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THESIS

ENVIRCNHENTAL INFLUENCES CN REGRESSICN FACTOR" FCR ESTIKATIJG

505-DAY PRODUCTION FROM PART LACTATICKS

By

George R. FritZ, Jr.

AN ABSTRACT

Submitted to the College of Agriculture
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of

LmfiTER OF SCIENC
Department of Dairy

Year 1958

Approved <??i;zx E). 7)2Cflbiillu/L0L/

ABSTRA”‘T GEORGE R. FRITZ, JR.

Cumulative milk and fat production on test day from 11,420 Michigan
D.H.I.A. - IBM records for the period 1955 to July 1957 were analysed, and
used to derive regression factors for estimating 505-day production from
part lactations. The data included 8,995 Holstein, 1,457 Guernsey, 651
Jersey, and 519 Brown Swiss records.

Linear regression coefficients were used as the variable measuring
the relationship between cumulative production on test day and the sum of
the first ten test days. The regression coefficients were calculated
within each herd, season, lactation, and age group. finalyses of variance
and visual inspection of the milk and fat regression coefficients for the
first, third, and seventh cumulative months of the Holstein data were used
to determine the importance of season, lactation, and age on the part to
whole relationship. From these techniques, season was not considered an
important influence for the present study. Visual inspection of the mean
age coefficients within lactation numbers failed to reveal where the groups
should be separated or combined; consequently, the data were grouped as a
whole within each breed.

Intra-herd extension factors were computed as the weighted average
regression coefficient within herds, seasons, lactations, and ages for each
of the nine cumulative test days. Each regression coefficient included in
the average was weighted by the number of records determining its value.
For comparison, inter-herd extension factors were also derived disregarding
herd, season, lactation, and age effects. Although the inter and intra—herd

factors were not tested for significance, the marked similarity between the

ABSTRACT GEORGE R. FRITZ, JR.
Holstein factors suggests that herd has little or no influence on the part
to whole relationship.

Correlations between cumulative part and 505-day production ignoring
herd, season, lactation, and age differences were not less than .7 for
the first month, increased steadily as the lactation progressed; and were
.9 by the fifth test day for all breeds. These findings support data in
the literature that suggests production records of only one or two months
are valuable guides to what a cow will produce in that lactation. Further-
more, estimating 505Pday production from such records would be useful tools

in early culling and prOgeny testing.

MROI‘II'E'TTJ‘LL DIFLUEICCES Cl-I REGRESSICN FACTOR" FCR ESTII‘IATII‘V‘

505-111?! PRODUCTION FROM PART MCTATIOIIS

By

George R. Fritz, Jr.

A THESIS
Submitted to the College of Agriculture
Michigan State University of Agriculture and

Applied Science in partial fulfillment of
the requirements for the degree of

I-RSTER OF 3013.2: 3

Department of Dairy

Year 1958

TABLE OF CON

ITRCDUCTICN . . . . .
REVIEW CF LITERATURE . .
MATERIALS AND PROCEDURE .

Source of data . . .
Measure of relationship
Determining influence of

Determining influence of

e o o
o o o
o o o
o o o
o e 0
season

age and lactation

Computing extension factors . .

Measure of relationship

Influence of season .

Influence of age and lactation

Unweighted extension factors .

Weighted extension factors . .

Average test day production . .

Comparison of inter and intra-herd extension factors

APPLICATION OF EXTENSION FACTORS .

Inter-herd factors . .
Intra-herd factors . .
SUI-332A RY O I O O O o 0

REFERENCES . . . . . .

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Factors for Lnbtndlnfi Cumulacive
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Factors for Extending Cumulative
to a 50f-Dsy Basis - Guernsey .

Factors for Extending Cumulative
to a 5CZ-Dav Sasis - Jersev . .

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Factors for extending Cumulative
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ACKNOWLEDGEMENTS

The author wishes to thank Dr. D. E. Madden for suggesting the re-
search tOpic and his patient guidance throughout the investigation.

Appreciation is also extended to Dr. L. D. McGilliard for his
friendly council during the investigation and helpful suggestions in
preparation of the thesis.

Thanks are expressed to Dr. N. P. Ralston, Head of the Dairy Depart-
ment, for teaching and research assistantships affording the Opportunity
for graduate study and valuable teaching experience.

To Mr. Robert P. Witte for his invaluable assistance in formulating
the machine procedures, and to Mr. Robert C. Lamb for his aid in pro—
cessing portions of he data go sincere thanks.

host of all,the author is ever indebted to his family and Kiss

Mar aret Rood for their continued and buoyant encouragement.

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also be possible by extending incomplete records.

Several workers have reported the ability to estimate the complete
lactation yield by applying multiplicative and regression factors to an
incomplete record or to production tests made during certain portions of
the lactation. These techniques assumed that similar relationships be-
tween production during different portions of the lactation and the total
yield exist for all cows.

Previous work has indicated that (l) breed, (2) age and (3) season of
freshening, (4) milking frequency, and (5) stage of gestation influence
the quality and/or quantity of milk.and fat produced during all or certain
portions of the lactation. Whether these factors exert an influence on
the relationship between an incomplete record and its 505-day equivalent
has not been determined. Recently, several workers have delved into this
problem with limited success by studying the differences between extension
factors computed for different seasons, ages of freshening, and milking
frequencies. To assure maximum accuracy of the estimated 505—day pro-
duction, all environmental agents influencing the part to whole relation-
ship must be compensated for in the method used in deriving the predicting
factors.

The present study was initiated to (l) examine the importance of
breed, herd, lactation number, season, and age of freshening on the relation-
ship between milk and fat produced on test day and production for the com-
plete lactation, and (2) to compute factors for extending incomplete

records to a 505-day basis.

REVIEW OF LITERATURE

Voelker (1957) found that sixteen per cent of all production re-
cords available (l,6§6) in the South Dakota College herd since 1897 were
incomplete due primarily to low production. The per cent of records
terminating in the first to the ninth month, respectively, were 5, ll, 9,
ll, 15, 15, 18, 12, and 6.

Two methods of deriving factors to es fimate 505—day production from
yields of less than 505-days have been used in the past. The simplest
procedure is the ratio of the complete production to partial production.
It has a general predicting equation of the following form: I = cX, where
Y is estimated production for 505—ddys, c the ratio of complete production
to partial production, and X the actual production for less than 505—1ays.

The second technique is to fit by "least souares" a regression
equation of total production on partial production. The regression pro-
cedure has a prod ictin equation of at least two parameters and is some—

7

what more compleXi in applica tio.. In its simplest form (linear regression),
L. 1 ,L o i‘? 1 A e L. .L w

the general equation has tne StrUCCUTGO Y = ai-oa, where Y is eSULmQUCQ

production for 505—day s, a the point where the reg res on line intercepts

D

the y axis, b the regression coeifioient measuring the average change in Y

'With each unit change in X, and1ithe actUal production for les sthan 335-
d 513’s 0
Unless a regression of total production on month of production utiliz-

ing all nine months is used as a basis of predicting total production, it

is necessary to have different equations for each.month regardless of the

method (ratio or regression) since cows do not produce the "ame quantity
of milk and fat throughout the lactation. Consequently, a, b, and g_in
the two general equations will take on different values depending on th
month or length of lactation from which the total yield is being estimated.

Both methods will extend an incomplete record, but the regression
equation adjusts for the incomplete repeatability of different portions
of the lactation at the same time. Unless some adjustment is made after
the incomplete record has been extended by the ratio equation, estimates
of total production by the two methods would vary for the same lactation.
The difference between the estimates would be the amount that must be
added to 0X to equal ai'bX. This difference is (b - c)(X.- E) where b
represents the linear regression of total on part, g_the ratio of total to
part, and X and i represent part and average part production. The differ-
ence (b - c) is negative and largest (c)'b) during the early (1-5) cumular
tive months, least (c'Vb) during the center (4-6), and positive and small
during the longer (7-9) cumulative parts (Madden gt El! 1959). Total
production estimated by the ratio method would have a tendency to over-
estimate for the high producers (X)i) and underestimate for the low pro-
ducers (1“?) during the first 5-4 months of the lactation. The increased
variability of estimated 10-month production from records of one, two, and
three months duration was shown to be 12-47 per cent by the ratio method
as compared to the linear regression equation (Harvey 1956).

Gaines (1927) examined milk and fat percentage data from the Guernsey

and Holstein Advanced Registries. He found that a one or two day test

conducted between the fourth and seventh month of the lactation best repre-

sented a cow's average total production for twelve months. his conclusion
was based on a study of the correlations between the monthly and yearly fat
percentages which were the largest for the four middle months, ranging from
.76 - .80 and .82 - .85 for the one and two day tests, respectively.

A similar conclusion was drawn by Cannon gt El. (1942) while working
with 400 Holstein records from the Iowa State College herd and 1,289 D.H.I.A.
lactation reports. Predicting factors (regression) for each month of a
10-month period were calculated from butterfat yield for a single day for
the two groups of data separately. Production predicted for ten months
from the fifth month was considered the most accurate since it had the low-
est standard error of estimate, 45.8 and 15.6 for the college and D.H.I.A.
factors, respectively. Tests during the sixth month were the next most
accurate followed closely by the seventh and fourth. These findings of
Gaines and Cannon indicated that there is less accuracy in predicting a
cow's lactation yield from a single test in the initial and final months
than there is from.a test in the middle portion of the lactation.

In view of Gaines' and Cannon's results, it seems logical that the
first 4-5 consecutive months production couldn't be less accurate than a
test of.production for a single day as a means of predicting total pro-
duction. Kennedy and Seath's investigation (1942) of the value of incomr
plete records as a basis for culling and progeny testing supports this
proposition. They found correlations between short-time and complete re-
cords of 505-days duration increased from an average of .62 for the first
to .78 by the end of the first four months of the first lactation. Records

of 80 Holsteins and 80 Jerseys having complete records for their first two

lactations in the Louisiana State University herd were used for their
analysis. Rendel 23.2l: (1957) discovered that milk yields as short as
the first 70 days of the lactation were excellent guides to predicting
total production. High correlations (.8) between records of that length
and total production were found in 5,109 production records of six main
dairy breeds in England and Wales. When Voelker (1957) extended current
two-year-old records in the South Dakota College herd, the correlations
between the actual 505-day and estimated yield from l-9 months production

were .68, .74, .76, .85, .89, .92, .94, .95, and .99, respectively.

Cannon gt.§l, (1942) also computed ratio factors to estimate what a
cow would produce when only a portion of the lactation record was known.
The predicting factors ranged in magnitude from 7.#7 at the first month to
almost unity at the ninth. Differences were noted between the college and
D.H.I.A. values, especially during the first four months. This was
probably due to differences in management and not separating the D.H.I.A.
data by breeds.

Gifford (1959) made an intensive study of correlations between indi-
vidual months of consecutive lactations with 2,600 pairs of records from
99 herds in Iowa Cow Testing Associations. He found that each month was
more closely correlated with the production of the other months in the
same lactation than with the production for the same month in a subsequent
lactation. This suggests that there are certain environmental factors in-
fluencing production during all or nearly all portions of a specific lac-
tation which are not constant from.one lactation to the next. The study

also indicated that short-time records of only a few months had a high

value as indicators of a cow's real producing ability. Real producing
ability is a cow's capacity to produce under normal conditions.

The large genetic correlations (.9 or larger) between cumulative
part and complete milk and fat production found by Madden _e_t_ al- (1955)
demonstrated that genetic factors influencing one portion of the lactation
also influenced all others as well. These results were derived from.599
records completed by 255 Holsteins in the Iowa State College herd from
1940-52. Madden also studied the influence of age at freshening on the
part to whole relationship by comparing ratio factors computed for dif-
ferent ages from actual cumulative production. Two age groups were used,
records initiated before three years of age and those started after three
years. This grouping procedure was determined from plotting average
monthly production for the various ages of freshening and noting a distinct
difference between the lactation curves of the cows under three years as
compared to those of cows over three years of age. Because the extension
factors were so dissimilar in the initial months, it was concluded that
separate factors were necessary for the two age groups at least for the
first 150 days. The extrapolation factors for milk for the initial 50
days were 9.56 and 7.81 for the ages under three and over three years,
respectively. The differences between the two sets of factors diminished
as the lactation advanced. These findings demonstrated that young cows
start producing at a lower level than the older cows but do not decrease
in production as fast in the latter half of the lactation. Similar results

regarding young cows were noted in a later paper by Madden §t__l, (1956)

when ratio factors were obtained from 6,495 Holstein H.I.R. records.

Kendrick (1955) investigated the influence of season and level of pro-
duction in addition to age at freshening by compiling ratio factors from
756 Ayrshire Herd Test records. Factors were compared for three age groups
(under 50 months, 51-44 months, and 45 months and older), two seasons
(April-September, and October—March) and two levels of production. The
production levels were determined by the first 120 days production of each
lactation record. Below average production was designated "low" and above
average "high." The data supported findings of Madden gt_gl. (1955) that
separate factors would be necessary for different ages at freshening because
of the larger factors found for the younger cows. After the sixth month,
the factors deve10ped apparently were not affected by season of freshening
or level of production.

As a supplement to Kendrick‘s sample of Ayrshire data, Harvey (1956)
obtained an additional 2,151 Herd Test records for statistical analysis.
The combined 2,867 Ayrshire records were separately analysed for three age
groups, cows calving at 52 months or less, between 55-46 months, and 47
months of age or older. Linear and quadratic equations were fitted to
tbm accumulated milk and fat production data for the nine consecutive test
days. From the small differences between the multiple and simple cor-
relations, Harvey concluded that the curvilinearity of the relationship

mall when averared over

C

l‘etween part to whole accumulated production was

(0

all “eras. It is rerences have masked the true pic-

In a more recent paper,

'1 L.» n o ‘r' _|_.' _0 fl: ' __ r‘_o "J- P P
TQLZlenyhips ceanQH production lor a single or cuaulativc test day .Ld

505—day production. Age at calving, milking frequency and level of pro-

duction were considered as havin

us

possible influence on how extension
factors should be developed. The 6,715 Holstein H.I.R. records studied
were gro pod according to milking freeuencies (3x and Ex , and age groups
previously used in the study at Iowa (Hadden §t_gl, 1955 . Linear and
ression equations were fitted 90 the ata to determine the
influence of level of production on the part to whole relationship. The
mall differences found between the simple and multiple correlatio s ind i-
cated that linear reg re ssiona dequately described the relationship of
part to whole cumulative production for high as well as low producing
cows. No significant differences were found between extension factors

for 2x and 9x frequencies. This suggests that a Similar relationship i

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335—day production regard-

prevalent between the incomplete and complete

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Lolav

n

Guer
been -
lO -

”62

’7) -
h, L-
‘19.”!‘0

L

1

sin,
ions

b
9

lot

62 Hols

r;
8 COI‘I‘

l4:/
rg

I‘,
~.

100 l

.‘1

.b

breeds were:
3

o r- H
field (Rendel st 1;. l07 and total-

mh .
—— "/‘

J. A" o 1 “-1 o J. c_ n. __ . I . .. A
o-daue is lepcited ir mos LGCtlfl: PlOérnmS, production accumulated for

(

used to predict 505—dey production. By using accumulated production, the
any environmental factor influencing the vield of any one test
def would be diluted and have an Opportunity to be cancelled if the in-
fluence were random from month to month. Production on test day is con-
verted to cumulative-to—date production by multiplying by 50.5, the
average number of days in a month.

Lactation number as well as herd, season, and age differences were
considered as possible important influences on how extension factors
should be computed. From previous studies with Ayrshire Herd Test records
(Kendrick 1955; Harvey 1956) and Holstein Herd Improvement Records
(Madden 23 _l. 1959), it was suggested that separate extension factors
should be develOped for different seasons and ages of freshening. This
was considered necessary because of climatic changes and production
characteristics of the younger cows reflected a different part to whole re—
lationship when factors were developed and compared for different seasons
and ages.

The question, can partial records of cows freshening for the second
time be accurately extended if treated in the same manner as those
freshening for the first time at the same age, has not been examined pre-
viously. The first, second, and third lactations of the Guernsey and

Holstein data were plotted separately with age of calving along the

abscissa and number of records along the ordinate in Figures 1 and 2.

12

 

 

 

 

 

 

{'3 I3 E LEGEND:
5 LACT. RECORDS
0 " " a 692
m n
m ----- 2 444
9, 9 v ---.-3 349
g ..
c: 7 "
o \
U .\ J
g 5 .\."\ I‘.
m _ " ." ‘.
O 3 ~ \
m '- I ' \ I \ \ K ' [Xv] ‘-
55’ I p ,"Y ,/'\,’ ‘ \1’ \\ \\ I
g .Liin_nnliniliiiilnlnninnii'in
z m 22 25 30 34 38 42 46 50 54 .58 62 66 70
AGE AT CALVING (MONTHS)
FIG.| FREQUENCY OF GUERNSEY RECORDS' BY
AGE AND LACTATION NUMBER
’5‘ '3 E . LEGEND:
8 LACT. RECORDS
m ” ' | 4095
m " ----- 2 2677
CL
v 9 t ----- 3 2:34
(.0 , h-
o
a: 7 -
O \ ./'\
U ' \\ .I ~ '\
g 5 " \ I \
\ . \
3 ’- \’\ .\’
L- . \
a: 3 *l \\ .\.
DJ "' / \\ \o
g | _ I \ \"'\
\
g .L I l [J l l l l l l l l l L J l l l l 1 14 L 1 LJ

 

 

IS 22 26 30 34 38 42 46 5O 54 58 62 66 70
AGE AT CALVING (MONTHS)

FIG.2 FREQUENCY OF HOLSTEIN RECORDS BY
AGE AND LACTATION NUMBER

15

The first lactation curve intercepts the second lactation curve at 55
months of age. The second lactation curve intercepts the third at 47-48
months. Similar characteristics were observed by Madden §§_§l, (1959)
with Holstein data. They assumed since about preportional percentages

of first lactations were initiated after 56 months (10%) as second lac-
tations prior to 56 months (12%)and the most important production infor-
mation was lost in first lactations, a division of ages into under-three-
years and over-three—years was sufficient. To answer the question of the
effect of early and late first calving on the part to whole relationship,
it was necessary to make further refinements in grouping the data by ages.

In order to consider the postulated environmental influences, the
data were grouped by two 6—month seasons of freshening, three lactation
numbers, and eight ages. The two seasons were used to measure a management
system of dry roughage feeding (October-March) and pasturing (April-
September) as well as climatic conditions in Michigan. A similar group-
ing was used by Kendrick (1955).

Since the need for extending first lactations is the most important,
it would be logical to group them separately, but there was no assurance
that all subsequent lactations could be treated as a single group. Con-
sequently, the first two lactations were individually separated from all
others. This grouping also facilitated determining if possible the signi-
ficance of early and late first calving on the part to whole relationship.
The majority of records falling in the third lactation group would likely
be from.mature cows if the records were plotted by age.

The age groups were divided by 6~month intervals, but all records

14

initiated at less than 24 months were in a single group and all 60 months
or over in another.
MEASURE OF RELATEQNSEEE.

Linear regression coefficients within herds, seasons, lactations, and
ages were used as the variable measuring the relationship between the pro -
duction for the cumulative part and the complete ten test days. All re-
cords in the same herd having the same lactation number, season and age of
freshening would be exposed to similar environmental conditions. Because
the hereditary relationship between the part and whole production has been
found to be close to 1 (Madden gt_al, 1955), the hereditary differences in
production should not change the part to whole relationship. Any variation
between the intra-herd coefficients for the various season, lactation numr
her, and age groups would reflect the significance of the environmental
agents under consideration. Although it was a more cumbersome statistic
with which to work, the regression coefficients were used instead of
ratios because it was decided to deve10p regression factors after deter-
mining which environmental agents were important. Regression factors will
adjust for incomplete repeatability of different portions of the lactation
at the same time the incomplete record is extended.

At least two observations were necessary to fit a regression line by
"least squares" to each intra-herd,~season,'1actation, age group; there-
fore, all records not meeting the requirement were eliminated from the
study. The number of usable records remaining within the four breeds
were 8,995 Holstein, 1,457 Guernsey, 651 Jersey, and 519 Brown Swiss. The

linear regression coefficients were then calculated to the nearest one

15

hundredth of a pound for each intra-herd, —season, -1actation, -age group
separately for the nine cumulative test days.
DETERI-III‘IING INFLUENCE OF 53M or?

To acertain if season of freshening should be considered in computing
predicting factors, analyses of variance were performed on the first,
third, and seventh cumulative test days of the Holstein data. The re-
gression coefficient within each herd, season, lactation, and age group
was used as the observed variable. Only three test days were analysed
because previous investigations (Harvey 1956; Madden n_t_a__. 1959) had
shown the correlations between cumulative part and the complete lactation
were least for the first month and increased progressively as the lac-
tation continued. These correlations were all .9 by the fou rth month.
The three test days analysed were the most convenient to process and yet

L“

ma“ked one low, middle, and high correlations previously found.

DETWWTING I: B“ U""CL‘ OF was . mom: oz:

 

To determine how ag es and lactation numbers should be grouped or
separated, unweighted means of the int ra— nerd reare ess ion coefficients
for ages within the three lactation groups were scrutinized for the same
three test days utiliZe d in tb e analysis ofs son.

CCAPUTING EXTZYSICN FACTORS

as the average regression coefficient

rs
2L
( L)
:5
L‘)
H e
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0
$3

.5;
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O
04

within herds seasons lactations ana ates for each c.mulet ive test dav.
3 , 3 u

The regression coefficients derived fluctuated quite radically from on

(1"
FJ.
:3
f)
.— J
H
DJ
H
(D
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(0
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month to the nex

ent in the averag e by the number of records included reduo d the variacion

16

from month to month, and the weighted average coefficient was taken as the
I
extension factor.

7 an,

wSULTs AJD DISCUSSION

KEASURE CF RELAT ONSHI?

 

Linear regression coefficients within herds, seasons, lactation numr
bers, and ages were utiliZed to measure the relationship between pro-
duction during parts of the lactation and complete production for ten
test days. Young cows begin their lactation at a relatively low level of
production and decline gradually after reaching their peak production. In
contrast, older cows have a higher initial and peak production and decline
quite rapidly as the lactation advances. The question naturally arises is
the part to whole relationship on a cumulative production basis more ac-
curately described by curvilinear regression rather than linear regression.
Both Harvey (1956) and Madden eg_g;, (1959) have demonstrated that the
curvilinearity of cumulative part to whole production was slight when
averaged over all herds. This was done by fitting linear and quadratic
equations to the data separately and comparing the simple and multiple
correlations. The differences were found to be small for both Ayrshire
and Holstein records. The curvilinearity of cumulative part to whole
production on an intra-herd basis of the present data was not determined.
Linearity was assumed for the present investigation.

The regression coefficients within herd, season, lactation, and age
for total production on the amount for the first test day assumed a wide
range of positive and negative quantities. But, as additional production
information was added in succeeding test periods, the variation in the re-

gression coefficients for subsequent test days decreased and the frequency

of negative values was reduced.

_ 17 _

18

INFLUTVCE OF 833 CW

 

The structure of the analysis of variance prepared to determine the
importance of season on the relationship between the part and complete
lactation is presented in Table 1. The significance of the analysis is
weakened by all herds not having proportional numbers of cows freshening
in both seasons. Consequently, if the Mean Square for interaction (Herd
x season) is used to test the significance of the Variation attributed
to herds and seasons, the probabilities will be inexact and indicate
trends rather than precise differences. An analysis of a preportional
group of observations would be more conclusive in answering the question
of seasonal influence on the part to whole relationship, but these do not
occur.

Variation due to season was significant for the first test day of
fat production exclusively. Highly significant herd differences were
noted for the first test day of milk production. Herd, season inter-
actions were highly significant for the first test day of fat, and for the
seven cumulated test days of milk and fat. Significant differences in
fat production due to season; especially for the first test day, would
be expected since a direct relationship of season of the year and per cent
of butterfat has been found regardless of the stage of lactation (Becker and
Arnold 1955; Wylie 1925). The lowest fat test usually occurs during June-
July and the peak test in December-January. Because the smallest per—
centage of incomplete records are terminated in the first month of the
lactation (Voelker 1957) and the seasonal effect for the first month is

expected, season was not considered an important environmental factor

Table l. AYRLISIS CF VAXIdTICH N RJGRISSION CCEFFICIZNTS FOR HERBS

RTE SEASCNS - Holstein

 

 

 

c 1‘1 "~' 7v ‘-
Test Day yource nF “a a Fee
a r. I‘- R ‘.
AécaLl Jxlgl L‘O ‘oCC‘fiL 5.3.31“?

 

(D
cl"
6
(L)
5
I
(I)
>-\
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9
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m
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1*

:U
(3
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Ho
DJ
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{‘1
H
H
O\
5‘:-
)
F4
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(D
1D
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}.J
\ T)

'4

F" -1—

 

 

Between Seasons 1 5O 40

\

Herd X Season 9 421 59** 15**

 

Ar— *1??? < A 1. .2 .- 1. .L-,-..., 'J. - .z.~_ .1-..”
c5 . .cl due co dlsrreporclcn~lio- chase 3;: a .

fl
0* O c-
'1 :1 V. J . ,1 :1 4.x h J. __ . _ - 1. - 1-.. -~ ~. g
9‘? QCZcS . "u. lt‘SCI‘tfi‘, .2.” v.18 VCU. ..C‘_-‘c 8313311 Cz.C.LLlClv3.'.d, 11/ “1,sz
, ’ ‘ . ‘ .“ 4' .‘r‘. “4' w. 1 . o -
L..-C1 :ecr‘rcs 1.1 the .mr. uC ,c. se: :30. sensual».

influencing he relationship between the part and whole lactation.

IKFLUENCE OF AGE AXE LACTATION

 

The unweighted average regression coefficients of total on part lac-
tation for cows of the same age in the same lactation for the Holstein
data are presented in Table 2. No distinct pattern was observed where
ages differed within or between lactation groups. The number of coef-
ficients determining averages for the 50-55 and 56-41 age groups of the
first and second lactations were the most nearly proportional. Yet the
relationship between the age coefficients for a given month was not con-
sistent for the three days analysed.

A comparison of records initiated before and after 56 months of age
for the first and second lactations showed less overlapping of the two
lactations than reported by Madden at _a_1_. (1959). Only 7.0 per cent of
the first lactation records were initiated after 56 months and 5.2 per
cent prior to 56 months for the second lactations. Upon these findings,
age and lactation number were ignored and regressions were averaged over
all ages and lactations within each breed.

Probably a more adequate evaluation of the age, lactation influences
could have been obtained with an analysis of Variance by testing the dif-
ferences between lactation numbers having records in the same age groups.
Following this the data could be regrouped accordingly; igg. if there
was no difference between lactation numbers for the same ages, the lac-
tations could be combined. Then the ages could be tested with Duncan's
(multiple Range Test to determine where they should be separated.
UNWEIGHTED EXTENSION FACTORS

Extension factors based on cumulative production would be expected

TABLE 2.

UNVEIGETED AVERAGE REGRESSICN CCEFFICIEITS FOR.AGES
AID LACTATION GROUPS - Holstein

 

Age Group

 

TeSt LaCto .
Day GrOUP —24 24-29 50—55 556941 42—47 48-55 54—59 60/
(No. of Coefficients)
1 55 495 518 12 _- _- __
2 -- 1 55 206 48 9 4
5 -- -- 1 27 195 176 769
(Lbs. of Milk)
1 50/ 6065 6055 6089 "" "" ‘-
1 2 --" '06]. 5055 4017 6046 14.62 —7901+4
5 -—- --- 2705’“ #020 6027 4082 [+075
1 -.49 1.89 2.95 2.60 _— -- __
5 2 —-- -.56 5.47 2.27 1.51 2.04 4.09
5 -—- --- 2013 [+095 1060 2064 1085
1 1.40 1.49 1.55 1.45 __ _- _-
7 2 -—- 2'59 1009 10115 089 all 1050
5 --- -__ 08hr“ 1077 1019 1012. 1.48
(Lbs-
1 5.42 5.29 5.55 5,35 __ __ _
l 2 --- .b 7.88 5.50 5.20 —1,04 1.12
5 ——- ——- 12.25 5.84 1.10 5.92 2.69
1 1.84 .98 2.55 2.25 -_ -_ __
5 2 -—- . l 5.79 1.14 -1.18 1.79 4.77
5 _-— -""'" Lac/1 097 2.55 2.._9 106;;-
7 l 1.18 1057 1.21 .75 —— —— __
2 ——— _ll.5fi OM 1041. 1.24 1.56 1072
5 —-— -—_ lo 25 —1056 l 0514 e 97 1 0:7

 

[x
I

systematically to approach unity as the lactation progressed. The average
intra-herd factors computed did not exhibit this characteristic except for
the Holsteins. The observed fluctuation from one test day to the next
could possibly be explained by the use of intra-herd regression coefficients
as a measure of relationship and the relatively small numbers of records
controlling their value. Regression coefficients produced by the minimum
of only two records falling in a single herd, season, lactation, age group
could easily change the differences between each other in their part to
whole relationship from one month to the next. Consequently, if there

were sufficient numbers of coefficients of this nature, the changing rela-
tionship would be reflected in the unweighted averages. When the data

were scrutinized, it was found that 45-55 per cent of the intra-herd re-
gression coefficients were the products of two observations. The number

of intra-herd, -season, -lactation, ~age regression coefficients for the
four breeds were: 2,699 Holstein, 440 Guernsey, 208 Jersey, and 98 Brown
Swiss. The number of regressions might seem sufficient to average out much
of the random variation among the coefficients, but the results indicate
that the variation among individual regressions was so large and the

number of regressions per subclass was so small that sampling variation
caused the average coefficients to fluctuate widely.

WEIGHTED EXTENSION FACTOP“

 

When each intra-herd, -season, ~lactation, -age regression coefficient
was weighted by the number of records controlling its value, the trends in
the average regression coefficients were smoothed out to a considerable

extent. By weighting in this manner, the average regression coefficients

were determined more by the regressions fitted to many records within a

single herd, season, lactation, age group and the corres so nding coef-

J.

ficients have less tendency to deviate excessively from one test day to

1

the next. The weighted intra-herd extension factors (b) are presented

in Tables 5-6.
A more accurate method of weighting would have teen to weight each

e coef‘

*‘0

intra-herd, season, lactation, a icient by the inverse f its

-
V

variance. Coefficients with the least varia ation would therefore be given

more va us in determining the average coefficient.

 

p a
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A
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5
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(‘1‘

tions (3) of cumula tive test do”r pro-

:3
8.]
3:
$ ;4
I 1.:
Ho
:5
c!-

‘L r 1 ,‘ n .
between herds an; Cows are 1

1 .... 1 , 'L‘- ‘ f"- u .3 - 1.
larger breeze (“cl t in a.- crown HnLCS/o lie valiacicn 1w cumulceive
'- ‘ - ,. ‘ 4 . ., . .L n " .‘
PT-5u0t1_n 1.3re_sec e. a Lecr: "ins ‘foC -tr all breeds.
n J— a‘ I ‘ p .L' J-H no +. A ”r. J 1‘ »-
uOTTTTflol «Jr- (a) L... dun/3” "fljsl‘v ”1‘79 44-t u 0' fr... «“0 L1 Tl 3...».4 9h .. .u

ih T: b-e 7. T.“" ch“”€ auitc cltsely with t“-cc r:p;rL-C i. the ‘i* “"uro
"‘s U “+010 crd sr‘un le s correl:ti;ns are very closely matchsr :13 3.0

'. le‘3t .9 1‘y the ftpr*h moith. The Gnome" v an” J rrey 5:; similar t0

etch 0+“or inf :lthough L“1?; 10*cr in the initial 5t:ge :f the lectction

are .9 ”CV the fifth month

.fih' ~_-~ r, 13 any? n51 arm a firm .T'T‘D‘ Uffififi T""rY‘11‘-Yh‘f’/\T Ifl'fi“"
Vb.4nb k.‘ I.‘-..'4R ul- IT..;.:.J"1..4. .I_J .4... 4-.-.LL'. F.5‘-.L\..~

 

m- 11-1 1 - w- 1 ‘1 . l m. .-.- ,7 :on, .
.Le no tools inter-nor- e - tot: re ression 1 series her- 21-1ersnces

Q .4

TABLE 5. .EG.ESSION FACTORS FOR EXTENDIKG CUfiULATIVE TEST DAY
PRODUCTION TO A 505-DAY BASIS - Holstein*

 

Test Day A a B b c

 

(Lbs. of 11111:)

 

1 50.4 12.5 5.09 5.19 7.65
2 100.4 25.8 2.91 2.62 5.85
5 146.4 55.4 2.11 2.15 2.65
4 188.9 45.8 1.72 1.69 2.04
5 228.5 52.5 1.47 1.61 1.68
6 265.5 60.0 1.51 1.57 1.45
7 500.5 67.0 1.20 1.51 1.28
8 552.5 75.0 1.11 1.19 1.16
9 561.2 78.1 1.05 1.11 1.07
10 584.7 82.0 1.00 1.00 1.00
(Lbs. of Fat)
1 1.95 .59 4.04 5.52 7.12
2 5.70 1.00 2.54 2.42 5.75
5 5.50 1.56 1.96 1.89 2.62
4 6.78 1.64 1.64 1.77 2.05
5 8.17 1.96 1.44 1.51 1.70
6 9.49 2.22 1.50 1.45 1.46
7 10.75 2.46 1.19 1.28 1.29
8 11.91 2.67 1.11 1.15 1.17
9 12.98 2.86 1.05 1.08 1.07
10 15.88 5.00 1.00 1.00 1.00
* .A is cumulative test day production

a is the standard deviation of cumulative test day production
B is the inter-herd regression of whole on cumulative part production
b is the intra-herd regression of whole on cumulative part production

c is the ratio of whole to cumulative part production

25

TABLE 4. REGRESSIOH FACTORS FOR EXTEKDING CUKULATIVE TEST DAY
PRODUCTION TO A 505—DAY BASIS - Guernsey*

 

T6 st Day A a B b C

 

(Lbs. of Mi k)

1 57.1 8.5 4.79 5.50 7.19
2 72.8 16.4 2.79 2.05 5.66
5 105.0 25.5 2.05 2.08 2.54
4 154.2 50.0 1.67 2.01 1.99
5 16143 55.8 1.45 1.42 1.66
6 185.9 41.0 1.50 1.01 1.45
7 209.5 5.7 1.19 1.50 1.27
8 51.0 49.8 1.12 1.19 1.15
9 250.4 55.5 1.06 1.08 1.07
10 266.7 56.7 1.00 1.00 1.00
(Lbs. of Fat)
1 1.72 .46 5.97 2.97 7.40
2 5-52 .85 2.51 2.12 5.35
5 4.79 1.15 1.96 2.54 2.66
4 6.16 1.41 1.65 1.65 2.07
5 7.44 1.66 1.45 1.77 1.71
6 8.66 1.88 1.51 1.20 1.47
7 9.80 2.10 1.21 1.16 1.50
8 10.90 2.29 1.15 1.20 1.17
9 11.88 2.47 1.06 1.11 1.07
10 12.75 2.64 1.00 1.0 1.00

* A is cumulative test day production

J

a is the standard deviation of cumulative Lest day production

3 is the inter-herd regression of whole on cumulative part production

b is the intra-herd reorescion of whole on cumulative pert production

x.)

D

EtiO 01

O
H
U)
ct-
3
(D
"5

whole to cumulative nort 1

1 r”
l :““

26

'11-“ v1 ‘J"!"".‘f"‘" (n? lfimf‘ '9 HA. Hafmmm 'r'vq In?" or! '7 'o m'v‘r'fi hivr
“‘u .5 5. R—du¢\~~-j \ -. F‘;I\J.~VR.J : b3 H..-.J.- .L.‘~.- ‘JvanLJh—I Ir-l *H~‘ M‘—
9"" .1‘1' n (\‘7 A A ‘,‘ 1'“ ‘3‘"3‘ « - - ~-*
11.0., ‘vT-JTI'w'-‘ TV 38 5x'5—Dsbf 14146 14' - JD... 530".

 

 

Test Day .A a B b C
(TL... Of Itl 11:)
1 52.6 7.7 4.75 5.51 7.14
2- (31:00 . 1405’ 2.80 10; 5.54
5 92.1 20.6 2.09 2.07 2.55
4 117.5 26.5 1.71 1.99 1.98
5 140.5 51.5 1.48 1.57 1.26
6 161.9 55.3 .5: 1.29 1.44
7 82.1 40.2 1.20 1.01 .28
8 201.0 45.9 1.1: 1.15 1.16
9' :18. 47.1 .1006 1005 1007
10 252.7 50.0 1.00 1.00 .00

0 '~‘

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cumulative test day production

:0
H.
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(—
3"
J
U}

enlard deviation of cumulative test day production

U1
Ho
0)
d"
i ‘5‘
(D

inter-herd regression of whole on cumulative part production

0 is ‘h intra-herd regression of whole on cunulative part production
c is the ratio of whole to cumulative part l,roductior

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6O As—Ju-n-lb _'I\a.- r...le.\—7M FLR wLfi-L--.'-f -...4 4c.~.cu.s-IV.4 1.14.]. Me's.-
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I‘..c.~.-eTIc.. -o u. 90/— .1 1....)14 - crow-r11 o-..-1ss

 

 

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\11—I=-\;IIOH O\1) 00-40\ \flbvaror—J

O\’)OD\IO\

I-J

(L123. of ..:1:;)
42.9 11.2 5.11 4.05 7.79
85.8 22.2 2.80 5.47 5.90
25.9 51.7 2.07 1.66 2.65
65.2 40.5 1.69 1.57 2.05
197.8 48.1 1.46 1.60 1.69

250.5 55.1 1.50 1.28 1.45
260.5 61.5 1.19 1.29 1.28
288.2 66.4 1.12 1.19 1.16
515.1 70.9 1.06 1.07 1.07
554.2 75.2 1.00 1.00 1.00

(Lbs. of Fat)
1.72 .55 4.40 5.25 7.67
5.54 .95 2.72 2.66 .95
4.86 1.29 2.08 1.76 2.71
6.29 1.61 1.75 1.75 2.09
7.65 1.91 1.50 1.52 1.75

1.48
1.53
1.17
1.14 1.07
1.00 1.00

H
0
I\)

8.91
10.12
11.25
12.28
15.19

H
o
H

\O

0 Com .,':-l-’
b

.
\fl O\\J‘ o)
O

H l--' H H H
O
O O H mm
o O\\N mm
0
V)
.4

\N P.) [O F1) [0
o o

 

U}

is cumulative test day production

H.
U)
(+-
o )4
(D
U)

tandard deviation of cumulative test day production

H.
U)
C‘.‘
IS‘
0

inter-herd regression of whole on cumulative part production
is the intra-herd regression of whole on cumulative part production

is the ratio of whole to cumulative part production

TR

 

 

 

 

 

 

e is standard error of estimate ignoring herd,

age differences

season,

M‘E'V 7. CORRE-LTICNS BT1U33N CLE JJLLTIVS TLST DAY L E TCTLL

PL«CDUCTI (-13 34:11) «.JT. #8:? D:.SAD L‘Rilf 3:3 CF 43,111....«1‘: *

Test Day Breed
Holstein Brown Swiss Guernsoz, Jersey
r e r e r e r e
(Lbs. of Silk)
1 .76 61.1 .76 57.1 .72 44.1 .75 58.6
2 .85 48.9 .82 48.9 .81 56.2 .81 51.5
9 .88 4?.1 .87 41.2 .85 51.6 .86 26.9
4 .22 55.5 .91 55.2 89 27.8 .89 25.7
5 .54 50.9 .9 29.8 .91 24.1 .92 20.5
6 .96 25.7 .95 24.6 .94 20.5 .94 17.0
7 .98 18.6 .97 19.1 .96 16.1 .97 15.5
8 .99 14.8 .99 15.5 .98 11.2 .98 9.6
9 1.00 7.1 1.00 7.2 .99 5.9 1.00 5.2
(Lbs. Of Fat)
1 .77 2.6 .76 2.6 .70 2.4 .71 2.4
2- OBZL 200 08 2.0 079 200 .81 108
5 089 106 :88 106 081:" 106 087 105
4 .9- 1.4 .91 1.4 .88 1.4 .90 1.5
5 .94 1.2 .94 1.2 .91 1.2 .92 1.1
6 096 1.0 096 1.0 0911' 100 005 .9
7 .97 .8 .97 .7 .96 .8 .97 .7
8 099 05 099 05 09' 05 0‘; 05
9 1.00 .5 1.00 .5 .99 .5 .99 .5
a:

r is correlation ignoring herd, season, la eta tion and 86 e differences

.'

lactation and

I
_.C 6.13

Po

nsinn

z
05'

n‘ ‘_
LI 54.»

[K

._ -12 a.
J—IuCh—jr 'J ‘Ur

:rS

4"

in {‘f

_ j
HOLT.

Vb a
O

.18 OCT?“ '1“

n 4
’ U

n ,
1.111111 1.

.0 7.4.1
1. '31.]. .1 f1

.4.

prfil'Yt

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\—

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1

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it u:

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an

to a

APPLICATICNC T*"33»'.TZI'”ICI\T FASTOZS

The general regression equation is more readilv understaneatle for
predictint milk and fat production fro; an inconplete record when in one

A
fsrg= Y— Y‘ ‘:(X ~ X

\_l

Estimated production Y ’s a function 0 the average ton month production
(f) .dded to the product or the extons ion fetter (b) times the difference
between t‘1e incomplete production record (1) and the avero e production
for a similar length of lactation (A).

I-«wm-fi-fi- vhfi?“ \ fifir‘.“ ’1

.Ltéu—l-i :5A‘JI‘IBJ AM“

 

2 LL. ., . n . .u .., . 1 ,1. .,_J.- M MFR-”
, .5, the ave 2 Q8 nine: 1 01 days in a month. as an I‘lupulgql‘h, iaa ine

Table 5, tLe evcrete Holstein mil“ production for four test lays (A4) is

ied tv 30.; equ: ls 5,761.45, the aver: e for four

L3ch8 9 cductien. Similarly, tl1e ten month average proluotion (A13) is
534.7 tin .03 30.50 rll,735.53 lbs. of mi k. SuLstitutin" taese Values

into the tredicting equation above and using the epprcuriete in
tensicn factor (3) frcn Table 5, 11,755.55 (I) plus 1.72 (BL) times

,000 (x) minus 5, 7 1 45(1) equ els 10, 49 5.66 118. of milk the estiLated

a

uOfi-dm product ion ( ).

IETZA-HIRD FACTCRS

 

The ten month lactation herd avernse will be eveilaole so the a Mi~yzax

\_-

.fi
4.

rom his arm meal herd Simmery report, but it is not likely thet he will know

_ 5Q _

51

J“ Q ~ .. '2‘,“ . ,f ‘ ‘ o
the as: r" 0. manual; 0 :l tive plosu ct ion

lactation for his herd. 'T

o / n o o 7
ed in Taslcs 5-6 and n13 ten month lactation hera average. The c

 

represents the ratio of ten north proo“c ion to ave “’e ouaLlative
o . v n A
Liontlfl 3 production. It may se expressed as- c I ; . since g_ana
X
Y are "no.1n rueatitiee, A can se computed Lv dividing the tzn Icnth lec-
f";
o o o & Q o
tatlen he‘d averaac “y the appropriate g_value; 1.e. 3- ” i. The esti-

mate of X assumes that any herd has a similar rela ticnslip of cumulative
part to whole ten month production as the breed average.

For an ex wiple of practical application, assume an estimate of 3’?~
-y mi k production is desired for a 301 stein cow having produced 5,000
lbs. in four months of an incomplete record in a herd with a 10,000 lb.
507- d. ay herd avera :e. From Table 5, 10, 000 (T) divided by 2.04 (c) equals
an estimated four m nth lactation herd average of ',901.%1L: .(Fl).
Substituting these Values into the predicting equation and using the ap-
propriate intra-herd extension factor (b) from Table 5, 10,000 (Y) added
t0 1069 (b4) times the di feronce between 5,000 (X) andL ' .,901. 96 (X)

A
equals 10,165.69 lbs. of milk the estimated 505-day production (Y).

susmar

Cumulative test day production for milk and fat from ll,#20 Hichigan
D-H.I.A. - BK records for the period 195) to July 1937 were analysed and
used to derive regression factors for extending a partial record to a
505-day basis. The data included 8,995 Holstein, 1,457 Guernsey, 651
Jersey , and 519 Brown Swiss records.

Linear regression coefficients were used as the variable measuring
the relationship between cumulative production on test day and the sum
of the first ten test days. The regression coefficients were calculated
within each herd, season, actation, and age group. Analyses of variance
and visual inspection of the milk and fat regression coefficients for the
first, third, and seventh cumulative months of the Holstein data were used
to determine the importance of season, lactation, and age on the part to
whole relationship. From these techniques, season was not considered an
important influence for the present study. Visual inspection of the mean
age coefficients within lactation numbers failed to reveal where the groups
should be separated or combined; consequently, the data were grouped as a
whole within each breed.

Intra-herd extension factors were computed as the weighted average
regression coefficient within -erds, seasons, lactations, and ages for
each of the nine cumulative test days. Each regression coefficient in-
cluded in the average was weighted by the number of records determining
its value. For comparison, inter-herd extension factors were also derived
disregarding herd, season, lactation, and age effects. Although the inter

and intra-herd factors were not tested for significance, the marked

_ 52 _

similarity between the Holstein factors suggests that herd has little or
no influence on the part to whole relationship.

Correlations between cumulative part and 505-day production averaged
over all herds, seasons, lactations, and ages were not less than .7 for
the first month, increased steadily as the lactation progressed; and were
.9 by the fifth test day for all breeds. This supports the literature that
suggests production records of only one or two months are valuable guides
to what a cow will produce in that lactation. Furthermore, extension of

such records to a 505—day basis would be useful tools in early culling and

progeny testing.

(1)

(2)

(5)

(1+)

(5)
(6)

(7)

(8)

(9)

(10)

(11)

(12)

(15)
(11+)

EFERENCES

Becker, R. B., and Arnold, P. T. Dix. Influence of Season and

Advancing Lactation on Butterfat Content of Jersey Milk.
J. Dairy SCio, 18: 5890 19550

Cannon, C. Y., Frye, J. B., Jr., and Sims, J. A. Predicting
505-Day Yields from Short-Time Records. J. Dairy Sci.,

25: 991. 1942.

Gaines, R. L. The Deferred Short-Time Test as a Measure of the
Performance of Dairy Cows. J. Agr. Research, 553 257. 1927.

Gifford, W. The Relative Accuracy of various Portions of the
Lactation as Indicators of the Permanent Productivity of Cows.
Unpublished Ph.D. Thesis. Iowa State College Library, Ames.
1959.

Harvey, W. R. Unpublished data from Ayrshire Herd Test records.

1956.

Kendrick, J. F. Unpublished data from Ayrshire Herd Test records.
1955.

Kennedy, 0. M., and Seath, D. M. The Value of Short-Time Records
for Culling and for Progeny Testing of Dairy Cattle. J.
Animal SCio’ 1: 5480 1942.

Madden, D. E., Lush, J. L., and McGilliard, L. D. Relations
Between Parts of Lactations and Producing Ability of Holstein
COWS. J. Dairy SCio, 58: 12640 19550

, McGilliard, L. D., and Ralston, N. P. Relations
Between Monthly Test-Day Milk.Production of Holstein-Friesian
COWB. J. Dairy 8010, 59: 952. 1956.

_, McGilliard, L. D., and Ralston, N. P. Relations
Between Test-Day Milk.Production of Holstein Cows. J. Dairy
Sci. 1959. (In press).

Iichigan D.H.I.A. - IBM Annual Herd Summary. Iimeo. 1955.

Annual Herd Summary. Mimeo. 1956.

 

Annual Herd Summary. Mimeo. 1957.

 

Rendel, J. M., Robertson, A.,.Asker,.A.‘A., Khiskin, S. S. and
Ragab, M. T. The Inheritance of Milk Production Characteristics.
Jo Agr. 801-, 48: [+26- 19570

_ 54 _

(15) Voelker, H. H.

Use of Extended Incomplete Lactation Records.

J. Dairy SCio, 40: 6510 1957.

(16) wy11e, c. E.

Factors Influencing Two- Day Official Butterfat

TeStS Of COLTS. J. Dairy 8010, 6a 2940 19250

55

to on U 31 0:4 LY

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lv‘fi-A. h H—J»-.~ i. .1 - -;