Front Cover
 Table of Contents
 Review of literature
 Environmental conditions and herd...
 Materials and methods
 Results and discussion
 Summary and conclusions
 Literature cited

Group Title: Bulletin - University of Florida. Agricultural Experiment Station ; no. 754
Title: Sire by herd interaction for milk production in Florida DHIA herds
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00027184/00001
 Material Information
Title: Sire by herd interaction for milk production in Florida DHIA herds
Series Title: Bulletin University of Florida. Agricultural Experiment Station
Physical Description: 19 p. : ; 23 cm.
Language: English
Creator: Verde, Omar Gerardo, 1940-
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1972
Subject: Dairy cattle -- Breeding -- Florida   ( lcsh )
Milk yield -- Florida   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
non-fiction   ( marcgt )
Bibliography: Bibliography: p. 18-19.
Statement of Responsibility: O.G. Verde ... et al..
General Note: Cover title.
Funding: Bulletin (University of Florida. Agricultural Experiment Station)
 Record Information
Bibliographic ID: UF00027184
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 000929623
oclc - 18432759
notis - AEP0415

Table of Contents
    Front Cover
        Front Cover
    Table of Contents
        Table of Contents
        Page 1
    Review of literature
        Page 2
        Page 3
        Page 4
    Environmental conditions and herd size
        Page 5
        Page 6
        Page 7
    Materials and methods
        Page 8
        Page 9
        Page 10
        Page 11
    Results and discussion
        Page 12
        Page 13
        Page 14
        Page 15
    Summary and conclusions
        Page 16
        Page 17
    Literature cited
        Page 18
        Page 19
Full Text

Bulletin 754 (technical)




0. G. Verde, C. J. Wilcox, F. G. Martin, and C. W. Reaves
Florida Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville
J. W. Sites, Dean for Research


_ _-_I I

December 1972


Drs. D. E. Franke, M. Koger, and R. L. Ott contributed to
this investigation in the statistical analyses and in review of
the manuscript. Mrs. Sara Harr Rice programmed and carried
out the analyses. The Facultad de Ciencias Veterinarias de la
Universidad Central de Venezuela provided financial support for
the senior author. Sincere appreciation is extended to all.

This public document was promulgated at an annual cost
of $843.03 or a cost of .28( per copy to provide information
on one type of genotype by environment interaction to re-
searchers in quantitative genetics.


Introduction 1
Review of Literature 2
Environmental Conditions and Herd Size 5
Materials and Methods 8
Results and Discussion 12
Summary and Conclusions 16
Literature Cited 18

Sire by Herd Interactions for Milk Production
in Florida DHIA Herds
O. G. Verde, C. J. Wilcox, F. G. Martin, and C. W. Reaves1


In recent years a considerable increase in milk production
has taken place in many dairy cattle populations. Average pro-
duction for all U. S. cows tested under the Dairy Herd Improve-
ment Association (DHIA) program increased from 7,189 pounds
of milk and 284 pounds of fat to 12,750 pounds of milk and 483
pounds of fat in the 45 year period, 1925 to 1970 (6).2
Milk production depends on the combined influence of several
genetic and nongenetic factors. Some nongenetic factors orig-
inate in changes in physiological functions of the animal's body,
e.g., length of lactation, age or lactation number, and length of
previous dry period. Other nongenetic factors are environmen-
tal in the strictest sense, including year of calving, month of
calving, nutrition level, and specific management practices.
Production may be increased by improving the environment
or by changing the genetic make-up of the animal. Improvement
of both generally has been a major objective of dairy cattle
breeders. Improvement in environment can be obtained by im-
provements in feeding and management, etc. Selection has been
a widely used tool in making genetic improvement.
An important concern of dairy geneticists is the interrela-
tionship of selection procedures and the commercial conditions
under which animals produce. Some maintain that selection
should be practiced in an environment comparable to the one
in which the strain or breed is expected to perform. Others
believe that the environment provided should be the one that
permits the maximum expression of the trait being selected.
Still others have suggested that for milk yield of the dairy cow
neither belief is of major concern, since they believe one of the
major genotype by environment interactions, that of sire by
farm, is relatively small.

'0. G. Verde: Former Research Assistant, Dairy Science Department.
Present address: Facultad de Ciencias Veterinarias de la Universidad
Central de Venezuela, Maracay.
C. J. Wilcox: Professor (Geneticist), Dairy Science Department.
F. G. Martin: Associate Professor (Associate Statistician), Statistics
C. W. Reaves: Former Extension Dairyman, Dairy Science Department.
2Numbers in parentheses refer to Literature Cited.

Interest in the entire topic has increased since the de-
velopment of artificial insemination (AI). Concern has been
expressed about the existence and magnitude of genotype by
environment interactions, i.e., that the best genotype in one
environment is not necessarily the best in another environment.
The presence of genotype by environment interactions would
make it necessary to evaluate sires on a within-environment
basis for use in any environment.
The main objective of this investigation was to estimate
the magnitude of genotype by environment interactions in
Florida, where the environment for dairy cattle is unique in
many ways.


Genetic-environmental interactions exist whenever the phen-
otypic differences among two or more genotypes are genuinely
different from environment to environment. The actual phen-
otypic value is not simply the sum of the genotypic and the
environmental values.
Haldane (9) discussed the nature of interactions in detail
in 1946 and gave examples to illustrate his discussion. He con-
sidered two genetically different populations and two different
environments, illustrating several types of genotype-environ-
ment interaction. Falconer (7) has been credited with a dif-
ferent approach to the problem and its effects on the selection
of breeding-stock. He examined the interaction by considering
its effects on the correlation between the same genetic material
exposed to two different environments. He reasoned that if
there were no appreciable genetic-environmental interactions
the same genetic basis would exist for the expression of the
phenotypes in both environments. Therefore, the correlation
between these expressions should equal unity.
In recent years, refinements of these general concepts have
been used to determine the magnitude of such interactions for
milk yield in dairy cattle. Estimation of the fraction of the
total variance that corresponds to the genotype by environment
interaction variance, comparison of the ranking of animals
based on their genetic merit in several environments, and the
correlation procedure proposed by Falconer are methods which
have been used.
Hickman and Henderson (12) analyzed nearly 4,000 lac-
tation records from daughters of 126 sires in 1,094 herds over

a period of 8 years. They reported that the fraction of the
total variance due to herd by sire interaction was approximately
2% for both milk and fat yields. Legates et al. (14) used nearly
25,000 lactation records of daughters of Guernsey, Holstein,
and Jersey sires in artificial breeding associations throughout
the U. S. during the period 1946-50. The percentage of the
total variance associated with herd by sire interactions for
milk yield, fat percentage, and fat yield ranged from 0.0 to 2.1
in all cases, with the exception of fat percentage in Jersey
cows, in which a value of 9.9% was obtained. Whether or not
the latter value is atypical is not known. A similar approach
was used by Mason and Robertson (17), Wadell and McGilliard
(31), and Touchberry et al. (26). They obtained estimates of
zero for the fraction of the total variance contributed by genetic-
environmental interactions.
Van Vleck et al. (29) examined first and second milk and
fat DHIA records of AI daughters in New York. The inter-
action component was less than 4 c of the total variance. Bur-
dick and McGilliard (3) reported that interactions between Al
sires and Michigan DHIA herds ranged between 0.0 and 4.09
for all variables studied, except fat percentage in Guernsey
records in which a value of 9.09% was detected. They stated
that the evidence to date suggested that ranking of sires by
performance of their daughters in DHIA would be generally
the same in any of the environments examined. Kelleher et al.
(13) analyzed nearly 38,000 records from nine mid-western
U. S. states. To ensure orthogonality in the distribution of rec-
ords and to permit more exact testing of hypotheses, equal
numbers of observations were chosen at random within each
herd-year-season. Sire x herd-year-season interactions ac-
counted for less than 3.5% of the total variance.
In 1960, Robertson et al. (21) studied data from England,
Wales, and Scotland, representing 57 Holstein and 19 Ayrshire
bulls used in AI centers. Progeny by each bull were evaluated
using contemporary comparisons. Herds were divided into three
categories: low, medium, and high yield. Three breeding val-
ues were estimated for each sire, one at each herd level, and
correlations between the breeding values were calculated. Cor-
relations ranged from 0.87 to 0.96. From a practical standpoint
there seemed little need to attempt to evaluate daughters of
an AI bull only in high producing herds. Further, daughter
records from all herds could be used with equal confidence re-
gardless of level of production.

Carter (5) investigated correlations between ranks of bulls
at different fat levels of contemporaries and the normal AI
evaluation; 33 Holstein bulls were included. Records were ad-
justed for twice-a-day milking (2X), 305-day length of lacta-
tion and age (mature-equivalent basis, ME), and were divided
into five groups according to the fat level of contemporaries.
Correlations between ranks of bulls in each group and those of
regular AI proofs ranged between 0.81 and 0.90.
Van Vleck (28) studied first and second lactation records
of New York AI Holstein daughters. Records were divided
into four groups according to level of the adjusted herd-mate
averages. Genetic correlations between the expression of the
same genotypes in different environments were estimated for
69 sires and were higher than 0.93 for both milk and fat pro-
duction. These high correlations also indicated that sires could
be evaluated in all levels of herds and that the ranking of bulls
will be similar, no matter where the daughters were located.
Similar analyses were carried out by McDaniel and Corley (18)
for 40 Holstein bulls; correlations obtained ranged between
0.89 and 0.94.
Both methods, estimation of the fraction of the total variance
accounted for by genotype x environment interactions and cor-
relations between ranking of bulls, were used by Lytton and
Legates (15) and by Mao and Burnside (16). Lytton and Le-
gates utilized first available DHIA records of 10,548 AI daugh-
ters of 46 Holstein sires used in the northern and southern re-
gions of the United States. Correlations between average breed-
ing values of sires in the two regions for milk yield, fat yield and
fat percentage approached 1.00. Furthermore, estimates of the
variance components for sire x region interactions were essen-
tially zero. Mao and Burnside found no interaction of im-
portance between sire proofs and herd environments when
herds were grouped according to ten environmental factors.
In other investigations, however, genetic-environmental
interactions were large enough to be considered of practical
importance. Bereskin and Lush (1) indicated that performance
of bulls in high-level herds might not be very indicative of their
performance in low-level herds. Thomas et al. (24) reported
that the fraction of variability accounted for by interactions
for milk and fat yields in DHIA records of Guernsey, Holstein,
and Jersey cows ranged from 5.3 to 20%, with most of the
values greater than 10%. Salazar (22) studied three Holstein
herds in Colombia and obtained values ranging from 5 to

10 % as the fraction of the total variance due to interactions
for milk yield, fat yield, and 4'c fat corrected milk yield. The
three herds represented quite different management and clima-
tological conditions, and the sires were of diverse background,
being from Colombia, the United States, and Holland.
To summarize, most estimates of several types of genotype
by environment interactions for milk production have been very
close to zero. In several instances, however, estimates obtained
have been of considerable practical importance.


Florida's climate is characterized by considerable sunshine
and mild temperatures in winter, with greater intensity of sun-
shine than areas of the northern United States. Florida borders
the Gulf of Mexico and the Atlantic Ocean and extends into the
Caribbean Sea. It reaches from 24'30' to 31 0' N. latitude, the
southern end being subtropical. The average rainfall and tem-
perature by months for 30 years are given for three areas of
the state in Table 1.
In the northern half of the state from 1931 to 1960, 69r;
of the rainfall occurred from May to October, inclusive. On the
lower east coast 73r fell in this period. This uneven distri-
bution resulted in dry periods in winter and spring, although
normally some rain falls every month. Generally speaking, the
best growth and quality of forage occurs when the soil is neither
extremely dry nor extremely wet. The favorable season for
forage production can be extended by use of adapted temporary
winter and summer grazing crops, which are used to a limited
Heavy rains usually act against maximum milk production
both from effect on quality of forage and on the cow. Wet pas-
tures and muddy lots increase foot rot and other health prob-
lems. These problems are accentuated in large herds and re-
quire special attention to grading of lots and lanes, some high
ground in pasture, and hard surfacing of holding lots.
High temperatures, high humidity, insects, and muddy lots
are all conducive to lowered production, although management
can alleviate these effects by provision of ample feed, fresh
water in convenient places, shade, insect control, and dry lots
with attention to natural or artificial ventilation.
The mean annual relative humidity at eight Florida weather
stations was 78.2; (20). Hourly wind movement averaged

Table 1. Average Florida Rainfall
and Temperature, 1931-601

inches degrees
Month rain F

Jan. 2.53 57.0

3.24 58.7

4.02 62.8

3.44 68.8

3.35 75.3

6.13 80.1

7.62 81.4

6.90 81.5

6.55 79.1

4.40 71.6

1.95 62.8

2.52 57.4

North Central

Lower East Coast

inches degrees inches degrees
rain F rain F

2.10 60.5

2.16 66.9

2.72 62.1 2.02 67.6

3.92 65.7

3.39 70.8

3.40 76.4

7.07 80.3

8.16 81.6

7.12 81.7

7.21 80.0

4.27 74.0

1.85 66.2

2.03 61.3

2.82 70.0

3.90 73.6

5.49 77.0

7.44 80.2

6.65 81.5

6.82 82.0

9.47 81.0

8.15 77.4

2.84 72.0

2.17 68.2

Total or average 52.65

67.7 52.94 71.7 59.93 74.8

IBased on reference 27.

10.3 miles, an asset to livestock in dissipating heat. The highest
temperature seldom exceeded 100F. In a 17-year period in
Gainesville, temperatures of 100F were reached in only four
of 204 months (June for three years and August in one year).
August had the highest mean maximum temperature for the
17 years-90.7F. The mean maximum and mean minimum
temperatures for the hottest months are given for three loca-
tions in Table 2. Although daytime highs for these months
averaged near 90, the mean minimum was just below 70, re-
ducing the 24-hour average.

Some of the most important characteristics of the Florida
dairy cattle population, as compared to the United States, are
shown in Table 3. Herd size increased from 210 cows in 1958
to 424 cows per herd in 1970, a 102 percent increase in 12
years. The increase has been accomplished by purchase of out
of state cattle, mostly heavy springing heifers, and by an in-






Table 2. Temperatures of Hottest Months
in Three Florida Locations

Mean Maximum Temperature (F)
Gainesville Tampa Moore Haven

89.7 88.3 89.0

90.1 89.1 89.5

90.7 89.7 90.3

88.9 88.5 88.5

Mean Minimum Temperature (F)
Gainesville Tampa Moore Haven

68.8 72.4 68.5

70.7 73.8 70.1

70.9 74.0 71.1

69.0 72.6 69.7

Based on reference 20.

Table 3. Characteristics of Florida and U. S.
Dairy Cattle Populations1

Tested Cows
Official DHI


Average yield

Average herd size

Owner Sampler


Average yield

Average herd size

Non-tested Cows2


Average yield

Average herd size

All Cows


Average yield

Average herd size














United States













1. Based on references 6 and 8; slight discrepancies in U. S. figures may be noted
because of the methods of estimation.

2. Includes some cattle on unofficial testing programs.

crease in heifers raised. The increase in herd size accelerated
the change to labor-saving equipment and improved methods
of feeding and milking. Large herd size doubtless accentuated
problems mentioned earlier. Group handling and feeding in
bunks may have resulted in less attention to individual cows.
Small cows or cows of the smaller breeds might not get full op-
portunity to feed under these conditions.
The breed composition of cows in Florida changed gradually
from about 25;% Holsteins in 1950 to about 60% in 1970 (33).
The number and percent of Brown Swiss including crosses in-
creased also, whereas the percentage Jerseys and Guernseys
decreased. Changes in breed numbers were accomplished by
cattle purchases and by use of semen of larger breeds for pro-
ducing replacements. The latter method was followed by a
number of herds in the use of Brown Swiss semen on grade
Jerseys or Guernseys.
The change of breed of cows on official DHI test has not
been quite as rapid as in the overall state herd. Percentages
for each breed overall and on official DHI test are shown in
Table 4.


Data used in this investigation were obtained from DHIA
milk production records of dairy cattle located in Florida. They
are stored at the University of Florida and made available for
research through the courtesy of the Dairy Extension Service.
Three breeds were considered: Guernsey, Holstein, and
Jersey. Because of a limited volume of records, it was not pos-
sible to extend the investigation to other dairy breeds. Records
were available in the form of punched IBM cards. Each card
represented a single lactation record of a cow and contained the
following information.
1. Herd identification 9. Date of calving
2. Cow identification 10. Previous dry period
3. Breed of cow 11. Days milked
4. Sire identification 12. Days milked 3X
5. Breed of sire 13. Milk yield
6. Dam identification 14. Fat yield
7. Breed of dam 15. Condition affecting
8. Date of birth record

Table 4. Florida Cows Completing Official DHI Lactation Records
and Estimates of Overall Breed Composition, 1969-70.1

Official DHIA Overall
Number Percent Number Percent

Ayrshire 527 2.8 1,888 1.0

Brown Swiss 765 4.0 5,296 2.7

Guernsey 3,867 20.5 26,437 13.7

Holstein 10,604 56.2 114,538 59.3

Jersey 2,998 16.0 42,908 22.2

Other 95 0.5 1,949 1.0

Total 18,856 100.0 193,006 99.9

iBased on references 8 and 33.

Analyses were carried out on a within-breed basis. Only
first-lactation records of 100 to 305 days in length, with no ab-
normal condition, were used if they were produced by cows
milked twice-a-day (2X). A record coming from a cow without
a previous dry period and with age at freshening equal to or less
than 35 months was considered a first-lactation record. The
main reason for using only first-lactation records was to avoid
estimates biased by selection, as discussed by Henderson et al.
(11). Included were only those sires with 10 or more daughters
located in two or more herds during 1958 to 1967.
Months of calving were grouped in two seasons of six months
each. Season 1 included January through June, and Season
2 included July through December. These periods were chosen
because variation between seasons seemed to be greatest, and
variation within seasons least, when a gross comparison was
made between monthly mean yields as reported in Annual Sum-
maries published by the Florida Agricultural Extension Service.
Higher averages were observed during months included in
Season 1. Dependent variables analyzed were milk yield, fat
yield and fat percentage. Records were adjusted for year, season,
age at calving and lactation length, using factors obtained from
least squares analyses (30).

The mathematical model assumed was:

Yijk = / + hi + pj + (hp)ij + eijk, where
Yijk the adjusted first lactation record of the kth
daughter of j th sire in the i th herd,
S = the overall mean,
hi = the effect of the i th herd, the sum of all effects,
genetic and environmental, which made the i th
herd different from the mean of all other herds.
pj = the effect of the j th sire, believed to be entirely
genetic in nature, and which was the total of all
influences which made the progeny of the j th bull
different from the mean of all progeny groups.
(hp).. = the effect of the interaction between environmen-
S tal and/or genetic portions of the jth herd effect
and the jth sire effect.
eijk = the random error affecting the record of the kth
daughter of the jth sire in the ith herd.

The hi, pj, (hp)ij and eijk were assumed to be random, with
expected values of zero and variances ah2 r2, o2p and 02
respectively. It was further assumed that all effects were un-
correlated, e.g.,
E[hi, hi] = E[pj, pJ] = E[(hp)ij, (hp)j] =
E[eijk, eijk] = E[h pj] = E[hi, (hp)ij ]
E[pj, (hp)ij] = E[hi, eijk] = E[pj,eijk] =
E[ (hp) ij ,eijk] = 0

Least squares techniques would provide the best possible
estimate of the interaction component, r p. The interaction
sum of squares adjusted for herd and sire effects can be ob-
tained by computing the sum of squares error for the model
containing ,, h, p and (hp) and subtracting the quantity from
the corresponding sum of squares error for the model contain-
ing /I, h and p. However, even with absorption of one of the
effects, no computer program was available at the University
of Florida at the time capable of analyzing these data with the
large number of levels for each factor.

Since the purpose of the study was to obtain estimates of
variance components, Henderson's method I (10) was used to
complete the analysis. With this method, the sums of squares
are first obtained using standard formulas for the two-way
classification with interaction adjusting for the unequal num-
bers of observations but not for the non-orthogonality between
the two factors. These quantities are then divided by their

Table 5. Sources of variation, degrees of freedom and expected mean squares
for subclasses included in genotype-environment interaction analyses.

Sources of variation d.f. Expected mean squares

Herds h-1l 02 + K72hp + K8h + K9 2p

Sires p-1 2 + K4 02 + K5 a + K6 G2

Herd x sire hp-h-p + 1 2 + K, + K2 2 + K3 2
e hp 2 h 3 p

Remainder N-hp O2

1. h = number of herds; p = number of sires; hp = number of herd-sire cells;
N = total number of observations.

Xn2 7n2 Ern2
K1 = (n.. -E iij j ij + ij i];
Sn.j i i. n..

En2 2 -2
K2 = [i i. i i ]; K6 = [n.. n
n.. j n.. n..

n.2 En2 En2 Z n2
K3 [J_ i_ ii; K7 = [ iii ii];
n.. i ni. i ni. n..

En2i EE n2
K4= [z i j i ji ; K8 [n.. i.; and
3 n.j n.. n..

Z n2 Z n2 Z n2 E n2
K5 = [ i i i.]; K9 [C j ij i j].
n.j n. i ni. n..


n.. = the total number of observations,

nij = the number of observations in the ith herd from the jth sire,

ni. = the number of observations in the ith herd, and

n.. = the number of observations in the jth sire.

degrees of freedom to yield "mean squares". As pointed out by
Henderson, the herd x sire interaction will include, because of
the non-orthogonality of the data, sire and herd effects. As a
consequence of this, negative values are possible. Therefore,
these quantities should not be called mean squares. We will,
following the suggestion of Searle (23), call these quantities
analogous mean squares.
In order to estimate the variance components, cr2, 0r2 a2 and a2
h, p hp el
the expectations of the analogous mean squares were obtained.
These expectations (along with the sources of variation and their
degrees of freedom) are presented in Table 5. The expectations
were then set equal to the calculated values and the resulting set of
equations solved for the estimates of the variance components. In
order to assure an unbiased estimate of C2, the error mean square
was based on the within herd x sire subclass sum of squares.
After a2 is eliminated in the expectations, a system of three
equations with three unknowns remains. By solving these equa-
tions, estimates of 2 a2 ,and r2 were obtained. Once the
components of variance associated with herd, size, herd x sire
interaction and remainder were calculated, the corresponding
percentage of the total variance for each component for ad-
justed first-lactation records was estimated by the formula:

% of the total variance = -
2 + 2 2+ 02p + O2
(Th p
-2 2 2 2
S2= O' h or Or or -hp or (


A brief description of data used in this investigation is
shown in Table 6, with overall means and standard deviations
for the dependent variables in Table 7. Phenotypic correlations
involving these variables are shown in Table 8 and are in close
agreement with values reported previously (2, 4, 19, 25). Most
phenotypic correlations reported for milk and fat yields are
between 0.80 to 0.92. Negative phenotypic correlations between
milk yield and fat percentage generally range from -0.16 to

-able 6. Description of Data.

Number of records

Number of sires

Number of herds

Number of sire x herd cells

Average age at calving (months)

Average lactation length (days)

Table 7. Overall meanss and Standard Deviations.

Milk vield

Mean St. dev.

7,114 Ib 1,733 lb

10,388 Ib 2,152 Ib

6,931 lb 1,445 Ib

Fat yield

Mean St. dev.

324 lb 77 lb

381 Ib 77 lb

345 lb 72 Ib

tat percentage

Mean St. dev.

4.57% 0.40%

3.70% 0.34%

4.99% 0.42%

Table 8. Phenotypic Correlations


Milk yield

Fat yield


Milk yield

Fat yield


Milk yield

Fat yield

Fat percentage































Fat yield




-0.26. For correlations between fat yield and percentage, values
a little bit larger than the ones found in this investigation have
been obtained. Knowledge of phenotypic correlations is neces-
sary in the design of efficient selection programs. These esti-
mates do not suggest that unique environmental factors in
Florida are altering phenotypic interrelationships of the three
measures of milk production to any marked degree. The total
variance was partitioned as shown in Table 9.
Tables 10, 11 and 12. present analogous mean squares, com-
ponents, and percentages of the total variance accounted for
by each component.

Table 9. Degrees of Freedom and Expected Analogous Mean Squares

Sources d.f. Expected Analogous Mean Squares

Herds 68 02 + 3.95702 + 19.5460o + 3.60602

Sires 53 2 + 12.84902 + 10.04002 + 27.43602
e hp h p

Herd x sire 185 02 + 2.885S 2.90802 1.30402

Remainder 1,191 02

2 2
Herds 57 02 + 5.376o + 19.619 h + 4.912 p
e hp
2 2 2
Sires 39 02 + 12.807hp + 10.0030 + 30.800"p

Herd x sire 157 02 + 2.686 -2.4852 1.783
e + p p

Remainder 996 02


Herds 53 02 + 6.23202 + 34.9942 + 5.62902

Sires 60 02 + 15.074o2 + 12.59902 + 32.85302

Herd x sire 257 o2 + 2.9900p 2.9410o 1.16102

Remainder 1,660 02

Table l0. Genotype-environment Interaction Analyses for Guernseys


Herd Sire Herd x sire Remainder

Milk yield1
Mean square 33,787,091 37,727,622 -6,105,742 1,372,758

Component 1,582,143 995,597 532,998 1,372,758

Percentage 40 25 2 35

Fat yield1
Mean square 73,198 78,523 15,149 2,729

Component 3,519 2,228 1,609 2,729

Percentage 42 26 2 32

Fat percentage
Mean square 0.7078 1.1152 0.1137 0.1213

Component 0.0217 0.0159 0.0266 0.1213

Percentage 12 9 14 65

IUnit of measure for yields was pounds

2Negative estimate.

Results obtained were very similar to most previous findings.
Five of the six sire x herd interaction components of variance
for yields were negative. Negative sire, x herd interaction com-
ponents suggested that such interactions were zero or very
For yields, these results were in excellent agreement with
most previous research in other environments, which indicated
that the interaction component accounted for little (47c or less)
or none of the total variation.
The fat percentage interaction component in Guernseys com-
prised 14% of the total variance, the value for Jerseys was 5%,
and the value for Holsteins was positive but essentially zero.
This variation in estimates (ranging from 0 to 14%) can also
be seen in research at other stations. Whether or not this is a
real effect of practical importance awaits further investigation.

Table 11. Genotype-environment Interaction Analyses for Holsteins


Milk yield1



Fat yield1
Mean square



Fat percentage
Mean square




45,987,140 45,340,150

2,068,156 840,596















Herd x sire Remainder

-4,442,584 3,106,791

-339,249 3,106,791

2 52












1Unit of measure for yields was pounds.

2Negative estimate.


Studies of sire x herd interactions were carried out on
Florida DHIA milk production records by means of standard
analyses of variance. Holstein, Jersey, and Guernsey records
were adjusted for year, season, age at calving, and lactation
length, using the constants obtained from least squares analyses.
Sources of variation included were herd, sire, herd x sire, and
remainder. Estimates of variance components were obtained
using Henderson's Method I. Equating analogous squares to
their expectations and solving the resulting system of equations
yielded negative sire x herd interaction components for milk
and fat yields in most of the analyses, suggesting that the inter-
action component of variance was negligible or, zero. Some
variation (0 to 14%) was detected in the interaction component
for fat percentage.

The practical consequences of these results implied that
there is little need to concentrate the daughters of AI bulls, on
which evaluations for milk and fat yields are based, in higher
producing herds. Further, daughter records from all herds can
be used, regardless of level of production, with equal confidence.
These results and other reports give no support to the sugges-
tion that it would be much easier to detect genetic differences
at high levels of management, at least under dairy cattle con-
ditions present in Florida or the remainder of the United States.
Another conclusion, based on negligible genotype-environment
interaction components, is that in the process of improving the
genetic composition of dairy cattle, choice of bulls may depend
exclusively on their genetic merit without taking into considera-
tion their place of origin. These results do not mean that geno-
type by environment interactions for milk yield are necessarily
unimportant in other environments, e.g., conditions existing in

Table 12. Genotype-environment Interaction Analyses for Jersevs


Herd Sire Herd x sire Remainder

Milk yield1
Mean square 20,362,273 14,701,305 -98,617 1,077,726

Component 499,570 151,215 156,674 1,077,726

Percentage 27 8 8 57

Fat yield1
Mean square 46,126 34,070 1,762 2,882

Component 1,175 578 173 2,882

Percentage 25 13 2 62

Fat percentage
Mean square 1.1115 0.9696 0.0966 0.1528

Component 0.0239 0.0115 0.0092 0.1528

Percentage 12 6 5 77

1Unit of measure for yields was pounds

Negative estimate

developing dairy production countries. Nor do results suggest
that these interactions are unimportant in other traits of dairy
cattle. Further work on the magnitude and practical importance
of interactions for fat percent is also suggested.


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