds each.
To accomplish this, the herds ranked 49, 50, and 51 were
assigned to both the first and second quartiles, and the
herds ranked 148, 149, and 150 were assigned to both the
third and fourth quartiles.

Results for season alone and for season plus age
x season interaction are shown in Figures 3 through 8, and
the numbers of observations for each age-season combination
are listed in Table 3. The drylot herds showed more vari-
ation with season than did the pasture herds, even though
one might expect the drylot herds to receive a more adequate
and uniform supply of feed. The May-June was much more
unfavorable in the drylot herds than in the pasture herds.
Age x season interactions were present but dissimilar be—
tween groups of herds, and seasonal variation was much less
for two-year-olds than for older cows in the drylot herds.

From 1958 to 1960 (Figure 5) the greatest seasonal

44

 

 

 

 

Figure 3. Season constants for pasture and drylot herds
Pasture Drylot
4001 400 i
200- 200 j
Lb
000‘ OOOq
Milk
-200« -200 4
-400- -400 4
l 2 3 4 5 6 l 2 3 4 5 6
Season Season

Figure 4. Season plus age x season constants for pasture
and drylot herds

 

5? yrs.
3 yrs. --------
24 yrs. --—-

Pasture Drylot
600‘
400‘

Lb

200-
Milk

0.0j
-200~
-400.

-600-

 

 

 

 

 

45

commmm

 

 

 

||||| mm«
2.2:: mm
uma

 

 

ooml

00ml

oo¢I

ooml

0.0

com

00¢

00m

00m

samumumemm nmuuem «assuage sumo .omummma
.m .62.

xHHE no flaws» ha mmafluumso GH none: Eoum museumcou cammmm

XQHZ

ma

46

variation occurred in the first quartile herds, whereas

the least variation occurred in the fourth. November-
December effects were unusual in that the second and fourth
quartiles had only slightly favorable effects, and the
third quartile had unfavorable effects. Age x season in-
teraction was most predominant in the second and fourth
quartiles (Figure 6).

During 1962 to 1964 seasonal variation (Figure 7)
was greatest in the first quartile herds, intermediate in
the second, and least in the third and fourth. The quar-
tiles differed in seasonal effects in that January-February
and March-April were less favorable in the third and fourth
quartiles. The most unfavorable season was May-June in
the fourth quartile, whereas in the others it was July—
August. Age x season interactions were largest in the two
lowest quartiles (Figure 8). Cows four years or older var-
ied more with season than did younger cows in all four quar—
tiles and in the drylot and pasture herds (Figure 4).

Higher producing herds exhibited the most seasonal
variation during 1962 to 1964 (Figure 7). This relation-
ship between production and seasonal variation was not as
distinct from 1958 to 1960 but might be partially explained
by the fact that herd rankings were based on 1960 to 1964
production. Age x season interactions may be more pronounced
in lower producing herds as evidenced by Figures 4 and 8,
but this hypothesis is not supported by the 1958—60 results

shown in Figure 6.

47

Figure 6. Season plus age x season constants for herds
in quartiles by yield of milk 1958—60

 

 

 

 

 

 

 

 

First Quartile Second Quartile
600‘ / 600 -
k I
400e 400 ’
2001 200
Lb
000‘ 0.0
Milk
-200. -200.
-400« -400
-600- 3’ —600
1 fi 1— i 1 I I I l *1
1 2 3 4 5 6 l 2 3 4 5 6
Season Season
52 yrs.
3 yrs. “"-'---
24 yrs. —‘-"-
Third Quartile Fourth Quartile
600‘ “
4001
200-
Lb
0.03
Milk
-200.
-4001
-600,
I I l l l l l l 1

 

 

Season Season

48

commmm

 

 

 

T com!

r 000!

1 oovl

l

ooml

1.0.0

.r oom

. 00¢

loom

loom

 

 

emlmmma
xHHE mo mama» >3 mmaauumsv CH momma Eoum musmumcou commmm .5

de2

m4

omnfim

49

Figure 8. Season plus age x season constants for herds
in quartiles by yield of milk 1962-64

 

 

 

 

 

 

 

 

 

 

First Quartile Second Quartile
‘ 1
600' 600 4
400« 400
200- 200
Lb 0.0. 0.0
-200. —200
Milk
-400q -400 '
-600. -600
-800. -800 j
a r I 1 IL I 1 i f |
l 2 3 4 5 6 l 2 3 4”' 5 6
Season Season
52 yrs.
3 yrs."--“--
24 yr5r-----
Third Quartile Fourth Quartile
600‘
400.
200 .
Lb '
0.0-
Milk
-200,
-400.
—600.
? 1 1 I

 

I ‘ T f T _l
l 2 3 4 5 6 l 2 3 4 5 6
Season Season “

50

Patterns of Seasonal Calving

Table 3 lists the number and percentage of cows
calving in each season for the three ages. Most two-year—
olds, about 55%, calve in July through October; but as they
get older, the calving distribution becomes more uniform
throughout the year. Differences in the seasonal calving
distribution between the quartiles and pasture vs. drylot
are small and inconsistent, indicating that establishing
a favorable market for milk is the most important factor
in deciding when the cows should calve. The age composi—
tion of the herds varied slightly with about 2.5% more two-
year-olds in the top two quartiles and about 5% more in
the drylot herds.

If older cows are better producers because of hav—
ing survived more culling, then March-April with 13% more
cows at least four years old includes animals of higher
average ability than does July-August. Thus using herd-
mates of all ages would be another source of bias in addi-
tion to that caused by age x season interaction in compar-
ing cows that freshened in March-April with those calving

in July-August.

Effects of Age

Constants for ages in Table 4 show that in the 198
herds from 1958 to 1964 three-year-olds had the highest
production with two-year-olds intermediate. The estimate

for two-year-olds is 56 lb larger than the weighted average

Number of cows of three ages calving in each

Table 3.
season.
total.
seasons.

a. 198 herds, 1958—64
Age 1 2
_<_2 1057 828

(.25) (.21)

3 840 839
(.20) (.21)

24 2374 2367
(.55) (.58)

Total 4271 4034
11% 11%

b. 198 herds, 1958-60
Age 1 2
$2 410 242

(.26) (.17)

3 304 291
(.20) (.20)

24 844 906
(.54) (.63)

Total 1558 1439
11% 10%

c. 198 herds, 1962—64
Age 1 2
5? 512 461

(.25) (.23)

3 407 440
(.19) (.22)

gfi 1178 1109
(.56) (.55)

Total 2097 2010

12%

12%

3
875
(.26)

606
(.18)

1915
(.56)

3396
9%

251
(.22)

197
(.17)

693
(161)

1141
8%

3
507
(.28)

330
(.19)

950
(.53)

1787
10%

4
2724
(.31)

2105
(.24)

3919
(.45)

8748
24%

1065
(.32)

770
(.23)

1508
(.45)

3343
23%

4
1273
(.31)

993
(.25)

1787
(.44)

4053
24%

5
2668
(.27)

2395
(.24)

4805
(.49)

9868
26%

1038
(.27)

970
(.26)

1807
(.47)

3815
27%

5
1259
(.28)

1080
(.24)

2193
(.48)

4532
26%

Number in parentheses is per cent of season
Number with % is per cent of total over all

6 Total
1588 9740
(.23) 26%
1479 8264
(.21) 22%
3863 19243
(.56) 52%
6930 37247

19%

6 Total
709 3715
(.23) 26%
675 3207
(.22) 22%
1650 7408
(.55) 52%
3034 14330
21%

6 Total
636 4648
(.23) 27%
579 3829
(.21) 22%
1561 8778
(.56) 51%
2776 17255
16%

Table 3, continued

d. First Quartile 1958-1960

Age I

32

>4

Total

1
88
(.23)

84
(.22)

205
(.55)

377
10%

2
44
(.13)

67
(.19)

237
(.68)

348
9%

3
65
(.22)

52
(.17)

182
(.61)

299
8%

e. First Quartile 1962-1964

Age
52

>4

Total

1
124
(.26)

96
(.20)

259
(.54)

479
11%

2
113
(.25)

103
(.23)

239
(.52)

455
11%

3
146
(.29)

97
(.19)

258
(.52)

501
12%

f. Second Quartile 1958-1960

Age
5?

2%

Total

1
117
(.26)

77
(.17)

252

(.57).

446
12%

2
70
(.18)

67
(.17)

259
(.65)

396
10%

3
49
(.20)

31
(.13)

161
(.67)

241
6%

52

4
338
(.35)

217
(.22)

416
(.43)

971
26%

366
(.36)

247
(.25)

390
(.39)

1003
23%

4
230
(.29)
181
(.22)

397
(.49)

808
21%

5
297
(.30)

267
(.27)

434
(.43)

998
27%

331
(.30)

272
(.24)

513
(.46)

1116
26%

5
311
(.29)

286
(.26)

491
(.45)

1088
29%

6
184
(.25)

169
(.23)

387
(.52)

740
20%

185
(.26)

163
(.23)

364
(.51)

712
17%

6
224
(.27)

173
(.21)

433
(.52)

830
22%

Total
1016
27%

856
23%

1861
50%

3733

Total
1265
30%

978
23%

2023
47%

4266

Total
1001
26%

815
21%

1993
53%

3809

Table 3, continued

g. Second Quartile 1962-1964
Age 1 2 3
S? 151 133 133

(.26) (.25) (.29)

3 105 105 84
(.18) (.19) (.19)

zfi 325 298 233
(.56) (.56) (.52)

Total 581 536 450
12% 12% 10%

h. Third Quartile 1958-1960
Age 1 2 3
5? 87 70 67

(.24) (.19) (.21)

3 64 83 61
(.18) (.22) (.19)

24 208 221 189
(.58) (.59) (.60)

Total 359 374 317
9% 9% 8%

i. Third Quartile 1962-1964
Age 1 2 3
52 127 105 142

(.21) (.20) (.29)

3 115 114 83
(.20) (.22) (.17)

24 350 300 261
(.59) (.58) (.54)

Total 592 519 486
12% 11% 10%

53

4
364
(.34)

264
(.24)

452
(.42)

1080
23%

318
(.34)

226
(.24)

394
(.42)

938
24%

4
355
(.29)

289
(.24)

571
(.47)

1215
25%

5
348
(.28)

297
(.23)

619
(.49)

1264
27%

5
279
(.26)

274
(.25)

530
(.49)

1983
28%

5
345
(.26)

324
(.25)

636
(.49)

1305
27%

6
168
(.22)

157
(.20)

444
(.58)

769
16%

173
(.20)

191
(.23)

480
(.57)

844
22%

6
137
(.18)

143
(.19)

467
(.63)

747
15%

Total
1297
28%

1012
22%

2371
50%

4680

Total
994
25%

899
23%

2022
52%

3915

Total
1211
25%

1211
22%

2585
53%

4864

Table 3, continued

j. Fourth Quartile 1958-1960

Age
52

>4

Total

1
127
(.29)

89
(.21)

215
(.50)

431
12%

2
65
(.17)

80
(.21)

239
(.62)

384
11%

3
81
(.24)

59
(.17)

199
(.59)

339
10%

k. Fourth Quartile 1962-1964

Age
_<_2

24

Total

1. Pasture Herds

Age
<2

>4

Total

1
129
(.24)

109
(.21)

294
(.55)

532
12%

1
109

(.22)

94
(.19)

294
(.59)

497
14%

2
141
(.23)

137
(.23)

326
(.54)

604
14%

2
91
(.19)

101
(.21)

285
(.60)

477
13%

3
128
(.27)

87
(.18)

258
(.55)

473
11%

3
96
(.25)

71
(.19)

210
(.56)

377
10%

54

4
246
(.30)

191
(.24)

376
(.46)

813
23%

271
(.27)

253
(.26)

464
(.47)

988
23%

4
332
(.37)

217
(.24)

3343

(.39)

892
24%

5
200
(.25)

188
(.23)

417
(.52)

805
23%

276
(.26)

240
(.22)

549
(.52)

1065
25%

5
272
(.28)

230
(.24)

466
(.48)

968
27%

6
169
(.23)

158
(.21)

411
(.56)

738
21%

166
(.25)

143
(.21)

361
(.54)

670
15%

6
101
(.23)

101
(.23)

238
(.54)

440
12%

Total
888
25%

765
22%

1857'
53%

3510

Total
1111
26%

969

. 22%

2252
52%

4332

Total
1001
28%

814
22%

1836
50%

3651

55

Table 3, continued

m. Drylot Herds

Age 1 2 3 4 5 6 Total
5; 153 141 152 409 382 135 1372
(.26) (.29) (.38) (.38) (.34) (.24) 33%

3 131 107 32 277 273 119 989
(.23) (.22) (.20) (.26) (.25) (.22) 23%

24 296 244 170 380 449 295 1834
(.51) ((.49) (.42) (.36) (.41) (.54) 44%

Total 580 492 404 1066 1104 549 4195

14% 12% 10% 25% 26% 13%

of the three- and four-year-olds. Most studies, Allaire
and Gaunt (1965), Robertson and Barker (1966), Tucker et
al. (1960), and Tucker and Legates (1962) have shown the
average production of older cows exceeds the average of
two-year-olds. The discrepancy between the results of this
study and other research may be due to variations in the
age-yield relationship among herds (Castle, 1953; Hickman
and Henderson, 1955; and Searle and Henderson, 1959) and
geographic areas (Miller, 1964; Tucker and Legates, 1962;
Fairchild et al., 1966) or to differences between ML age
estimates and observed means of age groups. The age con-
stants for the 198 herds from 1962-64 agree better with the
literature. Extensive variation exists among the age con—
stants listed in Table 4 indicating variation in the age-
yield relationship among herds or groups of herds in this

study and a lack of correspondence between level of herd

56

production and age-yield relationships.

Since age constants and age x season interactions
varied from one set of herds to another and seasonal vari-
ation was only mildly related to level of herd production,
interactions of herds with age, season, and age x season
are probably important sources of variation, or the number
of cows within herds was too small to estimate the true
herd effect for age and season. Differences from herd to
herd in the way calves are raised and how heifers are fed
before freshening and during lactation could cause differ-
ences in changes of production with age. Since only com-
pleted records were used in this investigation, extreme
variations in culling rates between age groups from herd
to herd could also contribute to herd x age interactions.
Unusual season or age x season effects between herds could
arise from fluctuations in management due to competition
or lack of competition for the dairyman's time from other
enterprises or from his response to changes in temperature
or length of daylight hours. Other causes might be modi-
fications of the way dry cows and/or springing heifers are
handled or variations in the length of the dry or open
periods of cows throughout the year.

Estimates of year effects in Table 5 infer that
yearly environment and/or genetic values declined from 1958
to 1960 and then improved from 1960 to 1964. The decline

in production during the early years apparently was not

57

Table 4. Maximum likelihood estimates of age effects
(in 1b ME milk)

4 yrs. or

 

 

 

Data Years 2 yrs. 3 yrs. older
198 Herds 1958-64 +28 +92 ~120
198 Herds 1958-60 -54 +93 -39
198 Herds 1962-64 -44 +24 +20
First Quartile 1958-60 -78 +79 -1
Second Quartile " -171 +104 +67
Third Quartile " +8 +158 -l66
Fourth Quartile " -55 —33 +88
First Quartile 1962-64 -77 +90 -13
Second Quartile " +241 -94 -147
Third Quartile " -l67 +73 +94
Fourth Quartile " -202 +56 +146
Drylot " +131 +17 ~148
Pasture " +23 +31 -54
Table 5. Constants (in lb of ME Milk) for years 1958-64
from 198 herds
Year Constant No. Records
1958 —436 4304
1959 -515 4693
1960 ~602 5332
1961 -179 5662
1962 +241 5687
1963 +673 5973
1964 +818 5595

58

due to expanding herd size since herds expanded in size
during both the increasing and decreasing production phases.
With the number of herds and cows involved, it would be
unusual for year to year variations in genetic values to

be as large as the changes shown in Table 5. In late 1960
dairy scientists at Michigan State University suggested
feeding more grain to dairy cows could be a profitable
practice, but the idea did not get much emphasis from ex-
tension personnel until late 1961. Therefore, feeding more
grain to dairy cows could explain some or most of the in-
creases in yearly effects since 1960, but without informa-
tion about feeding of grain for the herds this is only spec—

ulation.

Genetic Variation Between Seasons

Evidence (Allaire and Henderson, 1966) and suspic-
ions of unequal culling rates throughout the year suggest
genetic differences could contribute to differences ob-
served between seasons.

The results of the analyses for genetic differences
are shown in Table 6. The three seasonal groupings chosen
were defined in Methods. In addition, two-year-olds and
older cows were analyzed separately in one seasonal group-
ing to determine the effects of selection on the statis-
tical model. All differences between seasons were genetic

in seasonal grouping A. But in groupings B and C a solu-

tion was impossible because mean square for variance between

59

seasons within sire (equation IV, page 33) became negative
when the expected component of residual variance was re-
moved. Equation IV was negative again when two-year-olds
and older cows were analyzed separately using seasonal

grouping A.

Table 6. Variance components from genetic and environ-
mental season analysis of DHIA data

Components of variance(a)

 

 

 

Season
Classification E S GS ES SEAS
Jan-June vs.
Jul-Dec A 4576 397 239 —30
sp-yr-olds A2 4287 233 147
gfi—yr-olds A3 4857 286 78

Oct-Apr vs.
May-Sept B 4487 455 317

Nov-Apr vs.
May-Oct C 4503 456 425

(a) E-residual, S-sires, GS-genetic season, ES-environmental
season, SEAS-season variance component from mean square for
diffegent sires in different seasons with GS=0. Variances

x 10“ .

Because of the unexpected difficulties concerning
equation IV, the dummy herd data were analyzed to evaluate
the statistical model. Results of these analyses (Table
7) were variable and differed from expectation. GS and “
ES were expected to be zero when data (a), (b), and (c)

were analyzed, whereas the expectations of GS and ES were

60

zero and 1250, respectively, when data (d) and (e) were
analyzed. Negative components in (c) developed when re—
sults for seasons within sires and different sires in dif-
ferent seasons were both negative after component of resid—
ual variance was removed. In none of the analyses did the
results suggest that all of the seasonal differences were

genetic.

Table 7. Variance components from genetic and environ-
mental season analysis of dummy herd data

Components of variance

 

No.
Data Records E S GS ES
Season = 0
(a) all 6126 356 25 ~13 13
(b) 2~yr~olds 2392 355 34 17 11
(c) 2 3 years 3734 350 23 ~17 ~10
Season = 50
(d) 2~yr~olds 2392 355 34 ~148 1276
(e) 2.3 years 3734 350 23 ~16 1270

The results in Table 7 do not explain the diffi-
culties with equation IV so perhaps residual and sire vari-
ances estimated from variance within sire within season
and variance among sires in the same season are too large.
Ratios of the components of variance for sires, seasons,
and residual were compared with the reports of other work-
ers (Table 8) to determine whether the components for sires

and residual variance might be the source of the difficulties

61

in solving equation IV. Minor differences exist between
the present study and the others in Table 8 in that the
investigators studied fat yield, and their components of
variance for seasons measure variation among seasons among
years. The ratios from A and B and those of C except sea-
sons/sires agree with the other studies. Therefore, since
error could not be located in the expected mean square for
equation IV, unusual relationships were suspected within
the sire groups which made paternal sisters in seasons B
and C more alike than paternal sisters within the same

season 0

Table 8. Ratios of variance components for sires, seasons,
and residual

Source §£§. SEAS/E SEAS/S
Barr (1962) .08 .04 .54
Bereskin (1963) .11 .03 .26
Henderson (1956) .13 .09 .71
Van Vleck et a1. (1961) .11 .04 .39
Table 6
A .11 .05 .53
A2 .05 .03 .63
A3 .06 .02 .27
B .09 .07 .70

C .10 .09 .93

62

Table 8 shows the ratios of the components for
sires or seasons to residual are smaller in A2 and A3 than
in the others. The values shown in Table 6 confirm that
the components for sires and seasons from A2 and A3 are
unusually small. It seems unlikely that the sire component
from two-year-olds and from cows three years or older should
be smaller than the sire component from all ages together.
The sire component among two-year-olds might be expected
to be largest since selection tends to leave only good cows
in each progeny group, thus removing some of the differences
between progeny groups. According to the results of the
maximum likelihood analyses the component of variance for
seasons among the two—year-olds should be smaller than the
component obtained from the older cows. Evidently, unusual
relationships exist among sires and seasons within the age
groups in these data.

A negative correlation between the genetic value
of the cows calving within a season and the environmental
effect of a season would cause Cov(GS)(ES) to be negative.
This negative covariance would make the result for equation
IV smaller and more apt to be negative after the residual
variance component was removed.

The results from analyzing both the actual and the
dummy herd data for genetic differences between seasons
were inconclusive. Although about 8,000 of the 18,500

records in the actual data were in single daughter sire-

63

season groups, it is doubtful whether eliminating the single
daughter progeny groups would make the analysis any more

useful.

CONCLUSIONS AND APPLICATIONS OF RESULTS

Variation in milk yield with season of calving is
smaller for two-year-olds than for older cows and slightly
less for three-year-olds than for cows four years or older.
In five of the six two—month seasons the effect for season
plus age x season interaction was closer to zero for young
cows than was the effect for the older cows. Therefore,
comparing two-year-olds with contemporaries in any lacta-
tion is likely to underestimate the environmental oppor-
tunity during the most unfavorable season Of the year (July
and August) and overestimate the environmental opportunity
during the favorable season (November to April). Biases
could result from a comparison between sires whose two—year-
old daughters do not have the same calving distribution
through the year. A less likely source of bias among sires
might occur where the age composition of the herdmates for
the daughters differs markedly between sires. This bias
is not likely because age composition of groups of herds
in this study varied only slightly. Any differences between
herds in age composition would probably be temporary because
of the biological dynamics of age.

Large age x season interactions occurred frequently,
but their statistical significance is unknown. First quar-

tile herds had the smallest interactions and fourth quartile

64

65

herds the largest, which suggests that better management
may reduce age x season interactions or that genetic dif-
ferences may exist between the best and poorest herds which
cause different age x season interactions. When all 198
herds for 1958-1964 were analyzed, age x season interactions
caused differences as much as 200 lb milk between age groups
in certain seasons. If these age x season interactions are
real and not due to sampling, cows should be compared with
herdmates of their own age to measure accurately the envi~
ronmental opportunity. On the other hand, if age x season
interactions are sampling variation, then larger herdmate
groups are preferred, i.e., herdmates in any lactation.

Age x season interactions varied widely from one
set of herds to another indicating herd x age x season in-
teractions. Correction factors for age for different sea-
sons have been studied and are now being used (McDaniel
and Corley, 1966). However, their usefulness is question-
able if herd x age x season interaction is as prevalent
as appears in this study. With an interaction of this sort
the general correction factors would be in error frequently,
and a sire would have to have his daughters distributed in
an appropriate set of herds to avoid incorporating bias.

The need to have daughters in a set of herds whose average
age x season interaction effects were the same as the pop~
ulation from which the factors were derived would be true

whether ages were corrected by the old factors of Kendrick

66

(1955) or the new factors of McDaniel and Corley.

For evaluating females within a single herd, apply-
ing the new age-season factors when herd x age x season
interaction exists will seldom be appropriate and may in-
crease occasionally the bias due to season, since only a
small percentage of the herds fits the average situation.
In general, with herd x age x season interaction the reduc—
tion in age-season bias from using age-season factors will
be small compared to the total bias from this source. The
most satisfactory way of dealing with herd x age x season
interactions is to compare cows within herd-season-age
groups.

Variation from one group of herds to another in
effects of age suggests a herd x age interaction. The
overall effect was for three-year-olds to have the highest
production. No relationship was evident between the age
effects and the level of herd production. The two-year—
old age constant should be largest in the low production
level herds and smallest in the high herds according to
Searle and Henderson (1959). Biases arising from herd x
age interactions could be minimized by comparing cows with
herdmates of the same age or by correcting first lactations
to a standard age at first calving (Johansson, 1961).

McDaniel and Corley (1966) reported a region x
age interaction, and Michigan was in a region in which

the old age-correction factors for two-year-olds (Kendrick,

67

1955) were too large. The age constants from the 198 herds
for 1958-64 agree with their work, but the results from

all the analyses suggest a larger error occurs because the
factors for three-year-olds are too large.

The analysis for genetic differences between sea~
sons did not function adequately, leaving the question un-
answered. However, if genetic differences between seasons
did exist, they could be minimized most easily by using
only two—year-old cows compared with two-year-old herdmates,
because they are relatively unselected and selection would
be the primary source of genetic differences between seasons.

This study indicates a need for further research
in several areas. Firstly, a measure of the three-way in-
teraction between herds, ages, and seasons is needed to
determine the appropriateness of age-season correction fac-
tors. If the variation due to age x season interaction
'is significantly larger than that due to herd x age x sea-
son interaction, then the reduction in bias by using age-
season factors will be worthwhile. Also, if some method
could be found of classifying herds into groups with like
age x season interactions, the use of age-season correction
factors would be fitting. ‘Developing a suitable method
of correcting for age—season effects would allow the use
of cows in any lactation as herdmates, thereby permitting
larger herdmate groups and reducing chance variation.

Secondly, since the production of two—year-olds seems to

68

deviate less from the yearly herd average in most of the
seasons than does the production of older cows, an evalu-
ation of averages of herdmates in any lactation that are
regressed toward the yearly herd average should be examined
for use in evaluating two-year-old records. In the USDA
system the adjusted herdmate average is calculated as:
breed season average + [n/(n+l)] (herdmate average-breed
season average). This method does not always move the ad-
justed herdmate average toward the yearly herd average.
Lastly, further study should be made concerning genetic
differences between seasons. This is a challenging prob~
lem because of the confounding between genetic and environ-

mental influences of seasons.

SUMMARY

Maximum likelihood was used to study the effects
of three ages (52, 3, 24 years), six seasons of calving
(January-February, March-April, etc.), and their interac-
tions on the 305 day-2x-ME milk of completed lactations
of Holstein cows in Michigan DHIA. Maximum likelihood
utilizes the probable producing ability of the cow and,
therefore, should remove genetic differences between sea-
sons from seasonal effects on lactational milk yield. Two
values of repeatability, 0.4 and 0.55, made little differ-.
ence in the constants for age, season, and age x season
interaction effects.

Data were 37,247 records in 198 herds on test con~
tinuously at least from 1958 to 1964, 4195 records in 51
drylot herds, and 3651 records in 51 pasture herds. The
drylot herds used no pasture during 1963-64 or 1962-64 and
were paired with 51 pasture herds which used at least 85
days of pasture during the same years and were from the
same counties. The drylot and pasture herds were matched
as closely as possible for years on test, herd size, and
registered or grade cows.

Yields were largest in the January-February season.
After this they declined steadily, were least in July~

August, and sharply improved again. Below average

69

70

production existed from May until October. The best and
worst seasons differed by 776 lb milk. The magnitude of
seasonal influence did not change from 1958-60 to 1962-64.
Comparisons were made between the pasture and drylot herds
and between quartiles of the 198 herds ranked on the DHIA
herd average of milk for 1960 to 1964. The drylot herds
showed more variation with season than did the pasture herds.
For 1958-60 the greatest seasonal variation occurred in
the first quartile herds, whereas the least occurred in
the fourth. During 1962-64 seasonal variation was largest
in the first quartile herds, intermediate in the second,
and least in the third and fourth. Seasonal effects dif-
fered some among the quartiles and between pasture and dry-
lot herds.

Interactions of age with season were present in
that the total change associated with season was about 250
1b less for two-year~olds than for three-year-olds, while
three-year-olds in turn varied 60 lb less than cows four
years or older. July-August was much more detrimental to
yield of the two older groups than to two-year-olds, whereas
March-April calvings were distinctly more favorable to the
two older groups. Cows of all ages yielded least follow~
ing July-August calvings, while maximum yields were asso-
ciated with January-February calvings for the three-year—
olds and November-December calvings for the others. Al—

though the seasonal pattern was similar, age x season

71

interactions varied among the quartiles and between the
pasture and drylot herds, indicating herd x age x season
interactions may be an important source of variation. Age
x season interactions seemed to be largest in the lower
producing herds.

Age constants varied widely among the sets of herds.
For the 198 herds during 1958-64 the three-year-old constant
was largest and the four years or older constant smallest.

An analysis of variance within herd and year, within
sire-season groups, between sire groups within season, be-
tween seasons within sire, and between different sires in
different seasons was unable to partition seasonal differ-
ences into genetic and environmental components because
of excessive variation among paternal sisters within sea-
son.

Interactions of herds with age, season, and age x
season appeared large enough to be a source of errors in

the ranking of bulls tested in a limited number of herds.

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