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LIBRARY
Michigan State

University

 

 

This is to certify that the

dissertation entitled

GENETIC ASSESSMENT OF
BIOLOGICAL MERIT IN CATTLE

presented by

Just Jensen

has been accepted towards fulfillment
of the requirements for

 

Ph.D degreein Animal Science

Date—(Eaumag #2, /?70

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

PLACE It RETURN BOX to remove this checkout from your record.

TO AVOID FINES rotunon orbdon dd. duo.
r.___—__—__
DATE DUE DATE DUE DATE DUE

P ,____

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU Is An Affirmative Action/Equal Opportunity Institution

G E N E T I C A S S E S S M E N T O F

B I O L O G I C A L M E R I T I N C A T T L E

By

Just Jensen

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Animal Science

1989

(,7 ‘_,.> {I 4% *—l {215

ABSTRACT

GENETIC ASSESSMENT OF BIOLOGICAL MERIT IN CATTLE

By

Just Jensen

The goal of this work was the construction of a total merit
selection criterion for use in cattle populations. The topics
addressed relate to estimation of genetic parameters, the genetics of
beef production and its energetic efficiency, and between and within
breed genetic parameters for dairy production and calving traits.

The estimation of genetic parameters from large populations poses
severe computing problems. Algorithms that reduce the computer
resources needed were reviewed. Strategies for sampling data from
populations undergoing selection were compared using a model of
breeding events in cattle populations. Genetic parameters estimated
using recent data only were unbiased if all relationships between
animals were taken into account.

Genetic parameters of beef production and its energetic efficiency
were estimated in an experiment with 650 calves from 31 sires. No
interactions between sire and proportion of roughage in the diet were
found. Daily gain was negatively correlated with feed conversion

ratio, but positively correlated with daily feed intake.

Residual intake and partial requirements for productive and
nonproductive use of energy were estimated for each bull. There was
considerable genetic variation in residual intake and partial energy
requirement for both productive and nonproductive use of energy.
Consideration of body composition had no significant influence on
residual intake. Feed conversion ratio and partial energy requirements
were phenotypically uncorrelated to body composition. Selection for
leaner animals would increase partial energy requirements. Milk
production had a positive genetic correlation to daily gain and
nonproductive use of energy, but was not correlated with appetite of
the growing bull.

The effect of immigration of Brown Swiss genes into the Red Dane
population on dairy production and calving traits were estimated from
data on 170,166 cows. Heterosis was 7.1 to 7.7% for production traits.
Brown Swiss were 2.6 to 6.2% inferior to Red Dane. Heterosis effects
for calving traits were small compared to additive breed differences.

Genetic improvement of calving traits was possible. Dairy
production was not genetically correlated with maternal effects on
calving traits but had antagonistic correlations to direct effects on

calving traits.

ACKNOWLEDGMENTS

First, I would like to extend thanks to my committee members for
their interest and support; Dr. Ivan Mao, Dr. Roy Emery, Dr. Bill
Magee, and Dr. Jim Stapleton. During my stay Ivan has extended a lot
of support as professor, colleague, and most importantly as a good
friend.

Many other friends, especially among graduate students, have
endured my harassments during the coffee breaks. Gwang-Joo Jeon has
received many punches, but always responded in ways that made me smile.
Terri Moore was able to at the same time make my stay a joy and almost
unbearable.

I am grateful towards my family for their support and
encouragements, even though they often times did not understand what I
was doing.

Many thanks are extended to Sheryl Hulet for the help in preparing
the manuscript in the final stages and to make the office environment
more humane.

Finally I want to thank the Danish Agricultural and Veterinary
Research Council and various grant funds belonging to Dr. Ivan Mao for
financial support. Computing support by the National Pitsburgh

Supercomputing Facility is acknowledged.

iv

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

INTRODUCTION

Chapter 1. Transformation algorithms in analysis of single

trait and of multitrait models with equal design
matrices and one random factor per trait: A review

Introduction

Models .
Transformation Algorithms
Backtransformation
Numerical Example .
Numerical Strategies
Convergence Criteria
Discussion

Chapter 2. A sthochastic model of breeding schemes in cattle

Chapter 3.

Chapter A.

Populations

Introduction

Overview of Model

Model Description .

Simulation of Yearly Breeding Events
Example .

Estimation of genetic parameters using sampled
data from populations undergoing selection

Introduction . .
Materials and Methods
Results and Discussion
Conclusions

Performance testing of dual purpose bulls for beef
traits. Genetic parameters of growth, feed intake,
appetite and carcass composition

Introduction . .
Materials and Methods .
Results and Discussion
Conclusions and Implications

ll

19
20
24
25
27

29
3O
31
33
39
43

49
SO
52
S9
66

69
7O
71
78
87

Chapter

Chapter

Chapter

Chapter

SUMMARY

LIST OF

Performance testing of dual purpose bulls for beef
traits. Residual intake and energy requirements
for growth and maintenance

Introduction .

Materials and Methods

Results and Discussion

Conclusions and Implications

Performance testing of dual purpose bulls for beef
traits. Genetic and phenotypic correlations between
partial energy requirements and beef traits of young
bulls and the milk yield of their female halfsibs
Introduction . . . . . . . . . .
Materials and Methods .
Results and Discussion
Conclusions and Implications

. Additive and heterotic effects of immigration of

Brown Swiss genes into the Red Dane Cattle
population on dairy production and calving traits
Introduction . .
Materials and Methods
Results and Discussion
Conclusions .

. Genetic parameters of dairy production and calving

traits in Danish Red Cattle
Introduction
Materials and Methods
Results and Discussion

AND CONCLUSIONS

REFERENCES

vi

89
9O
91
98
109

112
113
114
119
131

134
135
136
142
157

159
160
161
166

172

181

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

10.

11.

12.

13.

14.

LIST OF TABLES
Data used in numerical example

Estimates of genetic correlation from round 30 and at
convergence in a small simulated population

Basic parameters for simulation model

Typical population means, heritabilities, standard
deviations, partial economic weights, phenotypic
(above diagonal) and genetic (below diagonal)
correlations to be used in simulation model

Level of significance for effects of population
size, bull use and interaction between population
size and bull use

Genetic level in year 25, averaged over 10 replicates

Genetic standard deviations in year 25, averaged
over 10 replicates .

Total genetic drift accumulated in year 25. SD on 10
replicates

Parameters used in simulation of dual purpose and
dairy populations

No. of animals included in analysis, averaged
over 15 replicates .

Average estimates of genetic parameters in dual
purpose populations

Average estimates of heritability of milkfat in
dairy populations

Average no. of rounds to obtain a certain number
of significant digits in estimates of genetic

parameters

Energy content (Mj) and dry matter intake of
diets used

vii

21

26

35

35

45

46

48

48

54

6O

6O

62

66

73

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

Distribution of observations on years and treatments

Mean, heritability and phenotypic standard deviation
for production traits . . .

Genetic (under diagonal) and phenotypic (above
diagonal) correlations among traits measured in
production period 1 (28 d to 200 kg LW)

Genetic (under diagonal) and phenotypic (above
diagonal) correlations among traits measured in
production period 2 (200 kg LW to slaughter)

Genetic and phenotypic correlations among similar
traits measured in production period 1 and 2

Genetic (under diagonal) and phenotypic (above
diagonal) correlations among traits measured
at slaughter

Genetic correlations between growth, feed conversion
and appetite in production period 1 and 2 and traits
measured at slaughter

Mean, heritability and phenotypic standard deviation
for estimates of energy requirements

Genetic (below diagonal) and phenotypic (above
diagonal) correlations among partial energy
requirements and residual intake in production
period 1 (28 d to 200 kg LW)

Genetic (below diagonal) and phenotypic (above
diagonal) correlations among partial energy
requirements and residual intake in production
period 2 (200 kg LW to slaughter)

Genetic and phenotypic correlations among partial
energy requirements and residual intake in
production period 1 and 2

Factor loadings for phenotypic factors

Factor loadings for genetic factors

Genetic correlations between selected production

traits and partial energy requirements in
production period 1

viii

75

80

81

82

83

85

87

99

105

107

108

120

123

125

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

Genetic correlations between selected production
traits and partial energy requirements in
production period 2

and genetic correlations between selected
traits and residual intake in period 1

Phenotypic
production

and genetic correlations between selected
traits and residual intake in period 2

Phenotypic
production

Correlations between predicted breeding values of
sires for milkfat production and predicted breeding

values for traits measured on male progeny

No. of observations,

mean, and phenotypic SD for
traits analyzed . . . . .

Coefficients of crossbreeding parameters for cows
and progeny in various crossbreeding systems
Average and SD of various proportions of genes and
loci in cows and progeny and correlations between

cow and progeny proportions

Levels of significance for crossbreeding effects
in LS-model [1]

Crossbreeding parameters estimated in Model [1]
Crossbreeding parameters estimated in Model [2]

Crossbreeding parameters for production traits
estimated in Model [3] and Model [4]

Estimates of F1 heterosis from different models
Response in FAT from various crossbreeding systems

Response in calving traits from various
crossbreeding systems depending on estimation model

Number of observations for each trait (on diagonal)
and combination of two traits (off diagonal)

Genetic parameters of production traits and
their SE in parenthesis

Genetic parameters for milkfat production and

direct effects on calving traits and their
SE in parenthesis

ix

127

128

129

131

138

139

143

146

147

149

150

152

155

156

162

167

169

Table 46. Genetic parameters for milkfat production and
maternal effects on calving traits and their
SE in parenthesis . . . . . . . . . . . . . . . . . . 170

Table 47. Genetic correlations between maternal and direct
effects for calving traits and their SE in
parenthesis . . . . . . . . . . . . . . . . . . . . . 171

LIST OF FIGURES

Figure l. Heritability based on true BV. Avg. of 15
dual purpose populations . . . . . . . . . . . . . . . 63

Figure 2. Heritabiulity based in true BV. Avg. of 15
dairy populations . . . . . . . . . . . . . . . . . . . 64

xi

INTRODUCTION

Selection of parents of the next generation of animals is the tool
that has been used for the genetic improvement of cattle populations.
The goal of selection is to ensure that future animals will outperform
the current animals in production.

There are several alternative breeding schemes that can accomplish
a set of defined breeding goals, but in order to choose the most
efficient one, alternative schemes must be compared. Stochastic
modeling, which simulates real events is a useful tool in comparing
breeding schemes. Also, data generated from stochastic models can be
used to test the properties of statistical models and methods used in
estimation of genetic parameters.

Crossbreeding or immigration of genes have been popular for
genetic improvement in many European dual purpose and dairy cattle
breeds. In Danish Red Cattle genes have been imported from the Brown
Swiss breed. Data have been accumulated that makes it possible to
evaluate the impact of crossbreeding in terms of, additive genetic and
heterotic effects.

Efficiency, defined as either economic efficiency or biological
efficiency has received increased attention in recent years as a
desirable selection goal in cattle. However, maximizing efficiency of
producing dairy and beef products is not necessarily the same as
maximizing the output of milk and beef per animal or production unit.
A major obstacle in selection for biological efficiency is that it
requires measures of feed intake. Such measures are expensive or

impossible to obtain on a large scale under commercial conditions.

Intake and other measures for efficiency may be possible in dual
purpose populations, however, since relatively few animals are
performance tested for beef production. Selection for biological
efficiency may therefore be incorporated in the performance test, if
efficiency can be measured on the young bull, and is genetically
related to overall biological efficiency of males and females in the
production system.

Efficiency of whatever trait is a ratio of output to input.
Groups of traits other than dairy and beef traits, that are related to
economic merit, may be calving traits, fertility, and type or
management traits.

In order to make selection decisions based on many traits
simultaneously, information on these traits must be combined into an
overall index for economic merit. This means that each trait should
have assigned a weight according to its importance relative to the
overall economic merit. Determination of such weights requires
extensive economic analysis and long term projection of the dairy and
beef production enterprises and also requires knowledge of biological
parameters of the underlying genetics of the traits of interest. Such
biological knowledge, especially relationships among traits of
different groups, is not available. Therefore, the first step in a
study of economic merit should be to obtain such biological
information, while deferring economic considerations.

Knowledge of genetic parameters are also necessary in predicting
the results of various breeding programs. Selection decisions made

today have their main impact several years in the future. It is

therefore important to be able to predict genetic changes accurately
and study alternatives before implementation. Since exact knowledge of
genetic parameters is not possible in reality, they must be estimated.
Most of the data available for such estimation are field data. There
are several problems in the estimation of genetic parameters from field
data that need to be addressed.

The improvement of beef traits in dual purpose populations relies
mainly on tests of future artificial insemination bulls based on their
own performance. Bulls selected after the performance test would then
be tested for breeding value for milk production based on a progeny
test. Those bulls would have daughters producing in commercial herds.
These daughters would be measured for all other traits of interest.
Selection occurs both after the performance test for beef production
and after progeny test for dairy production. The very best bulls are
selected as sires of the next batch of bulls to be performance tested.
The use of field data from populations undergone such a selection
scheme can potentially cause bias in estimates of genetic parameters.
The current method of choice for the estimation of genetic parameters
is restricted maximum likelihood (REML) due to the desirable
statistical properties of this method. In order to account for biases
due to selection, all data that led to the current population should
ideally be included in the analysis. Use of all data on several traits
in REML estimation often leads to models that require amounts of
computation that cannot be done with current computers. It is
therefore necessary to develop strategies for sampling of data for use

in analyses. This sampling should be done in such a way that resulting

models are computationally manageable and biases in estimates is
minimized.

This thesis is organized in eight chapters covering three main
topics. The first topic is computation algorithms and data sampling in
alleviating computation difficulties in the estimation of genetic
parameters. The second topic relates to beef production and its
biological efficiency and the genetic relationships between these
traits measured on the growing young bulls and the dairy production of
female relatives. The third topic deals with estimation of
crossbreeding effects and genetic parameters on dairy production and
calving performance in a population importing genetic material.

Chapter 1 reviews transformation algorithms in the estimation of
genetic parameters in a class of single and multiple trait models.
Chapter 2 describes a stochastic model which simulates breeding events
in dual purpose and dairy populations. The model was used in Chapter 3
for the purpose of generating data used to compare different strategies
of data sampling for the estimation of genetic parameters in
populations undergoing selection.

Chapter 4, 5, and 6 reports on an experiment designed to study 1)
the possibility of including selection for energy efficiency in the
performance testing of young bulls, 2) alternative expressions for
energy efficiency of growing young bulls, and 3) the relationships of
beef characteristics in growing young bulls with the dairy production
of female halfsibs.

In Chapter 7, between breed additive genetic and heterotic effects

on dairy production and calving traits is reported. Chapter 8 presents

genetic parameters of dairy production and calving traits.

CHAPTER 1

Transformation Algorithms in Analysis of Single Trait
and of Multitrait Models With Equal Design Matrices

and One Random Factor per Trait: A Review

Introduction

Estimation of (co)variance components by use of restricted maximum
likelihood (REML) methods as proposed by Patterson and Thompson (1971)
has become increasingly popular due to its desirable statistical
properties. However, it often requires heavy computing due to its
iterative nature and the need for inverting one or more large matrices
in each iteration round. Several algorithms for obtaining REML
estimates of (co)variance components exist, but the expectation
maximization (EM) algorithm (Dempster et a1. 1977) has been most
frequently used due to the relative ease of programming required, and
expressions that are intuitively easy to understand. Unfortunately,
the EM algorithm in general converges slowly. Several suggestions have
been made to speed up convergence such as the common intercept approach
(Schaeffer, 1979) or nonlinear adjustment (Misztal and Schaeffer,
1986). However, application of these techniques in multitrait models
is unclear, because more parameters usually must be estimated than in
single trait models. Also, the convergence rate generally decreases as
the number of parameters to be estimated increases.

Other algorithms for REML estimation of (co)variance components
such as Fisher scoring (Patterson and Thompson, 1971), Newton Raphson
(Jennrich and Sampson, 1976) or a procedure developed in principle by
Anderson (1973) and used by Meyer (1985) generally converge in fewer
rounds, but each round requires more computation and more complex
programming than the EM algorithm. In order to avoid inverting large

matrices, an algorithm for single trait models developed by Smith

(1986) and Graser et a1. (1987) maximizes the likelihood function
directly using a grid search. For multitrait models, maximization of
the likelihood function directly becomes more complicated. Yet another
approach has been the use of transformations applied to different
elements in the EM algorithm. For a large class of models these
transformations offer an alternative that drastically reduce the
computational requirements of the EM algorithm.

The purpose of this paper is to review recent developments in the
use of transformation algorithms in single and multiple trait models
with equal design matrices. The model is assumed to contain only one
random factor per trait. The models studied represent a limited subset
of all possible multitrait models, but a large proportion of the models
usually used in single trait analysis. The single trait analysis will

be presented as a special case of the multitrait analysis.

Models
Let Y be a nxt matrix of observations on n individuals each with
records on t traits. Now, let the model for the ith trait, i.e., the
th

i column in Y, be

where bi is a fxl vector of fixed effects, “i is a qxl vector of random
effects, X and Z are known matrices relating observations in yi to
classes in hi and “i; and e1 is a nxl vector of random residuals. The
model for all t traits simultaneously would then be:

y - (IC*X)b + (It*Z)u + e
where y - vec Y, "*" denotes the direct product operation (Searle,

1982),

b' - [b1. bé. .bg].
u' - [ui, ué,...,ué], and
e' - [ei, eé,...,e£].

The expectations, E(), and (co)variances matrices, V(), are
E(y) - (It*X)b, E(u) - O, E(e) - 0,

V(y) - G*ZAZ' + R*I ° V(u) - G*A; and V(e) - R*In

n'
where G and R are (co)variances matrices of the t traits for the random
factor and the residual, respectively, and A is the numerator
relationship matrix for elements in ui. Under these assumptions the
mixed model equations that would yield the best linear unbiased
estimator (BLUE) of the fixed effects and the best linear unbiased

predictor (BLUP) of the random effects can be written as (Henderson,

1973):

l

R’1*x'x R‘ *x'z 6 (R'1*X')y

R‘1*z'x R'1*z'z + c‘1*A’1 a (R'1*z')y
[1]
As in practice, (co)variances are unknown, G and R in [1] contain a
priori estimates.

Let C, a generalized inverse of the coefficient matrix in [1], be
partitioned by denoting the ijth submatrix of C corresponding to the
1th and jth subvectors of u as cij'

Utilizing expressions by Dempster et al. (1977), the EM algorithm

th

to estimate the ij element in G and R are:

A "t ’1“ '1
gij(k+1) ' [ui(k)A uj(k) + tr(A Cij(k))]/q [2]

iimam) ' [éi(k)éj(k) + tr<313(k)>l/n [31

10

for the kth round of iteration, where Bij is the submatrix of VCW'
corresponding to the ijth pair of traits, where V - [XEZ]. These
expressions are due to Henderson (1984), and correspond to the REML
estimators given by Patterson and Thompson (1971) and Harville (1977)
but extended to multiple traits.

In estimation of (co)variance components or in prediction of the
random elements in u, we are not interested in solutions for the fixed
effects. Therefore, the equations in [1] corresponding to fixed
effects can be absorbed to give

[R'1*z'xz + c'1*A'1]u - (R’1*z'u)y [4]
where M - I - X(X'X)'X' is a projection matrix. In cases where X
describes more than one classification factor or includes covariates,
it can typically be partitioned as X - [X1 5 X2] such that Xin is
diagonal and thus can be absorbed easily. Equations corresponding to
X2 must then be absorbed either as a block or generally easier by using

Gaussian elimination or sweeping operations (Dempster, 1969, Goodnight,

1978). A detailed [4] denoting parts by t traits is

 

 

 

 

, . _ -
rllzouz + gllA‘l r1221” + gle']. ... rltzonz + gltA-l 61
r212'nz + 321A'1 rZZZ'MZ + gzza‘l --- thZ'MZ + gZCA'l 62
rtlz'xz + gtlA‘l rtZZ'MZ + gtza‘l --- rttz'nz + gttA‘l at J

L. .. L

rllz'uy1 + rIZZ'Myz + ---.+ rltZ'Myt
r212'ny1 + rZZZ'MyZ + ---.+ thZ'Myt
= [5]

2

 

 

rtlz'uy1 + rt z'My2 + ---‘+ rttZ'Myt

ll

1, respectively.

where rij and gij are the ijth elements of R'1 and G-
Simplifications of the EM-REML estimators in [2] and [3] are
possible in many cases:
1) If the individuals in u are unrelated, then A - I, and [2] becomes
gij<k+1> ' lfii<k>fij<k> + t‘(°ij<k>)1/q¥
2) If there is only one trait in the analysis (single trait analysis)
the (co)variance matrices G and R are scalars. The computations
necessary to evaluate [3] reduce to:
cr(311) - r(X) + q - a tr[(Z'MZ + aA‘l)‘1] [6]
and 6'6 - yiyl - B'Z'My - G'Z'My - aa'a [7]
where r(X) is the column rank of X and a - rll/gll' Proof of

equation [6] can be found in Schaeffer (1983), and equation [7] is due

to Thompson (1969).

Transformation Algorithms
Canonical Transformation

It is clear from [5] that if covariances were zero, the multitrait
analysis would split into t single trait analyses. The purpose of the
canonical transformation is to obtain a set of canonical variates,
between which, all covariances are zero, without loss of any
information contained in the original variables.

Let data for the jth individual observation be arranged in a txl
vector yj, and let P - G + R be the phenotypic (co)variance matrix,
V(yj) - P. If a linear transformation on yj is performed with a
transformation matrix Q, i.e., ycj - Qyj; then:

V(ycj) - Q(P)Q' - Q(G + R)Q' - QGQ' + QRQ'

- CC + RC [8]

12

where subscript c denotes canonical scale hereonafter.

If Q is chosen such that Gc is diagonal and Rc - It' the variables
in ycj are called canonical variates which have unit residual variances
and are uncorrelated. Such a transformation was first suggested for
animal breeding problems by Thompson (1976) and has been applied to
practical animal breeding data in several publications (Arnason, 1982,
Arnason, 1984, Taylor et al., 1985, Schaeffer, 1986 and Meyer et al.,
1987).

The diagonal elements of Gc are the eigenvalues of RC.1 and Q is
the matrix of corresponding eigenvectors. The matrix RG'1 is generally
not symmetric, which complicates the calculation of eigenvalues and
eigenvectors. Schaeffer (1986) gave an alternative method of computing
Q which only involves obtaining eigenvalues and eigenvectors of
symmetric matrices.

After transformation to the canonical scale, the mixed model
equations in [5] contain t diagonal blocks corresponding to the t
canonical variates. The equations for the ith block are:

[z'xz + Aila'116C1 - z'xyci [9]
where 11 is the ith diagonal element of Gc’ Expressions for estimating
the variances now reduce to the single trait form. Formulas for
estimating the covariances reduce to crossproducts of the solution
vectors and the residuals. At convergence such crossproducts are
expected to be zero. Let

cC - (Z'MZ + AilA'1)°1.

Then, for the (k+l)th round of iteration, estimators of the elements in

GC are.

l3

gcii(k+l) ' [fiéiA'lfici + tr(A'ICCH/q [10]

gcij(k+l) - [ficiA-lecjl/q' for 1/3 [11]
and those in R are:

feii<k+1) - [éciéci + r(X) + q - Ail tr(A'1CC)]/n [12]

fcij(k+l) - [ééiécj]/n, for ifj [13]
where ééiécj - yéiuycj - fiéiz'xycJ - Aifiéificj, for all 1 and j.

The estimation of the covariances is much simplified, because the
traces in [2] or [3] for that case reduce to zero due to the block
diagonal structure of the multitrait mixed model equations on the
canonical scale.

The (co)variance estimates on the canonical scale are in GC and
RC, which must be transformed back to the original scale by:

a(k+1) ' Q lacQ'T [1“]
and fi<k+1) - q'lfiCQ'T [15]
where Q.1 is the transpose of Q'l. In practice G and R may be very
close to positive semi-definite of the conclusion of an iteration.
However, they can be very close to, but never be positive semi-
definite.

The new estimates of G and R are then used to obtain a new Q
transformation matrix and a new Gc' the diagonal matrix of
corresponding eigenvalues, so the process from [9] through [15] can be
iterated until a convergence criterion is met.

This procedure yields the same results as the straightforward
multitrait estimators in [3] and [4], and a proof of such equivalence

was given in principle by Meyer (1985).

Other algorithms that incorporate the canonical transformation in

l4

REML procedures for estimating the (co)variance matrices G and R have
been presented by Meyer (1985) and Schaeffer (1985). The algorithm by
the latter author estimated only the genetic and residual variances on
the canonical scale. The variance estimates at convergence were then
backtransformed to obtain both variances and covariances on the
original scale by use of the inverse of the initial Q transformation
matrix. Such a procedure would generally yield estimates that are
dependent on the initial values chosen for G and R, Buttazzoni and Mao,
(1987, unpublished results). Meyer (1985) showed another algorithm
which estimate the off-diagonal elements of Gc and Rc and utilize a new
Q in each round of the interation process. She also used an
alternative algorithm given in principle by Andersen (1973), mainly to
speed up convergence. However, it requires the inversion and storing
of t qxq matrices in each iteration so the procedure tends to be

computationally demanding.

"Cholesky" Transformation
After canonical transformation, a multitrait analysis of t traits
can be accomplished by t separate single trait analyses.

h

The model for the it canonical variate could be written as:

yci - Xbci + ZuCi + eCi [16]
The (co)variance matrices of the random vectors are
V(uci) - AiA and V(eci) - In'
Further we have C°V(eci'°cj) - O and Cov(uci,ucj) - 0, i.e.,

residual variances are unity and all covariances between traits are

zero. The goal of the "Cholesky" transformation is to diagonalize

15

V(uci). To do so, the relationship matrix is decomposed such that A -
LL', where L is a lower triangular positive definite matrix and LL'1 -
I. The model [16] is rewritten as:
yci ' Xbci + ZLL-luci + eci
- Xbci + 2*uc11 + eci [17]

where 2* - ZL, and “c1' - L'luci, and subscript 1 denotes "Cholesky"

1.

scale.

The variance of ucli is

V(ucli) - V(L-1uci) - L-1(A1A)L-T

- A I [18]

i q'
The mixed model equations for the ith canonical variate after
absorption of fixed effects are now:
[z*'uz* + A;1116C11 - z*'xyci [19]
The quadratic and bilinear forms used in the estimation of
(co)variance components [10] through [15] are in principle not altered
by the "Cholesky" transformation but computations in each round become
easier. This is illustrated by the following:
Goliacli ' GciL-TL-lficj ' GéiA-1ch [20]
fiéliz*'xycJ - G'L'TL'z'uycj - fiéiZ'MyCJ [21]
tr(A'1CC) - tr[A'1(Z'MZ + AilA'1)'1]
- tr[L'TL’1(z'xz + AiIA'1)°1]
- trIL'1(Z'MZ + AilA-1)-1 L'T]

- tr[(L'Z'MZL + Ail

L'A'lL)'1]
- tr[(Z*'Mz* + AilI)'1]. [22]

The computational advantage of the "Cholesky" transformation is,

therefore, that A°1 drops out of the expressions used in estimating the

16

elements of G and R (Meyer, 1987). This can also be seen in [20],
[21], and [22]. Thus, the inverse of A no longer needs to be computed
and stored. The matrix L can easily be computed from a list of
pedigree information following rules given by Henderson (1976) and
Quaas (1976). As shown by Meyer (1987), L can be processed one column
at a time, overwriting the original arrays. The use of the "Cholesky"
transformation of the solution vectors in [17] was first suggested for
animal breeding problems by Smith (1986) and by Smith and Graser

(1986).

Householder transformation
In order to evaluate the traces in [22], a matrix of order qxq
would still need to be inverted for each trait in each round of the
iteration process. To ease the computational burden in obtaining these
inverses, Dempster et a1. (1984) suggested the unique spectral
factorization of the coefficient matrix. Let the coefficient matrix in
[19] be [H + Aill] then the unique spectral factorization of H is
a - PDP' [23]
where D is a diagonal matrix with the eigenvalues of H as diagonal
elements and P is the matrix of corresponding normalized mutually
orthogonal eigenvectors of H, i.e., P' - P'l. Hence, P'HP - D is an
orthogonal similarity transformation of H into D.
By applying this transformation to the coefficient matrix in [19]
we get:
P'[H + AiII]P - [D + 1,111 [24]
The coefficient matrix is now diagonal. However, finding the

eigenvalues and eigenvectors of a large matrix can be computationally

17

very demanding, and as shown by Smith and Graser (1986) not necessary.
A series of q-2 Householder transformations (Householder, 1958) is a
less demanding alternative, and is usually an initial step in finding
eigenvalues and eigenvectors. A description of the Householder
transformation can be found in most textbooks on linear algebra.
Programs for performing the transformation are available on all
reasonably equipped computer installations. Computing algorithms can
be found in textbooks on numerical analysis such as Kennedy and Gentle
(1980) or Stoer and Bulisch (1980). Other advantages of the
Householder transformation are that it is numerically stable and can be
employed on matrices too large to store in computer memory (Hansen and
Lawson, 1969).

Let P be the product of q-2 Householder transformation matrices.
Then P'P - PP' - I, i.e., P is orthogonal. The idea of the Householder
transformation is to choose a matrix, P, such that by premultiplying by
P' on both sides of the equation in [19]:

P'[z*'Mz* + AilI]PP'Gcli - P'z*'xyC1

or [T + killlficlhi - P'Z*'Myci [25]
the resulting T - P'Z*'MZ*P is symmetric and tridiagonal and aclhi -
P'acli' where subscript h denotes Householder scale. The estimates of
Gc and Re can now be computed using [10] through [15] but with 8C1
being replaced by ficlhi' Z'Myci by P'Z*'Myci, and tr(A‘IC) by tr[(T +
Ailr)‘1].

Once T is found, the equation system in [25] can be solved in
linear time by Gaussian elimination. The expression tr[(T + A'il)'1]

can be computed in linear time by the following recursion formulas, as

18

shown by Smith and Graser (1985) who attributes the derivation to R.L.
Quaas:

1I)'1] - z wi

tr[(T + Xi
where wl - tll' d - tll’ and u - t21/d, for i - l, [26]
and for i>1, d - tii - ti(i-l) u,

wi - (l + ti(i-l) u w(i_1))/d,

and u - tii/d‘ [27]
where tij is the ijth element of (T + Aill). Smith and Graser (1985)
also showed that the evaluation of tr[(T + Ai11)'1] can be incorporated
easily into an algorithm for solving [25] by Gaussian elimination so
that solutions and traces can be obtained in linear time.

The tridiagonal matrix T needs to be found only once no matter how
many traits are included in the analysis or how many iterations are
needed to obtain convergence of the (co)variance estimates.

The proof that the quadratic and bilinear forms and the traces
calculated on this new scale are the same as if they were calculated on
the canonical scale directly follows the same logical steps as the
proof that the "Cholesky" transformation did not alter these

quantities. Smith and Graser (1985) also proved this for the

Householder transformation directly.

Application of transformation in single trait analysis
The mixed model equations for a single trait analysis
corresponding to [19] are
[z*'u2* + aI]G - Z'My [28]

where a - 02/03. If we let G - (Z*'MZ* + aI)’1, then the EM-REML

l9

estimates of the variances are:

03(k+1) - [6'6 + 02(k) tr(C)]/q [29]
a§(k,1) - [6'3 + a§(k)(r(X) + q - atr(C))]/n [30]
where 6'8 - y'My - G'Z*'My - afi'fi [31]

The only difference in [29] and [30] from [2] and [3] is the appearance
of a§(k), since this was factored out of the single trait mixed model
equations in [28]. If A - I, 2* reduces to 2. Instead of iterating
from [28] through [31], a better alternative would be to apply the
Householder transformation on [28] so that solutions and traces can be

obtained in linear time.

Backtransformation

At convergence the estimates of Cc and Rc are transformed back to
the original scale using [14] and [15]. The solutions to the
tridiagonal systems in [28] can be backtransformed to the original
scale using a two—step procedure:

1. To undo the Householder and the "Cholesky" transformation,
multitrait solutions from [25], or single trait solutions from [28],
are premultiplied by the inverse of the transformation matrices, L'1
from [17] and P' from [25]:

fici - LP ficlhi [32]
where a "~" superscript denotes a solution obtained at convergence.
The corresponding prediction error variances estimated as if parameter
(co)variances were known are computed as (Jensen and Mao, 1987):

V(uC1 - 661) - LP[T + Ai11]'1P'L’ - C11 [33]
The inverse of [T + kill] can be obtained with minimal computational

effort (Smith and Graser, 1986). The diagonal elements in Cii and gel

20

will be used in the next step.

2. Solutions on the canonical scale are backtransformed to the
original scale: Let the solutions for the jth individual be arranged
in a txl vector ucj and the corresponding estimated prediction error
variances in a txt diagonal matrix Cj'
Then fij - Q-[k)fijc [34]
and V(uj - aj) - Q‘]k) cJQ'Ek) [35]
The solutions contained in fij at convergence are not BLUP, but in the
case where the (co)variance matrices are unknown, they are the best

approximations when uncertainty about fixed effects and the unknown

variances are taken into account (Gianola et al., 1986).

Numerical Example

This numerical example demonstrates the equivalence of the
straight-forward multitrait approach and the multitrait approach that
uses the three transformations.

Consider the data in Table l, which is a modified subset of data
used by Meyer (1986). The same starting parameters were also used
here:

G _ 12 9 and R _ 160 75

9 10 75 140

The three sires were assumed to be related according to the following

relationship matrix:

21

A - 1.00 0.25 0.25

0.25 1.00 0.50

0.25 0.50 1.00

 

 

 

 

 

 

 

 

 

Table 1.
Data used in numerical examplea.
Sire l Sire 2 Sire 3
Trait l 2 l 2 1 2
Herd 1 106 31 115 40 127 51:
120 49*
129 60*
145 59
Herd 2 105 21 109 30
120 50 121 48
98 32 132 55
111 48
117 29
101 22
Herd 3 132 53 137 49
117 41 139 67
129 49 131 44
125 55
119 37

 

aData consist of paired subset of data used by Meyer (1986) with two
modifications. Observations marked were moved from herd 3 and all
records for trait 2 were reduced by 100.

The solutions to the usual multiple trait mixed model equations
from [1] are:

8' - [122.337, 113.961, 127.393, 47.163, 38.3732, 48.2362],

and fi' - {-2.20238, 0.52125, 2.41526, -2.00205, 0.551105, 2.1183].
First round estimates of G and R using [2] and [3] are, respectively,

A 15.0460 11.7839 A 106.4670 81.6079

6(1) "' and R(1) _
11.7839 12.3598 81.6079 120.7820

22

These values would then be used in [1] and the process iterated until
convergence.

The matrix Q computed from the initial values of G and R and used
to transform the data into the canonical scale for the first round of

the iteration process was:

Q - 0.048206 0.0459666

-0.0776011 0.0861689

with G - 0.0889006 O

0 0.0261515

The Cholesky decomposition of the relationship matrix is:

r- G

L - 1.0 0 0
0.25 0.968246 0

0.25 0.451848 0.856349

 

 

h

The matrix Z*'MZ* is:

z*'uz* - 1.59375 -1.79932 -O.428174

-l.79932 2.84514 -0.866008

 

 

-0.428174 -0.866008 2.35278

In this case, only the elements (3, 1) and (l, 3) with the value -
0.428174 need to be annihilated by the Householder transformation in
order to tridiagonalize the above matrix. The corresponding P matrix

is

23

P - 1 0 0
0 -0.972835 -0.231500

0 -0.23150 0.972835

 

 

In practice the matrix P would not be computed. Instead, vector valued
functions of q-2 individual transformation matrices should be computed
and stored. These vectors can be stored as q columns in a triangular
qxq matrix.

After applying the Householder transformation we obtain:

F 1

1.59375 1.84957 0
T - 1.84957 2.42868 0.88407

0 0.88407 2.76923

 

 

The mixed model equations for the first canonical variate shown in [25]

are:
F 12 8423 1 84957 0 . PA 1 p 2 83947 I
. . SCll ' .
1.84957 13.6772 0.88407 §C12 - -2.34557
0 0.88407 14.0177 sc13 2.97471

 

 

 

 

 

 

which have solutions
Sél - {-0.198195 - 0.159058 0.222242].
The solutions for the second variate is:
8&2 - {-0.0016072 -0.00532212 -0.0108284]
The corresponding traces of the inverse coefficient matrices for the
first and second variates are 0.225935 and 0.0742087, respectively. So

the first round estimates of GC and RC become, respectively,

24
Gc(1) - 0.113302 -0.00041382 , and Rc(l) - 0.864277 0.126558

-0.00041382 0.0247856 0.126558 0.446563

Backtransformation to the original scale using [14] and [15] yields
exactly the same results as the straightforward multiple trait

procedure.

Numerical Strategies

Numerous numerical strategies can be employed in order to make
procedures as efficient as possible in terms of numerical stability and
amount of computation involved. Most of these strategies can be found
elsewhere in the literature. A couple of "tricks" probably not found
in the literature in relation to the canonical transformation are
discussed below.

In the iteration process, transformations must be performed in
each round. To ease these computations, compute first Y'MY, the matrix
of sum of squares and crossproducts, and P'Z*'MY a qxt matrix of
"single trait” left hand sides. These matrices can then be transformed
to the canonical scale using:

P'z*'MYC - P'z*'MYQ' [36]
and YéMYC - QY'MYQ'. [37]
Let Q(k+l) be the canonical transformation matrix for the next round in
the iteration process, a "round to round" transformation matrix can
then be computed as Qr - Q(k+l) Q'l, which can be used after the
initial round in [36] and [37] in place of Q in order to minimize the
numerical effort involved.

An algorithm applying the "Cholesky" transformation directly from

a list of pedigree information was given by Meyer (1987). Stoer and
Bulirsch (1980) outline an algorithm for the Householder transformation
that avoids actually setting up the transformation matrix. Instead, q-
2 vector valued functions of P are computed. These vectors can be
stored in the same space as the original matrix to be reduced, thus

saving both computer time and memory.

Convergence Criteria

The purpose of this section is to illustrate the effect of choice
of convergence criteria on the estimates obtained. The algorithm
employing the transformations requires limited computational effort in
each round of the iteration process which allows for a conservative
convergence criteria without excessive computing costs. The estimates
of G and R are generally updated in an approximate geometric
progression (Misztal and Schaeffer, 1986). This means that the changes
in the estimates of G and R become smaller and smaller in later rounds
of iteration. Small changes per round, however, can accumulate to a
considerable amount over many rounds of iteration.

A simulation study was conducted to illustrate the effect of
choosing a conservative stopping criteria instead of a fixed number of
iterations. A total of 600 observations on two traits using true
population parameters as the starting values was simulated. The 600
individuals simulated were descendants from 30 unrelated sires and were
distributed in 100 herds. The number of herds per sire group was on
average 7.97. The parameters generally slowest to converge are the

genetic covariances or equivalently the genetic correlations, so this

26

parameter was used to illustrate convergence rates. The true
population genetic correlation was 0.82. Estimates from round 30 and
at convergence along with the number of rounds necessary to reach
convergence are shown for 10 replicates in Table 2.

The norm of the matrix of differences of the parameter estimates
was used as a convergence criterion, i.e.,

“C(kfl) ‘ C(k)“

and

“R(k+l) ' 30¢)“-
Both norms were required to be less than 10-6. As can be seen from
Table 2, dramatic changes in parameter estimates can occur even after
round 30. Also that the number of rounds needed to reach convergence
vary wildly from sample to sample.
Table 2.

Estimates of genetic correlation from round 30 and at convergence in a
small simulated populationa.

 

Genetic Correlation No. of roundsb

Replicate Round 30 Convergence for convergence
1 0.43 0.42 400
2 0.84 0.95 2200
3 0.21 -0.02 4400
4 0.67 0.67 100
5 0.89 0.91 400
6 0.70 0.79 500
7 0.96 1.00 4800
8 0.52 0.60 500
9 0.51 0.51 200
10 0.78 0.83 400

 

8See text for description of population
Convergence only tested for each 100 rounds.

27

Discussion

The transformation algorithms reviewed in this paper offer a very
useful alternative for EM-REML estimation of (co)variance components
for a class of models frequently used in animal breeding. The class
includes all single trait models with two variance components. Also
included are multitrait models with equal design matrices and one
random factor per trait.

By employing a series of transformations, the problem of slow
convergence of the EM algorithm would be largely alleviated since the
computations necessary in each round of the iteration process can be
performed in linear time. However, there are some initial computing
efforts necessary. If the relationship matrix is included, a Cholesky
decomposition of the relationship matrix must be found. This can be
done directly from a list of pedigree information. Further, if the
Householder transformation is used, it would require about the same
amount of numerical work as computing an inverse of the same matrix but
this has to be done only once, no matter how many rounds of iteration
the problem requires. If (co)variance components are to be estimated
from an animal model, which tends to have a coefficient matrix that is
large and sparse, the Householder transformation is not well suited for
sparse matrix methods. In this case, tridiagonalization may be
obtained by other transformations such as the Givens rotations which is
better suited for sparse methods. A comparison of these transformation
techniques applied to sparse matrices in animal breeding problems is
needed.

When the computations necessary in each round of the iteration

28

process can be evaluated in linear time, the use of conservative
convergence criteria is possible. As demonstrated by the simulation
example, the number of iterations needed to reach a certain degree of
convergence can vary a great deal from sample to sample, and that
considerable change in parameter estimates can accumulate in later
rounds. These factors stress the need for a conservative convergence
criteria. More research work needs to be done to determine optimum

convergence criteria.

CHAPTER 2

A Stochastic Model of Breeding Schemes in Cattle Populations

29

30

Introduction

Traditional methods of optimizing breeding schemes have generally
involved the maximization of discounted economic returns in
deterministic models. Such models predict expected genetic gain by the
use of gene flow theory (Hill, 1974) or by the use of asymptotic theory
(Rendel and Robertson, 1950).

The expected genetic gain from a genetic improvement program is
influenced by many factors. Some of these factors relates to the
population itself such as average genetic production potential and
amounts of phenotypic and genetic variation present in the population.
Other factors are more external to the population and includes factors
such as climate, economic environment, skills of producers,
availability of infrastructure to provide test results, etc. All these
factors can be accounted for in both deterministic and stochastic
models.

However, some important factors are more difficult to take into
account in deterministic models. These factors include the variance of
the expected genetic gain due to random genetic drift (Falconer, 1981),
the buildup of inbreeding and the reduction of genetic variance due to
both inbreeding and linkage disequilibrium or Bulmer effect (Bulmer,
1971).

Many researchers today are facing the task of analyzing data
originating from populations undergoing intense selection. Statistical
models for such analyses need to take the selection incurred into
account. To test and validate such models, data from simulated

populations are a very useful tool.

31

This chapter reports on the construction of a stochastic model of

breeding events in dual purpose and dairy cattle populations.

Overview of Model

Cattle are primarily used for production of milk and beef. The
model constructed can be used to simulate either populations reared
solely for the production of milk (Single purpose populations) or
populations used for the simultaneous production of milk and beef (Dual
purpose populations). Genetic improvement of dual purpose cattle poses
problems beyond what is faced in single purpose populations, since more
traits must be taken into consideration.

Genetic improvement in cattle populations have four pathways: cows
to bulls, bulls to bulls, cows to cows and bulls to cows. The
importance of these pathways differ, due to generation interval,
selection intensity and accuracy of prediction of the genetic merit of
animals.

Young bulls, that are sampled for possible use in artificial
insemination (AI), are born out of contract matings. A contract mating
is usually an agreement between an AI organization and the owner of a
cow with outstanding credentials. Such cows are usually found in
commercial herds. Upon agreement, the cow is mated to a bull proven to
be superior and the resulting young bull is transferred to a central
testing facility at about six weeks of age in order to be tested for
beef production traits. This test is based on his own performance.

The performance test is concluded when the bull is around one year of

age so his breeding value for beef production can be predicted. Young

32

bulls who meet the criteria are then progeny tested for milk production
and other traits that can only be measured on females. Each bull is
mated to a random sample of cows from the population, and his breeding
value for direct calving difficulty can be predicted when the offspring
are born. Most of the female progeny will be bred shortly after one
year of age and start lactating after two. At this time, bulls can be
evaluated for effect on maternal calving difficulty and on female
fertility. When the progeny have concluded their first lactations, the
bulls can then be evaluated for milk production. Earlier evaluations
on milk production may be done on records in progress. Those bulls
that are promising in the preliminary evaluations are further progeny
tested for management traits on a subsample of their daughters. These
daughters are recorded for management traits during their first
lactations. Commonly management traits are those related to the ease
with which the cow can be managed in the herd or to her ability to
function in the herd. In some populations some of these traits are
traditionally called type traits.

After breeding values of a bull are predicted for all traits, a
total merit index is computed by weighing each trait according to its
partial economic importance. The best bulls is then used in the bull
to cow path and the very top bulls are used in the bull to bull path,
i.e. in the contract matings to produce the next generation of young
bulls.

In the cow to cow path, selection is usually less accurate and
less intense due to the low reproductive rate in the bovine. Another

reason is the large rate of replacement of cows due to reasons not

33

directly related to production, such as disease or infertility.
However, milk production in the first lactation receive the primary
selection emphasis.

The most intense selection is in the cow to bull path since very
few cows are needed to produce bulls for future use in Al. These cows
are selected among those with the highest predicted breeding values.
Contract matings between these cows and the very best bulls are then
arranged to start the next cycle.

The model, called DPSIM, is simulated at the animal level and is
aggregated such that year can be used as the unit of time. Similar
breeding schemes were also studied by deterministic models using

asymptotic theory by e.g. Petersen et a1. (1973).

Model Description

Traits

The selection process in both single and dual purpose cattle takes
many traits into consideration. These traits can be grouped into the
following categories:

(1) Growth traits measured during performance testing of males;

(2) Calving ease and stillbirth;

(3) Female fertility traits;

(4) Milk production traits;

(5) Management traits;

The traits in the categories (2) and (3) are lowly heritable, and
can be strongly influenced by management in the herd. These traits were
therefore not considered in the model. Each of the trait categories

would normally consist of several traits, but heretofore each were

34

modeled as one trait. The three remaining traits were denoted as
GROWTH for growth traits, YIELD for milk production traits and TYPE for

management traits.

Parameters

The program starts by calling subroutine DPPARL that reads basic
parameters chosen for this particular run of the model. The parameters
that can be varied in the model are defined in Table 3, together with
abbreviations subsequently used. Typical values for these parameters
are also shown in Table 3. Typical population means, heritabilities,
phenotypic standard deviations, phenotypic and genetic correlations,
and partial economic weights of the three traits are shown in Table 4.
Genetic parameters shown for growth traits were estimated by Jensen and
Andersen (1984) and for type traits by Jensen (1985). For milk
production, genetic parameters were estimated by Pedersen (1985) and
Pedersen and Gj¢l Christensen (1984).

The genetic parameters are converted into additive genetic and
environmental (co)variance matrices called VG and VE, respectively. In
order for VG and VE to be valid (co)variance matrices they must be
positive definite. Therefore, the eigenvalues of VG and VB is
computed. If any eigenvalue is negative, the corresponding (co)variance

matrix is invalid and the computations cannot proceed.

35

 

 

 

Table 3.
Basic parameters for simulation model.
Typical

Name Description value
NYEAR No. of years to be simulated 25
NT No. of traits to be simulated 3
NBSIRE No. of sires in base population 25
NYBPET Performance test capacity for beef 25
NBDPET No. of bull dams required to produce one

young bull for performance testing. 3
NBSY No. of bull-sires per year 2
NBCY No. of cow-sires per year 4
NHERD No. of herds 50
NCPH Avg. no of cows per herd 40
PYBPGTY Pct. of young bulls tested for yield .50
PYBPGTT Pct. of young bulls also tested for type .50
PCTT Pct. of progeny recorded for type .50
INVCR Involuntary culling rate for cows .20
SRDTM Survival rate of daughters from test matings .75
SRDCTM Survival rate of daughters from contract matings .85
SRDNM Survival rate of daughters from normal matings .75
SRYB Survival rate of young bulls on performance test .85
Table 4.

Typical population means, heritabilities, standard deviations, partial
economic weights, phenotypic (above diagonal) and genetic (below
diagonal) correlations to be used in simulation models.

 

 

Population Economic Correlations
Irai; mean Heritability SD weigh; GROWTH YIELD TYPE
GROWTH 1200 .50 75 3 --- .10 .10
YIELD 250 .25 35 50 .40 --- .10
TYPE 7 .40 1 500 .30 .20 ---

 

Base population

The subroutine DPBASE is used to simulate the base or founder

population. For males the base population consists of NBSIRE

individuals born in year zero and NYBPET individuals born in year one.

The bulls born in year zero is to be performance tested for GROWTH in

36

year zero and the bulls born in year one provide for the utilization of
the performance testing facility in year one. For females, first NHERD
herds with an average of NCPH lactating cows per herd are simulated.
The herd sizes are sampled from a Poisson distribution with a mean
equal to NCPH. The total number of females in a herd is usually about
twice the number of lactating cows due to the rearing of replacement
stock. Therefore, twice as many females as lactating cows are
simulated in each herd according to an age distribution of 30%, 20%,
25% and 25% percent of the females is born in year -2, -1, 0 and 1,
respectively. The cows born in or before year -2 would be lactating in
year 0, so that information for selection decisions on females is
available in year 1. The females born in year 1 makes up for the time
lag between the first matings and the birth of the first batch of
calves. All animals simulated in the base population are assumed to be
unrelated and sampled from a large population of females.

The true breeding value of an individual in the base population is
computed as:

a1 - chi [1]
where at is a 3 by 1 vector of true additive breeding values for the
ith animal, 21 is a vector of trivariate normal deviates with mean zero
and (co)variance matrix I3; and LG is a matrix satisfying LGL'G - VG'
The phenotypic values for the ith animal is then computed as:

pi - m + 8i + LEei [2]
where pi is the 3 by 1 vector of phenotypic values, m is the 3 by 1

vector of population means, e1 is a vector of trivariate normal

deviates with mean zero and (co)variance matrix I3, and LE is a matrix

37

satisfying LEL'E - VE. A11 random variables in the model are simulated
using IMSL STAT/LIBRARY subroutines (IMSL, 1987).

All traits are simulated simultaneously for all animals although
in reality a trait cannot be measured before certain events have
occurred. However, the phenotypic values are never used until these
events have occurred. For males, only GROWTH is possible and only at
the conclusion of the performance test. For females only YIELD and
TYPE are possible since these traits are sex limited with YIELD being
measured at the conclusion of first lactation. TYPE is measured on a
cow only if her sire is selected to be progeny tested for TYPE, and
only if the cow belongs to the subgroup of cows in the progeny group

that is recorded for TYPE.

Prediction of breeding values

After the base population is generated, and at the end of each
year, the breeding values of all living animals are predicted using
single trait selection index procedures (Hazel, 1943). The procedure
used is an approximation of a true multiple trait selection index
(Hazel, 1943), but was chosen due to its popularity in practice. In
fact the most appropriate procedure would have been the use of multiple
trait mixed linear models (Henderson, 1973). However, use of such
models would drastically increase the computational requirements of the
model. The mixed models, however, could easily be incorporated if
certain research projects would require this.

For males an index for growth (TC) is computed as:

Ic ' h6(Pc ' me) [3]

38

where, hg is the heritability for GROWTH, pc is the individuals
phenotype for growth and me is the population mean for GROWTH. The
breeding values of bulls for YIELD (IY) and TYPE (IT) are computed
based on progeny data as:

IY ‘ bYG‘Y ' my) [4]

IT - bT(xT - mT) [5]
where iY and iT are the average of the phenotypic values of the
progeny, mY and mT are the population means for YIELD and TYPE,
respectively. The coefficients bY and bT are computed as:

bY - 2nY/(nY + (4-h§)/h$> [61

bT - 2nT/(nT + (4-h%>/h%> [71
where, respectively, “Y and nT are the number of progeny recorded for
YIELD and TYPE, and h% and h% are the corresponding heritabilities.

A total merit index is computed for each bull by linearly weighing
the predicted breeding value for each trait by a partial economic
weight as:

IP - vGIG + vYIY + leT [8]
where VG, vY and VT are the partial economic weights for GROWTH, YIELD
and TYPE, respectively. If an index for a trait is missing the
corresponding term in [8] is dropped.

Females are evaluated for YIELD only. The index for YIELD (IY) in
females is computed as:

IY - h§<py - my) [91
where pY is the phenotypic value of YIELD in first lactation. Females

that not yet have finished a lactation are evaluated as:

39

where IYS and IYD are the predicted breeding values for YIELD of the
individual's sire and dam. The index IY is then transformed into
economic units by multiplying it by the economic weight for YIELD. This
provides for the possibility of avoiding selection for any trait, by
setting the corresponding partial economic weight equal to zero. If
all economic weights are set equal to zero, the model will perform

random matings.

Simulation of Yearly Breeding Events
Culling

Culling of animals is performed by subroutine DPCULL. Voluntary
culling is culling of low producing excess cows, while involuntary
culling is culling due to other factors such as disease or infertility.

A cow is culled due to involuntary reasons if a unit uniform
random variable is less than INVCR. Voluntary culling of cows is then
done on a within herd basis. The total number of lactating cows in
each herd is counted and compared to the herd size determined in
DPBASE. If there are excess cows, those with the lowest IY indexes
are culled.

No culling of young stock is simulated directly, but only progeny
surviving until breeding age are generated, as will be described in
section 3.5.2. Also males that survive the performance test for GROWTH
are not culled either. It is assumed, that semen is collected after the
performance test as an insurance against the possible loss of a bull
due to disease or accidents etc. However, no bull is allowed to be

used in breeding if he is more than seven years old.

40

Hating

Subroutine DPMAPR simulates mating and production, and is the core
of the model. Matings are of three kinds and will be described in the
sequel.

Test Matings. The number of young bulls that finish the
performance test for GROWTH in the current year is counted, and the
total number is called NYBAV. The number of young bulls to be progeny
tested is then computed as:

NSIPGT - NYBPET*PYBPGTY [11]
The variables NYBPET and PYBPGTY is defined in Table 3. If NSIPGT is
greater than NYBAV, all performance tested young bulls are also progeny
tested, thus no selection for GROWTH takes place. If NSIPGT is smaller
than NYBAV, then the NSIPGT bulls with the highest 10 indexes are
chosen for test matings. The cows to be used in test matings can be
chosen in several ways. Most populations use strategies such that a
bull is mated to a random sample of cows from the population. The
strategy chosen here is to use all first lactation cows (two year olds)
in the test matings. The bulls to be progeny tested are mated at
random to the first lactation cows using a uniform discrete random
variable.

The sex of offspring is determined by a unit uniform random
distribution with the sex ratio assumed to be .5. Only female
offspring of test matings that survives to breeding age are generated.
The offspring is determined to survive if a unit uniform random
variable is less than SRDTM (Defined in Table 3).

Contract Matings. The objective of contract matings is to produce

41

young bulls which are to be performance tested for GROWTH next year. In
dairy populations only young bulls which are to be pregeny tested for
milk yield are produced. This is the only type of mating in the model
where both male and female progeny are generated. The test capacity on
the performance test station is NYBPET. The bull sires to be used in
contract matings are selected as the NBSY sires with the highest IP
indexes, as long as the sire is seven years old or younger. The cows
for contract matings are selected among cows that are more than two
years old, i.e. second or later lactation, based strictly on ly. The
number of cows required for contract matings is computed as:

NCCM - NYBPET*NBDPET [12]
If NCCM is smaller than the number of cows available for contract
matings, all available cows is used in the contract matings. The
selected sires and dams are mated at random by use of a uniform
discrete random variable. Again sex of the offspring is determined by
a unit uniform distribution with a sex ratio of .5. Male offspring
survives to breeding age if a unit uniform random variable is less than
SRYB, and female offspring survives to breeding age if a unit uniform
random variable is less than SRDCTM. These survival rates, as defined
in Table 1, thus include survival from birth and to breeding age.

Matings to generate producing females. For these matings the top
NBCY sires are selected based on IP' Only sires seven years or younger
are used. All females of breeding age, not used in test matings or
contract matings, are mated to these sires. Again, the selected sires
and the cows are mated at random using a discrete uniform distribution

and only female offspring are generated. The survival rate employed

42
for female offspring of normal matings is SRDNM as defined in Table 3.

Control of inbreeding

Close inbreeding is avoided. As explained in the preceding
section groups of selected sires and dams are mated at random within
the group. However, if they happen to involve matings between father-
daughter, dam-son, or full- or half-sibs, the mating is avoided.
Instead the cow is assigned to the best bull in the group that meets
the above mentioned requirements against mating of close relatives. If
no such bull can be found in the group, the cow is culled. This
generally only happens in very small populations. After a mating is
accepted and the offspring survives to breeding age, the inbreeding
coefficient of the offspring is calculated using a modified version of

the algorithm given by Quaas (1976).

Generation of progeny records

The true breeding value of a surviving offspring is computed as:

so - .5(aS + a0) + CF*LM21 [13]
where, no is a 3 by 1 vector of true additive breeding values of the
offspring for the three traits; as and 8D are the corresponding vectors
of true additive breeding values of its sire and dam, respectively; LM
is a matrix satisfying LMLfi - .SVG, the (co)variance matrix of
Mendelian deviations in a non-inbreed population, and :1 is a vector of
trivariate normal deviates with zero means and (co)variance matrix I3.
The factor CF accounts for the inbreeding present in the parents and is
computed as:

CF - (1 - .5(FS + FD))‘5 [14]

43

where, FS and FD, respectively, is the inbreeding coefficient of the
sire and dam.

The vector of phenotypic values of an offspring is then computed
as:

pO - m + a0 + LEei' [15]

Progeny testing for type

The main selection pressure when selecting bulls is usually on
milk production. Therefore, only bulls with acceptable predicted
breeding values for YIELD are progeny tested for TYPE. Such schemes
are practiced in order to save costs by avoiding testing bulls that
would not be used anyway. Each year bulls are evaluated for YIELD on a
preliminary basis using the DPEVAL routine, The number of sires with
new progeny test results for YIELD is counted as NSPGTY. The number of
sires to be progeny tested for TYPE is then computed as:

NSPTTR - NSPGTY*PYBPGTT [16]
The NSPTTR bulls out of the NSPGTY that have the highest IY indexes in
the preliminary evaluation is then progeny tested for TYPE. The number
of progeny recorded for TYPE in each progeny group is computed as:

NPRT - NPROG*PCTT [17]
where, NPROG is the number of cows in the progeny group that were

recorded for YIELD.

Example
Description of example
As a genetic improvement program progresses, some buildup of

inbreeding is inevitable. Inbreeding reduces the genetic variance, the

44

very factor a genetic improvement program tries to exploit. Another
factor that reduces genetic variance is Bulmer effect (Bulmer, 1971),
which arises from the mating of selected parents. Chance plays an
important role, especially in small populations. Random fluctuation in
the genetic level due to chance is called genetic drift (Falconer,
1981). Such genetic drift induces a variance in the expected genetic
gain from a selection program. Inbreeding and genetic drift are
strongly influenced by the number of males and females used as parents
in each generation. The model was therefore used to study the effects
of cow population size and number of tested bulls used per year on the
genetic response, the buildup of inbreeding, reduction of genetic
variance and genetic drift.

The size of a cow population in the model is determined by the
number of herds (NHERD) and average herd size (NCPH). Tested bulls
that are used in the bull to bull and the bull to cow paths are
denoted, respectively, NBSY and NBCY (Table 3). A total of nine
situations were investigated. Three cow population sizes were selected
by setting (NHERD,NCPH) to (50,40), (25,40) and (25,20), which
correspond to cow population sizes of 2,000, 1,000 and 500 cows,
respectively. For each cow population size, three levels of bull use
were simulated by setting (NBSY,NBCY) to (1,2), (2,4) and (4,8) for

each of the three cow population sizes.

Results of example runs
Each of the nine situations were simulated 10 times and
comparisons were made, based on the data on animals born in year 25.

The following characteristics were computed for each replicate:

45

Genetic mean and standard deviation for GROWTH, YIELD and TYPE and
average inbreeding coefficient. Genetic drift was measured as the
standard deviation of the genetic means in year 25 calculated from the
10 replicates within a given situation.

The genetic means, genetic standard deviations and the average
inbreeding coefficients from each replicate, a total of 90
observations, were subjected to a two way analysis of variance to
determine the effect of cow population size, level of bull use and
interaction between the two effects. The significance levels obtained
are shown in Table 5. There were no effect of interaction for any of
the characteristics studied. Population size had a significant
influence on the genetic mean for YIELD and on the genetic standard
deviation for TYPE. Level of bull use had a significant influence on
the genetic mean in GROWTH, on the genetic standard deviation for YIELD
and TYPE, and on the average inbreeding coefficient.

Table 5.

Level of significance for effects of population size, bull use and
interaction between population size and bull use.

 

Characteristics Population size Bull use Interaction

 

 

 

Genetic mean

male GROW .1231 .0078 .8202
female YIELD .0001 .3262 .1984
female TYPE .2907 .7335 .4076

Genetic stand. dev.

GROWTH .2522 .1346 .8435
YIELD .6469 .0073 .2607
TYPE .0608 .0001 .9701

Avg. inbreeding .7010 .0001 .4549

 

46

The genetic means in year 25 for GROWTH, YIELD and TYPE are shown
in Table 6. All situations showed a considerable progress for all
three traits. There were no differences among population sizes in
genetic progress made in GROWTH. However, the intermediate level of
bull use of (2,4) gave a higher response in GROWTH than that of (1,2)
or (4,8) bull sires and cow sires per year. This was in contrast to
standard theory for deterministic models that would predict the highest
response for models with the highest selection intensity, i.e. (1,2) in
this comparison. The same tendency, although insignificant, can be
seen for YIELD. The reason for the highest response at the
intermediate level of bull-use is probably due to a greater risk in
relying on very few bulls per year in the (1,2) case. On the other

hand, if (4,8) bulls are used, the selection intensity becomes too low.

 

 

 

 

 

 

Table 6.
Genetic level in year 25, averaged over 10 replicates.
Situation Male Female
Cow-population size Bull use
NHERD. NCPH NBSYL,NBCY GROWTH YIELD TYPE

50,40 1,2 151 62.8 1.02
50,40 2,4 160 64.3 1.02
50,40 4,8 159 60.8 .93
25,40 1,2 138 52.3 .82
25,40 2,4 158 57.7 .91
25,40 4,8 147 56.2 .98
25,20 1,2 134 51.6 .94
25,20 2,4 156 49.5 .94
25,20 4 8 148 48.0 .80

 

For the genetic progress in YIELD, population size was a highly

significant factor, such that the genetic progress obtained increased

47

with increasing population size. The number of young bulls progeny
tested per year was the same in all situations. Decreasing the
population size meant that the number of cows available for test
matings also decreased, leading to a reduction of the accuracy in which
breeding values of the bulls were predicted. Lower accuracy means more
mistakes in the selection decisions, with the result that genetic
progress is reduced.

None of the factors studied had a significant effect on the
genetic progress in TYPE.

The genetic standard deviations in year 25, averaged over the 10
replicates are shown in Table 7. Level of bull-use had a significant
effect on the genetic variation in YIELD and TYPE such that use of
fewer bulls reduced the genetic standard deviation with up to 15
percent of the genetic standard deviation in the base population. Most
of the reduction is due to Bulmer effect, since the inbreeding
accumulated only would reduce the genetic standard deviation with a
fraction (l-F)'5, where F is the average inbreeding coefficient.

The average inbreeding in year 25 is also shown in Table 7.
Population size had no effect on the accumulated inbreeding, but
inbreeding increased markedly as fewer bulls were used per year as bull
sires and cow sires.

Table 8 shows the estimates of the variation due to genetic drift. The
number of replicates simulated per situation was too low to obtain
accurate estimates of this variation. However, results showed that
there were considerable genetic drift in all the situations

investigated. This means that the genetic progress made in a

48

particular improvement program can deviate substantially from the

expected progress, due to random genetic drift.

Table 7.
Genetic standard deviations in year 25, averaged over 10 replicates.

 

Situation Genetic SD

 

 

 

 

 

 

 

 

 

Avg.
Cow-population size Bull use Inbreeding
NHERD- NCPH NBSY, NBCY GROWTH YIELD TYPE
50,40 1,2 47.1 15.3 .58 .074
50,40 2,4 47.7 16.1 .62 .063
50,40 4,8 48.4 16.0 .63 .040
25,40 1,2 47.1 15.5 .55 .075
25,40 2,4 49.1 15.3 .60 .059
25,40 4,8 48.3 16.2 .60 .043
25,20 1,2 46.3 15.1 .56 .078
25,20 2,4 46.9 15.7 .60 .066
25,20 4,8 47.8 15.9 .61 .042
Base population 53.0 17.5 .63 ---
Table 8.
Total genetic drift accumulated in year 25. SD on 10 replicates.
Situation SD of genetic mean
Cow-population size Bull use
NHERD, NCPH NBSYllNBCY GROWTH YIELD TYPE
50,40 1.2 23.0 6.14 .33
50,40 2,4 18.4 7.63 .24
50,40 4,8 15.5 4.14 .13
25,40 1,2 14.0 5.46 .14
25,40 2,4 19.0 5.51 .28
25,40 4,8 23.1 5.96 .28
25,20 1,2 16.7 5.32 .25
25,20 2,4 15.8 7.37 .38
25,20 4 8 11.9 2.80 .23

 

CHAPTER 3

Estimation of Genetic Parameters Using Sampled Data From

Populations Undergoing Selection

49

50

Introduction

Genetic parameters of economically important traits in livestock
populations are usually estimated from field data. Such data often
originates from populations that have been subjected to intense
selection for one or more traits. The selection over time alters
genetic (co)variances due to accumulation of inbreeding and gametic
phase disequilibrium (Bulmer, 1971, Falconer, 1981). However, genetic
parameters of the base population prior to selection must be known in
order to draw general inferences about the population in terms of
genetic and phenotypic relationships among traits, to predict gains
from breeding programs, and to predict breeding values of animals.

Henderson (1975) and Goffinet (1983) argued that in prediction of
breeding values, all data used in the selection decisions that led to
the current populations must be included in analysis in order to
alleviate selection bias.

The problem of genetic parameter estimation under a selection
model was considered by Schaeffer (1987). He showed that for certain
translation invariant selection rules the usual REML estimation is not
biased by selection. However, in most practical situations the
selection rule is not translation invariant, i.e. selection is across
fixed effects in the model. Sorensen and Kennedy (1984) showed that
minimum variance quadratic unbiased estimation (MIVQUE) of variance
components was not biased by selection from an animal model with a
complete relationship matrix. A practical problem with MIVQUE,
however, is it's dependency on the prior values assumed for iteration.

Most livestock populations undergo selection for more than one

51

trait simultaneously. An example is the simultaneous selection for
beef and milk production traits in many European cattle breeds.
However, multitrait selection has been practiced also in single purpose
cattle populations. Therefore, data on multiple traits should be
included in simultaneous analyses.

In many practical situations only more recent data from the
current population is available, and thus raise the question of
applicability of analysis results to the unselected population. A
population undergoing selection for several traits can be thought of as
existing in a three dimensional space defined by time, animals, and the
traits under selection. Data from a population can be stratified
according to one or a combination of these dimensions. Common ways of
sampling have been to analyze only data from a certain time period. For
example, analyzing data on type traits on Holstein cows who calved
between 1982 and 1988 in Michigan and Wisconsin can be thought of as
sampling according to a combination of time, space and traits. Using
only sample data could be due to limited data source in some cases.
However, if a large volume of data is available, sampling of data can
be repeated and estimates from different samples can be averaged and
can be used to compute SE of estimates.

For most estimation problems in animal breeding the model of
choice would be a multiple trait animal model. However, use of such
models to estimate genetic parameters can be impossible due to
computational difficulties or the animal model might not be feasible
due to lack of pedigree information. In such cases simplified

operational models, usually sire models, are used.

52

Another common concern has been the use of data on progeny of
highly selected sires, since the variance among those sires is smaller
than among unselected sires. Van Vleck (1985) suggested the inclusion
of these sires but to treat the effect of them as fixed in the model.
The advantage would be a more precise estimation of other fixed effects
in the model and more degrees of freedom in the estimation of residual
variances.

The objective of this study was to investigate different methods
of sampling data from populations undergoing selection in estimating
genetic parameters and to investigate the efficiency of different

operational models.

Materials and Methods
Simulation of Data

Data was simulated for a small dual purpose population, selecting
for both beef and milkfat, and for a larger dairy population selecting
for milkfat only. A traditional AI breeding scheme was simulated for
both populations, each for a 15 y period. A detailed description of
the simulation model was given in Chapter 2 so only a brief description
of the simulated populations is given below.

The simulation model was designed to generate data that resembled
the data structure found in real cattle populations. Basic parameters
describing the simulated populations are given in Table 9. The traits
simulated were assumed to be affected by a large number of loci, each
with small effects (Infinitesimal model). Only additive genetic

effects were considered and all loci were assumed to be unlinked. The

53

base population were in Hardy-Weinberg equilibrium. For a dual purpose
population, the traits simulated were growth measured on young bulls
sampled as potential future AI sires and first lactation milkfat
production on cows in commercial herds. The genetic parameters assumed
for the unselected base populations were heritabilities of .25 and .50
for milkfat production and growth, respectively, and corresponding
phenotypic standard deviations were 35 kg and 75 g. The genetic
correlation between milkfat production and growth was assumed to be .20
and the relative economic importance of the two traits were 8:1. The
performance test for growth of future AI bulls at a central test
station was concluded before one year of age so that selection on
growth were possible before the bulls were used in breeding. The final
selection of bulls was based on a total merit index weighing each trait
with the corresponding economic weight. For dairy populations only
milkfat production in commercial herds was simulated. The populations
were simulated over a 15 y time horizon. The simulation of both the
dual purpose and the dairy populations were replicated 15 times.

Since data were simulated, the breeding value and residual
deviation was known for each animal. These values were used to obtain
direct estimates of genetic and residual variance. The animals were
grouped according to year of birth and the mean and variance of true
breeding values and residual deviations were computed for each year of
birth. The variances for each year of birth were used to compute true
heritabilities for each year, and used as reference for the values to

be estimated later.

54

 

 

 

Table 9.
Parameters used in simulation of dual purpose and dairy populations.
Dual Purpose Dairy

No. of years to be simulated 15 15
No. of traits 2 1
No. of sires in base population 25 25
Performance test capacity for beef 25 ~-—
No. of bull-dams selected/year 75 36
No. of bull-sires selected/year 2 2
No. of cow-sires selected/year 2 2
No. of herds 4 20
No. of cows 200 1000
No. of young bulls tested for milkfat/yr 4 12
Involuntary culling rate/cow/year .20 .20
Survival rate of daughters from test matings .75 .75
Survival rate of daughters from contract matings .85 .85
Survival rate of daughters from normal matings .75 .75
Survival rate of young bulls < 1 yr .85 .85

 

Sampling of Data for Estimation

In this study, only data sampling in term of time was considered.
The 15 y of data were divided into three consecutive 5 y periods. A
total of three schemes of sampling data over time were compared:

Scheme 1: All data over time and all relationships between animals
were used;

Scheme 2: Only data in the last 5 y was used, but relationships
were traced all the way back to the base population;

Scheme 3: Only data from the last 5 y were used and relationships

were only traced for the last 5 y, also.

Models
Simulated data were analyzed for each of the three sampling
schemes according to the following three models. For dairy

populations, of course all matrices pertaining to growth were deleted.

55

Yu 0 xx hr! 0 Kill ‘111 ex

5'14 0 x“ bM 0 2M2 81112 ‘ M

7M 0 x” bit 0 xs ‘Mf 0 2M3 8M3 ‘M
l 3 l

where ya and yM were vectors of observations on growth and milkfat
production, respectively; bG and bM were, respectively, vectors of
fixed effects of management groups for growth and milkfat production
with XG and XM the corresponding incidence matrices.

Model [1] was a full animal model, where 3G1 and 8M1 were random
vectors of additive breeding values for growth and milkfat,
respectively, for all animals either with or without own performance
record, and 2G1 and 2M1 were the corresponding incidence matrices.

Model [2], was a combined animal-sire model, where ‘62 was a
random vector of additive breeding values for growth for all males, 3M2
was a random vector of additive sire effects for milkfat, and 2G2 and
2M2 were the corresponding incidence matrices. This model was
practical, since growth was measured on bulls during the performance
test before being used in Al and milkfat was measured on female
offspring of these bulls. The computational requirement for Model [2]

is much less than that for Model [1].

56

Model [3] was a modification of Model [2]. The submodel for growth
was unchanged but in the submodel for milkfat st was a vector of fixed
sire effects on second crop daughters, 3M3 was a vector of random sire
effects on first crop daughters, XS and 2M3 were the corresponding
incidence matrices. A sire that had both first and second crops of
daughters in data would thus have two effects in the model. The fixed
sire effects were included in an attempt to control selection bias, but
still use records of daughters of selected sires to obtain better
estimates of the fixed effects and the residual variance in the model.

In the absence of selection, assumptions first moments of random

vectors in the models were

YM beM
and
E yG - chG for Model [3].
YM beM + xsst

The expectation of all other random vectors in the models were
zero. The second moments of these random vectors in the models were

assumed to be:

2
V 8G1 ' ”0,3 aGM,a * A

2
8M1 aGM,a aM,a

57

V 8(:2 ' ”G,e (“cx,a)/a * Am
2
8M2 (UGM,a)/4 (0M,a)/4
v e - 02 o * I
G G,e
2
6M 0 0M,e
and
V e - 02 0 * I
G G,e
2 2
(M 0 014,8 + (30M,a)/4

where 0G,a' 0M,a were the additive genetic variances for growth and
milkfat production. respectively and aGM,a is the additive genetic
covariance between the two traits, ”G,e and 0M,e were the environmental
variances for growth and milkfat, respectively, and * denotes direct
product. All residual covariances were assumed to be zero since all
males were measured for growth only and females for milkfat only. In
Model [1], the relationship matrix A considered all known sires and

dams, but for Model [2] and [3], Am considered only sires and maternal

grandsires.

Estimation Algorithm

Heritabilities, genetic and phenotypic correlations and phenotypic
SD were estimated using a multivariate restricted maximum likelihood
(REML) algorithm. The multivariate restricted likelihood function were

maximized using derivative free methods as described by Meyer (1989).

58

Let the model for t traits be:

y - Xb + Zu + e [4]
where y is a vector of observation vectors for all traits; b is a
vector of fixed effects for all traits; u is a vector of random
additive genetic effects of the same animals for the t traits; and e is
a vector of random residuals corresponding to y. X and Z are known
design matrices corresponding to, respectively, b and u; since V(u) -
G and V(l) - R, V(y) - 262' + R - V.

Assuming normality, the log likelihood is:

L - c -.5[1n|VI + inle'a'1x*| + (y-X8)'V'1(y-Xb)] [5]
where c is a constant and X* is the largest submatrix of X with full
column rank. Following the notation of Meyer (1989) and dropping c, an
alternative form of [5] is:

-2L - 1nIRI + lanl + 1n|c| + y'Py [6]
where C is the largest full rank submatrix of the coefficient matrix of
the mixed model equations from [4] and

P-V'l-V'1X*(X*'V'1X*)'1X*'V°1.

The form of the likelihood function given in [6] was minimized using a
quasi-Newton method given by Dennis et a1. (1983) and using code from
IMSL (1987). This method requires many evaluations of [6] in order to
locate its minimum. The four elements in [6] were computed in each
evaluation following the strategy outlined by Meyer (1989), which
involves, in each iteration setting up the mixed model equations from
[4] in tableau form followed by the elimination of all equations by

absorption or Gaus-elimination.

59

Information accumulated on the estimation algorithm

Since use of multiple trait derivative free REML is relatively
new, is was considered useful to accumulate information on the
convergence pattern of the algorithm. For each model run the total
number of rounds to convergence and the number of rounds until a
specified degree of convergence was obtained. The degree of convergence

was computed by [7] which is modified from Misztal et a1 (1988):

 

H le(“*1)-x||
Ctn - . {7]
leII
where x(n+1) was the vector containing the intermediate solution from

the n'th evaluation and x was the vector containing the final solution
obtained at convergence. The absolute value of 10310 CE“) is
approximately the number of significant digits in x. The convergence
criteria was chosen such that the estimates was accurate to
approximately 5 significant digits. Expression [7] was then used to
obtain the number of rounds the iterated when estimates was accurate to

l, 2, 3, or 4 significant digits.

Results and Discussion

Biases in Genetic Parameter Estimates Due to Data Sampling

Table 10 shows the average number of bulls and cows included in
analysis. Estimates of the genetic parameters for the dual purpose
populations are shown in Table 11. For milkfat all heritability
estimates were unbiased, regardless of model, if all data and all
relationships were included in the analysis. However, SE of the
heritability estimate increased from .06 in the full animal model to

.12 in the combined animal-sire model and further to .15 if sire

60

effects on second crop daughters were treated as fixed. If only recent
data, were used, but relationships were traced all the way back to the

base population, estimates from the full animal model were still

 

 

 

unbiased.

Table 10.

No. of animals included in analysis, averaged over 15 replicates.
Dual Purpose Dairy

Years included 1-15 11-15 1-15 11-15

Bulls 420 147 198 70

Cows 2198 741 10588 3519

 

 

 

 

 

 

Table 11.
Average estimates of genetic parameters in dual purpose populations.
Milkfat Growth
Sampling
Model scheme h2 SD h2 SD rA SD
(True parameters .25 .50 .20 )
[1] 1 .25 .06 .64b .17 .26 .21
2 .25 .09 .62 .22 .06b .28
3 .20a .10 .50 .24 .04 .34
[2] 1 .25 .12 .78b .12 .32 .32
2 .21 .17 .48 .26 .34 .41
3 .21 .16 _ .60 .31 .20 .42
[3] 1 .27 .15 .77b .14 .25 .38
2 .36b .20 .56 .28 -.11b .24
3 .36b .22 .55 .31 .16 .52

 

8Significant at 10% a-level.
Significant at 5% a-level.

If only recent data and recent relationships were used there was a
tendency (P<.10) for both the full animal model and the combined

animalosire model to yield estimates that were biased downwards.

61

However, this tendency was not significant for the combined animal size
due to the large variance among estimates. Use of recent data and
relationships only in the combined animal-sire model with sire effects
on second crop daughters treated as fixed surprisingly yielded an
upward bias in the heritability estimate for milkfat. This finding was
the main reason for also simulating the larger single purpose dairy
population in order to check if this result could be repeated in a
larger population. Results are shown in Table 12. In all cases for
dairy population, heritability estimates were biased downwards, even if
all data were included in the analysis. Treating sire effects of second
crop daughters as fixed did not alleviate any bias due to selection.

All estimates of heritability of growth were biased upwards when
all data and all relationships were included in the analysis. Again
this was an unexpected result, and we lack a reasonable explanation.

On the other hand the estimates from analyses using recent data only
were all essentially unbiased.

The genetic correlations estimated from all data were all unbiased
regardless of models used, but were associated with large SE, therefore
no definitive trend could be observed. When only recent data were
included in the analysis, SE were even greater and in fact there were
not enough information in the simulated data to estimate the

correlation with reasonable precision.

62

 

 

 

Table 12.
Average estimate of heritability of milkfat in dairy populations.
Sampling
Model Scheme Heritability SD
(True parameter .25 )
[2] 1 .20* .06
2 .20* .08
3 .19* .08
[3] 1 .22* .07
2 .20* .08
3 .20* .08

 

Changes in Underlying Genetic Parameters Due to Selection

The additive genetic variance would decrease over time due to
buildup of inbreeding and gametic phase disequilibrium or Bulmer effect
caused by directional selection (Bulmer, 1971, Falconer, 1981).
Inbreeding was negligible in our simulated breeding schemes so only
Bulmer effect needs to be considered. In simulated populations,
additive genetic variance can be computed from the true breeding values
and residual variance from the residual deviations of each individual.
Average heritability, based on true breeding values and residual
deviations, were plotted as a function of time in Figure 1 for dual
purpose populations and in Figure 2 for dairy populations. In both
cases a considerable decrease in heritability was observed. The
magnitude of such decreases is dependent on the selection intensity
among parents and the mating structure.

Estimated parameters were compared to the expected or true
underlying parameters using heritability estimates for milkfat. Use of

recent data only gave estimates which essentially reflect the

63

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64

 

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65

population of the same time period, since the estimate obtained is an
unbiased estimate of the heritability in the population of the same
period. Even the use of a relationships matrix which tied recent
animals to the original base population, failed to produce unbiased

estimates of the base population parameters.

Convergence Pattern of the Estimation Algorithm

Table 13 shows the average number of iteration rounds needed to
obtain a certain number of significant digits in the estimates of the
genetic parameters. The analysis on the dual purpose populations with
two traits in the analysis required considerable more iterations than
the single trait analysis on the dairy populations. Changing the model
from a full animal model to a combined animal-sire model also increased
the number of iterations. Thus, although the amount of computation per
round is less for the combined model the total amount of computation
for a given analysis was not reduced significantly. Changing the model
such that sire effects of second crop daughters were treated as fixed
increased the number of iterations in the dual purpose populations, but
not in the dairy populations. By comparing the number of iterations in
Table 13 and SE of estimates in Table 11 and 12 it appears that the
number of iterations is inversely related to SE of the estimates. In
other words, the more information available on the set of parameters

the less rounds of iteration is necessary.

66

Table 13.
Average no. of rounds to obtain a certain number of significant digits
in estimates of genetic parameters.

 

No. of significant digits
Sampling
Model scheme 1 2 3 4 5

 

 

 

 

 

 

Dual purpose populations

 

1 1 55 78 98 118 125
2 74 92 117 121 121
3 84 100 117 128 128
2 1 73 99 116 119 119
2 112 144 196 221 239
3 114 172 219 236 293
3 1 72 99 113 114 114
2 127 158 206 253 279
3 175 200 230 255 273
Dairy populations

9 16 24 26 26
2 12 21 28 31 31
3 12 21 28 31 31
3 1 9 17 24 25 26
2 12 23 28 29 29
3 11 22 28 29 29

Conclusions

Selecting parents of following generations would change the
variance in the progeny generation from what could be expected in a
random mating population. Sorensen and Kennedy (1984) showed that for
an infinitesimal model with selection within fixed effects, that a
MIVQUE estimator using models that took all relationships into account
yielded unbiased estimates of base population parameters. Results from
this investigation using a REML estimator confirms this result, even
though selection in this case resembled real populations with selection

across fixed effects. However, this conclusion might be dependent of

67

the selection intensities applied, a factor that was kept constant in
the present investigation.

The combined animal-sire models also seemed to provide unbiased
estimates of base population heritability for milkfat in the dual-
purpose situations if all data were included in the analysis. The
inclusion of a trait recorded on the bulls themselves might be the
reason for this observation. The single trait sire models for the
dairy populations were unable to yield unbiased estimates of base
population parameters in any of the cases.

If only recent data, but a complete relationship matrix were
incorporated in the model, the estimates of heritability for milkfat
were still unbiased, albeit with a greater SE.

Using recent data only and recent relationships only is
essentially equivalent to redefining the base population to be the
selected population. The estimates obtained were unbiased estimates of
the genetic parameters in this redefined base population. Sorensen and
Kennedy (1984) discussed methods of obtaining the genetic parameters in
the current selected population. However, such an approach does not
seem useful in practice, since it is dependent on the selection
intensity among the ancestors to the current generation, the mating
structure used, and the amount of inbreeding present in the current
population. If these factors can be quantified, a more practical
approach might be to develop correction factors to adjust the estimate
results for biases due to selection. This subject seems to warrant
further research. Treating sire effects on second crop daughters as

fixed did not reduce selection bias in the populations investigated.

68

The reason for this might be that a large proportion of the populations
was used for testing so that the number of second crop daughters was

relatively low.

CHAPTER 4

Performance Testing of Dual Purpose Bulls for Beef
Traits. Genetic Parameters for Growth, Feed Intake,

Appetite and Carcass Composition

69

70

Introduction

Genetic parameters for growth traits of young bulls are well
documented, e.g., Andersen, 1977, and Hanset et al., 1987. However
only few estimates of genetic parameters exist for feed intake,
appetite and carcass composition due to the high costs associated with
measuring these traits. Also the genetics of the partial energy
requirements of young bulls for maintenance and growth are not well
understood.

In most European countries milk and beef are, to a large extent,
produced from dual purpose cattle. To facilitate selection for beef
traits most countries have established test stations, where future AI
bulls are tested mostly for growth traits based on own performance.

Due to the relatively small number of animals tested it is possible to
measure feed intake without excessive cost. This may facilitate
selection for feed conversion ratio and appetite expressed as average
daily feed intake. Appetite may be an important trait since energy and
protein intake might be a major limiting factor of production in the
lactating cow. (Andersen, 1989, Holmes, 1988, Korver, 1988). The total
utility of measuring feed intake during the performance test depends on
the genetic correlation between feed intake of the growing bull and the
overall merit in the production system.

An experiment was carried out to estimate genetic parameters of
growth, feed intake, feed conversion ratio, appetite and carcass
composition. Furthermore the experiment was designed such that partial
energy requirements for growth and maintenance could be estimated.

This paper presents the experimental plan and genetic parameters for

71

growth, feed intake, feed conversion ratio, appetite and carcass
composition of young bulls. In subsequent Chapters we examined
alternative ways of describing energy requirements and estimate their
relations to the aforementioned production traits and the milk yield of

female halfsibs.

Materials and Methods

Animals

The experiment was conducted in Denmark at the experiment station
”EGTVED" under supervision of the National Institute of Animal Science.
From 1978 to 1982, it was planned to purchase 144 bull calves each year
from commercial dairy herds. In each of the first three years the
calves were the progeny of six sires of Holstein Friesian (HF)
descent. In 1981 they were the progeny of three HF and three Brown
Swiss (BS) sires, and in 1982 the calves were progeny of seven BS
sires. Very little variation in the proportion of HF or BS genes
existed among the bulls used in the experiment. The effect of
proportion of HF or BS genes, therefore, could not be studied. Sires
were used in one year only. Therefore, over the 5 yrs a total of 31
sires were used. All the sires were young bulls sampled either in
Denmark or in North America. Very few genetic relationships existed

among the bulls, and they were assumed unrelated in all analyses.

Feeding
All calves were brought to the test station before three weeks of
age and started on test at an age of 28 days. In the first production

period (Pl) from 28 d to a live weight (LW) of 200 kg, all calves were

72

fed restricted amounts according to live weight, such that energy
intake was about 75% of expected ad libitum intake for animals of
similar weight. In the second production period (P2) from 200 kg
liveweight until slaughter, the calves were randomly placed on four
different treatments. Treatment 1 was concentrates fed ad libitum from
automatic feed hoppers. Treatments 2, 3 and 4 were all rations based
on concentrates and roughages fed ad libitum, which were composed such
that 75%, 50% and 25% of expected energy intake were from the
concentrate component, respectively. In 1978 and 1979 concentrates
were fed in fixed amounts based on weight, and roughages were fed ad
libitum. In the last 3 yrs roughages and concentrates were fed as
total mixed rations. The roughage component in the diet was changed
every year as indicated in Table 14. Also shown in Table 14 is the
energy and dry matter content of the major feedstuffs used. A detailed
description of procedures used in feeding and handling of the animals
was given by Bailey et a1. (1985), who used data from the first two
years to estimate effects of treatment and slaughter weight on growth,
feed efficiency and carcass composition.

The animals also were randomly assigned to three slaughter weight
groups. Target slaughter weights were 340, 470 and 600 kg liveweight.
Thus it was planned to have two calves in each sire by treatment by

slaughter weight subclass.

73

 

Table 14.

Energy Content (Mj) and Dry Matter Content of Diets Used.

Year Treatmenté HILLS QMZkg

1978 l 6.07 .862
2 2.71 .420
3 1.74 .293
4 1.29 .232

1979 1 6.08 .863
2 3.65 .569
3 2.60 .444
4 2.03 .374

1980 l 6.14 .864
2 5.70 .837
3 5.19 .836
4 4.76 .836

1981 l 6.24 .861
2 5.64 .816
3 4.76 .824
4 4.76 .829

1982 l 6.32 .871
2 5.05 .895
3 4.99 .804
4 4.20 .824

 

8Treatment 1, 2, 3 and 4 were respectively, 100%, 75%, 50% and 25% of
expected energy intake from concentrate.
Recordings

Calves were weighed at the first day of test and then every 14 d
(i.e., at ages 28, 42, 56 d and so on). Feed intake was recorded daily
and summed over the 2 week intervals between weighings. In production
period 2, all calves were fed ad libitum and the animals were fed three
to four times daily to ensure that they had feed available at all

times. Weighbacks were performed twice weekly. The energy content of

74

the roughages used was determined both in vitro via chemical
composition, and using in vivo experiments with sheep reared close to
the maintenance level in order to obtain the digestibility of the diet.
Energy intake was expressed as net energy intake computed according to
the Danish feed evaluation system based on Scandinavian feed units
(SFU) (Moller et al., 1983). That system expresses feed energy content
as net energy for lactation at a certain level of production. Another
measure of energy intake is metabolizable energy (ME). Since the
Danish net energy system assumes a nearly constant net energy
efficiency the net energy intake can be converted to ME by ME - 4.16 +
1.17 NE which gave an R2 of .96 based on information given by Van de
Honing and Alderman, (1988). Since this simple linear relationship
exists the genetic parameters to be estimated later are invariant to
choice of feed evaluation system. Live weight and carcass weight were
recorded at slaughter. Carcasses were graded for conformation and fat
cover using a scale from one to 10 with 10 being the best for
conformation, and a scale from one to five for fat cover with three the
optimum grade and a grade of 4 or 5 indicates too fat animals. One
side of the carcass was dissected into lean, fat and bone following
anatomic lines at the Danish Meat Research Institute. Samples were
taken to determine nitrogen and fat content of the lean meat and for
determining palatability using test panels. However, only the
dissection data will be used in this report. Procedures used for
dissection of carcasses were described by Andersen et a1. (1977). A
total of 650 bulls completed the experiment, and their distribution

over years and treatments is shown in Table 15. The number of bulls

75

per sire by treatment by slaughter weight subclass were 2 with a few

exceptions of 1 due to death.

 

 

 

 

Table 15.
Distribution of Observations on Years and Treatments.

Treatmenta
Year 1 2 3 4 Total
1978 28 34 35 31 128
1979 34 30 33 35 132
1980 31 33 36 30 130
1981 46 46 16 14 122
1982 35 33 35 35 138
Total 174 176 155 145 650

 

8Treatment 1, 2, 3 and 4 were respectively, 100%, 75%, 50% and 25% of
expected energy intake from concentrate.
Definition of Traits
Based on weights at start and end of each production period, total
feed intake in each production period and carcass composition, the
following 17 traits were defined as below:

In production period 1, P1(28 d to 200 kg liveweight):

WGT28 Weight in kg at 28 d.

DC Average daily gain in g.

EI Total energy intake in mJ.

FCR Feed conversion ratio, EI/(Total weight gain),
calculated using the Danish feed evaluation system.

DEI Daily energy intake (appetite), EI/(Days on test).

DMI Total dry matter intake in kg.

Similar traits except WGT28 were defined in production period 2
from 200 kg LW to slaughter. In all analysis measurements in different

production periods were treated as different traits. In tables a

76

postscript of P1 or P2 is used where necessary to indicate production
period.

At slaughter:

DRSPCT Dressing percentage.

CARGRD Carcass grade. Scale 1-10 with 10 being the best
grade.

FATGRD Fat grade. Scale 1-5 with 3 being the optimum value.

LEANPCT Percent lean meat in carcass.

FATPCT Percent fat in carcass.

EICG (Total energy intake)/(Total carcass gain).

In computing total carcass gain it was assumed that the dressing
percentage of 28 d of age was 50, following definitions given by

Andersen (1977).

Estimation of genetic parameters

The 17 traits defined in the preceding paragraph were analyzed
together with traits describing energy requirements to be reported in a
companion paper. All traits were analyzed simultaneously by a multiple
trait model with equal design matrices for each trait. The model for
each trait was:

yijklm - ti + gj + (tg)ij + pk + Skl + eijklm [1]
where: yijklm is a record for the mth bull of year-treatment subclass i
slaughter weight group j and the progeny of sire l of breed k; ti is
the fixed effect of the 1th year-treatment with i-l,2...20; gj is the
fixed effect of the jth slaughter weight with j-l,2,3; (t8)ij is the
interaction between 1th year-treatment and the jth slaughter weight; pk
is the fixed effect of the kth breed with k-l,2; Skl is the random
effect of the 1th sire within the kth breed, where the total number of
sires were 31; and eijkl is the random residual.

Preliminary single trait analysis based on a model including all

77

factors in [l] and all other two-way interactions were conducted.
Since the results indicated that other interactions were insignificant,
they were dropped from the model.

In matrix notation the multitrait model for all traits
simultaneously was:

y - (I*X)b + (I*Z)u + e [2]
where y was a vector of observations for all traits, b a vector of
fixed effects, u a vector of random sire effects and e a vector of
random residuals. X and Z were incidence matrices corresponding
respectively to b and u; I was an identity matrix of order equal to the
total number of traits in the analysis
Assumptions on expectations and variances were:

E(y) - (I*X)b, E(u)-0, E(e)-O;

V(y) - G*(ZZ') + R*In. V(u) - G*Iq; and V(e) - R*In;

where G and R were sire and residual (co)variance matrices, I and In

q
are identity matrices, respectively, of order equal to the number of
sires, q-3l, and the number of observations, n-650 and "*" denotes the
direct product operator. All sires were assumed unrelated. Since
relationships existed among very few sires, taking additive genetic
relationships into account would therefore be inconsequential to the
results reported. The elements of G and R were estimated by use of
restricted maximum likelihood (REML) in the multiple trait model
including all traits simultaneously. An expectation maximization (EM)
algorithm augmented with canonical and Householder transformations, as

described by Jensen and Mao (1988) was used. No standard errors on

genetic parameters are given, since no such statistics have yet been

78

developed for estimates from multitrait models.

Results and Discussion
Interactions

Preliminary single trait analysis were used to check for all two
way interactions. Components of variance due to sire by treatment and
sire by slaughter weight group interactions were estimated using a
single trait REML algorithm. In all cases estimates of zero were
obtained. Estimation of variance components usually requires
considerable amounts of data in order to obtain estimates with
reasonable accuracy. To investigate how small interaction components
could be detected, data were simulated using exactly the same design as
the real data. Magnitude of components of variance due to sire and the
two interaction components were varied. Components as small as one
percent of total phenotypic variance could be detected. In conclusion,
therefore, no interaction existed between sire and treatment or sire
and slaughter weight group in this experiment.

Andersen et a1. (1981) expressed concerns about selecting bulls
tested on concentrate diets when roughage is the main component in the
diet of milk producing daughters of these bulls. Performance testing
systems were therefore changed in several European countries from
feeding mainly concentrates to feeding diets containing a large
proportion of roughages. The lack of evidence in sire by treatment

interaction from this study suggested such a change is not necessary.

Mean, Phenotypic Standard Deviation and Heritability

The means and phenotypic standard deviations in Table 16 show good

79

accordance with results from the literature, e.g., Andersen, 1977.
Heritability estimates (Table 16) for average daily gain were .354 and
.373 for production period 1 and 2, respectively. These estimates were
somewhat lower than usually found for average daily gain from test
station data. However several recent estimates were in the same range:
Andersen et a1. (1987) found estimates of .392, Hanset (1987) found

.44 and Oldenbroek et al. gave estimates of .36 for veal calves and .59
for young bulls, both estimates from data on Dutch Red and White
cattle. Dijkstra et a1. (1987) gave estimates of .12 and .14 for veal
calves and young bulls respectively in the Dutch Holstein breed.

The heritability estimates for total energy intake, feed
conversion ratio, appetite and total dry matter intake were lower than
the estimates for daily gain in the corresponding production periods,
except for appetite in production period 2. Again the results were
well in line with the recent literature estimates cited above.

For dressing percentage and carcass grading the heritability
estimates were in the range from .31 to .39 which were slightly lower
than those in the literature cited earlier. For percent lean and
percent fat in the carcass, very high heritability estimates of .706
and .894, respectively were obtained, in comparison to estimates at .52

and .44 found by Andersen (1977).

80

Table 16.
Mean, Heritability and Phenotypic Standard Deviation for Production
Traits.

 

Phenotypic standard

 

Traita Mean Heritability deviation
WGT28 48.7 .394 6.58
DGPl 893 .354 63.5
EIPl 2932 .313 225
FCRPl 19.4 .195 1.35
DEIPl 17.2 .246 .711
DMIPl 393 .259 30.4
DGP2 1225 .373 133.0
EIP2 12231 .266 1116
FCRP2 42.3 .267 4.51
DEIP2 50.8 .412 2.48
DMIP2 1971 .264 214
DRSPCT 53.0 .333 1.45
CARGRD 6.08 .386 .961
FATGRD 2.87 .310 .354
LEANPCT 67.5 .706 1.985
FATPCT 15.3 .894 2.092
EICG 9.28 .315 .790

 

8See text in Materials and Methods for definition of traits.
Genetic and Phenotypic Correlations Among Traits Measured in Production
Period 1

As shown in Table 17, weight at 28 d was positively correlated to
daily gain but negatively to total energy intake and total dry matter
intake both on the phenotypic and the genetic level. The reason for
such negative relations was that a high starting weight leads to a
lower need for weight gain in order to reach 200 kg live weight. Also
it seems logical that the correlation between weight at 28 d and daily
gain would tend to make the correlation between weight at 28 d and

total energy intake negative. Daily gain and feed conversion ratio

81

were strongly negatively correlated as expected for animals fed
restricted amounts of feed. Both genetic and phenotypic correlations
between daily gain and appetite were positive with estimates of .707
and .325, respectively, which were partially due to the feeding system,
because animals were fed restricted amounts according to weight.
Efficient animals would grow faster, and thereby advance into the next
weight class and thus receive more feed.

Table 17.

Genetic (Under Diagonal) and Phenotypic (Above Diagonal) Correlations
Among Traits Measured in Production Period 1 (28 d to 200 kg LW).

 

 

Traita WGT28 DG 81 FCR DEI DMI
WGT28 --- .174 -.442 .149 .558 -.369
00 .435 --- -.850 -.830 .325 -.826
El -.698 -.916 --- .820 -.101 .989
FCR -.093 -.889 .776 --- .240 .854
DEI .746 .707 -.709 -.314 --- .000
DMI -.661 -.900 .989 .794 -.639 ---

 

3See text in Materials and Methods for definition of traits.

Genetic and Phenotypic Correlations Among Traits Measured in Production
Period 2

Estimates are shown in Table 18. Total energy intake, total dry
matter intake and feed conversion ratio were all very highly correlated
both phenotypically and genetically. This was expected, since energy
content of the feed and dry matter content are closely related. The

close correlations between total energy intake and feed conversion

82

ratio were caused by the fact that intake was measured in a fixed
weight interval. Both genetic and phenotypic correlations obtained in
production period 2 between daily gain and feed intake traits were
almost identical to the corresponding estimates obtained in production
period 1. This is in contrast to an expectation of a lowered
correlation when changing the feeding regimen from restricted feeding
to ad libitum feeding. Andersen et a1. (1987) found a genetic
correlation of -.72 between daily gain and feed conversion ratio when
bulls on performance test were fed ad libitum whereas their
corresponding estimate for animals under restrictive feeding was -.98.
Table 18.

Genetic (Under Diagonal) and Phenotypic (Above Diagonal) Correlations
Among Traits Measured in Production Period 2 (200 kg LW to Slaughter).

 

 

Traita DG EI FCR DEI DMI
DC --- -.725 -.862 .336 -.716
El -.876 --- .907 .143 .997
FCR -.905 .979 --- .103 .902
DEI .594 -.195 -.232 --- .146
DMI -.885 .998 .979 -.218 ---

 

6See text in Materials and Methods for definition of traits.

The genetic correlation between average daily gain and appetite
was estimated at .594 and between appetite and feed conversion ratio
the estimate was -.232. Both estimates are comparable to those
obtained by Andersen et a1. (1987). Brown et a1. (1986) obtained a
genetic correlation of 0.84 and 0.59 between daily gain and appetite

for Angus and Hereford bulls, respectively, on postweaning gain test

83

under an ad libitum feeding regimen. Their estimates of the genetic
correlation between appetite and feed conversion ratio were .47 and .05
for the two breeds mentioned above, results that deviate substantially
from the estimates obtained in this investigation. Reasons for this
deviation might be due to the different breeds involved and the fact
that they used cattle tested in fixed time interval instead of fixed
weight interval.

The genetic correlation between appetite and total energy intake
was -.709 in production period one, but only -.195 in period 2. The
corresponding phenotypic correlations were-.101 and .142, for
production period 1 and 2, respectively. The negative phenotypic
correlation in period 1 was due to the restricted feeding according to
weight over a fixed weight interval. Fast growing animals moved faster
to the next weight class and thus received more feed. However, these
fast growing animals would reach 200 kg live weight in a shorter time
and therefore had a lower total energy intake. In production period 2
with ad libitum feeding a large appetite was not necessarily related to
a high daily gain. The phenotypic correlation between appetite and

total energy intake was therefore positive in production period 2.

Phenotypic and Genetic Correlations between Similar Traits Measured in
the Production Periods Before and After 200 kg Live Weight

All phenotypic correlations (Table 19) were low, ranging from .084
to .194. This clearly shows that similar measures taken in the two
production periods, which differed in age and weight of the animals as
well as feeding should be regarded as different traits. For daily gain

the estimate was .189, which is consistent with estimates obtained for

84

similar weight intervals by Jensen and Andersen (1982), Andersen (1977)
and Hanset et a1. (1987). The genetic correlation between average
daily gain in the two production periods was .471. Oldenbroek et a1.
(1987) found estimates at .61, Dijkstra et al. (1987) found .53, Jensen
and Andersen (1982) at .70 and Andersen (1977) found .85. The lower
estimates found in this investigation might be due to the different
feeding systems used in the two production periods. However, for total
energy intake, total dry matter intake, and feed conversion ratio the
genetic correlation between the two production periods was around .60.
This is higher than Oldenbroek et a1. (1987) who found an estimate of
.49 for feed conversion ratio. The correlation for appetite was low
.127, which is because average daily feed intake is influenced more

than the other traits when changing the feeding regimen from restricted
feeding to ad libitum feeding.

Table 19.

Genetic and Phenotypic Correlations Among Similar Traits Measured in
Production Period 1 and 2.

 

 

Genetic Phenotypic
Traita correlation correlation
DC .471 .189
El .559 .194
FCR .577 .159
DEI .127 .084
DMI .626 .192

 

3See text in Materials and Methods for definition of traits.

85

Genetic and Phenotypic Correlations between Traits Measured at
Slaughter

As shown in Table 20 the correlation between dressing percentage
and carcass grading were estimated at .478 and .351, respectively,
genetically and phenotypically. It is interesting to note that neither
dressing percentage nor carcass grading were highly correlated to
carcass composition, but there is a strong genetic correlation between
fat grade and percent fat in the carcass with an estimate at .65.
However the corresponding phenotypic correlation was low. Percent lean
and percent fat in the carcass were highly correlated since they make
up about 83% of total carcass weight and there is only limited
variation in the proportion of bone in the carcass (Andersen, 1977).
Total energy intake per unit of carcass gain is related to carcass
composition such that selection for leaner carcasses would decrease the
feed intake per kg carcass gain. Again the corresponding phenotypic
correlation was low.
Table 20.

Genetic (Under Diagonal) and Phenotypic (Above Diagonal) Correlations
Among Traits Measured at Slaughter.

 

 

Traita DRSPCT CARGRD FATGRD LEANPCT FATPCT EICG
DRSPCT --- .351 .094 .118 .032 -.143
CARGRD .478 --- .112 .236 -.079 -.295
FATGRD -.065 -.157 --- -.261 .343 -.085
LEANPCT .043 .373 -.664 --- -.899 -.361
FATPCT .011 -.189 .658 -.920 --- .226
EICG -.220 -.290 .048 -.482 .465 ---

 

8See text in Materials and Methods for definition of traits.

86

Genetic and Phenotypic Correlations between Traits Measured in
Production Period 1 and 2 and Traits Measured at Slaughter

As shown in Table 21, all traits measured in production period 1
had low genetic correlations to carcass traits, except net energy
intake per kg carcass gain and this was probably due to the part-whole
relationship. Daily gain in production period 2 was genetically
correlated to dressing percentage and body composition such that
selection for higher daily gain would tend to lower dressing percentage
and increase the percentage of lean meat in the carcass at a given body
weight. These results are similar to results obtained by Andersen
(1977). Total net energy intake, total dry matter intake and feed
conversion ratio all had positive genetic correlations to percent fat
in the carcass. Thus selection for leaner animals would reduce total
feed requirement. This is probably to some extent caused indirectly by
daily gain, since fast growing animals are leaner at a given weight
because they are less mature at that weight. Also fast growing animals
reach a fixed weight in shorter time, thus reducing the accumulated
maintenance requirement. Appetite is also related to carcass
composition such that selection for higher daily feed intake will
yield leaner animals with an estimate of the genetic correlation
between appetite and percent fat in the carcass at -.397 when slaughter
weight is held constant. All the corresponding phenotypic correlations
are not shown, but were of same sign, although much lower in magnitude
than, the corresponding genetic correlations. Exceptions were the
correlations between daily feed intake and percent lean at -.134 and

daily feed intake and percent fat at .157. The latter corresponded to

87

an environmental correlation between percent fat in the carcass and
daily feed intake at .33. This implies that an animal who has a large
daily feed intake due to environmental reasons tends to be fat, whereas
if it is due to its genotype it will not be fat at a fixed weight and
tend to grow faster.

Table 21.

Genetic Correlations Between Growth, Feed Conversion and Appetite in
Production Period 1 and 2 and Traits Measured at Slaughter.

 

 

Traita DRSPCT CARGRD FATGRD LEANPCT FATPCT EICG
WGT28 -.245 -.282 .214 -.l43 -.073 -.156
DGPl -.042 .129 .244 .175 -.205 -.524
EIPl .071 .008 -.307 -.082 .172 .581
FCRPl —.117 -.235 -.247 -.244 .178 .688
DEIPl -.207 -.118 .130 -.041 -.l40 -.033
DMIPl .082 .000 -.297 -.119 .190 .649
DGP2 -.249 .144 -.263 .592 -.619 -.788
EIP2 .203 .005 .053 -.476 .523 .877
FCRP2 .189 -.084 .060 -.457 .484 .904
DEIP2 -.184 .290 -.391 .413 -.397 -.l61
DMIP2 .195 -.017 .069 -.489 .528 .881

 

8See text in Materials and Methods for definition of traits.

Conclusions and Implications
No interaction between genotype represented by paternal halfsib
groups and rations of differing proportion of roughages were found in

this experiment. In several European countries the feeding of bulls on

88

performance test have been changed from diets based mainly on
concentrates to diets with a large proportion of roughages. The reason
for this change was concern about the roughage intake of daughters of
bulls selected on a concentrate diet, (Andersen at al. 1981). The
results of the present experiment did not support such concerns.

All the traits analyzed show additive genetic variances and
heritabilities in a range that would allow for considerable response to
genetic selection. Selection for daily gain would as a correlated
effect improve feed conversion ratio and increase appetite. However,
in ad libitum fed animals, the literature cited earlier indicates that
the correlation between daily gain and feed conversion ratio might be
lower in ad lib. fed animals than found in this investigation. The
relatively low correlations between the same trait measured before and
after 200 kg live weight and on different feeding systems, indicate
that animals must be tested for these traits during age or weight
intervals and feeding systems that are similar to normal practice in
commercial production to ensure genetic progress in this environment.

Results indicate that selection on daily gain or appetite will
decrease carcass fatness at a given weight, but there is a positive

environmental correlation between appetite and carcass fatness.

CHAPTER 5

Performance Testing of Dual Purpose Bulls For Beef Traits.
Residual Intake and Energy Requirements For

Growth and Maintenance

89

90

Introduction

Supply of feed energy is a major cost factor in any cattle
production system. Selection for more efficient use of energy may
therefore be profitable. Genetic improvement of feed efficiency
requires measures of feed intake. For dual purpose cattle, feed intake
can in principle be measured on different groups of animals: (1)
Progeny groups under field conditions; (2) Bull-dams either in
commercial herds or on special testing stations, most probable in
connection with breeding schemes using multiple ovulation and embryo
transfer (MOET); (3) Future AI bulls while they are being performance
tested for beef traits. In this paper we are concerned only with the
third possibility.

The total utility of measuring feed intake on future AI bulls
depends on the genetic correlation between efficiency traits measured
on the growing bull and the same traits in other groups of animals,
primarily lactating cows. Traditional measures of feed efficiency such
as feed conversion ratio are closely correlated to the level of
production as shown in Chapter 4. The total intake of metabolizable
energy can be partitioned into productive (growth) and nonproductive
(maintenance and efficiency of the digestive tract) use of energy.
These parts are collectively called partial energy requirements. The
nonproductive use of energy is a major part of the total use of feed
energy (Andersen, 1978). Residual intake, defined as actual energy
intake minus predicted energy intake, has been suggested as a measure

of efficiency that is independent of level of production (Koch et al.,

91

1963. Brelin and Brénning, 1985). A lower residual intake would
indicate a better efficiency. However, errors introduced by use of an
inappropriate model in predicting intake would be included in this
measure as would errors of measuring feed intake. The genetic nature
of residual intake and partial energy requirements is not well
understood.

The objective of the present paper therefore was to explore
different measures of the young growing bulls' energy requirements for
growth and main-tenance and their residual intake, and to estimate the
genetic parameters of these traits. A necessary requirement for the
use of such measures in performance testing of future AI bulls is that
they can be obtained on the live animal. The previous chapter reported
genetic parameters of traditional beef production characteristics of
the same young bulls. In a following paper, we will report phenotypic
and genetic correlations between residual intake and partial energy
requirements defined in this paper, and traditional beef production
characteristics. Genetic correlations to the milkfat production of

female halfsibs also will be reported.

Materials and Methods
Animals and records
An experiment was carried out in Denmark at the experiment station
"EGTVED" under the supervision of the National Institute of Animal
Science. A total of 650 bull calves of 31 Holstein Freisian (HF) or
Brown Swiss (BS) sires completed the experiment. The experiment was

carried out in yearly batches, with a batch initiated in each of the

92

years from 1978 to 1982. All calves started in the experiment at the
age of 28 d. In the production period from 28 d and until the animals
reached a live weight of 200 kg (P1) feeding of calves was restricted,
at a level of 75% of expected ad libitum intake. In production period
2 (P2), from 200 kg live weight to slaughter, the animals were placed
at random on four treatments with ad libitum feeding. Treatments 1, 2,
3 and 4 were respectively, 0%, 25%, 50% and 75% of expected energy
intake from roughages. The 0% treatment was concentrates fed from
automatic feed hoppers, while the other treatments were fixed amounts
of concentrates and roughages fed 3-4 times daily to ensure that feed
was available at all times.

Live weights of the animals were recorded at the age of 28 d and
thereafter biweekly throughout the experiment. Feed intake of a young
bull was recorded as a sum of daily intakes in the weighing intervals.
All feed given at each feeding was weighed. Weighbacks were taken
twice a week. Feed intake was then recorded as the sum of all feed
given in a two week period minus weighbacks. The periods when feed
intake was recorded coincided with the intervals between body weight
measures.

Energy intake was computed according to the Danish feed evaluation
system based on Scandinavian feed units (SFU). That system expresses
feed energy content as net energy for lactation (Moller et al., 1983).
Since the Danish net energy system assumes a nearly constant net energy
efficiency, the net energy intake (NE) can be converted to
metabolizable energy (ME) by ME-4.16 + 1.17NE which gave an R2 of .96.

This equation assumes both ME and NE to be measured in mJ and is based

93

on information given by Van der Honing and Alderman (1988). Since this
simple linear relationship exists the genetic parameters to be
estimated later are invariant to the choice of feed evaluation system.
Records on a total of 18,111 weighing intervals were available.
The number of intervals available for an individual animal ranged from
16 to 45 depending on the animal's growth rate and slaughter weight.
Animals were slaughtered at 340, 470 or 600 kg live weight. At
slaughter, live weight and cold slaughter weight was recorded and the
left half of the carcass was dissected into lean, fat, and bone,
following anatomic lines, at the Danish Meat Research Institute. A
detailed description of the experiment and the procedures used were

given in Chapter 4 and Bailey et a1. (1985).

Estimation of partial energy requirements for individual bulls

The total energy intake (E1) of an animal can be partitioned into:

EI - NPE + PE,
where NPE is nonproductive use of energy and PE is productive use of
energy. Both components can be further subdivided. The PE is energy
used for growth, mainly in the form of fat or protein. Fat has a
higher capacity for storing energy than protein, and 1 g of protein is
accompanied by about 5 g of water (Webster, 1977). Therefore, storage
of one g of lean meat should require much less energy than storing one
g of fat. However the synthesis of protein is a very complex process
that requires more energy than synthesis of the same amount of fat.
This means that the partial energy requirement for growth might not be
as highly dependent on the composition of the weight gain as the energy

content of fat and lean would indicate (Pullar and Webster, 1977,

94

Kielanowski, 1976). Such association perhaps is different in ruminants
as in single-stomach animals (Geay, 1984). The maintenance

requirement might be dependent on the composition of the body weight
maintained.

Based on the considerations mentioned above, simple models for
estimating partial energy requirements were defined. The partitioning
of energy intake into productive and nonproductive use of energy for
each individual bull was based on the biweekly measures of energy
intake and live weight. The following alternative multiple regression
models were used to obtain estimates of partial energy requirements for
individual young bulls within a production period:

1:1i - 611 + 661(ci) + bw1(w2/4) + e1 [1]

£11 ' b11 t bGZ(Gi) t bw2(wi/A) t wa2(c,wi/4) + 61 [21

where E11 was the energy intake (mJ) in the 1th

two week weighing
interval for an individual bull; G1 was the total live weight gain in
kg in the 1th weighing interval; W1 was the average weight in kg in the
1th weighing interval; bll' bGl etc. were partial regression
coefficients; and e1 was a random residual.

The intercept in each model, bIl and bI2' describes a baseline
intake not associated with growth rate or metabolic weight. The
regression on metabolic weight, le and bW2' denote the energy
requirement for maintaining one kg of metabolic body weight in a
weighing interval. The regression on growth, bGl and bGZ' in a
weighing interval expressed the energy requirement for one kg of body

weight gain.

The intercept together with the regression on metabolic weight

95

estimates the nonproductive use of energy. The intercepts in the
models indicate use of energy not associated with other factors in the
model and is the part of nonproductive use of energy independent of
body weight. Since the energy expenditure at zero metabolic weight and
zero gain is expected to be zero, deviations of this intercept from
zero might also indicate lack of fit of the model used. As the animal
grows larger the composition of body weight gain changes (Geay, 1984).
Interactions between productive and nonproductive use of energy can
therefore be expected.

In model [2] an interaction between growth and metabolic weight
was included with bGW2 as the corresponding partial regression
coefficient. The reason for including the interaction in the model was
to account for the changes in the composition of body weight gain and
of the body weight maintained as metabolic weight changes. Instead of
using the interaction term in model [2], it might have been desirable
to use a regression on lean and fat depositing separately. However,
this requires knowledge of body composition and change in body
composition throughout the production period and under practical
conditions such information is not available.

All estimates of baseline intake and weight dependent
nonproductive use of energy were divided by 14, so that they were
expressed as energy requirement per day, instead of per two weeks.

Since the feeding regime was different in production period 1 and
2, each of the models was applied within each period. For ease of
reference in tables the coefficients were labeled BIl, 861, and BWl for

model [1] requirements and 812, BG2, 8W2 and BGW2 for the requirements

96

estimated in model [2].
Several other, more complex, models were investigated. However,
they did not provide enough additional information beyond the models

above to warrant reporting.

Residual intake
The residual efficiency, here termed residual intake, is defined
as the total energy intake minus predicted total energy requirement in
a given production period (Brelin and Brénning, 1982). The total
energy requirement can either be predicted from feeding standards or
derived directly from analysis of the experimental data. Earlier
analyses of residual intake of growing cattle have been presented by
Brelin and BrAnning (1982) and Brelin and Martinsson (1986). In this
investigation, total energy requirement was estimated directly from the
data, because this gave the possibility of taking carcass composition
into account in the prediction. The residual intake was therefore
estimated as the residual from the following two alternative models:
yijk ' ‘1 + 8j + (t5)ij + Pk + b1(“l§§) + b2(Gijk) + b3(Dijk)

+ eijk [31

yijk - ti + gJ + (tg)ij + pk + bh(Wi§§ ) + b5(Gijk) + b6(Dijk)

+ b7j(Kijk) + b8j(Fijk)

+ eijk [4]
where: yijk was the total energy intake in production period 1 or 2 for
a bull of the kth breed in slaughter weight group j and year-treatment
ich

1; ti was the effect of year-treatment; gj was the effect of jth

slaughter weight group; (tg)ij was the interaction between ti and gj;

97

pk was the effect of kth breed; wijk was the average weight in the
production period; Cijk was the total live weight gain in the
production period; Djk was the number of days in the production period;
and b1 through b6 were corresponding regression coefficients. In model
[4], carcass measures were considered, where Kijk was the dressing
percentage; Fijk was the percent fat in the carcass; and b7j and b8j
were corresponding heterogeneous regression coefficients within
slaughter weight group. In [3] and [4], eijk was a random residual and
was defined as alternative measures of residual intake in each
production period.

The residual intake from [3] is hereafter denoted as RES, while
that from [4] is RESC with post letter "C" indicating the consideration
of carcass composition in the prediction of energy requirement. Other
more complex models were fitted in order to estimate residual
efficiency. However, estimates from those models were very highly
correlated with those from the simple models presented and hence only

the simple models were reported in this paper.

Estimation of genetic parameters
Nine traits were defined by parameter estimates from models [1]
through [4] for each of the 650 bulls in each production period. Since
there were two production periods, a total of 18 traits were analyzed.
These traits were analyzed together with traditional beef
production characteristics which were reported in Chapter 4. All
traits were analyzed simultaneously using a multiple trait model with

equal design matrices for each trait.

98

The model for each trait was:

yijklm ' ‘1 + gj + (t5)ij t Pk + skl + eijklm [51
where yijklm was the record of a trait for a bull in year-treatment i,
in slaughter weight group j, of breed k and of sire 1; t1 was the
fixed effect of the ith year-treatment; gj was the fixed effect of the
jth slaughter weight group; (tg)1j was the interaction between t1 and
g1; pk was fixed effect of kth breed; skl was the random effect of 1th
sire within the kth breed and eijklm was a random residual. Note that
for the four residual intake traits from [3] and [4], the fixed effects
needed to be repeated in [5] so that degrees of freedom would be
accounted for properly. Precise description of assumptions for the
model were given in Chapter 4.

Variance-covariance matrices corresponding to sire and residual
effects were estimated by restricted maximum likelihood (REML)
utilizing the expectation maximization (EM) algorithm augmented with
canonical and Householder transformations, as described in Chapter 1.
No standard errors on genetic parameters are given, since such
statistics have not yet been developed for estimates from multitrait

models.

Results and Discussion
Table 22 shows simple means, heritability estimates and phenotypic
standard deviations for partial energy requirements from model [1] and

[2] for both production periods 1 and 2.

Table 22.

99

Mean Heritability and Phenotypic Standard Deviation For Estimates of

Energy Requirements.

 

Production period

 

Traitsa

28d to 200 kg_1ive weight

h2

h2

200 k LW t lau hter

 

Mean 0P Mean 0P
Model [1]
811 -4.01 .252 1.49 -3.31 .185 15.3
BGl 9.26 .106 22.1 23.0 .188 51.4
BWl .604 .067 .062 .684 .208 .199
Model [2]
BIZ 1.90 .258 4.86 1.45 .154 75.9
BG2 -27.1 .258 75.5 ~21.5 .161 712
BW2 .539 .199 .154 .626 .142 1.07
BGW2 1.03 .248 2.03 .560 .142 10.3
Model [3]
RES 0 .077 96.5 0 .275 619.7
Model [4]
RESC 0 .082 96.4 0 .363 600.8

 

8See text in Materials and Methods for definition of traits.

Baseline intake

Average model [1] energy requirements showed a slightly negative
baseline intake in both production periods. The baseline intake
reflects energy intake corrected for weight-dependent nonproductive use
of energy and productive use of energy (weight gain) and might
therefore be said to reflect a baseline metabolism. The use of energy
cannot be negative, but the estimates were expressed at zero production
and zero metabolic weight, a state that no animal can, of course,
attain. For selection purposes, variation among animals is more
important than the actual level of the estimates obtained, since

ranking of animals might be a primary goal. The standard deviation of

100

15.3 mJ/d in production period 2 showed that there were considerable
variation in energy requirement at constant production and at constant
metabolic weight. The heritability was estimated at approximately .2
which is the same level as the traditional feed conversion ratio

obtained in Chapter 4.

Partial energy requirement for growth

The average model [1] energy requirement for one kg of body weight
gain were 9.26 and 23.0 mJ in production periods 1 and 2, respectively.
The partial energy requirement for growth is generally thought to be
dependent on the composition of the body weight gain (Webster, 1980).
In older animals, a larger proportion of the body weight gain consists
of fat (Andersen et al., 1984 and Geay, 1984), but in this experiment
the composition of the gain is not known for each animal in each
individual weighing interval. However the partial efficiency for fat
and protein gain is very different. In a literature review, Geay
(1984) gave preferred values of .20 and .75 for protein and fat
accretion on an energy basis, respectively, based on pooled data from
52 experiments. The large differences in the partial efficiencies of
protein and fat accretion tend to diminish the relation between body
composition and energy requirement for growth. This might especially
be true in the present experiment since bulls of dairy breeds have
relatively small amounts of fat deposition.

The feeding level and production in production period 2 was much
higher than in period 1, with average daily gains of 1225 g vs. 893 g,
respectively. The efficiency of energy utilization is dependent on the

production level (Milligan and Summers, 1986, Andersen, 1980). This

lOl

might be a reason for the big difference in the partial energy require-
ment for growth in the two production periods. Also the composition of
the body weight gain can be of importance.

A detailed analysis of the genetic and phenotypic correlations
between partial energy requirements and carcass composition at
slaughter will be reported in a subsequent paper. The heritability of
model [1] energy requirement for body weight gain was estimated at .106
and .188 for production period 1 and 2, respectively. These estimates
together with the phenotypic standard deviations of 22.1 and 51.4 mJ/kg
shows considerable variation among animals in partial energy
requirement for growth and also that a significant proportion of this

variance is due to additive genetic effects.

Weight dependent nonproductive use of energy

The average model [1] requirements for weight-dependent
nonproductive use of energy were .604 in production period 1 and .684
in period 2, both expressed in mJ per kg metabolic weight per day.
These values correspond to predicted maintenance requirements, and are
almost twice the values assumed in most systems of estimating energy
requirements, e.g., NRC, (1978). However, the weight-dependent nonpro-
ductive use of energy is very dependent on production level, and the
values used in several energy systems were estimated in fasting animals
or in animals close to weight equilibrium. Andersen (1980) found esti-
mates at .541, .468 and .355 mJ/kg3/h/d for ad libitum feeding, 85% and
70% of ad libitum intake, respectively, based on data from a

crossbreeding experiment.

102

The nonproductive use of energy is dependent on weight or age of
the animals. Van Es (1980) estimated the maintenance requirement in MB
of bulls that were crosses between Hereford and Freisian to be .607
mJ/kg3/4/d at 250 kg live weight and .573 at 450 kg live weight.
Hilligan and Summers (1986) stated that the maintenance requirement
decreases with increasing weight or age. However, this decreasing
effect might have been counteracted in the present experiment by the
change in the feeding strategy before and after 200 kg liveweight.
Thorbek (1980) estimated the maintenance requirement of calves weighing
from 100 to 275 kg liveweight using respiration chambers and found
estimates varying from .377 to .486 mJ/d, but found no relation to
liveweight. Larsen (1979) cf. Andersen, (1980) using a similar
approach as in the present investigation found estimates at .688
mJ/kg3/a/d on bull calves fed concentrates ad libitum, a result very
similar to the results obtained in this study. The considerable
variation among different estimates of weight-dependent nonproductive
use of energy found in the literature might well be ascribed to
differences in level of intake in the different experiments.

The heritability estimates for weight-dependent nonproductive use
of energy were .067 and .208 for production period 1 and 2
respectively. In comparison Larsen (1979) cf. Andersen (1980) obtained
a figure of .31 from a small experiment. Andersen (1980) demonstrated
differences among different crosses between beef breeds and dual
purpose breeds for weight-dependent nonproductive use of energy. Also,
Ferrell and Jenkins (1985) based on an extensive literature review

concluded that there are considerable differences among cattle types in

103

energy requirements for maintenance and growth. The heritability
estimates, together with the phenotypic standard deviations, show
considerable variation among animals for the weight dependent non-
productive use of energy, and also show that the nonproductive use of

energy can be altered through genetic selection.

Interaction of energy requirements

The baseline intake for this model was slightly above zero in both
production periods (Table 22). The interpretation of the partial
requirements for growth and weight-dependent nonproductive use of
energy was difficult, due to the interaction between the two factors.
However, the results indicated that this interaction was important.
The standard deviation of model [2] requirements were all larger than
corresponding model [1] requirements, a feature that may render model
[2] more useful in distinguishing among animals.

The heritability of model [2] partial energy requirements were
higher than corresponding model [1] requirements in production period
1, whereas the opposite were the case in period 2. The interaction
term showed heritability estimates at a level similar to the
heritability of conventional measures of feed efficiency reported for

the same animals in Chapter 4.

Residual intake

The last two rows of Table 22 shows means, heritability estimates
and phenotypic standard deviations for the two alternative expressions
for residual intake. The average is zero due to the method used in

determining residual intake. The phenotypic standard deviation of

104

residual intake is smaller in production period 1 than in period 2,
which is partly due to the fact that intake was obviously easier to
predict in production period 1, where the animals were fed restricted
amounts according to live weight. The phenotypic standard deviation
for residual intake was slightly less than than 100 mJ in period 1 and
slightly more than 600 mJ in period 2, or 3.3% and 5.1% of total energy
intake in the respective production periods. These percentages corres-
pond very well to the 4.3% found by both Brelin and Branning (1982) and
Brelin and Martinsson (1986) working with intake on an ME basis.
Residual intake is, by definition, independent of daily gain.
Therefore, intake also can be expected to have a low correlation with
feed conversion ratio, since the feed conversion ratio is closely
correlated to daily gain. Thus, there is considerable variation in
feed intake that is unrelated to production level in terms of average
daily gain.

Correction for carcass composition in predicting residual intake
only reduced the phenotypic standard deviation by 3% in production
period 2 and did not reduce the standard deviation in period 1 at all.
However, the correction increased the heritability estimate from .275
to .363 in production period 2. This increase might be an effect of a
very high heritability of percent lean and percent fat in the carcass
found in this experiment (Chapter 4). Brelin and Branning (1982) found
a heritability estimate for residual intake at .27, a result well in

line with the results in this study.

105

Table 23.

Genetic (Below Diagonal) and Phenotypic (Above Diagonal) Correlations
Among Partial Energy Requirements and Residual Intake in Production
Period 1 (28 d to 200 kg BW).

 

Model Model

 

 

 

 

Model [1] Model [2] [3] [4]

Traita 811 861 8W1 812 802 BW2 BGW2 RES RESC
Model [l]

811 --- -.087 -.643 .306 -.039 -.277 .033 -.139 -.142
861 -.605 --- -.668 -.021 .277 - 252 -.005 -.072 -.072
Bwl -.760 .019 --- -.176 -.205 .379 .012 .242 .252
Model [2]

812 .473 -.433 -.099 --. -.907 -.942 .949 -.122 -.123
802 -.273 .400 -.140 - 957 --- .759 - 947 .041 .043
8w2 -.435 .341 .141 -.985 .942 --- -.903 .190 .189
BGW2 .230 -.285 .110 .957 -.987 -.949 --- -.075 - 075
Model [3]

RES .063 -.040 -.101 -.137 .132 .098 -.104 --- .988
Model [4]

RESC .067 -.O38 -.099 -.171 .174 .133 -.l45 .981 ---

 

aSee text in Materials and Methods for definition of traits.

Correlations among traits in production period 1

Genetic and phenotypic correlations among traits measured in
production period 1 are shown in Table 23. For model [1] energy
requirements, the phenotypic correlation between baseline intake and
requirement for growth was close to zero, whereas baseline intake and
weight-dependent nonproductive use of energy were negatively correlated
with an estimate at -.643. Genetically, baseline intake and requirement
for growth and weight-dependent nonproductive use of energy were
strongly negatively correlated.

The model [2] partial energy requirements were all very highly

intercorrelated. With only one exception, all phenotypic and genetic

106

correlations had absolute values above .95. This means that they
varied together as a unit, since knowledge of any one of the partial
energy requirements could lead to a precise prediction of the remaining
requirements. This may make model [2] easier to use in comparing
energetic efficiency of different animals.

Partial energy requirement from model [1] were generally much less
correlated to model [2] requirements than were requirements estimated
within the same model. Even coefficients with similar biological
definitions, but estimated in different models were generally not very
highly correlated, which implies that the biological interpretation of
a partial energy requirement was very dependent on the model used in
its estimation. This dependency have probably contributed to the large
variation in estimates of partial energy requirements found in the
literature.

The two expressions of residual intake in production period 1 were
very highly correlated. Consideration of carcass composition in
calculating residual intake added very little information. Residual
intake in production period 1 had low correlations to all estimates of

partial energy requirements both phenotypically and genetically.

Correlations among traits in production period 2

The genetic and phenotypic correlations among partial energy
requirements and residual intake in production period 2 (Table 24) were
in most cases in reasonably good agreement with the corresponding
estimates from production period 1. There were a few exceptions, for
example the phenotypic correlation between model [1] requirements for

growth and weight-dependent nonproductive use of energy was -.668 in

107

production period 1 but .141 in period 2. As in period 1, partial
energy requirements from the same model were more closely correlated to
each other than were similar requirements from different models.
Results involving residual intake in production period 2 also were
similar to those in period 1. Again, consideration of body composition
in computing residual intake did not add significant information. The
phenotypic cor-relations between residual intake and the partial energy
requirements were low. However, there were relatively strong genetic
correlations between residual intake and model [1] partial energy
requirements.
Table 24.
Genetic (Below Diagonal) and Phenotypic (Above Diagonal) Correlations

Among Partial Energy Requirements and Residual Intake in Production
Period 2 (200 LW to Slaughter).

 

Model Model

 

 

 

 

Model [1] Model [2] [3] [4]

Traita BIl BGl BWl 812 BG2 BW2 BGW2 RES RESC
Model [l]

811 --- -.453 -.932 .349 -.187 -.317 .156 -.032 -.026
8G1 —.298 --- .141 -.l79 .176 .112 -.104 .027 .012
8W1 -.901 -.110 --- -.327 .150 .322 -.l4l .139 .134
Model [2]

812 .550 -.340 .420 --- -.970 -.993 .965 .019 .016
802 -.439 .440 .258 -.977 --- .963 -.994 -.039 -.034
BW2 -.536 .263 .449 -.993 .956 --- -.970 .012 .014
BGW2 .440 -.387 -.284 .983 -.996 -.971 --- .028 .022
Model [3]

RES .196 -.556 .165 .232 -.337 -.l33 .282 --- .970
Model [4]

RESC .080 -.467 .245 .048 -.152 .042 .102 .939 ---

 

aSee text in Materials and Methods for definition of traits.

108

Correlations between production periods 1 and 2

Phenotypic correlations between partial energy requirements or
residual intake measured in production period 1 and the corresponding
measures in period 2 were all low (Table 25). The genetic correlations
were also relatively low and even negative for model [1] weight
dependent nonproductive use of energy. Only model [2] energy
requirements showed significant correlations at approximately .4
between the two periods. In comparison, Jensen et a1. (1989) found
genetic correlations between the two production periods at .56 and .58

for energy intake and feed conversion ratio, respectively.

Table 25.
Genetic and Phenotypic Correlations Among Partial Energy Requirements
and Residual Intake in Production Period 1 and 2.

 

 

Genetic Phenotypic

Traita correlation correlation
Model [1]

fill .076 .047
861 .284 .002
BWl -.239 .045
Model [2]

812 .395 .061
862 .404 .081
BW2 .397 .043
BGW2 .437 .072
Model [3]

RES .190 .098
Model [4]

RESC .248 .093

 

8See text in Materials and Methods for definition of traits.

109

Conclusions and Implications

It is well known that growth rate shows good responses to genetic
selection and as a correlated effect the feed conversion ratio is
reduced. As noted by Webster (1977), this reduction is mostly achieved
by shortening the production period so that the accumulated maintenance
requirement is reduced if animals are slaughtered at a constant weight.
He also noted that selection for increased growth rate probably would
have limited effect on the partial requirements for growth and
maintenance. This study showed that it is possible to measure partial
energy requirements for growth and nonproductive use of energy based on
live animals. Hence it is possible to include selection for partial
energy requirements in large scale programs for genetic improvement.

The partitioning of energy intake into productive and
nonproductive use, by the relatively simple models used in this study,
yielded three or four coefficients for each animal. Coefficients from
the same model were highly correlated. Also, vectors of coefficients
instead of single values must be used as comparison criteria. Choice
of model for computing the partial energy requirements is important
because coefficients with similar biological interpretation, but from
different models, were not as highly correlated as were different
coefficients within a given model. The reason for the high correla-
tions between partial requirements within a model might be due to the
arbitrary statistical partitioning of energy intake into productive and
nonproductive use. This partitioning does not necessarily reflect
specific physiological events but merely different aspects of the

animal's energy conversion system.

110

Residual intake as a criterion of energetic efficiency is easier
to use than the partial energy requirements in comparing animals. The
heritability estimates for residual intake when the animals were fed ad
libitum were slightly larger than those of partial energy requirements.
Results indicate that residual intake can be calculated without
correction for carcass composition. Another advantage of residual
intake is that it did not require the biweekly body weights that were
needed in the calculation of partial energy requirements, but only the
total energy intake and weight at start and end of the production
period.

Results obtained in the present investigation using simple models
clearly showed considerable variation among young bulls in partial
energy requirements and in residual intake. A significant proportion
of this variance was due to additive genetic effects. More research is
needed to find better models of energy conversion for individual
animals in ways that are suitable for inclusion in selection programs.
Such modeling work will require input from both physiologists and
geneticists.

The utility of measuring partial energy requirements and residual
intake of the young growing bulls on performance test is dependent on
their genetic correlations to the total merit of the animals in the
cattle production system. Total merit includes energy requirements of
the young bulls themselves, but also the energy requirement of other
groups of animals in the production system such as their female
relatives used as replacement heifers and lactating cows. This is an

area where much further research is needed. Some of this research

111

already is ongoing at several institutes. It is also unknown to what
extent the parameters estimated for each animal in the approach used in

the present investigation corresponds to energy chamber results.

CHAPTER 6

Performance Testing of Dual Purpose Bulls for Beef Traits.
Genetic and Phenotypic Correlations Between Partial
Energy Requirements and Beef Traits of Young Bulls and

The Milk Yield on Their Female Halfsibs

112

113

Introduction

Future selection programs for total merit in dual purpose cattle
might need to include selection for a more efficient use of energy from
feeds, which is a major cost factor in cattle production systems.
Measuring feed intake on each of the animals in the population might be
prohibitively expensive. However, feed intake measures can be obtained
with relative ease during performance testing of future AI bulls for
beef traits. Such performance tests are carried out in many European
countries. The total utility of measuring feed intake during the
performance test depends on the magnitude of the genetic correlation
between feed intake measured on the growing bull and overall merit of
cattle in the production system. Conventional measures of feed
efficiency of growing animals, such as total feed intake or feed
conversion ratio, are usually closely correlated to the level of
production in terms of growth rate, because increasing growth rate
reduces the time needed to reach a given slaughter weight, and
therefore reduces the accumulated maintenance requirement. Feed
conversion ratio or total feed intake are not necessarily related to
the partial energy requirements for productive and nonproductive use of
energy. An experiment, comprising 650 young bulls by 31 Holstein
Friesian or Brown Swiss sires was conducted at the experiment station
"EGTVED" in Denmark. The first group of traits measured on the young
bulls included growth rate, total feed intake, feed conversion ratio,
appetite, dressing percentage, carcass grading and carcass composition.
The second group of traits measured on the young bulls included

residual intake and estimates of partial requirements for productive

114

and nonproductive use of energy. Conventional beef production traits
measured in this experiment were studied in Chapter 4 and residual
intake and partial requirements for productive and nonproductive use of
energy were studied in Chapter 5.

Milk yield is economically the most important trait in selection
programs in most dual purpose cattle populations. The first objective
of this chapter was to investigate genetic and phenotypic correlations
between the two groups of traits measured in the experiment with young
bulls. A second objective was to investigate the relationships between
traits measured on the young bulls and the milkfat production of their

female halfsibs.

Materials and Methods

Animals and data

Data on 650 bull calves, the progeny of 31 Holstein Friesian or
Brown Swiss sires, were analyzed. The experiment consisted of two
consecutive production periods for each young bull. Production period
1 was from initiation of experiment at the age of 28 d and until the
animal reached 200 kg liveweight (LW), all animals were fed restricted
at approximately 75% of expected ad libitum intake. In production
period 2 , from 200 kg LW and until slaughter, the animals were placed
on four different treatments. The treatments were ad libitum feeding
of rations differing in energy concentration by varying the proportion
of roughage in the ration. Body weight was measured biweekly, feed
intake was recorded as the sum of biweekly intakes and carcass

composition and carcass grading were obtained at slaughter. A detailed

115

description of the experimental procedures was given in Chapters 4 and
5.

Energy intake was an important variable in our studies and needs
to be defined clearly: Energy intake was expressed as net energy
intake computed according to the Danish feed evaluation system based on
Scandinavian feed units (SFU) (Mdller et al., 1983). That system
expresses feed energy content as net energy for lactation at a certain
level of production. Another measure of energy intake is metabolizable
energy (ME). Since the Danish net energy system assumes a nearly
constant net energy efficiency the net energy intake can be converted
to ME by ME - 4.16 + 1.17 NE which gave an R2 of .96 based on
information given by Van de Honing and Alderman, (1988). Since this
simple linear relationship exists the genetic parameters estimated were
invariant to choice of feed evaluation system. Live weight and carcass
weight were recorded at slaughter.

The following production traits were defined (Jensen et al.
1989a). In production period 1 (28 d to 200 kg LW):

WGT28 LW in kg at 28 d.

DC Average daily gain in g.

El Total energy intake in mJ.

FCR Feed conversion ratio, EI/(Total weight gain).

DEI Daily energy intake (appetite), EI/(Days on test).
DMI Total dry matter intake in kg.

Similar traits except WGT28 were defined in production period 2
from 200 kg LW to slaughter. At slaughter the following traits were
obtained:

DRSPCT Dressing percentage.

CARGRD Carcass grade. Scale 1-10 with 10 being the best grade.
FATGRD Fat grade. Scale 1-5 with 3 being the optimum value.
LEANPCT Percent lean meat in carcass.

FATPCT Percent fat in carcass.

116

EICG (Total energy intake)/(Tota1 carcass gain).

Partial energy requirements for productive and nonproductive
purposes were estimated for each individual animal in each production
of the two periods separately (Jensen et al. 1989b). This was
accomplished by a statistical partitioning of energy intake using two
different models. The partial energy requirements estimated in the
first model were:

811 Baseline energy intake in mJ/d at zero metabolic weight
and at zero growth rate.

BGl Partial energy requirement in mJ for one kg of body
weight gain.

BWl Partial energy requirement in mJ/kg3/A/d for weight
dependent nonproductive use of energy.

The corresponding partial energy requirements estimated in the
second model were defined similarly to the estimates from the first
model and are denoted as B12, B62 and BW2. The second model also
contained an interaction between partial energy requirements for growth
and weight dependent nonproductive use of energy. This interaction
component was denoted as BGW2. The second model was called the
interaction model and the first model was called the no interaction
model.

Residual intake was defined as total energy intake in a production
period minus predicted intake in the same period. Two different
estimates of residual intake were obtained for each young bull and were
denoted as:

RES Residual intake.

RESC Residual intake corrected for carcass composition.

Since the feeding regime were different in the two production

117

periods, partial energy requirements and residual intake were estimated
within production period for each animal and the estimates for each
production period was treated as different traits. In tables a
postscript P1 or P2 in the abbreviations for traits identifies

production period.

Estimation of genetic parameters and breeding values

The genetic and phenotypic (co)variances were estimated for all
traits by use of restricted maximum likelihood (REML) in a multitrait
model including all traits simultaneously (Chapter 4).

Predicted breeding values for milkfat production of the 31 sires
used in the experiment were obtained from the national sire evaluation
program in Denmark. These predicted breeding values were correlated to
the sire solutions of various traits from the multitrait model used on
the experimental data. Such correlations are approximations to the
genetic correlations between traits measured on young bulls in the
experiment and milkfat production of their female halfsibs, and tend to
be biased toward zero. However, no correction was made for this bias.
The sires breeding value for milk fat production were denoted MILKFAT

in tables.

Analysis of estimated (co)variance matrices

Estimation of genetic and phenotypic (co)variance matrices for
many traits yield a plethora of variances and covariances. In order to
draw inferences from such a mass of parameters the information needs to
be further summarized, especially in this case where the traits

analyzed were to be highly intercorrelated. To gain more insight into

118

the covariance structure of the traits analyzed, the estimated
covariance matrices were subjected to a factor analysis.

The factor analysis extracted principal components followed by an
orthogonal VARIMAX rotation for easy interpretation (SAS Institute
Inc., 1985). The objective of the factor analysis is to identify a
small number of uncorrelated and unobservable underlying variables
called factors, such that the traits observed can be represented as
linear combinations of the underlying factors. The decision on how
many factors to extract is arbitrary. The rule followed was to include
as many factors as necessary to account for at least 95% of total
variance, which is the sum of the variances of the individual traits.
The results were presented as factor loadings for each underlying
factor. A factor loading is a correlation between the underlying
factor and the observed trait in question. Only loadings with a
numerical value greater than .3 were presented. A group of traits that
all have large loadings on the same factor vary largely together as a
group and are said to be controlled by the same underlying factor. The
factors were ordered such that the first factor explained the largest
proportion of total variance, the second factor the second largest
proportion of total variance and so on. The theory behind factor
analysis can be found in several texts on multivariate analysis, e.g.,
Morrison (1976). Application to animal breeding problems is scarce,
but has recently been used by Sieber et al. (1988), Sieber et al.

(1987) and Graf (1987).

119

Results and Discussion

Phenotypic factor analysis

The factor analysis was applied to the estimated phenotypic and
genetic covariance matrices separately. The phenotypic factor loadings
with a numerical value greater than .3 are shown in Table 26. A total
of 14 phenotypic factors were necessary to explain 95% of the total
phenotypic variance. This means that the 35 recorded traits can be
expressed as linear combinations of 14 uncorrelated variables or
factors. The most important phenotypic factor described average daily
gain, feed conversion ratio, total energy intake, total dry matter
intake, all measured in period 2, and energy intake per kg carcass
gain. The second factor described interaction model energy
requirements in production period 2. The energy requirements in
production period 1 were similarly described by factor 3. These
results indicates that the interaction model was superior to the no
interaction model in describing variation among animals in partial
energy requirements. Factor 4 described the production level in
production period 1 similarly to factor 1 for production level in
period 2. Factor 5 and 6 described appetite and residual intake in
production period 1 and 2, respectively. The same factor described
residual intake, whether or not carcass composition was used in
estimating residual intake. This shows that appetite and residual
intake was closely correlated and that there were variation in those
traits that could not be explained by variation in either partial

energy requirements or level of production in terms of growth rate.

120

 

 

 

 

Table 26.
Factor Loadings for Phenotypic Factors.
Factors

Traita l 2 3 4 5 6 7 8 9 10 ll 12 13 14
WGT28 - - 30 - - - - - - -.37 - 80 - -
DGPl - - - .96 - - - - - - - - - -
EIPl - - - .93 - - - - - - - - - -
FCRPl - - - .90 - - - - - - - - - -
DEIPl - - - - 86 - - - - - - .35 - -
DMIPl - - - .92 - - - - - - - - - -
DGP2 .89 - - - - 30 - - - - - - - -
EIP2 .93 - - - - - - - - - - - - -
FCRP2 .96 - - - - - - - - - - - - -
DEIP2 - - - - - .92 - - - - - - - -
DMIP2 .93 - - - - - - - - - - - - -
DRSPCT - - - - - - - - - - .75 .31 - -
CARGRD - - - - - - - - - - .86 - - -
FATGRD - - - - - - - - - - - - - .95
LEANPCT - - - - - - - -.93 - - - - - -
FATPCT - - - - - - - .94 - - - - - -
EICG .87 - - - - - - - - - - - - -
BIlPl - - - - - - - — - .95 - - - -
BGlPl - - - - - - - - .99 - - - - -
BWlPl - - - - - - - - - 72 -.64 - - - -
B12P1 - - .97 - - - - - - - - - - -
BGZPl - - .95 - - - - - - - - - - -
BW2Pl - - .92 - - - - - - - - - - -
BGW2P1 - - .99 - - - - - - - - - - -
B11P2 - - - - - - -,93 - - - - - - -
BGlP2 - - - - - - - - - - - - .97 -
BWIPZ - - - - - - .96 - - - - - - -
BIZP2 - .98 - - - - - - - - - - - -
BGZP2 - .99 - - - - - - - - - - - -
BW2P2 - .98 - - - - - - - - - - - -
BGW2P2 - .99 - - - - - - - - - - - -
RESPl - - - - .96 - - - - - - - - -
RESCPl - - - - .96 - - - - - - - - -
RESP2 - - - - - .93 - - - - - - - -
RESCP2 - - - - - .93 - - - - - - - -

 

8See text in

Materials and Methods for definition of traits.

121

Factor 7 described baseline intake from the no interaction model
in production period 2 and factor 13 described the partial energy
requirement for growth also estimated in the no interaction model in
period 2. Baseline intake and weight dependent nonproductive use of
energy were strongly correlated, since they had loadings of similar
absolute value but with opposite signs. Similarly, factor 9 and 10
combined described the no interaction model partial requirements in
production period 1.

Factor 8 described carcass composition in terms of percent lean
and percent fat in the carcass. It's interesting to note that carcass
composition traits were not grouped together with either production
traits or energy requirements, illustrating the low correlation between
carcass composition and feed conversion ratio or partial energy
requirements.

Factor 11 described carcass grading and dressing percentage and
factor 12 and 14 described weight at 28 d and fat grading,
respectively.

The factors describing partial energy requirements grouped traits
according to model used in the estimation of requirements and the
production period where requirements were measured. That was opposed
to a prior expectation of grouping according to a "biological"
interpretation, by grouping together say measures describing weight

dependent nonproductive use of energy.

Genetic factor analysis
For the genetic covariance matrix a total of 10 factors were

needed to describe 95% of total variance (Table 27). The genetic

122

factor analysis did not separate the traits analyzed into groups as
clearly as did the phenotypic analysis. Instead, several traits were
described by two or more factors.

Factor 1 on the genetic level described interaction model partial
energy requirements in production period 2, but was also correlated to
production level in terms of the growth rate in the same period and to
carcass composition. Factor 2 described mainly production level in
period 1, but was also correlated to production level in period 2. The
third factor mainly described interaction model requirements in
production period 1 but was also correlated to the appetite in the same
period.

The genetic factors 4 and 5 described residual intake and appetite
in production period 1 and 2 similarly to factor 5 and 6 on the
phenotypic level. Factor 6 on the genetic level mainly described the
carcass composition and fat grading. However, carcass grading was
described by factor 9 and 10. Factor 7 mainly described model the no
interaction model, partial energy requirements in production period 2,
but were also correlated to the level of production in this period.
Factor 8 and 9 mainly described no interaction model requirements in
production period 1 and was also correlated to the carcass grade.
Factor 10 described dressing percentage and was correlated to carcass

grade.

Table 27.
Factor Loadings for Genetic Factors.

123

 

Traita

 

WGT28
DGPl
EIPl
FCRPl
DEIPl
DMIPl

DGP2
EIP2
FCRP2
DEIP2
DMIP2

DRSPCT
CARGRD
FATGRD
LEANPCT
FATPCT

EICG

BIlPl
BGlPl
BWlPl
BIZPl
BGZPl
BW2P1

BGW2P1

BIlP2
BGlP2
BWlPZ
BIZPZ
BGZPZ
BW2P2

BGW2P2

RESPl

RESCP2

RESP2

RESCP2

MILKFAT

 

 

Factors
1 2 3 4 5 6 7 8 9 10
- .41 .68 - - - - .44 - -
- .95 - - - - - - - -
- .92 - - - - - - - -
- .90 - - - - - - - -
~ .58 58 - 39 - - - - -
- .92 - - - - - - - -
-.50 .51 - .41 - .32 .38 - - -
.65 .49 - - - - .37 - - -
.58 .57 - - - - .43 - - -
- - - .92 - - - - - -
.65 .48 - - .31 - .38 - - -
- - - - - - - - - .92
- - - - - - - - .67 .49
- - - - - .88 - - - -
-.47 - - - - .75 - - - -
.52 - - - - 71 - - - -
.64 .59 - - - - - - - -
- - .34 - - - - -.76 .42 -
- - - - - - - - 94 -
- - - - - - - .89 - -
- - .91 - - - - - - -
- 32 - .88 - - - - - - -
- - .92 - - - - - - -
.31 - .91 - - - - - - -
.33 - - - - - .83 - - -
- 33 - -.58 - .35 - - - 38
- - - - - - 37 - - -
.93 - - - - - - - - -
-.92 - - - — - - - - -
-.92 - - - - - - - - -
.93 - - - - - - - - -
36 - - - .87 - - - - -
- - - - .89 - - - - -
- - - .93 - - - - - -
- - - .90 - .34 - - - -
-.39 - - - .41 - - .61 - -

 

8See text in

Materials and

Methods for definition

of traits.

124

Production level was controlled by a combination of several
factors, namely, factor 1, which mainly controlled the interaction
model energy requirements in period 2; factor 2, which mainly
controlled production level in period 1; and factor 7, which mainly
controlled the nonproductive use of energy in production period 2.

The sires breeding value for milkfat production was also
controlled by a combination of several factors: Factor 1, which
controlled interaction model requirements in production period 2;
factor 5, which controlled residual intake and appetite in period 1;
and factor 8, which controlled the nonproductive use of energy in
period 1. The fact that the sires breeding value for milkfat pro-
duction was controlled by a combination of factors which mainly
controlled different traits on the young bull might lead to a way of
developing indirect selection criteria for milk yield based on a
combination of traits measured on the growing bull during the
performance test. It also shows that the genetic correlation between

milk and beef production traits is complex.

Genetic correlations between production traits and partial energy
requirements in production period 1

Genetic correlations between selected production traits and
partial energy requirements from both models are shown in Table 28.
The genetic correlations between production traits and no interaction
model partial energy requirements were generally low. Most pronounced
was an estimate at -.365 between daily feed intake and baseline intake.
The interaction model partial energy requirements in production period

1 were much more closely correlated to the production traits than the

125

no interaction model requirements, except for feed conversion ratio
which was essentially uncorrelated to interaction model energy
requirements in period 1. The interaction model energy requirements in
period 1 were genetically correlated to daily gain and appetite such
that higher daily gain or higher appetite tends to be associated with
higher requirements for growth and weight dependent nonproductive use
of energy, but to a lower baseline intake and also a smaller
interaction component. The interaction model energy requirement in
period 1 were also genetically related to body composition in terms of
dressing percentage and percent fat in the carcass, where the
corresponding phenotypic correlations (not tabled) were essentially
zero.

Table 28.

Genetic Correlations Between Selected Production Traits and Partial
Energy Requirements in Production Period 1.

 

 

Traita DGPl FCRPl DEIPl DRSPCT FATPCT
BIlPl -.128 -.032 -.365 -.013 .010
BGlPl -.023 .021 .033 - 172 -.002
BWlPl -.088 .214 .177 .213 .008
BI2P1 -.225 -.046 -.549 .140 .415
BG2P1 .224 -.003 .467 -.139 -.445
BW2P1 .154 .124 .515 -.149 -.422
BGW2P1 -.204 -.038 -.480 .160 .448

 

3See text in Materials and Methods for definition of traits.

Genetic correlations between production traits and partial energy
requirement in production period 2
The estimates are shown in Table 29. The no interaction model

energy requirements were genetically correlated to daily gain and feed

126

conversion ratio, such that selection for higher daily gain yields a
lower baseline intake and a higher energy requirement for gain and
weight dependent nonproductive use of energy. Results presented in
Chapter 4 showed that selection on daily gain would improve feed
conversion ratio. This is not contradictory to the results obtained
here because the increased growth rate decreases the time needed to
produce a young bull of a given weight so the accumulated maintenance
requirement is reduced. The correlations between interaction model
requirements and feed conversion ratio were similar to those between
interaction model requirements and daily gain, but of opposite sign due
to the definition of feed conversion ratio. The no interaction model
energy requirements were genetically correlated to dressing percentage
such that higher dressing percentage is associated with a higher
baseline intake and a higher energy requirement for growth, but a lower
weight dependent nonproductive use of energy. However, the interaction
model requirements were not related to dressing percentage. The
interaction model requirements in production period 2 were genetically
correlated to daily gain, feed conversion ratio and percent fat in the
carcass with absolute values of estimates in the range .5 to .6. The
corresponding phenotypic correlations (not tabled) were all close to

zero.

Table 29.

Genetic Correlations Between Selected Production Traits and Partial
Energy Requirements in Production Period 2.

 

 

Traita 0092 FCRP2 DEIP2 DRSPCT FATPCT
BIlP2 -.605 .729 -.072 .190 .353
80192 .156 -.384 -.434 .450 -.172
BW1P2 .641 - 616 .396 -.354 -.339
81292 -.576 .696 -.072 .080 .535
80292 .516 -.663 -.039 .137 -.503
BW2P2 .601 -.684 .165 .054 -.542
BGW2P2 -.533 .659 -.014 -.112 .506

 

8See text in Materials and Methods for definition of traits.

Correlations between production traits and residual intake

Table 30 and 31 shows phenotypic and genetic correlations between
selected production traits and residual intake in production period 1
and 2, respectively. Even though residual intake in production period
1 and 2 were almost uncorrelated (Chapter 5), their relation to the
production traits were similar in the two production periods.
Phenotypically, residual intake were not correlated to daily gain as
expected due to the definition of residual intake. However, the
genetic correlation were estimated at approximately .3. This was in
accordance with the genetic correlation between daily gain and energy
requirements, where high daily gain were associated with high energy
requirements for growth and for weight dependent nonproductive use of
energy. Residual intake and feed conversion ratio were positively
correlated phenotypically, with estimates around .4, but the
corresponding genetic correlation were close to zero. Appetite and
residual intake were highly positively correlated, which seems to

indicate that animals with a high appetite tends to use energy less

128

efficient than the average animal. This conclusion was supported by
the correlation between daily intake and energy requirements.
Phenotypic correlations between residual intake and body composition
were low. If body composition was taken into account when calculating
residual intake, the phenotypic correlation between residual intake and
body composition was expected to be zero. The estimates of the
corresponding genetic correlations were negative such that high
breeding value for dressing percentage and percent fat in the carcass
was associated with a low residual intake. This is in accordance with
the results of the factor analysis showing that residual intake and
appetite were controlled by the same underlying factor.

Table 30.

Phenotypic and Genetic Correlations Between Selected Production Traits
and Residual Intake in Period 1.

 

 

 

 

Phenotypic Genetic

Production correlation correlation
traita

RESPl RESCPl RESPl RESCPl
DGPl .003 .004 .319 .326
FCRPl .465 .462 -.044 -.062
DEIPl .783 .781 .598 .581
DRSPCT -.034 .029 -.l29 -.127
FATPCT -.048 -.004 -.058 -.240

 

8See text in Materials and Methods for definition of traits.

129

Table 31.
Phenotypic and Genetic Correlations Between Selected Production Traits
and Residual Intake in Period 2.

 

 

 

 

Phenotypic Genetic

Production correlation correlation
traita

RESP2 RESCP2 RESP2 RESCP2
DGP2 .015 .029 .234 .329
FCRP2 .396 .374 .160 .009
DEIP2 .808 .778 .886 .913
DRSPCT .025 -.017 -.l75 -.192
FATPCT .221 .000 -.129 -.457

 

8See text in Materials and Methods for definition of traits.

Correlations between breeding values of traits measured on male progeny
and breeding value for milkfat production

Correlations between sires' breeding values for beef and energy
requirement traits measured in the experiment and breeding values for
milkfat production from the National population is shown in Table 32.
As mentioned in the section Materials and Methods in this Chapter,
these correlations were not true genetic correlations but only
approximations. The correlation between daily gain and milk fat
production was .36 and .18 for daily gain in production period 1 and 2,
respectively. These results are in line with recent literature
estimates of the genetic correlation between daily gain of a bull and
the milk yield of his daughters, e.g. Van der Werf et al. (1987) who
found an estimate at .21. Breeding values for milkfat production were
uncorrelated to those for dressing percentage but highly negatively
correlated to those for percent fat in the carcass with a correlation
estimated at -.47. Also total energy intake and feed conversion ratio

were negatively related to milk fat production. Note that in this

130

case a negative correlation is advantageous. Appetite had a positive
correlation to milkfat production in production period 1 but a negative
although nonsignificant correlation in period 2. This latter result is
contradictory to the expectation of a positive correlation between
appetite of the ad libitum fed bull and the milkfat production of
female halfsibs, since intake might be a main limiting factor for milk
production of the dairy cow during first lactation. The correlations
between partial energy requirements in production period 1 and milkfat
production were similar to those obtained for the partial energy
requirements in period 2. High breeding value for milkfat production
were associated with high energy requirements for growth and weight
dependent nonproductive use of energy. This unfavorable relation is
offset in correlations between milkfat production and feed conversion
ratio or total energy intake because of the advantageous correlation to
daily gain. Milkfat production and residual intake were positively
correlated in production period 1 but negatively in period 2. However,

none of these correlations were significantly different from zero.

131

Table 32.
Correlations Between Predicted Breeding Values of Sires for Milkfat
Production and Predicted Breeding Values for Traits Measured on Male
Progeny.

 

 

Traita Correlationb Traita Correlationb
WGT28 .42 B1191 -.45
DGPl .36 BGlPl .21
EIPl -.43 BWlPl .33
FCRPl -.28
DEIPl .33 BI2P1 -.37
DMIPl -.40 BG2P1 -.31
BW2P1 .33
DGP2 .18 BGW2P1 .28
EIP2 -.30
FCRP2 -.26 BIlP2 -.l4
DEIP2 -.l6 BGlP2 .15
DMIP2 .12 BWlP2 .02
SLP ~.02 B12Pl -.27
CARGRD -.03 BGZPl .28
FATGRD .05 BW2P1 .24
LEANPCT .33 BGW2P1 -.28
FATPCT -.47
EICG -.27 RESPl .15
RESCPl .22
RESP2 -.34
RESCP2 -.l7

 

8See text in Materials and Methods for definition of traits.
If the correlations, I r I > .3, then P(r-0) < .10.
Conclusions and Implications
The factor analysis proved to be a valuable tool in analyzing
large correlation matrices to locate groups of traits that vary
together as units. The results of this analysis showed that the
partial energy requirements of individual bulls could best be estimated
in a model that included requirements for baseline intake, weight
dependent nonproductive use of energy, productive use of energy and an
interaction between productive and nonproductive energy use. The

partial energy requirements from this model were very strongly

132

intercorrelated and essentially controlled by a single underlying
factor.

The results also indicated that there was no strong relation
between carcass composition and partial energy requirements when
observed within a relatively homogeneous population. This is opposed
to a common assumption of a close relation between net energy
requirements of growing cattle and the proportion of fat in the carcass
(Robelin and Daenicke, 1980). The phenotypic correlations between
daily gain and partial energy requirements were very low. However,
there were genetic correlations, especially in production period 2,
such that selection for increased daily gain would increase the partial
energy requirement for growth and for weight dependent nonproductive
use of energy, but decrease the baseline intake. Increased growth rate
would also reduce the time needed for a young bull to reach a given
weight and thus reduce the accumulated maintenance requirement.

Residual intake was closely related to appetite. Selection for
increased appetite would increase residual intake and thus lead to less
efficient animals. The results reported in Chapter 4 indicated that
selection for increased appetite would lead to leaner animals at a
constant weight.

The genetic correlations between daily gain and milk production in
terms of milkfat were positive, with the highest correlation when daily
gain was measured in production period 1. This correlation was carried
over to total energy intake and feed conversion ratio due to the close
relation between these traits and daily gain.

The genetic correlation between milkfat production and appetite

133

was positive for appetite in production period 1, but negative in
period 2. This was in contrast to prior expectations, since feed
intake is a major limiting factor for milk yield in the lactating cow.

Correlations were also found between milkfat production and
partial energy requirements such that selection for increased milk
production would tend to increase the energy requirement for weight
gain and weight dependent nonproductive use of energy, but decrease the
baseline feed intake.

The factor analysis showed that the sires' breeding values for
milkfat production can partly be described by a combination of several
factors measured on young bulls. It might lead to a way of developing
indirect selection criteria for milk yield based on a performance test

of potential AI bulls.

CHAPTER 7

Additive and Heterotic Effects of Immigration of Brown Swiss
Genes Into the Red Dane Cattle Population on Production

and Calving Traits

134

135

Introduction

Although crossbreeding programs are common in swine, broilers, and
beef cattle such programs are rare in dairy or dual purpose cattle.
However, experiments have shown significant heterosis effects in
production traits (E.g. Christensen and Pedersen, 1988, Robison et al.
1981).

Many dual purpose or dairy populations throughout the world have
initiated immigration programs especially with germ-plasm from North
America. Import of genes to the Red Dane breed was initiated during
the seventies, first with imports in a planned experiment reported by
Christensen and Pedersen (1988), and then in a field study (Kim et al.,
1984). Later large scale imports of genes primarily from American Brown
Swiss have been made.

Immigration of genes can give rise to effects similar to what can
be expected in a crossbreeding program. These effects are due to
additive genetic differences between the breeds involved and heterosis.
Heterosis is defined as the deviation of the performance of crosses
from the expected performance based on the additive breeding value of
the breeds involved. These deviations are mainly caused by intralocus
interactions (Dominance) and interlocus interactions (Epistasis). 0f
epistatic effects, additive by additive interactions is generally
thought to be the most important (Christensen and Pedersen, 1988,
Kinghorn, 1980, Rendel 1953). Additive by additive epistatic effects
are often expected to be negative. The reason being that selection in
the parent breeds have favored gene complexes together instead of

single genes. Such gene complexes are then broken down in crossbreeding

136

programs (Kinghorn, 1983). Such effects are therefore often termed
recombination loss (Dickerson, 1969) or F2 breakdown (Hill, 1982).

Crossbreeding programs or immigration programs in cattle almost
invariably includes many types of crosses so that recombination effects
might become important in predicting responses to such programs.

The main objective of the present investigation was to obtain
crossbreeding effects between the Red Danish and the Brown Swiss breed
for production and calving traits and to investigate whether
recombination effects were of importance between the breeds involved.
These effects are between breed genetic effects. Within breed effects,

in terms of genetic parameters will be reported in a companion paper.

Materials and Methods

Definition of traits

Three production traits and three traits related to calving were
analyzed. The production traits were 305-d milk production in kg (MLK),
305 d butterfat production in kg (FAT) and 305 d protein production in
kg (PRT). All three traits were recorded during first lactation. The
calving traits were calving difficulty (DIF), calf survival (SURV) and
calf size (SIZE). The calving traits were recorded by individual
farmers on all calvings reported after October 1984. Farmers were
required to record SURV on all calvings while DIF and SIZE were
optional. DIF was recorded on a scale from 1 to 4; with 1 being easy
without help, 2 being easy with help, 3 being difficult but without
veterinary assistance, and 4 being difficult with veterinary

assistance. SURV was coded as l for stillborn, 2 born alive but dead

137

within 24 h, 3 born alive but dead after 24 h but before the first milk
test day and, 4 was born alive and still alive on first test day after
calving. SIZE was recorded as; 1 little, 2 somewhat below average, 3

somewhat above average, and 4 large.

Records

Pedigree information on 593,585 females born in the period from
1978 to 1988 inclusive was obtained from the Danish Dairy Records
Processing Center. Production and calving records on cows freshening in
the period 1980 to 1988 was obtained. Only records with known
calving/lactation number was included. This yielded a total of
1,034,156 records. The production and calving records were merged with
the pedigree file and all animals without production/calving records or
with parity number greater than 3 were deleted. This procedure left a
total of 858,464 records.

Three more steps of editing was done. In the first step,
production records with MLK, FAT or PRT outside the intervals
[l,500;l2,500], [70;425] and [50;375] kg, respectively, were deleted.
Other reasons for deletion were; days in milk less than 100-d, previous
calving interval outside the interval [280;500] d, age at first calving
outside the interval [19;42] months, sire of cow or sire of calf not
registered. The editing steps mentioned above reduced the dataset to
565,090 records. In the next editing step, second and third parity
records were deleted if one or more of the previous records were
missing. In other words all previous records were required to be
present for second and third lactation records. This rule reduced the

dataset to 504,065 records. In the third step, every herd-year group,

138

sire of cow group, and sire of calf group was required to be
represented with at least 5 records on first lactations/calvings. This
rule was applied iteratively until all three rules were satisfied
simultaneously. This finally left 308,382 records on 170,166 cows
available for analysis. In this investigation, however, only records on
first lactation/calving records were used. The amount of information on
each animal varied. The number of records for each trait together with

average and phenotypic SD are shown in Table 33.

 

 

 

Table 33.

No. of observations, mean, and phenotypic SD for traits analyzed.
Trait Abbreviation N Mean SD
Milk production, kg MLK 146179 5370 737
Fat production, kg FAT 146179 222.5 30.2
Protein production, kg PRT 110331 186.7 26.2
Calving difficulty DIF 74297 1.71 .73
Calf survival SURV 103830 3.75 .77
Calf size SIZE 80363 2.45 .72

 

For each record, the proportion of genes originating from
different populations were known from pedigree information. Genes from
a total of 10 different populations were present in data. However only
native Red Dane (R) and Brown Swiss (B) had gene proportions of more
than two percent. Therefore, all other breeds were combined into one
group called Other (0). For each record gene proportions on five
individuals were known; the calf born, the cow, the sire of calf, the
sire of cow (Maternal grandsire of calf), and the dam of cow (Maternal
granddam of calf).

Based on information on gene proportions, the expected amount of

139

heterozygosity in cow and offspring were computed, together with

proportion of pairwise non-allelic genes that were of different breed

origin. Examples of such coefficients involving R and B are shown for

different types of crosses in Table 34.

Table 34.

Coefficients of crossbreeding parameters for cows and progeny in

various crossbreeding systems.

 

 

 

 

 

 

 

Mating Cow
(Cow) x (Sire) 9(9) 9(8) hC aC
R,B R,B
RxR 1 0 0 0
BxB 0 1 0 0
Change of breed from R to B
RxB l 0 0 0
[RxB]xB .5 .5 1.0 .5
[(RxB)xB]xB .25 .75 .5 .375
[((RxB)xB)xB]xB .125 .875 .25 .2188
Change of breed from B to R
BxR 0 l 0 0
[BxR]xR .5 .5 1.0 .5
[(BxR)xR]xR .75 .25 .5 .375
[((BxR)xR)xR]xR .875 .125 .25 .2188

Continued breeding of crosses (Synthetic)

 

[RxB][RxB] .5 .5 1.0 .5
[(RxB)(RxB)]2 .5 .5 .5 .5
Rotgtional crossing

RxB l 0 0 0
[RxB]xR .5 .5 1.0 .5
[(RxB)xR]xB .75 .25 .5 .375
[((RxB)xR)xB]xR .375 .625 .75 4688

 

 

 

Progeny

P(R) 9(8) h§,3 aE’B
1 0 0 0

0 1 0 0

.5 .5 1.0 .5
.25 .75 .5 .375
.125 .875 .25 .2188
.0625 .9375 .125 .1172
.5 .5 1.0 .5
.75 .25 .5 .375
.875 .125 .25 .2188
.9375 .0625 .125 .1172
.5 .5 .5 .5

.5 .5 .5 .5

.5 .5 1.0 .5
.75 .25 .5 .375
.375 .625 .75 .4688
.6875 .3125 .625 .4297

 

Models

Crossbreeding parameters have traditionally been estimated by

least squares procedures. However, as shown by Kommender and Hoeschele

(1989),

the use of mixed models reduces the true SE of the estimates

140

obtained. Use of mixed models also should reduce biases resulting from
using data from populations undergoing selection. The crossbreeding
parameters to be estimated were between breed additive genetic
differences, dominance effects and additive by additive epistatic
effects. These effects were estimated both as effects of the cows
genotype and of the offspring (calf) genotype.

The model for calving traits were:

yijklmnopqr - H + SPEAE + Zthng + EaEJ(AXA)EJ
+ 2159A? + 21191091 + 2391(AXA)?J
+ hyk + m1 + tm + kn
+ 8o + 83(0) + 1/253(o) + 52(0) + eijklmnopqr [1]
Elements in the model with a superscript C (Cow) were considered

an effect of cow genotype and similar effects with superscript O

(Offspring) were considered and effect of the offspring genotype.

Definitions for the model are:

p is an overall mean;

p? is the proportion of genes in the cow from the ith breed (R,B,O); A?
is the additive genetic effects of the 1th breed on the cow
performance;

hgj is the proportion of loci with one gene from breed 1 and one gene
from breed j. Together the hEJ describes the degree of
heterozygosity of the cow due to breed origin;

DEJ is the dominance effect on the cow due to within locus interactions
of genes from breed i and j;

agj is the proportion of pairwise non-allelic genes in the cow that

were of different breed origin;

141

(AXA)Ej is the additive by additive recombination effects between breed
1 and j;

Similar crossbreeding effects were defined for the progeny genotype,
all denoted with superscript O.

hyk is the effect of the kth herd-year;

1th

m1 is the effect of the month of calving;

t is the effect of the mth

m age group at first calving, with ages

grouped in one month intervals;

h

kn is the effect of the nt sex of calf.

th

go is the effect of the o sire group;

th th

Sg(o) is the effect of the p sire of cow nested within the o sire

group;

h

53(0) is the effect of the pt maternal grandsire of offspring nested

within the 0th sire group.
58(0) is the effect of the qth sire of calf nested within the 0th sire
group
eijklmnopqr was a residual.
All effects except 53(0), 1/233(o), 32(0), and eijklmnopqr were

considered fixed. Model [1] was similar for production traits except

th

that kn was replaced with d where dn was the effect of the n group

n!
O O

of days in milk, grouped in 10 d intervals. Also, l/2sp(o) and Sq(o)

were dropped from the model. The proportion of R genes in cows and

offspring was not included in the model. The reason was that all gene

proportions sum to 1.0 and thus creating a linear dependence. The

proportion of R genes were therefore dropped from the model as a

constraint. This means that all effects are expressed relative to

142

native Red Dane genes.

Reduced models were also run. In model [2] all recombination
effects were left out. Model [3] and [4] were run only on production
traits and did not include effects of calf genotype. Model [3] included
recombination effects, whereas these effects were left out in model
[4]. The reasons for running models without recombination effects were
that several authors (e.g. Cunningham, 1987) maintains that
crossbreeding effects can be sufficiently described using models
including only additive and dominance effects.

The models took additive genetic relationships due to sires and
maternal grandsires into account. Genetic parameters used to obtain

C O

variances of s , s and e, and the covariance between sC

and so, where

applicable, were estimated from the same data and will be reported in
Chapter 8.

The models lead to systems of equations of order from 10,614 to
16,661 to be solved, so these systems had to be solved iteratively. SE
of estimates are functions of diagonal elements of the inverse of the
coefficient matrix and could therefore not be obtained. Tests of
various hypothesis were therefore instead obtained from least square

analysis with similar models, but with effects of sires ignored.

Results and Discussion
Gene and Loci Fractions
The average proportion of genes immigrated into R from B and O are
shown in Table 35 for genes in both cows and offspring. The average
proportion of B genes in cows were .101, which increased to .137 in the

progeny, a reflection of a continuing immigration of genes from B over

143

time since offspring of course were born later than cows. The
proportion of genes other than R and B1 (0)1 were 2-3% in both cows and
progeny. In order to estimate crossbreeding effects, there must be
variation in the different gene proportions. That such variation indeed
were present is illustrated by the SD of the gene proportion and is
also shown in Table 35.

Table 35.

Average and SD of various proportions of genes and loci in cows and
progeny and correlation between cow and progeny proportions.

 

Corr.
Cow/
Average SD Progeny
Proportion in cows
Genes from B .101 .145 .979
Genes from O .021 .071 .961
Loci with genes from both R & B .184 .258 .513
Loci with genes from both R & O .038 .132 .363
Loci with genes from both B & O .004 .025 .282
Pairwise nonallelic genes from R & B .138 .182 .967
Pairwise nonallelic genes from R & O .030 .096 .963
Pairwise nonallelic genes from B & O .002 .013 .972
Proportions in progeny
Genes from B .137 .203
Genes from O .027 .198
Loci with genes from both R & B .220 .234
Loci with genes from both R & O .053 .139
Loci with genes from both B & O .011 .040
Pairwise nonellelic genes from R & B .153 .208
Pairwise nonellelic genes from R & O .031 .108
Pairwise nonellelic genes from B & O .002 .010

 

The amount of dominance effects expressed by an individual is
proportional to the fraction of loci with genes from two breeds. In
cows, this proportion for (R,B) dominance interactions was on average

.184 for cows and .220 for progeny with SD .258 and .203, respectively.

144

This means that .184 and .220 of total dominance effects were expected
to be present in the overall average. The SD shows that there were
considerable variation among animals, both cows and progeny, in the
expected degree of dominance expressions. Finally, the degree of
additive by additive recombination effects is expected to be
proportional to the fraction of pairwise non-allelic genes descending
from two breeds. For R and B recombination effects this fraction was on
average .138 for cows and .153 for offspring with SD .182 and .208,
respectively. The fraction of loci with genes descending from two
breeds or the fraction of pairwise nonallelic genes from two breeds
were all small if not both of the R and B breeds were involved.

The 16 proportions of genes and loci computed for each cow/calf
pair, with averages shown in Table 35, were not independent of each
other. An optimum design for estimating crossbreeding effects would
have these effects orthogonal to each other. Such designs usually
cannot be obtained, even in planned experiments (Robison, 1981) and
certantly not when field data are used. The lack of orthogonality is
illustrated in Table 35 by the correlation between gene/loci
proportions for similar effects in cows and offspring. It is seen that
in many cases these proportions were highly correlated as were also
several other fractions. These correlations mean that the partial
effect of including/excluding a particular crossbreeding effect in the
model might be expected to be small even though interpretation of an
estimate might be dependent of what other effects that were included in
the model simultaneously. Biases in various estimates of crossbreeding

parameters were shown for various designs by Hill (1982).

145

Significance of Crossbreeding Effects

Levels of significance for partial F-tests in model [1] associated
with contrasts for various crossbreeding effects are shown in Table 36.
For production traits, all contrasts except effects of dominance in
progeny were highly significant. That the effect of progeny genotype on
subsequent production was significant was somewhat surprising. The
results in Table 36 also shows that both cow and progeny recombination
effects were highly significant. That the genotype of offspring might
influence subsequent production has been indicated on a within breed
basis in investigations by Skjervold and Fimland (1975).

For calving traits, the only significant individual effect were
effect of dominance in progeny for DIF and SIZE. However, the combined
tests shows significant additive, dominance and recombination effects
for both DIF and SIZE. The reason is that the different effect are
highly correlated as explained in the previous section. For SURV the
overall cow effect was significant even though none of the individual
effects were significant.

Most models used to estimate crossbreeding effects only include
additive and dominance effects (Cunningham, 1987). The models were
therefore run without recombination effects included. As can be seen in
Table 36 Rz-values were hardly reduced by leaving out the recombination
effects even though results from model [1] showed that these effects
were highly significant. Similar effects were seen for production
traits when leaving out effect of progeny genotype. One reason for this
is that the various effects are highly correlated, so that estimates of

remaining effects may change considerably when some effects are left

146

out of the model.

 

 

 

 

 

Table 36.

Levels of significance for crossbreeding effects in LS-model [1].
Effect MLK FAT PRT DIF SURV SIZE
Cow Additive .0001 .1308 .0038 .4255 .5647 .2832
Cow Dominance .0001 .0001 .0001 .3132 .7815 .2377
Cow A x A .0001 .0474 .0010 .4649 .6727 .1696
Progeny Additive .0001 .0001 .0002 .5806 .4940 .3342
Progeny Dominance .3497 .8484 .0031 .0001 .9941 .0001
Progeny A x A .0001 .0001 .0001 .6490 .6980 .1433
Overall Additive .0001 .0001 .0006 .1224 .1502 .0087
Overall Dominance .0001 .0003 .0001 .0001 .9789 .0001
Overall A x A .0001 .0001 .0001 .0001 .7899 .0179
Overall Cow .0001 .0001 .0001 .0005 .0002 .2621
Overall Progeny .0001 .0001 .0001 .0001 .6059 .0001
R2 - Model [1] .651 .663 .677 .219 .098 .213
R2 - Model [2] .650 .663 .677 .218 .098 .212
R2 - Model [3] .650 .662 .677

R2 - Model [4] .650 .662 .676

 

Crossbreeding Effects

The estimates of crossbreeding effects from model [1] are shown in
Table 37. Of particular interest in this model is the recombination
effects. For production traits the effect of recombination in the cows
own genotype were large and negative, with estimates of -1328, -32.8
and -53.6 kg, for MLK, FAT and PRT, respectively. This, however was to
some degree counteractered by a positive effect of recombination in the
genotype of calves, with estimates of 611, 17.3 and 22.5 kg MLK, FAT
and PRT, respectively. In general, most estimates for production traits
was surprisingly large, and similar effects of cow and progeny genotype
were generally opposite in sign. Whether these effects have an

underlying physiological explanation or are merely an artifact of the

147

model cannot be determined from the present data.

For calving traits, positive recombination effects for cow
genotype were found for DIF and SURV, but negative effects were found
for SIZE. The recombination effects of cow genotype were small for SURV
and SIZE, but for DIF the recombination effects of cow and offspring

genotype were of the same magnitude although opposite in sign.

 

 

 

 

 

Table 37.

Crossbreeding parameters estimated in Model [1].

Effect MLK FAT PRT 019 SURV SIZE
Ag 1065 14.3 40.5 -.44 .08 .22
Ag -815 -18.3 1.2 -.62 -.42 .90
03.3 848 26.1 32.0 .02 -.06 .09
03,0 46 9.2 2.2 -.53 .21 .27
0g,0 1369 85.9 40.2 -.62 -.30 1.36
AxAg B -1328 -32.8 -53.6 .09 .19 -.16
AxAE’O 1289 19.0 10.4 1.19 -.09 -.67
8x83 0 350 -11.2 12.5 1.11 .82 -4.37
A3 -850 -20.1 -29.0 .11 .04 -.11
A8 1238 23.0 -14.8 .41 .20 -.63
03,8 -2 .0 .0 .06 .10 .13
03,0 20 .3 2.7 .08 .01 .09
03,0 -67 -3.0 -.9 .01 .07 .19
AXAE’B 611 17.3 22.5 -.10 .03 .0
AxAg O -1150 -23.6 2.9 -.29 -.11 .38

AxAg 0 -3063 -173.7 -91.7 -.04 -.20 2.10

 

148

The estimates of crossbreeding parameters from model [2] with
recombination effects dropped are shown in Table 38. For production
traits, estimates of remaining crossbreeding parameters changed
dramatically when recombination effects were deleted from the model.
The effects of offspring genotype is now relatively small and do not
counteract effects of cow genotype. The model indicates that B is
inferior to R in production. A direct comparison of breeds and various
crosses will be discussed in a later section.

For calving traits results shows that B has considerable less
calving difficulty than R with an estimate of -.37 units in additive
genetic difference in maternal calving ability. For direct effects
(calf genotype) the effect is .06, e.g. an increase in calving
difficulty. That means that B cows calve easily, but B calves tend to
have difficult births.

Similar trends can be seen in SURV. B cows give birth to calves
with a higher survival rate, but B calves tend to have a lower survival
rate. Both cow and calf dominance effects tended to improve survival.
For SIZE, B cows give birth to larger calves, whereas there were no
direct additive effect on calf size. There were no maternal dominance
effects on calf size, but a positive effect on calf size from dominance

in the calf (Direct effect).

149

 

 

 

 

 

Table 38.

Crossbreeding parameters estimated in Model [2].

Effect MLK FAT PRT 019 SURV SIZE

Ag -60 -13.6 -4.1 -.37 .26 .07

Ag 304 .7 8.9 .33 -.44 .24
0g 3 409 16.2 13.6 .02 .05 .01
c

DR,O 242 9.8 7.8 '.04 .12 .09
0g 0 419 15.5 11.7 -.07 .04 -.03

Ag -83 -.2 .2 .06 -.07 -.01

A8 112 -1.0 -15.2 -.06 .11 -.14
o

DR’B -3 .0 .0 .06 .10 .13
0

03,0 19 .3 2.7 .08 .01 .09
o

DB’O -60 -3.1 -.9 .01 .06 .19

 

Crossbreeding effects on production traits estimated in model [3]
and model [4] with effects of calf genotype dropped in shown in Table
39. Again results show that B are inferior to R in production traits,
with an estimate of the additive genetic difference between R and B of
12-14 kg butterfat in favor of R. Recombination effects in this model
was negative, as expected, and with estimates of -l35, -2.6 and -14.5
for MLK, FAT and PRT respectively. Results from model [3] and [4] also
showed estimates of dominance effects on production traits ranging from

7.2% to 10.9%.

 

150

Table 39.
Crossbreeding parameters for production traits estimated in Model [3]

and Model [4].

 

 

 

 

 

 

 

 

Model [3] Model [4]
Effect MLK FAT 981 MLK FAT 981
Ag -28 -12.0 4.6 -114 -13.8 -4.1
A8 45 -2.3 -6.7 359 -.4 1.8
DE’B 461 17.3 20.4 398 16.1 13.6
og,o -19 7.5 1.2 256 9.9 7.4
0g,0 1010 79.2 28.3 407 15.3 12.1
AxAg B -l35 -2.6 -14.5 --- ---- ----
Axag O 577 4.6 13.2 --- ---- ----
AxAg O -1246 -128.1 -32.5 --- ---- --.-

 

Heterosis Effects

Heterosis expressed as the expected performance of F1 crosses
deviated from the average of the R and B purebreds is equal to the
dominance effects between R and B plus half the recombination effects
between the two breeds. The heterosis expected in F1 animals is
summarized in Table 40 for estimates from all models.

For production traits estimates from models [2], [3] and [4] are
all in very close agreement. Results from model [2] indicates that
effects of calf dominance on subsequent production of the cow seems to
be small. Estimates of F1 heterosis, expressed in percent of the
overall average, range from 7.1 to 7.6% when estimates from model [2],
[3] and [4] are considered. Individual estimates from model [1] are

lower, but the effect of heterosis in cow and calf are to some degree

 

151

additive and of the same sign. The exact degree of F1 heterosis
estimated in model [1] then depends on both the cow and the calf
genotype, and will be discussed in a later section where various
breeding systems are compared.

Estimates of heterosis estimates of 7.1 to 7.6% are in good
agreement with several literature estimates. E.g. Robison et al.
(1981), who found estimates of 5.1%, Rincon et al. (1982) with
estimates of 5.9% , Hollon et a1. (1969) who found an estimate of 8.7%
and Christensen and Pedersen, (1988) who found and estimate of 6.7%.
All the above results were estimated in models that ignored
recombination effects.

Both models show that calving difficulty increases in F1 animals,
both as a function of cow genotype and of offspring genotype. This is
in contrast to most literature reports that shows increased calving
difficulty when the offspring is crossbreed, but a decrease in calving
difficulty when the cow is crossbred. E.g. Vesely et a1. (1986), Kim
and Petersen (1985), and Christensen and Pedersen, (1988).

For calf survival estimates from model [1] and [2] are in good
agreement. (Table 40). Heterosis in both cow and calf have a positive
effect on calf survival. This again is in contrast to the literature
cited above, where most authors found that crossbreed offspring had
lower survival but that but that crossbreed cows increased the
survival rate of the offspring.

Calf size were not influenced by heterosis in the cow, but
crossbreed progeny were larger. The agreement between model [1] and

model [2] was very good for calf size.

152

 

 

 

 

Table 40.
Estimates of F1 Heterosis from different models.
MLK FAT PRT DIF SURV SIZE
Model [1]
Cow Genotype 185 9.7 5.2 .07 .04 .01
Calf Genotype 304 8.7 11 3 .01 .12 .13
Model [2]
Cow Genotype 409 16.2 13.6 .02 .05 .01
Calf Genotype -3 .0 .0 .06 .10 .13
Model [3]
Cow Genotype 394 16.0 13.2 --- --- ---
Model [4]
Cow Genotype 398 16.1 13.6 --- --- ---

 

Response to Various Breeding Systems

As discussed in the previous section, parameters estimated in
different models vary considerably. To gain a better understanding of
various effects, responses to different breeding systems were
estimated. The systems compared were: purebred R, purebred B, change of
breed from R to B by continued use of B bulls, change of breed from B
to R by continued use of R bulls. A synthetic breed consisting of 50%
genes from each of R and B and created by mating F1 animals and so on,
and finally a system using rotational crossing by using purebred B and
R bulls alternately in each generation starting out from R cows. The
coefficients needed for each program in the initial generations are
shown in Table 34.

The only production trait discussed is FAT, whereas all calving
traits are discussed. Estimated responses in FAT estimated in all four
models is shown in Table 41. All results are shown relative to purebred

R which always are zero. Estimated responses from models [2], [3] and

153

[4] all show good agreement, whereas model [1] differs in several
instances. All models predict lower performance of purebred B cows with
estimates of a 12-14 kg lower butterfat production of B cows estimated
in models [2], [3] and [4]. Model [1] only estimates a 6 kg genetic
inferiority of the B breed in comparison with R. The reason for this
can be seen in the system of change of breed from B to R. In generation
0, when the cow is purebred B, but carries an F1 offspring, model [1]
estimates a large positive effect on subsequent production when a cow
with B genes carry an F1 calf. On the other hand as seen in generation
0 of the system of changing breed from R to B, model [1] predicts a
slight decrease in production when an R cow carries F1 progeny. Change
of breed from R to B would increase production in generation 1 with 8-
10 kg FAT in first lactation. In subsequent generations production
would gradually regress bach to the B purebred level, as dominance
effects are lost and additive genetic effects of B becomes more
important.

Change of breed from B to R would yield even larger increases in
the production of F1 cows as compared to generation 0 cows. Model [2],
[3] and [4] estimates increases of 22-23 kg FAT. Model [1] estimates
much smaller increases due to the large positive effect of B cows
carrying F1 progeny. I.e. B cows would show a large increase already in
generation 0. In later generations production gradually approaches the
level of purebred R performance.

The use of a synthetic breed with 50% genes from each breed shows
a large positive effect of 10-16 kg FAT of the F1 cows. In generation 2

and all subsequent generations production regresses back to a level

154

slightly above that of purebred R cows.

The last crossbreeding system investigated was a two-breed
rotational system with alternate use of purebred bulls. Again estimates
from model [2], [3] and [4] are very similar, with large positive
effects in early generations, similar to the effects seen when changing
breed. In later generations production declines to a level 3.4 kg FAT
above that of purebred R cows, but 16-17 kg FAT above that of purebred
B cows. Estimates of effects of rotational crossing in model [1]
differs again considerable from the other models, due to the large
positive effect when a cow with a large proportion of B genes is mated
to an R bull.

Responses in calving traits, estimated in models [1] and [2] in
the same breeding systems are shown in Table 42. For DIF both models
predict a genetic difference between R and B of .31 to .33 units in
favor of B. This corresponds to .42 to .45 phenotypic standard
deviations.

In the system of change of breed from R to B the estimate in
generation 0 shows that when an R cow carries an F1 offspring DIF is
increased by .07 to .09 and then reduces in subsequent generations when
the cow either becomes crossbreed or carries a large proportion of B
genes. In the reciprocal system of changing breed from B to R it is
seen that B cows carrying F1 offspring do not experience increased DIF.
Model [1] even predicts an improvement in DIF, -.38 versus -.33 for the

purebred B cow carrying B offspring.

155

 

 

 

 

 

 

 

 

Table 41.

Response in FAT from various crossbreeding systems.

Mating Model

(Cow) x (Sire) Gen [1] [2] [3] [4]
Purebred R --- 0 0 0 0
Purebred B --- -5.8 -13.8 -12.0 -13.8
Change of breed from R to B

RxB O -1.4 -.1 0.0 0.0
[RxB]xB l 8.3 9.3 10.0 9.2
[(RxB)xB]xB 2 -2.3 -2.3 -1.3 -2.3
[((RxB)xB)xB]xB 3 -5.0 -8.3 -6.7 -8.1
Change of breed from B to R

BxR 0 12.9 -l3.7 -12.0 ~13.8
[BxR]xR 1 18.3 9.4 10.0 9.2
[(BxR)xR]xR 2 5.6 4.7 4.6 4.6
[((BxR)xR)xR]xR 3 1.9 2.3 2.3 2.3
Continued breeding of crosses (Synthetic)

RxB 0 -l.4 -.1 0.0 0
[RxB][RxB] 1 15.5 9.3 10.0 9.2
[(RxB)(RxB)]2 2 2.4 1.2 1.4 1.2
Rotational crossing

RxB 0 -l.4 -.1 0.0 0.0
[RxB]xR l 18 3 9.4 10.0 9.2
[(RxB)xR]xB 2 -.l 4.6 4.7 4.6
[((RxB)xR)xB]xR 3 14.3 3.6 4.3 3.5

 

Estimated effects on SURV from the various breeding programs is
also shown in Table 9 for both models [1] and [2]. Results shows that B
has a higher survival rate than R with a difference of .12 to .19
corresponding to .16 to .25 phenotypic SD. All crossbreeding programs
shows positive responses in early generations. Of course the system of
changing breed from B to R will eventually revert back to the purebred
R level. The largest discrepancies between estimated responses from
model [1] and [2] is in the rotational system. This indicates that

recombination effects might be of some importance for SURV.

156

Finally, effects of the breeding systems in SIZE is shown in Table 10.
Purebred B calves are .06 to .11 units larger than R calves,
corresponding to .08 to .15 phenotypic standard deviation units. From
the systems of change of breed it is seen that if a cow carries a
crossbreed progeny SIZE is increased considerably, whereas effects in
later generations are smaller.

Table 42.

Response in calving traits from various crossbreeding systems depending
on estimation model.

 

 

 

 

 

 

 

 

 

 

 

Mating DIF, Model SURV, Model SIZE, Model
(Cow) x (Sire) Gen [1] [2] [l] [2] [l] [2]
Purebred R --- .00 .00 .00 .00 .00 .00
Purebred B --- -.33 -.31 .12 .19 .11 .06
Change of breed from R to B

RxB 0 .07 .09 .14 .07 .08 .13
[RxB]xB l -.08 -.09 .17 .18 .10 .10
[(RxB)xB]xB 2 -.20 -.2O .17 .18 .09 .08
[((RxB)xB)xB]xB 3 -.26 -.26 .15 .19 .09 .07
Change of breed from B to R

BxR 0 -.38 -.28 .22 .33 .30 .20
[BxR]xR l —.14 -.12 .15 .21 .16 .11
[(BxR)xR]xR 2 -.06 -.06 .10 .11 .06 .05
[((BxR)xR)xR]xR 3 -.03 -.03 .06 .05 .02 .03

Continued breeding of crosses (Synthetic)

 

RxB 0 .07 .09 .14 .07 .08 .13
[RxB][RxB] l -.12 -.11 .16 .20 .13 .11
[(RxB)(RxB)]2 2 -.13 -.12 .19 .17 .09 .10
Rotational crossing

RxB 0 .07 .09 .14 .07 .08 .13
[RxB]xR 1 -.14 -.12 .15 .21 .16 .11
[(RxB)xR]xB 2 .oo .oo .18 .12 .07 .11
[((RxB)xR)xB]xR 3 -.19 -.16 .18 .24 .18 .13

 

157

Conclusions

For production traits, analysis indicate some effects on calf
genotype on the subsequent production of the cow. This was especially
so if recombination effects was included in the model. Whether these
effects was due to underlying physiological interactions or was an
artifact of the model could not be determined from the present data. If
recombination effects were removed from the model there were no effects
of calf genotype on the subsequent production of the cow. Models
without effects of offspring genotype indicated recombination effects
from -1.1% to -7.7% with small effects on MLK and FAT but relatively
large effect on PRT.

Most of the models used on production traits yielded F1 heterosis
of 7.1 to 7.7%. Such an effect should therefore be beneficial in
crossbreeding programs. Positive heterosis, however, was to some degree
counteractered by a large genetic difference between R and B in favor
of R, with R being 2.6 to 6.2% superior to R in FAT. The benefits to R
breeders in production traits is therefore minimal after the initial
generations where the cow expresses large levels of heterosis. For B
breeders, however there seems to be a large advantage in production
traits to be gained from introducing R genes into their population.

For calving traits results showed a large genetic difference in
favor of B for DIF and SURV. Heterosis effects tend to increase DIF,
both when the cow is crossbred and when the calf is crossbred. However
for calf survival both these effects were positive. Heterosis effects
on DIF and SURV were small compared to the additive genetic difference

between R and B.

158

The overall advantage of crossbreeding to R breeders is small. The
easiest breeding system for R breeders to implement seems to be the
creation of a synthetic based on R and B genes, which is also what
happens in practice (Table 35). This system would also reduce calving
difficulty and improve calf survival.

For B breeders there would be a large advantage in production by
introducing R genes into their population. However, this would have

some negative effects on calving difficulty and calf survival.

CHAPTER 8

Genetic Parameters of Dairy Production and Calving Traits
in

Danish Red Cattle

159

160

Introduction

Simultaneous selection for several characteristics requires
knowledge of genetic parameters in terms of SD, heritabilities and
phenotypic and genetic correlations. In most cattle populations the
major selection emphasis has been on milk production traits. However,
several other traits are of economic importance, for example dystocia
and stillbirth. Philipsson (1976) assessed the cost related to the
dystocia-stillbirth complex. He found costs associated with increased
dystocia and stillbirth amounting to more than 50% of calf value per
case of dystocia. These costs, however, are very dependent on calf
price so it is difficult to translate such calculations into other
economic conditions. Nevertheless, his results indicated that
selection for decreased dystocia and stillbirth might be worthwhile.
Result of evaluating sires for dystocia and stillbirth maybe more
important from another standpoint, that is to find sires suitable for
heifer matings, where the dystocia and stillbirth problems are most
prevalent. Meijering (1984) gave an excellent review of current
knowledge about the dystocia and stillbirth complex in cattle.

Genetic variation in dystocia and stillbirth stems from both the
genotype of the cow (maternal effects) and the genotype of the calf
(direct effects) and there may exist a genetic correlation between
these effects (Van Vleck, 1978). This complicates the estimation of
genetic parameters of maternal and direct effects on calving traits.
In order to separate these effects, models that simultaneously include

effects of both dam and progeny genotype must be used.

161

The objective of this study was to obtain genetic parameters of
production and calving traits in Danish Red Cattle and to study the

genetic and phenotypic relationships between these traits.

Materials and Methods

Definition of traits

Three production traits and three traits related to calving were
analyzed. The production traits were 305 d milk production in kg
(MLK), 305 d butterfat production in kg (FAT) and 305 d protein
production in kg (PRT). All three traits were lactation totals in the
first parity. The calving traits were calving difficulty (DIF), calf
survival (SURV) and calf size (SIZE). The calving traits were recorded
by individual farmers on all calvings. SURV must be recorded on all
calvings while DIF and SIZE were optional. DIF was recorded on a scale
from 1 to 4; with 1 being easy without help, 2 being easy with help, 3
being difficult but without veterinary assistance, and 4 being
difficult with veterinary assistance. SURV was coded as 1 for
stillborn, 2 for born alive but dead within 24 h, 3 for born alive but
dead after 24 h but before the first milk test day and, 4 for born
alive and still alive on first test day after calving. SIZE was
recorded as; l for little, 2 for somewhat below average, 3 for somewhat

above average, and 4 for large.

Records
A total of 170,166 cow-calf pairs were available for analysis. A
complete description of editing procedures was given in Chapter 7. The

number of observations on each individual trait or combination of two

162

traits are given in Table 43.

Table 43.
Number of observations for each trait (on diagonal) and combination of
two traits (off diagonal).

 

 

 

 

MLK FAT PRT DIF SURV SIZE
Milk prod. (MLK) 146,179
Fat prod. (FAT) 146,179 149,179
Protein prod. (PRT) 110,331 110,331 110,331
Calf diff. (DIF) 55,829 55,829 55,589 74,297
Calf survival (SURV) 80,456 80,456 79,525 73,968 103,830
Calve size (SIZE) 61,121 61,121 60,595 70,374 80,160 80,363

 

Precorrection of data

As reported in chapter 7, the Danish Red Cattle population
contains a large proportion of genes originating from American Brown
Swiss. Therefore, genetic effects of both additive genetic differences
between the breeds involved and heterosis are important. For calving
traits these effects were of importance in the genotype of the cow
(maternal effects) as well as that in the genotype of the calf (direct
effects). Other effects of importance was herd-year, month of calving,
age at calving, days in milk, sex of calf, and random effects due to
sire of cow and sire of calf. Thus, a total of 14 factors were
included in the model.

In the estimation of (co)variance components for multiple traits,
the mixed model equations needs to be constructed many times when
iterative estimation procedures are used. For models with many factors
this became prohibitively expensive. Data were therefore precorrected
for all fixed effects, with the exception of herd-year effects, which

had by far the largest number of levels. Additive correction factors

163
estimated from model [1] of Chapter 7 were used.

Models and sampling of data

The dataset included 1650 bulls that were either sire of cow or
sire of calf. All traits and all sires could not be included in the
analysis simultaneously due to computer constraints. Samples of data
were therefore taken. Each sample was constructed by first choosing 300
bulls at random and then selecting those records with both sire of cow
and sire of calf appearing in the sample of 300 bulls. This sampling
process was repeated eight times, and each sample was analyzed
separately. To further reduce computational cost, only two or three
traits were analyzed simultaneously. A total of seven analyses were
performed on each sample. FAT was included in each of the trait
combinations, while MLK and PRT was only analyzed together with FAT but
not together with any of the calving traits. Analyses were run for all
possible 2-traits-combinations of FAT, DIF, SURV and SIZE.

The model for the precorrected production traits was:
yijkl - hi + gj + SE(j) + iijkl [1]
where:
hi was the effect of the ith herd-year;
gj was the effect of the jth group of sires grouped according to year

of birth;
SE(j) was the random effect of sire of cow nested within the jth
genetic group; and

eijkl was a random residual.

For calving traits the model was:

C O O
yijklm ‘ hi + 81 + 58(1) + (1/2)sk(j) + 51(3) + eijklm [2]

164

where effects not previously defined were:
(1/2)sg(j) was the random effect of the kth maternal grandsire of

offspring (sire of cow) nested within the jth

genetic group.
s?(j) was the random effect of sire of offspring nested within the jth
genetic group.
The model [1] and [2] are now combined in matrix notation and

illustrated below for an analysis including one production trait and

one calving trait:

'- l
yc 0 xC bC 0 2M (1/2zM + 2D) ug eC
0
h “C A

 

 

where:

yP was a vector of production records;

yC was a vector of calving records;

XP and KC were incidence matrices for fixed effects;

bP and bC were vectors of fixed effects on the production and calving
trait, respectively;

ZP, ZM and ZD were known incidence matrices of random effects;

uP was a random vector of sire effects the on the production trait;

ug was a random vector of sire effects on maternal effects on the
calving trait;

ug was a random vector of sire effects on direct effects on the calving
trait;

Thus, the model was a sire model for production traits and

165

maternal effects on calving traits, but for direct effects on calving
traits the model was a sire and maternal grandsire model.

Expected first and second moments of random vectors in model [3] were:

and
y0 0 x0 bc
- a _ 2 1
M 2
u0 0M0 0M0,00
g ug ‘ L Symmetric 00C .

 

 

 

 

where A was the additive genetic relationship matrix accounting for
relationships due to sires and maternal grandsires, and SO was 1/4 of
the additive genetic (co)variance matrix.

The residual (co)variance matrix,

was a block diagonal matrix with one block (R1) for each cow calf pair

with data. There were three types of blocks: If both traits were

th

recorded for the i cow-calf pair, then {Ri} - R0 the 2X2 matrix of

residual (co)variances. If only one of the two traits was recorded then
{R1} was a scalar of the residual variance for that trait.

Note that SO was a 3X3 matrix, whereas R0 was a 2X2 matrix for the
model indicated. The phenotypic variance for the traits analyzed was
then:

02 _ 02

2
pP 9 + 0 eP

166

02pC ' 02MC + (5/4)°200 + ”M0,00 + 02eC

where a’eP and 02eC was the residual variances for production and calving
traits, respectively. The coefficient 5/4 stems from the fact that the
submodel for direct effects on calving traits was a sire and maternal
grandsire model.

The (co)variance matrices SO and R0 was estimated by a derivative
free REML algorithm for multiple traits using a computing strategy
similar to the one outlined by Meyer (1989). The restricted likelihood
function was maximized using a quasi-Newton method given by Dennis et
al. (1983) and using code from IMSL (1987).

Several parameters were estimated more than once from analyses of
the same data sample because only two or three traits were included at
a time in a given analysis. These estimates were then averaged to
obtain a single estimate of each parameter per sample. The estimates
from the eight samples were then averaged and the variance of the eight

estimates was used to obtain SE of estimates.

Results and Discussion
Production Traits
The genetic parameters estimated for production traits are shown

in Table 44. The heritability estimates for MLK and FAT were lower
than found in several recent reports in the literature, e.g., Cue et
al. (1987), Wade and Van Vleck (1989), Van Vleck et al. (1988) and Van
Vleck and Dong (1988). These authors found estimates ranging from .315
to .382. However, Meyer (1984) found estimates at .283 for MLK and .268

for FAT. For PRT, the heritability estimate was considerably higher

167

than those for MLK and FAT. Cue et al. (1987) found an estimate of the
heritability for PRT of .254, a value considerably lower than their
estimates for MLK and FAT. Van Vleck and Dong (1988) found and estimate
of .36, a value similar to those for MLK and FAT.

Genetic and phenotypic correlations between production traits are
also shown in Table 44. Phenotypic correlations were always higher than
the corresponding genetic correlations which are in agreement with most
literature results cited earlier. The phenotypic correlation between
MLK and FAT were estimated at .707 which is higher than the .57 by
Meinert et al., (1989) and deJager and Kennedy (1987). The genetic
correlation between MLK and PRT were estimated at .599. Most
investigators, however, have found that PRT are closer related to MLK
than FAT, e.g., deJager and Kennedy (1987) and Meinert et al. (1989).
The estimate of the genetic correlation between FAT and PRT of .628 are

well in line with the aforementioned literature estimates.

 

 

 

 

 

Table 44.
Genetic parameters of production traits and their SE (in parenthesis).
Correlationsa

Trait Heritability Phenotypic SD MLK FAT PRT

Milk yield (MLK) .259 736.6 --- .857 .821
(.030) (6.33) (.004) (.013)

Fat yield (FAT) .262 30.2 .707 --- .779
(.026) (.166) (.067) (.010)

Protein yield (PRT) .396 26.2 .599 .628 ---
(.040) (.339) (.082) (.057)

 

aPhenotypic correlations are above the diagonal, and additive genetic
correlations are below the diagonals.

168

Calving Traits

Direct Effects. Genetic parameters for FAT and direct effects on
calving traits are shown in Table 45. Heritability estimates for FAT
are repeated for easy reference. The heritability estimates for
direct effects on calving traits were well within the ranges given by
Philipsson et al., (1979). These ranges were based on a literature
review of work published before 1977. Weller et al., (1988), however,
obtained lower estimates of heritability for DIF of .031 and .027 for
SURV.

The residual correlations between FAT and calving traits were all
estimated to be essentially zero. Genetic correlation estimates between
FAT and direct effects on calving traits were small to moderate, but
were antagonistic. Selection for FAT would tend to increase direct
effects on DIF and decrease direct effects on SURV and SIZE, but none
of these correlations were very strong. It should be noted that the
estimates of genetic correlations between FAT and the calving traits
had relatively large SE. Philipsson (1976) concluded that milk
production were unaffected by dystocia and stillbirth, but he
considered only phenotypic relationships. Thompson (1980) found that
calving difficulty and production were uncorrelated when calving
difficulty was measured as a direct effect.

The residual correlations between calving traits (Table 45) showed
that larger calves experienced more difficulty at birth than smaller
calves. Calves with a more difficult calving had a reduced survival,
however, calf size and survival were essentially uncorrelated.

The genetic correlation estimates between direct effects on

169

calving traits were all greater than the corresponding residual
correlations, but were of the same sign. Selection for reduced direct
effects on calving difficulty would also improve survival but decrease
size. Again the genetic correlation between calf size and survival were
relatively low with an estimate of -.l78.

Table 45.

Genetic parameters for milkfat production and direct effects on calving
traits and their SE in parenthesis.

 

 

 

 

Correlationsa
Trait h2 0p FAT 019 SURV SIZE
Milkfat prod. (FAT) .262 30.2 --- -.007 .034 .023
(.026) (.166) (.027) (.010) (.022)
Calving diff. (DIF) .155 .734 .345 --- -.274 .343
(.036) (.011) (.220) (.006) (.007)
Calf survival (SURV) .068 .768 -.131 -.631 --- -.081
(.012) (.019) (.201) (.067) (.009)
Calf size (SIZE) .199 .721 -.240 .692 -.l78 ---

(.031) (.006) (.205) (.032) (.029)

 

aResidual above the diagonal and genetic below the diagonal.

Maternal Effects. Genetic parameters for FAT and maternal effects on
calving traits are shown in Table 46. The estimates for DIF and SIZE
were considerably lower than the corresponding direct effects with
estimates of .087 and .044, respectively. For SURV the estimate were
approximately the same as the estimate for heritability of direct
effects. All estimates agree reasonably well with normal ranges given
by Philipsson et al., (1979).

The genetic correlation between FAT and maternal DIF was estimated

at -.079, whereas the genetic correlation between FAT and direct DIF

170

was .345. For maternal SURV the genetic correlation with FAT was -
.147, a value similar to the genetic correlation between FAT and direct
SURV. The genetic correlation between FAT and maternal SIZE was .271,
whereas the corresponding correlation between FAT and direct SIZE was -
.240. Thus, selection for FAT would tend to produce cows that give
birth to larger calves, but the cows themselves would be smaller at
birth. The genetic correlations between the maternal effects on calving
traits was similar to the correlations between the direct effects
although lower in absolute value.

Table 46.

Genetic parameters for milkfat production and maternal effects on
calving traits and their SE in parenthesis.

 

 

 

 

 

 

Correlationsa

Trait h2 op FAT 019 SURV SIZE
Milkfat (FAT) .262 30.2 --- -.007 .034 .023
(.026) (.166) (.027) (.010) (.022)

Calving difficulty
(DIF) .087 .734 -.079 --- -.274 .343
(.016) (.011) (.119) (.006) (.007)
Calf survival (SURV) .086 .798 -.l47 -.464 --- -.081
( 021) (.019) (.185) (.061) (.009)
Calf size (SIZE) .044 .721 .271 .219 -.051 ---

(.011) (.006) (.213) (.021) (.070)

 

aResidual above the diagonal and genetic below the diagonal.

Genetic Correlations between Direct and Maternal Effects

Estimates of genetic correlations between direct and maternal
effects are shown in Table 47. Genetic correlations between direct and
maternal effects were all negative with estimates of —.474, -.366 and -

.560 for DIF, SURV and SIZE, respectively. Based on a relatively small

k

171

set of data, Philipsson (1976) found estimates at -.19 and -.53 for DIF
and SIZE, respectively, whereas his estimate for SURV was .07, a
result deviating considerable from our result. For DIF, Thompson
(1980) (Cf. Balcerzak et al., 1989) found estimates of -.38.

Table 47.

Genetic correlations between maternal and direct effects for calving
traits and their SE in parenthesis.

 

 

 

 

 

Direct
Maternal DIF SURV SIZE
Calving difficulty (DIF) -.474 .100 .110
(.080) (.052) (.057)
Calf survival (SURV) .299 —.366 .046
(.116) (.071) (.051)
Calf size (SIZE) -.397 .007 -.560
(.037) (.039) (.029)

 

The correlations between direct and maternal effects when
different traits were considered were all smaller in absolute value
than when the same trait were considered. The most notable correlations
were the genetic correlation between direct DIF and maternal SURV with
an estimate of .299 and between direct DIF and maternal SIZE with an
estimate of -.397. This means that selection for decreased direct DIF
would yield cows that gives birth to calves with decreased SURV and

increased SIZE.

SUMMARY AND CONCLUSIONS

The ultimate goal of this series of work is the construction of
total merit indices to be used as selection criterion in dairy and dual
purpose cattle populations. Parts of the series are included in this
thesis. These total merit indices will consider dairy and beef
production, calving characteristics, management or type traits and
fertility as well as biological efficiency traits. In order to
construct an index, genetic parameters involving all traits must be
known, but many especially genetic covariances are not known. To
estimate these parameters, however, strategies need to developed to
alleviate computational difficulties and to avoid biases due to
selection. Selective mating for genetic improvement has been and will
continue to be conducted on a within breed basis. However, utilization
of between breed genetic effects which involves crossbreeding needs to
be explored.

Therefore, this series of studies covered three main topics. The
first topic is computation algorithms and data sampling in alleviating
computational difficulties in the estimation of genetic parameters.
The second topic relates to beef production and its biological
efficiency, of young bulls of dual purpose breeds, and the genetic
relationships between traits measured on the growing young bulls and
the dairy production of female relatives. The third topic deals with
estimation of crossbreeding effects and genetic parameters on dairy
production and calving performance in a population importing genetic

material.

172

 

173

CHAPTER 1. Transformation Algorithms in Analysis of Single Trait and of
Multitrait Models with Equal design Matrices and One Random
Factor per Trait: A review.

Transformation algorithms for models with two variance components
per trait are reviewed and illustrated with a numerical example. The
emphasis is on multiple trait models with equal design matrices.
Algorithms of canonical, "Cholesky", and Householder transformations
are discussed. The series of transformations offers an alternative
that drastically reduces the amount of computation per round of the
iterative expectation maximization algorithm for estimating
(co)variance components by the restricted maximum likelihood method.
After all the transformations are carried out, no matrices need to be
inverted and the computations in each round of the iteration process
can be evaluated in linear time. Thus, in practice, once the initial
computing work is done, any number of iterations can be performed with
ease. This allows the use of conservative stopping criteria. The
stopping criteria often need to be conservative because considerable
changes in parameter estimates can occur during later rounds of the

iteration process, even though the change per round is very small.

CHAPTER 2. A Stochastic Model of Breeding Schemes in Cattle
Populations.
A stochastic model of breeding events in a dual purpose or in a
dairy cattle population was constructed. It was aggregated such that
year could be the unit of time.

The model primarily simulates performance testing of young bulls

 

174

for growth in a central testing facility and milk production of cows in
commercial herds. In dairy populations only milk production in
commercial herds is simulated. Primary use of the model is to study the
effects of population size, breeding structure, magnitude of underlying
genetic parameters and economic conditions on the genetic response from
a genetic improvement program. The build-up of inbreeding, the
reduction of genetic variance due to both inbreeding and Bulmer effect,
and random variation in response due to genetic drift can also be
studied. The model can generate data from simulated populations which
has been either undergoing selection for one or more traits or is
mating at random.

As illustration, the model was used to study the effect of

population size and number of tested bulls used per year.

CHAPTER 3. Estimation of Genetic Parameters Using Sampled Data from
Populations Undergoing Selection.

In populations undergoing selection, genetic variances and
covariances are altered in amounts dependent on selection intensity
among parents and the mating structure. In order to estimate the
genetic parameters of the unselected population using data from
populations undergoing selection all data that led to the current
population must be included in the analysis. this is often not possible
due to missing information or computer limitations. Therefore, often
only subsamples of data are analyzed and/or simplified operational
models are used. A simulation study was conducted to investigate
different sampling strategies and different operational models in dual

purpose populations selecting for beef and milk and in single purpose

175

dairy populations. Genetic parameters estimated by REML were unbiased
if all data and all relationships were included in analysis even though
selection was not within fixed effects. Use of a model including only
additive effects of males, where bulls had own record on growth and
daughter records on milk also seemed to yield unbiased estimates of
genetic parameters. Sire models used in dairy populations gave biased
estimates of genetic parameters, even when all data were included in
the analysis. Treating sire effects on second crop daughters as fixed

did not alleviate any selection bias in the populations investigated.

CHAPTER 4. Performance Testing of Dual Purpose Bulls for Beef Traits.
Genetic Parameters of Growth, Feed Intake, Appetite and
Carcass Composition.

Genetic parameters for growth, energy intake, feed conversion
ratio, average daily energy intake and carcass composition were
estimated in an experiment with 650 bull calves from 31 halfsib groups
of Holstein Friesian or Brown Swiss sires. All traits analyzed showed
an amount of additive genetic variance that allows for considerable
response to selection. No interaction between genotype (sire group)
and proportion of roughage in the diet was found. Daily gain was
strongly negatively correlated with feed conversion ratio but
positively correlated with daily feed intake or appetite. Results
indicate that selection for either daily gain or average daily energy

intake would decrease carcass fatness at a constant slaughter weight.

176

CHAPTER 5. Performance testing of Dual Purpose Bulls for Beef Traits.
Residual Intake and Energy Requirements for Growth and
Maintenance.

The residual feed intake and the partial requirement for
productive and nonproductive use of feed energy was estimated for each
of 650 bull calves of 31 Holstein Friesian or Brown Swiss sires. The
partial requirements for nonproductive use of energy, or more
conventionally the maintenance requirement, was further partitioned
into a part dependent on metabolic body weight and a part independent
of metabolic body weight. The partial energy requirements were
obtained for each individual bull based on biweekly measures of body
weights and energy intake. Two different models were used in
partitioning energy intake in the production period before 200 kg live
weight with animals fed restricted amounts, and again in the production
period after 200 kg live weight where the animals were fed ad libitum.
Genetic analysis of the partial energy requirements showed considerable
variation among bulls in requirements for both productive and
nonproductive use of energy, and also showed that these traits were
heritable to approximately the same degree as conventional measures of
feed efficiency.

Results indicated that it is possible to obtain individual
estimates of partial requirements for productive and nonproductive use
of energy from frequent measures of body weight and energy intake.
Biological interpretation of the partial energy requirements was very
dependent on the model used in the partitioning of energy intake,

because different partial requirements estimated in the same model were

177

more closely correlated than were similar coefficients from different
models.

Residual intake, defined as actual minus predicted energy intake,
was also computed for each bull in each production period. Residual
intake showed a larger degree of additive genetic variance than the
partial energy requirements when the animals were fed ad libitum,
whereas the opposite was the case when the animals were on a restricted
feeding regime. Residual intake estimates with and without correction
for carcass composition were very closely correlated. Thus residual

intake can be calculated without the knowledge of carcass composition.

CHAPTER 6. Performance Testing of Dual Purpose Bulls for Beef Traits.
Genetic and Phenotypic Correlations Between Partial Energy
Requirements and Beef Traits of Young Bulls and the Milk
Yield of their Female halfsibs.

Genetic and phenotypic correlations between growth, feed intake,
feed conversion ratio, appetite, carcass composition, residual intake
and partial energy requirement for growth and maintenance were studied
in an experiment on 650 bull calves of 31 Holstein Friesian or Brown
Swiss sires. The correlations between these traits and the sires
breeding value for milkfat production were also studied. The
phenotypic and genetic (co)variance matrices were analyzed by factor
analysis and accordingly interpreted. Energy requirements for growth
and maintenance were unrelated to growth rate phenotypically. However,
genetic selection for higher daily gain would increase the energy
requirement for growth and weight dependent nonproductive use of

energy, but decrease intake at constant growth rate and constant

178

metabolic weight. Feed conversion ratio and partial energy
requirements for growth and maintenance were all phenotypically
unrelated to carcass composition. However, selection for leaner
animals would increase the partial energy requirement for growth and
the weight dependent nonproductive use of energy, but decrease baseline
intake. The sires' breeding values for milkfat production and daily
gain of his male progeny bulls were positively correlated, especially
when daily gain were measured before 200 kg live weight. Appetite of
the ad libitum fed young bull was not correlated with the sires'
breeding values for milkfat production. Sires' breeding values for
milkfat production was negatively correlated to percent fat in the

carcass of the growing young bull.

CHAPTER 7. Additive and Heterotic Effects of Immigration of Brown Swiss
Genes into the Red Dane Cattle Population on Dairy
Production and Calving Traits.

Data on 170,166 cows were analyzed in order to estimate the
effects of immigration of genes into the Red Dane Cattle population.
Most foreign genes originated from American Brown Swiss. Effects on
first lactation production and calving traits were estimated.
Relatively small but negative recombination effects were found for
production traits. A model including both additive, dominance and
recombination effects indicated large effects of progeny genotype on
the cows subsequent production. If effects of progeny genotype were
ignored, however, recombination effects were small for milk and fat

production but still large and negative for protein production.

179

Heterosis for production traits, expressed as F1 heterosis was 4.4
to 7.7% depending on model used in estimation. Models without
recombination effects estimated heterosis effects for production traits
in the range 7.1 to 7.7%. The large positive heterosis for production
was to some extend counteractered by a large genetic difference between
Red Dane and Brown Swiss, with Brown Swiss being 2.6 to 6.2% inferior
to Red Dane in production.

For calving traits small recombination effects were found.
Heterosis for calving difficulty and calf survival tended to improve
calf survival, but also increased the level of calving difficulty.
Heterosis effects for calving traits were small, however, in comparison
to additive genetic differences between Red Dane and Brown Swiss, the
latter having considerable less calving difficulty and better calf
survival.

The advantages of crossbreeding to Red Dane breeders seems to lie
in the use of a synthetic breed consisting of genes from both breeds.
For Brown Swiss breeders, however, there seems to be a large advantage
in production traits, by introducing Red Dane genes into their
population. Such immigration, however, will increase calving difficulty

and yield a slight decrease in calf survival.

CHAPTER 8. Genetic Parameters of Dairy Production and Calving Traits in
Danish Red Cattle.
Data on 170,166 cow-calf pairs of Danish Red Cattle were analyzed
in order to estimate genetic parameters of first lactation production
and of calving traits recorded at first calving. The traits analyzed

were 305 days milk, fat, and protein production and calving difficulty,

180

calf survival and calf size. For calving traits effects due to both
genotype of cow (maternal effects) and genotype of calf (direct
effects) were considered. Genetic parameters were estimated using a
multivariate derivative free REML algorithm. Heritability estimates for
milk, fat, and protein production were .259, .262 and .396,
respectively. Heritability estimates for direct effects on calving
difficulty, calf survival, and calf size were .155, .068 and .199,
respectively, and the corresponding estimates for maternal effects were
.087, .086, and .044. Fat production had positive genetic correlations
to direct calving difficulty and a negative genetic correlation to
direct calf size. Fat production was not correlated with maternal
effects on calving difficulty and calf survival, but had a positive
genetic correlation with maternal effects on calf size. Genetic
correlations between direct and maternal effects were all negative with
estimates of -.475, -.366 and -.560 for calving difficulty, calf

survival and calf size respectively.

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181

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