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dissertation entitled
EFFECTS OF POPULATION STRUCTURE AND UNDERLYING MAGNITUDE

OF DOMINANCE GENETIC EFFECTS ON THE ESTIMATION OF
ADDITIVE AND DOMINANCE GENETIC VARIANCES

presented by

David Norris

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EFFECTS OF POPULATION STRUCTURE AND UNDERLYING MAGNITUDE OF
DOMINANCE GENETIC EFFECTS ON THE ESTIMATION OF ADDITIVE AND

DOMINANCE GENETIC VARIANCES

By

David Norris

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Animal Science

1998

ABSTRACT

EFFECTS OF POPULATION STRUCTURE AND UNDERLYING MAGNITUDE OF
DOMINANCE GENETIC EFFECTS ON THE ESTIMATION OF ADDITIVE AND
DOMINANCE GENETIC VARIANCES

By

David Norris

Five populations with varying percentages of animals in full-sib families were
simulated. For each population, three combinations of additive and dominance genetic
variances of different relative magnitudes were considered, thereby creating three
subpopulations. Constant residual variance and heritability in the broad sense were used
in all populations. Variance components were estimated using the tilde-hat
approximation to REML based on sire-dam model. Populations with few full-sibs (2%
and 10%) and small magnitude of dominance variance (50), resulted in inaccurate
estimation of dominance genetic variance. In populations with a large number of animals
and having dominance genetic relationships (10% or greater), estimates of dominance
genetic variances can be obtained with improved accuracy even when the dominance
genetic effect in the population is of small magnitude. Overestimation of additive effects
increased as both the number of full-sibs and the magnitude of dominance effects

increased.

ACKNOWLEDGEMENTS

I wish to greatly thank Dr. I.L. Mao for his advice and support during my graduate
studies at Michigan State University. I wish to also express my profound appreciation to
the members of my guidance committee, Drs. B.D. Banks, R.J. Tempelman, D. Hawkins
and M. Rye for their support and suggestions in this study.

I wish to acknowledge the following colleagues for their considerable help and
fi'iendship : Zhiwu Zhang, Chu-Li Chang, Kadir Kizilkaya, Dwayne Faidley, Renee Bell,
Elissette Rivera and Mara Preisler. Special thanks are extended to all faculty and staff in
the breeding and genetics program.

Special thanks are extended to my parents, sisters, Zuzo and Sibiya families for
their unwavering support. In a very special way, I wish to express my deepest gratitude

to my love, Boni, for her kindness and strong support during my studies. Above all, I

thank the Almighty God for His love and care for me.

iii

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. vi

LIST OF FIGURES ......................................................................................................... viii
CHAPTER 1

Introduction .............................................................................................................. 1
CHAPTER 2

Literature Review ..................................................................................................... 5

Total genetic effects and molecular basis of dominance ............................. 5

Estimation of genetic components ............................................................... 9

Reproductive technology and population structures .................................. 13

Estimation of nonadditive variance ........................................................... 17

Implications of excluding nonadditive effects in genetic evaluations ....... 19

Practical implication and application of nonadditive genetic effects ........ 22

Nicking ............................................................................................................................. 22

Heterosis .......................................................................................................................... 23

Inbreeding .................................................................................................. 26

Genetic gain from selection utilizing nonadditive genetic effects ............. 28
CHAPTER 3

Introduction ............................................................................................................ 35

Materials and Methods ............................................................................... 37

Data Structure ............................................................................................ 37

Data Simulation ......................................................................................... 37

Data analysis .............................................................................................. 4O

Variance component estimation ................................................................. 43

CHAPTER 4

Results and Discussion

Dominance genetic variance ...................................................................... 46
Additive genetic variance ........................................................................... 50
Estimates of heritability ............................................................................. 62

iv

Conclusions ............................................................................................................ 71

REFERENCES .................................................................................................................. 75

LIST OF TABLES

 

Table Page
1. Relationship coefficients of various gene actions .......................................................... 8
2. Numbers and types of close relatives in US Holsteins ................................................ 16
3. Summary of studies on dominance genetic variance ................................................... 18
4. Genetic variance, maximum inheritable fraction and maximum inheritable

variance for additive, dominance and additive x additive genetic effects ................... 32
5. Percentage of full-sib animals in different populations ............................................... 38
6. Underlying Parameters (additive and dominance genetic variances) .......................... 39
7a. Two percent animals in full-sib families with simulated values,

VA = 950, VI) = 50, VIE = 2000 .................................................................................... 56
7b. Two percent animals in full-sib families with simulated values,

VA = 800, VD = 200, VE = 2000 .................................................................................. 56
7c. Two percent animals in full-sib families with simulated values,

VA = 500, VD = 500, VE = 2000 .................................................................................. 56.
8a. Ten percent animals in full-sib families with simulated values,

VA = 950, VD = 50, VE = 2000 .................................................................................... 57
8b. Ten percent animals in full-sib families with simulated values,

VA = 800, VD = 200, VE = 2000 .................................................................................. 57
8c. Ten percent animals in full-sib families with simulated values,

VA = 500, VI) = 500, VE = 2000 .................................................................................. 57
9a. Twenty percent animals in full-sib families with simulated values,

VA = 950, VD = 50, VE = 2000 .................................................................................... 58
9b. Twenty percent animals in full-sib families with simulated values,

VA = 800, VD = 200, VE = 2000 .................................................................................. 58.
9c. Twenty percent animals in full-sib families with simulated values,

vi

vA = 500,vD = 500, vE = 2000 ................................................................................... 58

10a. Fifiy percent animals in full-sib families with simulated values,
VA = 950, VD = 50, VE = 2000 ................................................................................... 59

10b. Fifty percent animals in full-sib families with simulated values,
VA = 800, VD = 200, VE = 2000 ................................................................................. 59

10c. Fifty percent animals in full-sib families with simulated values,
VA = 500, VD = 500, VE = 2000 ................................................................................. 59

11a. Hundred percent animals in full-sib families with simulated values,
VA = 950, VD = 50, VE = 2000 .................................................................................. 60

11b. Hundred percent animals in full-sib families with simulated values,
VA = 800, VD = 200, VE = 2000 ................................................................................ 60

11c. Hundred percent animals in full-sib families with simulated values,
VA = 500, VD = 500, VE = 2000 ................................................................................ 60

12. Summary table for estimates of additive genetic variance under reduced and full
models ......................................................................................................................... 61.

13. Estimates of heritability (hz) under reduced and full models — two percent
animals in full-sib families .......................................................................................... 66.

14. Estimates of heritability (hz) under reduced and full models — ten percent
animals in full-sib families .......................................................................................... 67

15. Estimates of heritability (hz) under reduced and full models — twenty percent
animals in full-sib families .......................................................................................... 68.

16. Estimates of heritability (hz) under reduced and full models — fifty percent
animals in full-sib families .......................................................................................... 69.

17. Estimates of heritability (hz) under reduced and full models — hundred percent
animals in full-sib families .......................................................................................... 70

vii

LIST OF FIGURES

Figure 1. Mating system utilizing nonadditive information. ............................................ 34

viii

CHAPTER 1.

INTRODUCTION

The sustained ability to improve phenotypic performance of livestock with respect
to economically important traits is partially dependent upon accurate evaluation of
animals’ genetic merit. Knowledge of genetic variance and its distribution in the
population structure can lead to the design of optimum breeding plans (Miller et al, 1963;
Willharn and Pollack, 1985).

Animal breeders widely use mixed model methodology in genetic evaluations.
However, this methodology has typically considered only additive genetic effects.
Additive genetic effects arise from simple additive genetic contributions of separate loci.
Nevertheless, there is increasing interest on the utilization of nonadditive effects within
and between breeds and crosses (Smith and Maki-Tanila, 1990). Nonadditive genetic
effects arise from interaction of genes which could be between genes at same locus
(dominance) or at different loci (epistatic). Mixed-model methods can be readily applied
to the prediction of genetic merit and estimation of genetic variances for dominance,
epistatic and cytoplasmic effects. The relative importance of these nonadditive effects
can be described as the fraction of their variance in the total variance for a given trait

(Misztal, 1997). The non-inclusion of these effects is due to a general expectation of

small and insignificant nonadditive gene effects for quantitative traits of economic
importance (Lee and Henderson, 1969, Falconer, 1989 ).

Recent developments in computational techniques and computing algorithms
coupled with the discovery of rules to invert the dominance relationship matrix allow the
use of mixed model equations to infer upon dominance genetic effect for large data sets
(Hoeschele and VanRaden, 1991). These developments should trigger interest in
identifying traits that have significant dominance genetic variation and could therefore
benefit from evaluation with dominance included in the model.

A requirement for estimation of dominance genetic variance is measurements on
animals with dominance relationships greater than zero, such as full-sibs, three-quarter
sibs and clones (Van Vleck and Gregory, 1996). Increased use of artificial insemination
(AI) and multiple ovulation and embryo transfer (MOET) together with other
reproductive technologies such as embryo splitting and in vitro embryo production have
increased the relative number of animals with non-zero dominance relationships. The
advances made in these reproductive technologies necessitate the investigation of non-
additive genetic variances.

Animal breeders usually assume, in livestock selection theory, that selected males
and females are mated randomly. If overall genetic merit is not inherited additively, the
average progeny merit could be increased by mate selection which is the simultaneous
selection and mating of males and females according to predicted progeny merit (Jansen
and Wilton, 1984). Furthermore, if dominance genetic variance is important for
economically important traits in livestock, the incorporation of dominance genetic

relationships could improve the accuracy of genetic evaluations and allow the possibility

of greater exploitation of total genetic merit with further refined mating strategies. There
would be an expected acceleration in animal performance unlike if selection was based on
additive effects only.

There seems to be some connection between the magnitude of the heritability and
the nature of the character or trait (Falconer, 1989). It is a general agreement that
characters with lower heritabilities are those mostly associated with fitness such as
viability and fertility while the characters with higher heritabilities tend to be those
judged on biological grounds to be less connected with natural fitness (Falconer, 1989;
Walsh and Lynch, 1998). The low heritability of these fitness traits, their tendency to
show inbreeding depression and their favorable response to outbreeding (Larnberson and
Thomas, 1984) suggests the possibility of sizable non-additive genetic variance.
Selection accuracy for these traits under an additive model is therefore likely to be
reduced. It may be important therefore, to employ models that consider non-additive
genetic effects when dealing with these traits.

Previous studies on estimation of dominance genetic variance have been
inconsistent and thus inconclusive. However, there appears to be sizable dominance
genetic variation reported in species with higher fecundity such as poultry and fish and
small dominance genetic variance found in other species such as dairy and beef cattle.
The differences in magnitude of dominance effects in these studies could be attributed
partly to differences in the data structure. Poultry and fish have higher fecundity
compared with cattle and thus provide data with higher mean nonadditive genetic
relationships among individuals. Tempehnan and Burnside (1991) in their study of

additive and dominance genetic variation in dairy production traits observed a close

association between relative proportions of either variance component with the relative
density of its respective relationship matrices.
With this background in mind, this study aims to achieve two goals :
1) To test the hypothesis that the ability, and the accuracy to detect dominance genetic
effects depends on the density and size of full-sib families in the data.
2) To investigate the effect of ignoring and considering dominance genetic effects in the

model on the estimation of additive genetic variance.

CHAPTER 2.

LITERATURE REVIEW

Total genetic merit and molecular basis of dominance.

The genetics of any metric character is built around the study of its variation and the basic
idea in the study of variation is the partitioning into components attributable to different
causes (Falconer, 1989). The partitioning of the variance into its components makes it
possible to estimate the relative importance of the different causal components of
phenotype. This is of particular importance in assessing the role of heredity versus
environment in the determination of the phenotype.

The total genetic value of an animal is:

G = GA + GD + Gl
where GA = Sum of additive genetic effects

GD = Sum of dominance genetic effects.

GI = Sum of interaction or epistatic genetic effects
The total genetic variance is thus the sum of additive, dominance and epistatic variances :

0'02 2 0“2 + 502 + 6,2

The additive variance is used in genetic evaluations as it is assumed to be the

major cause of resemblance between relatives therefore mainly responsible for the

response of the population to selection. As shall be discussed later, it is becoming

increasingly necessary to consider other components of the total genetic variance in
genetic evaluations.

Genetic evaluation is based on the theory of covariances between relatives. In a
random mating population and in the absence of linkage, the genetic covariance between
relatives is a fimction of the additive and non-additive relationship between these
relatives and the components of genetic variance for the population (Freeman and
Henderson, 1959). Relationship coefficients for non-additive genetic effects were
established long before the respective variances could be estimated correctly (Van Raden
et al, 1992). Cockennan (1954) developed a useful method for expressing the variance-
covariance matrix of non-additive effects in non-inbred populations in linkage
equilibrium. He showed that for large, randomly mated populations in Hardy-Weinberg
and linkage equilibrium, the genetic covariance between any two relatives x and y can be
calculated as follows:

j 2

Cov(x,y) = X Z ai d 0'”
. . XY XY 11
I 1

Where, a,y and d,, are respectively, the additive and dominance relationships between
animals x and y, and i refers to the number of nonallelic genes acting together with j
allelic pairs.

Table 1 gives the coefficients of the variance components in the covariances of relatives
with two-factor interactions included. For a gene action whose coefficient of relationship
is zero, the estimation of variance for this effect is not possible. The smaller the
coefficient, the less precise the estimation or prediction (Misztal et a1, 1995). It is thus

difficult to estimate higher order epistatic effects.

The evolutionary implications of complex biochemical systems are based on the

aggregate characteristics of metabolic pathways as determined by the enzymes involved
(Dean et al, 1988). There are many examples of feedback mechanisms where the activity
of a biological process (enzyme activity, DNA transcription etc.) is directly or indirectly
regulated by the end product of that same process. Kinghom (1987) a selective advantage
in populations for stabilizing homeostatic systems which canalize the development of
genetically diverse individuals to the area of an optimum phenotype or adaptive norm.
Any cross between two breeds where one is at this adaptive norm and the other is not,
gives rise to a heterotic effect in the F1 cross and this effect may not be dependent on the
degree of heterozygosity.
Metabolic relationships are usually nonlinear rather than additive (Dean et al, 1988;
Kacser and Burns, 1981) and therefore biochemical systems often exhibit such
phenomenon as dominance, pleiotropy, and epistasis at the level of the phenotype, and
such phenomena are also to be expected with fitness and other quantitative traits.
Dominance genetic effects may therefore be built into the genetic system due to the
nature of the interlinking metabolic pathways. Kacser and Burns (1981) have
demonstrated that dominance gene action is a function of any enzyme pathway that,
because of the buffering of the system, the second quantity of an enzyme in a diploid
organism will always have less effect than the first one. It follows therefore that the larger
the effect of the gene on enzyme activity, the more dominant it is likely to be. Indeed, it
may be completely dominant on output as far as can be detected, and there are.

Table 1: Relationship coefficients of various gene actions

 

Variance components and the coefficients of their contributions

 

Relatives

Identicals
Full-sibs
Half-sibs
Parent-offspring
3/4 sib

General

1.0

0.5

0.25

0.5

0.3125

1.0

0.25

0.0625

1.0

0.25

0.0625

0.25

0.0977

1.0

0.125

0

0

0.0195

ad

1.0

0.0625

0.0039

(12

 

interactions of effects at different loci, particularly those involved in the same enzyme

pathway.

Estimation of genetic components

Prediction of genetic values when non-additive effects are important has been presented
by Henderson (1984). The animal model can be expanded to include dominance genetic
effects ((1). The model with dominance included is ;

y = Xb + Za + Zd + e

where :

y vector of observation
b = vector of fixed effects

vector of random animal additive effects

a
d = vector of random dominance effects
e = random residual error.
The assumptions are that : var(a) = A of, var(d) = D of , var(e) = I of
var(y) = ZAZ‘ + ZDZ‘ +1 of

The main expense in solving the mixed model equation is in the computing of the
relationship matrices, Al and D". These relationship matrices can be formed and
inverted for small populations, up to 5000 individuals (Misztal, 1995). For larger
populations, it is necessary to obtain inverses directly by using recurrence equations.

Cockerman (1954), as stated earlier, has shown a useful formula for calculating

genetic covariance between any two relatives for populations in Hardy-Weinberg and

linkage equilibrium. The dominance relationship between two non-inbred animals, x
and y (probability that they have the same pair of alleles in common) is a function of the
additive genetic relationship between fathers (p) and mothers (m) of x and y and can be
calculated as follows :

(1,,y = 0.25 (am, a"my + awn, am”) where a represents additive relationship.

Dominance genetic relationships, D can be calculated from knowledge of the
additive genetic relationship, A. With an idealized population, accommodation of any
number of nonadditive genetic effects is possible for prediction of genetic merit.

The prediction of dominance effects requires the inverse of D. Hoeschele and
Van Raden (1991) developed a procedure for obtaining D'1 directly for populations that
are not inbred by including sire and darn or sire and maternal grandsire subclass effects in
the model.

Animals receive half of their genes fiom the sire and half fi'om the dam and an
individual’s dominance effect could be expressed as

d = f5.D + 3

where f w represents the average dominance effect of progeny produced by sire
(S) and dam (D) and e is the Mendelian sampling deviation of the individual from the S x

D subclass effect. of , which is the variance of the S x D subclass effect is equal to the

covariance between full-sibs (of2 = 0.25 of). Var (e) is equal to 0.750;.

Hoeschele and Van Raden (1991) presented recurrence formulae for dominance
effects, using pairs of animals (sire and dam) and interactions between their parents.
Considering a particular sire and dam subclass (fs‘D), the combination effect results from

the interactions between the sire and parents of dam, D, interactions between the dam and

10

parents of the sire, S and interactions between the parents of S and the parents of the
dam, D. The recurrence equation is :

fso = 0-5 (fSSD +fs,DD +fss.o +fns,n) - 0-25 (fssso +fss,DD +fos,sp +fns.oo) + e

where SS and DS represent sire of sire and dam of sire, SD and DD represent dam of sire
and dam of dam.
Accurate estimation of dominance variance requires large amounts of data due to the
limited number of dominance relationships (Chang, 1988). A model that fully uses all
relationships in the model and is resistant to selection bias is required for accurate
estimation of dominance genetic effects (Misztal, 1995). Such requirements would lead
to creation of a large number of equations that exceed current capabilities of restricted
maximum likelihood (REML). Several alternative approaches have therefore been used to
estimate nonadditive genetic effects. The methods include derivative-free REML
(Meyer, 1989), Method R (Reverter, et al, 1994), tilde-hat approximation to REML (Van
Raden and Jung, 1988) and others.

Graser et a1, (1987) suggested a derivative-free REML algorithm for univariate
analyses to estimate the additive genetic variance and the error variance under an animal
model. Restricted maximum likelihood estimates of variance and covariance components
are obtained by direct maximization of the associated likelihood. Software written by

Meyer (1989) utilizes sparse matrix techniques to compute REML estimates of variances.

The log likelihood to be maximized is :

—2 log (1) = const. + log IRI + log IGI + log ICI + y‘Py

log (1) is the log likelihood function,

11

R = 16,2,

G = Ao,2 + Dod2

C is the full rank submatrix of the coefficient matrix in the mixed model equations

P is a projection matrix directing the absorption of the mixed model equations into the
phenotypic sums of squares and cross-products,

P = V" - V" X(X‘V"X)'X‘V" .

Details of this procedure are explained by Meyer (1989).

Reverter et al. (1994) presented an iterative procedure, Method R, to compute
estimates of variance components for large data sets. The advantage of the method as the
derivative-free REML is that it does not require the inversion of the coefficient matrix.
Method R is based on the linear regression coefficient ( R) of recent (more accurate) on
previous (less accurate) individual genetic predictions. Method R and its implementation
can be summarized as follows (Misztal, 1997):

Let ui be a random for effect i distributed as N (0, Gi of), let iii be BLUP of ui based on

all available data and let {if be BLUP of ui based partial data. Regression of predictions

based on full data from those based on partial data, ri is defined as :

Ti:

Three possible results can obtained for r,, (Culbertson, 1998) : ri > 1 denotes a variance
that is too small; ri < 1 denotes a variance that is too large; and ri = 1 denotes estimation

procedure has converged.

12

Early studies on dominance genetic effects were prompted by observations that
progeny from certain matings appear superior to those from matings of the same animals
with other animals. This specific combining ability usually called nicking was studied by
several investigators (Allaire and Henderson, 1965; Purohit et al, 1973) using a sire x
maternal grandsire interaction in the model. A general model method used for this
purpose was :

yum = H + h.- + 81+ gr+ (ssh. + er...
where u is effect common to observations in ith herd, si is an effect common to daughters
of jth sire, gk is an effect common to grand daughters of the kth maternal grandsire and
(sg)jk is an effect common to daughters of the jth sire having the kth maternal grandsire.
The magnitude of the component of variance of sire x maternal grandsire interaction was

used to evaluate the importance of specific combining ability.

Reproductive technology and population structures

The extent to which animals with superior genetic merit contribute to succeeding
generations is directly proportional to their reproductive capacity (Christensen, 1991).
Genetic progress has been limited by low reproductive rate and long generation interval
of cows. The development of artificial insemination coupled with the use of selection
index and more recently BLUP methodology have revolutionized cattle breeding in past
decades through the rate of genetic gain that was attained (Polge, 1986; Youngs et al,
1980). The development of embryo transfer (ET) and multiple ovulation and embryo

transfer (MOET) has made it possible to increase the rate of reproduction and has

13

decreased the generation interval of females considerably. MOET can increase genetic
gain per year substantially over that possible by AI alone through increased genetic
selection intensity for dams of bulls and dams of cows (Van Vleck, 1986; McDaniel and
Cassell, 1981). The advent of new technologies such as in vitro maturation and
fertilization of oocytes and cloning to further improve the reproductive rate of females
will continue to stimulate new breeding programs and applications in the firture
(Christensen, 1991).

The early incorporation of AI generally produced paternal half sister families
across herds. The additive model has generally been sufficient for genetic evaluations in
this type of population structure because of the small number of nonadditive genetic
relationships. Wide use of embryo transfer creates possibility for population structures
to change from paternal half sister families to hierarchical firll sister within sire families
with the result being propagation of animals with nonadditive genetic relationships.
Increased adoption of new reproductive techniques such as embryo splitting, cloning and
other techniques will firrther increase the relative number and size of nonadditive
relationships in the populations.

Significant amount of nonadditive genetic variation have been found in fish (Rye
and Mao, 1998), poultry (Wei and Vanderwerf, 1993); and pigs (Culbertson et al, 1998).
In all these species, there is a large number of full-sibs. Currently, the number of full-
sibs in cattle is not as large as in pigs and poultry (Table 2). The increase in the number
of animals with nonadditive relationships in cattle due to new reproductive technologies
will warrant greater exploitation of total genetic merit by including the nonadditive

effects in genetic evaluations.

14

Some environmental effects have been found to cause resemblance between
relatives. These environmental effects tend to make some sorts of relatives resemble each
other more than others. These are common environmental effects which have been found
to be important in certain relationships such as full-sibs (e.g pig litters and full-sib
families in fish). This is a component of environmental variance that contributes to the
variance between means of families but not to the variance within the families and
therefore contributes to the covariance of the related individuals (Falconer, 1981). This
environmental variation may also be regarded as non-random maternal environmental
variation. The sources of common environmental variance may include (Eisen, 1967) : 1)
maternally provided intrauterine and early postnatal nutrition, 2) transmission of either
antibodies or pathogens from dam to offspring and 3) maternal behavior patterns.
Common environmental effects may be confounded with genetic effects and thus could
seriously reduce the accuracy of genetic evaluations under inappropriate mating designs
(Rye and Mao, 1998). This might directly influence selection response in programs
involving family selection. It is important therefore to consider these effects in
evaluations involving full-sibs. In a study by Rye and Mao (1998), there was a small

Table 2: Numbers and types of close relatives in US Holsteins (Van Raden et al, 1992)

 

 

Family type Number of families Mean family size Largest family size
Clones 79 2 3
Full sisters 23,015 3 26

15

Three-quarter 5 5,779 l 3 421 5
sisters

Half sisters 291,587 40 76,698

 

l6

confounding between common environmental effects and genetic effects. However, the
inclusion of these effects in the model led to a decrease in the error variance, indicating
confounding of these effects with the residual variance. The study of dominance genetic
effects in swine by Culbertson et al (1998) did not include common environmental effects
which in swine are particularly important because of litter (full-sib) effects. The study

could be improved by considering these effects in the evaluations.

Estimation of Nonadditive Variance in literature

Evidence of dominance effects, though inconsistent were reported in several studies
(summary of these studies is presented in Table 3): Templeman and Burnside (1990)
reported dominance variance, as a percentage of total variation, at 6% for milk yield and
24% for fat. Van Raden et al (1992) estimated dominance variance at 3.5% and 3.3% of
phenotypic variation for milk production and fat yield respectively. Miglior et al (1995)
reported dominance variance for milk yield, milk fat % and somatic cell score to be 3%,
2.8% and 1.3% respectively. Lawlor et al (1992) estimated dominance component to be
12% for milk yield. Misztal (1997) estimated dominance variance at 12% of total
variance for stature in Holsteins. Misztal et al (1997) estimated dominance and additive
variances for 14 linear traits in Holsteins. The estimate of the dominance variance was
9.8 % of the phenotypic variance for body depth, 8.0 % for strength, 6.9 % for stature and

was less than 5 % for other traits.

l7

Table 3: Summary of studies on dominance genetic variance.

 

 

Reference Trait Dominance Species
variance(%)

Tempelman and milk yield 6

Burnside (1990) fat % 24 dairy

Van Raden et al. Milk 3.5

(1992) Fat 3.3 dairy

Miglior et al. Milk 3

(1995) Fat 2.8 dairy

somatic cell score 1.3

Lawlor et al.

(1992) Milk 12 dairy

Misztal (1997) stature 12 dairy

Misztal et al. body depth 9.8

(1997) stature 6.9 dairy

Wei and Werf egg number 20 poultry

(1993)

Van Vleck and ovulation rate 0.0

Gregory (1996) twinning (first parity) 21 beef
twinning (later parities) 3.5

Rodriquez- birth weight 18

Almeida et al. 205-d weight 28 beef

(1 994

Misztal et al. post-weaning gain 9.9 beef

(1998)

 

18

Wei and Werf (1993) reported dominance variance for several production traits in
laying hens. Ratios of dominance variance to total genetic variance were high for egg
number ( 10 to 20%), and low for egg weight and egg specific gravity (1 to 13%).

Misztal et al (1998) estimated dominance variance for postweaning gain at 9.9 %
in beef cattle. Van Vleck and Gregory ( 1996) estimated dominance variance as a
fraction of phenotypic variance to be 0.0 for ovulation rate and 0.209 (first parity), 0.035
(later parities) for twinning rate in beef cattle. In another beef cattle study (Rodriquez-
Almeida et al, 1994), dominance and 11 % of total variance for birth weight, birth hip
height, 205-d weight and 205 hip height, respectively.

Rye and Mao (1998) reported large dominance variance for growth rate in
Atlantic Salmon. They found dominance and additive by additive genetic variances to
be of equal or greater magnitude compared to additive variance. In a recent study by
Culbertson (1997) in Yorkshire swine, estimates were 25% and 78% of additive variance
for number born alive and 21 day litter weight respectively. Dominance variance for days

to 104.5 kg was estimated to be 33% of the additive variance.

Implications of excluding nonadditive effects

Exclusion of nonadditive effects in prediction models may lead to these effects
being confounded with other effects in the model. Misztal (1995) illustrated this
phenomenon using two models, the repeatability model and single record model.

Single record mode] :

y=XB+Za+Zd+Zaa+e

l9

where a, d, and aa are additive, dominance and additive x additive genetic effects

In this model, exclusion of the nonadditive effects will lead to these effects being
estimated as part of the residual effect.

Repeatability model :

y=XB+Za+Zp+Zd+Zaa+e

where p is permanent environment effect.
In the repeatability model above, dominance genetic effects become confounded with
permanent environmental effect if they are excluded in the evaluation model. The
additive x additive genetic effects become part of both the additive and permanent
environmental effect if they are ignored.

Rye and Mao (1998) in a study of nonadditive genetic effects for grth in
Atlantic Salmon observed a significant confounding of dominance, additive x additive
and common environmental effects with additive effects when these effects were ignored
in the model. The study found a substantial reduction in the estimates of additive genetic
variance (50 to 79%) when nonadditive genetic effects were estimated simultaneously
with additive genetic effects. Selection differentials have also been shown to be
overestimated for selection of fullsibs for moderately heritable traits in the presence of
significant dominance genetic effects (Tempelman, 1989).

Since genetic evaluations of farm animals are based on the additive model, the
current evaluations may be less accurate than they could be. The extend of the loss of
accuracy is dependent upon the magnitude of the variance of the nonadditve genetic
effects and the number of animals with nonadditive genetic relationships ( Van Raden et

al, 1992; Misztal, 1997). Misztal (1995) pointed out that though the number of animals

20

with nonaddtive genetic relationships may be small with respect to the whole population,
they may be exerting more influence on the population as in most cases these kind of
animals are the elite of the population. Fullsibs and clones forinstance are produced
through procedures that are expensive and therefore reserved for best future sires and

bulldams.

Potential benefits of including nonadditive genetic effects in genetic
evaluations.

Dominance genetic effects can have important implications for estimation of
breeding values in the genetic improvement of farm animals (Johansson et al, 1993).
Accuracy of genetic evaluations could be increased when dominance effects are
considered in animal models (Henderson, 1985; Henderson 1989; de Boer and Van
Arendonk, 1992; Van Raden et al, 1992; Johansson et al, 1993, Misztal, 1997, 1998).
Several studies have shown that heritability is overestimated in additive models when
nonadditive genetic effects are present. Maki Tanila and Kennedy (1986) have showed
that when dominance genetic effects are present the use of mixed models that include
additive and nonadditive genetic effects result in unbiased estimates of breeding values.

Improvement in estimation of breeding values is expected to be more pronounced
in populations with a large number of animals with nonadditive relationships (V arona et
al, 1996; Misztal, 1998). Varona et al. ( 1997) examined differences in breeding values
between dominance and additive models. The greatest breeding value differences

between the dominance and additive models were observed for parents with large number

21

of fullsib progeny. Animals with a large proportion of their information coming from
animals with dominance relationships changed the most.

If nonadditive genetic effects are important and the variances of these effects are
estimated accurately, predictors should have smaller prediction error variances than

predictors based on additive effects only (Henderson, 1989).

Practical implication and application of nonadditive genetic effects
Nicking

As already alluded above, the genetic merit of an animal is a combination of the
general combining ability which is the additive genetic effect, and specific combining
ability which is the dominance and epistatic effects. The specific combining ability is not
transmitted from generation to generation. However there has always been beliefs that
certain matings would give consistently better results than expectation, giving rise to a
phenomenon known as “nicking” (Johnson et al, 1940; Seath and Lush, 1940). If for-
instance a boar “nicks” with a particular sow, they would together give litters of fullsibs
whose genetic merit would be consistently greater than halfsibs of equal transmitting
abilities. This phenomenon of “nicking” has been observed in dairy cattle. With frozen
embryos, it is practical to implement sire-specific breeding programs that will take into
consideration the specific combining ability (Purohit et al, 1973).

Should this phenomenon of nicking be present with respect to economically

important traits, the nonadditive genetic merit of individuals and/or families could be
evaluated in addition to individuals’ transmitting abilities, and a breeding program could

be designed to capitalize on such genetic merit.

22

Heterosis

The advantages of crossbreeding are well documented. Animal breeders have
long known that crossbreeding of two lines has positive fitness related effects in the F1
progeny. An F1 performance that exceeds the average parental performance is generally
referred to as hybrid vigour or heterosis (Sheridan, 1981).

Pig breeders, poultry breeders and beef breeders widely use crossbreeding to
exploit heterosis. More than half of the improvement in production efficiency of beef
cattle results from utilizing crossbred cows (Cox, 1984). Gregory and Cundiff (1980)
stated that the basic objective of beef cattle crossbreeding systems is to simultaneously
optimize the use of both nonadditive (heterosis) and additive (breed differences) effects
of genes. Use of this nonadditive genetic variance is minimal in dairy cattle compared
with other species even though dairy cattle data often result from a mixture of genes from
different populations due to increased exchange of semen and embryos (Van Der Werf
and De Boer, 1989). Van Der Werf and De Boer, 1989) point out that estimates for
heritability of milk production traits in crossbred populations, using mixed models with
breed-group effects were higher than published values from pure breeds. They indicate
that nonadditive effects might have caused an increase in heritability estimates. Less
crossbreeding in dairy cattle has resulted because line formation was difficult, crosses
among breeds in temperate climates under developed management systems did not
exceed the best parental breed for milk production, intensive calf management reduced
the need for hybrid vigor, and because of less attention to performance components other

than milk volume that influence the life cycle efficiency of milk solids production

23

(Willham and Pollack, 1985). Swan and Kinghom (1992) pointed out that crossbreeding
can give rise to economic gains if milk pricing puts reduced emphasis on milk volume
and if nonmilk traits such as disease resistance were important in the breeding objective.

Heterosis is particularly strong for traits that are lowly heritable (Van Vleck and
Gregory, 1996). The reproductive complex or fitness traits in most species have
heritability of less than 0.15 but seem to have considerable nonadditive genetic variance
which could be exploited. Species that have low reproductive potentials such as cattle,
must therefore rely on exploiting the existing genetic differences among groups like
breeds (Willham, 1969).

The genetic phenomenon of heterosis among crosses and of inbreeding is
generally believed to be due to dominance of gene action at many loci (Hill, 1987,
Cunningham, 1986). The consequences of crossbreeding (heterosis) depend on gene
frequency differences among the breeds and degree of dominance (Willham, 1969). It is
widely assumed that increased heterozygosity in crossbred animals is the underlying
heterotic mechanism which gives rise to observed hybrid vigor (Kinghom, 1982). The F 1
is totally heterozygous with respect to breed of origin. Due to random association of
genes, the F2 cross is expected to be heterozygous in this respect at only half of all loci.
It follows therefore in this dominance model, that the F2 is expected to show half the
hybrid vigour of the F1.

There seems to be a linear relationship between degree of heterozygosity and
heterosis (McGloughin, 1980). However, in most data fi'om farm animals, heterosis in
the F1 crosses is more than twice that in the F2 crosses (Van Der Werf and De Boer,

1989). Epistatic effects which are often estimated as recombination loss could be

24

responsible to this deviation from linearity between degree of heterozygosity and
observed heterosis. Epistasis effects describe all multiple gene effects which involve
more than one locus. Example of epistatic effects are the additive by additive effect
which is the joint effect of two genes at two separate loci and the additive x dominance
effect which is the joint effect of a single gene at one locus and a gene pair at a second
locus. Considering only two loci, there are possible four additive by additive effects, four
additive x dominance effects and one dominance x dominance effect. These effects may
be positive or negative. There has been some discussion on the evidence of existence of
significant epistatic effects. A lot of studies in mice, dogs, corn and beef cattle suggest
that the additive-dominance model is adequate in predicting heterosis in crossbreds
(Cunningham, 1987). However, Sheridan (1981) presented evidence in chicken that
showed that the additive-dominance model is inadequate. Sheridan’s data showed
performance in the F2 to be substantially lower than what is expected.

As already pointed out earlier, the genetic variance is composed of nonadditive as
well as additive variation. In many livestock species, the commercial animal is a cross of
two or more breeds. Genetic evaluation of such populations require statistical models
that expand beyond additive variation with a single breed (Benyshek, 1998; Miller and
Goddard, 1998). A model that includes additive and nonadditive effects between and
within breeds is necessary. Genetic variation in crossbred populations is usually
estimated from within breed variance, i.e., predictions of random effects are adjusted for
fixed breed-group effects. This may not be adequate. Arnold et al. (1992) using a multi-
breed model included average nonadditive genetic effects (heterosis) to estimate genetic

variation. However, this model failed to account for within breed nonadditive effects.

25

Miller and Goddard (1998) propose to think of the population of breeds as a single
‘super—breed’ with all existing breeds tracing back to a common ancestral population.
The nonadditive genetic variation in this super-breed model includes between breed
effects (heterosis), sire x breed of dam effects and within breed variation. In deciding on
the model for genetic evaluation, the relative size of these three different types of
nonadditive genetic variation must be taken into account. If a large amount of the
nonadditive genetic variation which exists within the super-breed population, also exists
within the purebred population, then nonadditive genetic variation must not only be
accounted for within and between breeds in multi-breed evaluations but it must also be

accounted for in purebred genetic evaluations (Miller and Goddard).

Inbreeding

Inbreeding which is generated by mating of related individuals is known to result
in inbreeding depression. Inbreeding depression is the decrease in mean phenotypic
value with increasing homozygosity within populations (Falconer, 1989, de Boer and
Hoeschele, 1993). Research has shown that each percentage increase in inbreeding in
dairy cattle results in approximately 22 kg decrease in milk production (Schaeffer, 1991).
Widespread use of new reproductive technologies such as MOET which reduce the
number of breeding females have a potential of increasing the inbreeding in a population.

Characters that are closely related to fitness such as viability and fertility tend to
show higher levels of inbreeding depression than morphological characters such as body

weight or type traits. The latter traits are known to have higher additive variance than the

26

fitness related traits. These fitness traits which have lower heritability in the narrow
sense are likely to have a higher heritability in the broad sense (Falconer, 1989).
Selection theory helps to explain why the additive genetic variance for fitness related
traits should be low and why dominance should be directional for these traits (Falconer,
1989). Alleles with favorable effects on fitness should move rapidly towards fixation,
irrespective of their degree of dominance. Furthermore, dominant alleles with deleterious
effects will be removed rapidly. Deleterious recessive alleles will be maintained at low
frequency by mutation pressure.

It is widely appreciated that inbreeding is an inevitable consequence of dominance
gene action. Larger estimates of inbreeding depression are associated with higher
estimates of dominance variance (de Boer and Arendonk, 1992). When gene action
operates additively, the average phenotypic effect associated with alleles are independent
of the genetic background (Falconer, 1989). Characters that are of purely additive nature
cannot therefore exhibit inbreeding depression. With dominance, the average phenotypic
effect of an allele changes with a change in genotypic frequency, even in absence of allele
frequency change because allelic expression is a firnction of the genetic background.

Prediction of additive and dominance effects in non-inbred populations requires
knowledge of the additive and dominance variation in the base population. Inbreeding
complicates the genetic covariance structure of the population. It creates covariance
between additive and dominance effects in inbred populations (Kennedy et al, 1988).
With inbreeding, therefore, the computation of genetic covariances between two relatives
requires knowledge of : 1) the sum over loci of the squared effects of inbreeding

depression; 2) dominance variance in the inbred population and 3) covariance between

27

additive and dominance effects in the inbred population (Harris, 1964; de Boer and
Arendonk, 1992).

De Boer and Arendonk (1992) showed that a statistical model containing
individual additive and dominance effects but ignoring changes in mean and genetic
covariances associated with dominance due to inbreeding resulted in significantly biased
predictions of both effects. Bias was found to increase almost linearly with the

inbreeding coefficient.

Genetic gain from selection utilizing nonadditive genetic effects

The benefits of utilizing nonadditive genetic effects in genetic evaluations can be
measured by the genetic gain that can be obtained by considering these effects. F uerst et
al (1996) simulated a genetic model with different levels of additive, dominance and
additive x additive genetic effects to assess the impact of dominance and epistasis on the
genetic make-up of simulated populations. The results they obtained showed that in the
short term (3 -5 years), rapid selection response could be achieved under the additive
model while in the long term, more genetic gain could be achieved with the inclusion of
nonadditive effects. DeStefano and Hoeschele (1992) estimated by simulation that the
extra genetic gain by selection using dominance and inbreeding was from 1.5% to 8% of
the phenotypic standard deviation depending on the assumed variances and number of
animals in parental classes. Misztal (1995) pointed out that the extra gain found in this
study could have been underestimated because the sire model was used. Destefano and

Hoeschele, 1992 suggested that future changes in the population structure brought about

28

by widespread use of artificial insemination and an increase in the number and size of
full-sib families and clones, could permit more efficient utilization of nonadditive genetic
variance and thus more achievement of genetic gain than the gain obtained in the
simulated populations.

The genetic gain from selection considering nonadditive genetic effects can be
approximately obtained by computing the maximum fraction of the phenotypic variance
that can be explained by the additive and nonadditive effects (Misztal, 1995, Culbertson,

1997)

The variance of an animal’s predicted genotype :

. 2 2 2
var(g) = o"apa + 0'de 1" caapaa
p,, pd and p,, are the maximum inheritable fi'actions of variances. These are calculated

as the relative difference between each variance and its residual due to the Mendelian

sampling variance. The maximum inheritable fraction of the variance can be calculated

a?

i represents additive (a), dominance (d) and additive x additive (aa). 5i is the Mendelian
sampling variance.

Assumed variances for additive, dominance and additive x additive genetic variances

together with maximum inheritable fractions are shown in Table 4. The assumed

variances are 25% for additive genetic effect, 10% for dominance genetic effect and 5%

29

for additive x additive genetic effect. For the additive effect, the maximum inheritable
variance is 12.5%, the dominance effect has maximum inheritable variance of 2.5% and
the inheritable variance for additive x additive genetic effect is 1.25%. The maximum
inheritable variance for the additive effect is 5 times more than that for dominance effect
and 8 times more than the inheritable variance for the additive x additive variance.

Genetic evaluation with nonadditive genetic effects require a mating system to
exploit these effects. These nonadditive genetic effects may be exploited directly through
specific mate allocation (DeStefano and Hoeschele, 1992). Matings that produce
offspring with noticeable effects of inbreeding depression are avoided when mate
allocation is based on prediction of specific combining ability (SCA). Mating plans or
nonrandom matings produce higher average progeny merit than random matings in three
ways (DeStefano and Hoeschele, 1992) :
1) economic merit is a nonlinear function of the component traits;
2) traits have intermediate optima;
3) nonadditive genetic variance exists in the population

Misztal (1995) proposed a mating system (Fig l) to make use of nonadditive
information. The mating system accepts a list of cows to be mated and the selection
criteria proposed by the breeder. The system then considers mating each cow to a
number of sires and computes nonadditive genetic effects present. Combinations with
highest total genetic merit are selected. This system needs complete pedigree information
and complete results of recent evaluations to make nonadditive adjustments for each

potential mating.

30

Simultaneous consideration of selection and crossbreeding effects in breeding
programs can be canied out by incorporating crossbreeding effects into the selection
index framework and applying a mating algorithm to maximize predicted genetic merit of
progeny (Swan and Kinghom, 1992). Kinghom (1987) evaluated a number of strategies
for mate allocation. Mate allocation was carried out with the aim of maximizing mean
progeny merit and this was based on proportion of genes from each parental breed,
amount of heterosis expressed, estimated breeding values and costs associated with the
breeding program. The study found that the pattern of mate allocation in animal breeding
programs can have a large effect on progeny merit, especially where large nonadditive
effects such as heterosis are present (Kinghom, 1987).

Jansen and Wilton (1985) described an application of linear programming that
selects and allocates mates in a way that gives the best possible expectation for progeny
merit corrected for costs associated with the breeding program. They also found positive

effects associated with mate allocation schemes.

Table 4 : Genetic variance, maximum inheritable fraction and maximum inheritable
variance for additive, dominance and additive x additive genetic effects ( Misztal ,1995)

 

Maximum inheritable Maximum inheritable

 

Genetic effect, Variances,2 fraction (p) variance (oizp)
i (°/o)
Additive, a 25 50 12.5

31

Dominance, d 10 25 2.5

add x add, a 5 25 1.25

 

32

Juvenile crossclassified MOET schemes may be become possible with the advent
of efficient harvesting of female gametes, together with in vitro fertilization (Swan and
Kinghom, 1992). These schemes involve mating all selected males to all selected
females. This may work well with crossbreeding because sire by breed of dam effects
(and possibly sire by dam effects) can be estimated and used in the mate selection

process.

33

Fig l : Mating system utilizing nonadditive genetic information (Misztal, 1995).

Results of last evaluation

11

 

Selection
' ‘ I=i>
Criteria gags Mating
List of Recommendations
Cows to ==>
Mate

 

 

 

ii

Population Pedigree

34

CHAPTER 3.

Introduction

Most selection programs in farm animals are based on the assumption that non-
additive components of genetic variance are zero or that they occur in the covariance
between relatives with a coefficient sufficiently so small that they are of negligible
importance (Lee and Henderson, 1969). The paucity of records on close relatives make
estimation of non-additive genetic variance difficult.

The recent developments in statistical methods and computing algorithms
especially for the inverted nonadditive genetic relationship matrices and the new
reproductive technologies such as multiple ovulation and embryo transfer (MOET),
which creates animals with close relationships and thus nonadditive relationships, have
increased the opportunity to estimate nonadditive components of total genetic variance.

Previous studies on estimation of nonadditive genetic variance have been
inconsistent and inconclusive. However, sizable dominance genetic variation has been
reported in species with higher fecundity such as poultry and fish and small dominance
genetic variance found in other species such as dairy and beef cattle. The differences in
magnitude of dominance effects in these studies could be attributed partly to differences
in the data structure. Poultry and fish have higher fecundity compared with cattle and
thus provide data with higher mean nonadditive genetic relationships among individuals.
The objective of this study was therefore to test whether the ability to estimate dominance
genetic effects accurately depends on the density and size of full-sib families in the data.

When dominance genetic effect is significant, we intended to investigate the effect of

35

ignoring and considering dominance genetic effects in the model on the estimation of
additive genetic effects.

Accurate prediction of nonadditive effects may be important in selection of mates
based on their specific combining abilities. However, the importance and magnitude of
nonadditive genetic variance in many traits of economic importance is yet to be
determined conclusively. This study seeks to lay a foundation for addressing these

issues.

36

MATERIALS AND METHODS

Data Structure

Five populations with varying percentages of animals in full-sib families were simulated
(Table 1). Percentages of animals in full-sib families were 100, 50, 20, 10 and 2 percent.
The number of animals in each population was 10 000 and each full-sib family had 25
animals. For each population, combinations of additive variance, V A and dominance
variance VD variances were considered (Table 2): VA = 950 and VD = 50, VA = 800 and
VD = 200, VA = 500 and VD = 500, thereby creating a total of 15 sub-populations, each
with 10 000 animals. The residual variance and the broad sense heritability were constant
in all populations. The residual variance was 2000 such that the broad sense heritability

was 33%. Each sub-population was simulated for 50 replicates.

Data Simulation

Records were simulated according to the following sire and dam model :
Yijk = 11 + Si + mj + Sdij+ eijk
where u is the population mean,

si is the additive effect of sire ~ N ( 0, 1/4032 )

37

Table 5: Percentage of full-sib animals in different populations.

 

Percentage of animals in

 

Number of animals Number of full-sib families full-sib families
10 000 400 100
10 000 200 50
10 000 80 20
10 000 40 10
10 000 8 2

 

38

Table 6 : Underlying additive and dominance genetic variances.

 

 

Additive Dominance Residual
Variance Variance Variance
Case 1 950 50 2000
Case 2 800 200 2000
Case 3 500 500 2000

 

39

where

And

mj is the additive effect of dam ~ N ( 0, 1/4cr,2 )

sdij is the dominance effect due to interaction of sire and dam ~ N ( 0, l/4od2 )

eijk is the residual effect ~ N ( 0, of + 1/20,2 + 3/4od2)

Derivation of additive (a) and dominance ((1) genetic values:

a = .5as + .5ad + ma

(1 = fds,d + md

as and a,l are the additive effect of the sire and dam, respectively.

fdm is combination effect of sire with dam due to interaction of genes from the
sire with genes from the darn.

m, and md are the respective additive and dominance genetic effects due to

Mendelian sampling.

2
Var (m9 = 0.5 0A

2
Var (111,) = 0.75 GB

Data Analysis

The following sire-dam model was used to analyze simulated data from each

replicate of each of the designed sub-population:

yijk = l1 + Si + dj + Sdij+ eijk

40

where u is the population mean; si is the additive effect of sire I; d,- is the additive effect
of dam j; sdij dominance interaction effect of sire i and dam j; and eij is the random error
term of animal i.

The above sire-dam model can be written in matrix notation on an individual animal
basis as :

y = Za + Zd + e

where,
y is the data vector;
3 is the vector of random additive effects for sire and darn;
d is the vector of random dominance effects;
e is the vector of residuals; and
Z and D are known matrices corresponding to, respectively, to a and d.

The variances-covariance matrix associated with this model is:

u- -

 

 

A02 0 o
a a
Var d = 0 D0": 0
e o o R

where

of and of are additive and dominance genetic effects;
A is the additive genetic relationship matrix

D is the dominance genetic relationship matrix

R is the diagonal matrix of homogenous residual variances where R = 0'2c

41

Another sire-dam model (reduced model) which did not include dominance
genetic effects was used to analyze the same data as analyzed under the full model to
assess the impact on additive genetic variance when dominance genetic effects are
ignored in the evaluation :

Yijk = 11 + Si + dj +eijk
where yij is the phenotypic value of animal i, u is the population mean, si is the additive
effect of sire i, (I is the additive effect of dam and eij is the random error term. The above
sire-dam model can be written in matrix notation on an individual animal basis as:

y = Za + e
where,

y is the data vector;

a is the vector of random additive effects;

e is the vector of residuals; and

Z is known matrix corresponding to a

The variances-covariance matrix associated with this model is :

r- 2 -*

 

 

where of is the additive genetic effect; A is the additive genetic relationship among sires

and dams; and R = I ozc

Variance component estimation - Tilde-hat approximation to REML

42

REML procedure is widely preferred by animal breeders because of its desirable
properties. However, the use of this procedure has been limited by the need to calculate
the inverse of large coefficient matrices of the mixed model equations (Hoeschele, 1991).
Pseudo expectation could be used to obtain estimates with properties similar to those
obtained when using REML with reduced computational difficulties. In this approach, the
strategy is to find quadratics similar to those in REML but have expectations easier to
compute than those of REML and can be used in an iterative algorithm to obtain
approximate REML estimates (Van Raden and Yung, 1988). The quadratics are equated
to their expectations under the assumption that the a priori values of variances used to
produce mixed model solutions are true values.

Given a general model such as the one below ,

y: Xb + film, + e

i=1
where :
y is the observation vector,
b is the vector of fixed effects
ui is the i‘” vector of random effects,
e is the vector of residual effects, and
X and Zi are corresponding design matrices.

The mixed model equations are, assuming V(ui) = 10,2 and V(e) = 103:

43

X‘X X‘zl X‘z2 E X‘y

Z‘IX Z‘lZl +IkI Z‘lZ2 at = Z‘ly
Z‘,x Z‘, 21 Z‘,z, + 1k, in, Z‘zy
k,- = of / of where i = 1 pertains to additive genetic variance and i = 2 pertains to

dominance genetic variance.

Prior estimates of ki are inserted into the mixed model equations and solutions of

b and iii are estimated. From these estimates, the quadratic forms t‘rfiii and
y’y - b‘X‘y - Zfi‘,z,y are calculated. The quadratic forms are set equal to their
i=1

pseudoexpectations and solutions of of and of are computed. Estimates of of and of
are obtained through iteration until convergence is reached.
The expectations of fri'r‘ri involve computing the inverse of the left-hand side of

the mixed model equations. This can be avoided by using quadratics that resemble but

are not exactly the same as those mentioned above (Van Raden and Jung, 1988). To
obtain these quadratics, the equations for b and iii are absorbed into the mixed model

equations shown earlier to give:

Z‘,Mz,+rkl Z‘,Mz2 a, _ Zl‘My
Z‘, Mzl Z‘,Mz2 + 1k,

Where M = I - X(X‘X)"X‘.
Van Raden and Jung, (1988) proposed using the iii‘r'ii which they called the tilde-

hat quadratic. 6‘ equals D,"Z,‘My, where D," is a diagonal matrix whose diagonals are
those of Z‘,MZi + 1k,. The tilde-hat quadratic has an approximate solution for u,» only on

one side and should therefore closely resemble the REML quadratic.

44

Assuming that priors for each ki is equal to the true variance ratio of / of, the
expectation of the tilde-hat quadratic (Van Raden and Jung, 1988) is :

Effii‘fii) = tr[Z‘ilVIZiDi'qu2
Relationship matrices can be included in the quadratic as in REML. With the additive

relationship matrix considered, for instance, the expectations are:

Emi‘A‘lfii) = tr[D,‘12‘,Mz,]a,2

In this study, variance components were estimated using the tilde-hat
approximation to REML described above. The inverse relationship matrices, A" and D"
were computed directly by algorithms described by Henderson (1975) and Hoeschele and

Van Raden (1991). Computations were done using FORTRAN programs INVERS and

NONAD2 written by Hoeschele (1991).

45

RESULTS AND DISCUSSION

Dominance Genetic Variance

Estimates of dominance genetic variance under various population structures and
magnitudes of dominance genetic variance are presented in Tables 7a through 11c.
Estimates of dominance genetic variance under populations with 2% of animals in full-
sib families are presented in Tables 7a, 7b and 7c. Dominance genetic variance estimates
was biased upwards (185) in Table 7a. The simulated true value for this variance was 50.
Van Raden et al, (1992) pointed out that estimates of genetic variances are most precise if
the data contains large numbers of several types of close relatives and the number of
family types must equal or exceed the number of genetic variances to estimate. Additive
and dominance genetic variances can therefore be estimated from populations with full-
sibs and half-sibs. The population in Table 7a has only 8 full-sib families. This small
number of dominance relationships could have led to inaccurate estimates of dominance
genetic variance. Table 7b shows a population with 2% animals in full-sib families with
VD simulated at 200. The estimate of dominance genetic variance in this case was 188
and this was not significantly different from the simulated variance. This seems to
contradict the earlier explanation that the incorrect estimate of dominance genetic
variance obtained in Table 7a is due to the fact that there were few animals with
dominance genetic relationships. However, this may be an indication that the magnitude
of dominance genetic variance in the population is important in the estimation of this

parameter. Table 7c seems to support this theory as the estimate of dominance genetic

46

variance is close to what was simulated. Though the number of firll-sibs in the
population in Table 7c were small and similar to that in Table 7a, the higher magnitude of
dominance genetic variance resulted in more accurate estimates of dominance genetic
variance.

Tables 8a, 8b and 8c show populations with 10% of animals in full-sib families
but differing in the magnitudes of VD simulated. The same pattern as seen in Tables 7a,
7b and 7c emerges. In Table 7a where VD is 50, the resultant estimate of dominance
genetic variance is 158.37 which is a gross overestimation of what was simulated. The
dominance genetic variance is estimated at 188 in Table 8b which is close to 200, the
value that was simulated. In Table 8c, VD is 500 and the dominance genetic variance
obtained was 386.

Estimates of dominance genetic variance in populations with 20% of animals in
full-sib families are shown in Tables 9a, 9b and 9c. In the population shown in Table 9a,
VD is 50 and the estimate of dominance genetic variance obtained was 97. This seems to
be an improvement over the .estimates obtained in Tables 7a and 8a. The estimate of
dominance genetic variance in Table 9b is 231 which is close to the simulated dominance
genetic variance. VD in Table 90 is 500 and the estimate of dominance genetic variance
obtained was 543. The results in these tables follow the pattern of results found in
populations with 2% and 10% of animals in full-sibs except that in this case (20 %
animals in full-sib families), the estimate of dominance genetic variance is closer to the
simulated value though VD was small, 50.

Estimates of dominance genetic variance are presented in Tables 10a, 10b and ICC

for populations with 50% of animals in full-sib families. The estimate of dominance

47

genetic variance in the population in Table 10a in which VD was 50 is 85. The
dominance genetic variance estimate in Table 10b is 214, which compares well with the
simulated value of 200. In the population in Table 10c, the estimate of the dominance
genetic variance is 523 and this too compares well with the simulated dominance genetic
value.

Estimates of dominance genetic variance in populations with all animals in full-
sib families are presented in Tables 11a, 11b and 11c. Table 11a gives the estimate of
the dominance genetic variance in a population with VD at 50. The estimate obtained is
66, which compares well with the simulated value of 50. The estimate of dominance
genetic variance in Table 11b is 216, which is close to the simulated dominance genetic
value. VD in Table 11c is 500 and the estimate of dominance genetic variance is 501.

Estimation of nonadditive dominance genetic variance requires large data sets
(Chang, 1988; Misztal, 1995). The size of each population in this study is 10 000 though
each population was replicated 50 times. Misztal et al, (1998) pointed out that accurate
estimates of dominance variance require them to be derived from data sets with at least
30 000 to 100 000 animals for populations with many full-sibs. However, from Tables
70, 8b and 8c, it can be revealed that even when the number of animals with dominance
genetic relationships is small, as long as the magnitude of dominance genetic variance is
large, dominance genetic variances can be estimated with relatively good accuracy.

Results from populations with 50% and 100% show that when the number of full-
sibs is large, dominance genetic variance can be estimated with improved accuracy even
if the magnitude of the dominance genetic value in the population is small (50). It was

observed in populations with small number of full-sibs (2%, and 10%) that even though

48

dominance genetic variance estimates can be obtained with relatively good accuracy
when the magnitude of the dominance genetic variance is large, the estimates are not as
accurately estimated as those estimated in populations with a higher number of firll-sib
families .

The general conclusion that can be made is that in populations with small number
of full-sibs in the population (2% and 10%), accurate estimates of dominance genetic
variance would be difficult to obtain unless the magnitude of dominance variance is
large. In populations with a large number of animals having dominance genetic
relationships, estimates of dominance genetic effects can be obtained with improved
accuracy even when the effect in the population is of small magnitude.

Models with fewer nonadditive effects produce smaller standard errors of variance
estimates (Van Raden et a1, 1992). In this study, the magnitude of standard errors seem
to increase as the magnitude of dominance genetic variances increases irrespective of the
number of animals in full-sib families. On the same note, the standard errors seem to
decrease in magnitude as the number of animals with dominance genetic relationships
increase. It must be pointed out that the method used in the analysis does not generate
standard errors. The standard errors in this study were estimated fi'om the empirical
standard errors of the differences between the observed values and the simulated values.

Dominance genetic variation has been found to be important for several traits of
economic importance. Culbertson (1998) found dominance effects to be important for
reproductive and grth traits in swine. Wei and Van der Werf (1993) observed large
estimates of dominance variance for most of the traits they studied in poultry. Rye and

Mao (1998) also found dominance genetic effects to be important for grth in Atlantic

49

Salmon. In all these studies, the species were of high fecundity. This study has shown
that in populations with large number of animals with dominance genetic relationships
and the magnitude of dominance variance is small, dominance genetic variance can still
be estimated. It seems therefore appropriate to include dominance genetic effects in
genetic evaluations for these species especially with traits in which dominance genetic

variance is large.

Additive genetic variance

The same data was analyzed under a reduced additive model to assess the impact on
additive genetic variance when dominance genetic effects are ignored in the evaluation.
The results are presented in Tables 7a through Table 11c. Estimates of additive genetic
variances were also studied under various population structures and magnitudes of
dominance and additive genetic variance .

Presented in Tables 7a, 7b and 7c are the estimates of additive genetic variances
under reduced and full in populations with 2% of animals in full-sib families. In the
population shown in Table 7a, the simulated genetic variances, V A and VD were 950 and
50 respectively. The estimate of additive genetic variance obtained in this population
under the reduced model was 979 which seems slightly higher than the VA, However,
this was not significantly different VA (Table 12). Table 7b provides the estimates of
additive genetic variances under a population with simulated variances of 800 and 200 for
additive and dominance genetic effects respectively. The estimate of additive genetic

variance under the reduced model was 830 and this estimate under the full model was

50

800. These estimates were not significantly different. Estimates of additive genetic
variances under a population with simulated variances of 500 for both additive and
dominance genetic effects are presented in Table 7c. The estimate of additive genetic
variance under the reduced model was 557 and the estimate under the full model was 497.
These estimates were also found not to be significantly different. Under populations with
a small number of animals in full-sib families (2%), the estimates of additive genetic
variance are slightly higher under the reduced model than under the full model.
However, the difference is not significant.

Presented in Tables 8a, 8b and 8c are the estimates of additive genetic variances
under reduced and full models in populations with 10% of animals in full-sib families. In
the population shown in Table 8a, V A and VD were 950 and 50 respectively. The estimate
of additive genetic variance obtained in this population under the reduced model was
1048 which is significantly (P< 0.05) higher than the estimate of 959 obtained under the
full model. Under the full model, the estimate of the additive genetic variance
corresponds well with the simulated additive genetic value. Shown in Table 8b are the
estimates of additive genetic variances in a population with simulated genetic variances
of 800 and 200 for additive and dominance variances respectively. The estimate of
additive genetic variance obtained in this population under the reduced model was 920
which is. significantly (P< 0.01) higher than the estimate of 837 obtained under the full
model. In the population shown in Table 8c, the simulated genetic variances were 500 for
additive genetic variance and 500 for dominance genetic variance. The estimate of
additive genetic variance obtained in this population under the reduced model was 652

which is significantly (P< 0.01) higher than the estimate of 485 obtained under the firll

51

model. Under the full model, the estimate of the additive genetic variance corresponds
well with the simulated additive genetic variance.

Presented in Tables 9a, 9b and 9c are the estimates of additive genetic variances
under reduced and full models in populations with 20% of animals in full-sib families.
In the population shown in Table 9a, VA and VD were 950 and 50 respectively. The
estimate of additive genetic variance obtained in this population under the reduced model
was 995, which is significantly higher (P< 0.05) than the estimate in the firll model.
Presented In Table 9b are the estimates of additive genetic variances under a population
with simulated values of 800 and 200 for additive and dominance genetic variances
respectively. The estimate of additive genetic variance under the reduced model was 921
and this estimate was significantly higher (P< 0.01) than the estimate obtained under the
full model. Estimates of additive genetic variances under a population with simulated
values of 500 for both additive and dominance genetic variances are presented in Table
9c. The estimate of additive genetic variance under the reduced model was 826 and the
estimate under the full model was 474. These estimates were significantly different (P<
0.01).

Presented in Tables 10a, 10b and 10c are the estimates of additive genetic
variances under reduced and full models in populations with 50% of animals in full—sib
families. In the population shown in Table 10a, VA and VD were 950 and 50 respectively.
The estimate of additive genetic variance obtained in this population under the reduced
model was 1012 which is significantly (P< 0.01) higher than the estimate of .943 obtained
under the full model. Under the full model, the estimate of the additive genetic variance

corresponds well with the simulated additive genetic value. Shown in Table 10b are the

52

estimates of additive genetic variances in a population with simulated genetic variances
of 800 and 200 for additive and dominance effects respectively. The estimate of additive
genetic variance obtained in this population under the reduced model was 955 which is
significantly (P< 0.01) higher than the estimate of 788 obtained under the full model. In
the population shown in Table 10c, VA and VD were both set at 500. The estimate of
additive genetic variance obtained in this population under the reduced model was 896
which is significantly (P< 0.01) higher than the estimate of 481 obtained under the full
model.

A similar pattern of results, which is even more dramatic is shown in populations
with all animals in full-sib families (Tables 11a, 11b and 11c). In the population shown
in Table 11a, the estimate of additive genetic variance obtained under the reduced model
was 1010 which is significantly (P< 0.01) higher than the estimate of 948 obtained under
the full model. Presented in Table 11b are the estimates of additive genetic variances in a
population with simulated genetic variances of 800 and 200 for additive and dominance
effects respectively. The estimate of additive genetic variance obtained in this population
under the reduced model was 993 which is significantly (P< 0.01) higher than the
estimate of 809 obtained under the full model. In the population shown in Table 11c, V A
and VD were both 500. The estimate of additive genetic variance obtained in this
population under the reduced model was 905 which is significantly (P< 0.01) higher than
the estimate of 476 obtained under the full model. Almost all of the dominance genetic
variances become part of the additive genetic variance and there is a very small decline in

the error variances.

53

The dominance genetic variance fades into both the additive and residual genetic
variances under the reduced model. This is supported by Misztal (1995) where he
showed that in an animal model, with no permanent environment, the dominance genetic
effects become part of both the additive and residual effects when dominance effects are
not included in the model.

Results show that as the number of animals in full-sib families increase, the
estimates of additive genetic effects under reduced models become increasingly biased
upwards. Under the full model, the estimates of additive genetic effects are estimated
with increased accuracy. It is also apparent that as the number of animals in full-sib
families increase, most of the dominance genetic variance become part of the additive
variance and there is marginal decline in the error variances. Rye and Mao (1998) found
similar results in the study of non-additive genetic effects in fish. Considering
dominance genetic effects in animal models, increases the accuracy of genetic evaluations
(Henderson, 1989; de Boer and Van Arendonk, 1992, Johansson et al, 1993). This is
particularly true for populations with a large number of animals with dominance genetic
relationships GVIisztal, 1995).

As the number of full-sibs in the population increases and also as the magnitude
of dominance effects increases, a greater discrepancy results between the simulated
additive genetic effects and the observed estimates. Generally, accounting for
nonadditive genetic effects in dairy and beef cattle have led to less dramatic effect on the
estimation of genetic variances (Templeman and Burnside, 1991; Miglior et al, 1995;
Rodriquez-Alrneida et al, 1995). This may be an indication of the general effect of the

population structure.

54

Higher standard errors are likely to occur for estimates of dominance genetic
variation as compared to additive variation and generally the precision of dominance
genetic effects is expected to be much less than for estimation of additive genetic
variance (Tempelman, 1989). This is also the case in this study, the size of standard
errors for dominance genetic variance were higher than the standard errors for additive

genetic variances.

55

Table 7a : 2% animals in full-sib families with simulated values, V A = 950,
VD = 50, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 979.91 47.8 - 2034.07 12.3
Full 949.27 47.0 185.39 34.8 1918.87 12.4

 

Table 7b : 2% animals in firll-sib families with simulated values, VA = 800,
VD = 200, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 830.56 29.1 - 2194.60 7.6
Full 800.78 30.7 188.03 43.7 2076.82 12.1

 

Table 7c : 2% animals in firll-sib families with simulated values, V A = 500,
VD = 500, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 557.08 27.5 - 2459.14 8.5
Full 497.20 22.4 444.52 49.1 2071.61 7.7

 

56

Table 8a : 10% animals in full-sib families with simulated values, V A = 950,
VD = 50, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 1048.38 33.3 - 1973.07 7.6
Full 959.64 33.7 158.37 28.2 1923.49 8.1

 

Table 8b : 10% animals in full-sib families with simulated values, V A = 800,
VD = 200, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 920.97 33.2 - 2107.76 10.9
Full 837.93 36.8 187.78 31.4 2036.19 11.2

 

Table 8c : 10% animals in full-sib families with simulated values, V A = 500,
VD = 500, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 652.36 21.6 - 2386.92 8.4
2227.27 10.4

Full 485.16 23.3 386.27 39.8

 

57

Table 9a : 20% animals in full-sib families with simulated values, V A = 950,
VD = 50, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 995.38 21.4 - 2017.69 6.7
Full 945.53 23.3 97.30 21.3 2005.75 7.4

 

Table 9b : 20% animals in full-sib families with simulated values, V A = 800,
VD = 200, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 921.48 22.5 - 2081.37 20.9
Full 784.62 30.5 231.67 34.8 2036.1 6.08

 

Table 9c : 20% animals in full-sib families with simulated values, V A = 500,
VD = 500, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 826.29 24.2 - 2246.05 7.0
Full 473.99 24.9 543.19 43.6 2111.70 8.2

 

58

Table 10a : 50% animals in firll-sib families with simulated values, V A = 950,
VD = 50, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 1012.34 17.5 - 1996.03 6.3
Full 943.65 24.2 85.58 22.0 1984.48 6.5

 

Table 10b : 50% animals in firll-sib families with simulated values, VA = 800,
VD = 200, VE = 2000

 

 

Model Add SE Dom SE Resid SE
Reduced 955.03 14.9 - 2078.93 5.9
Full 788.42 31.7 214.08 32.7 2048.92 5.9

 

Table 10c : 50% animals in full-sib families with simulated values, VA = 500,
VD = 500, VE = 2000 -

 

 

Model Add SE Dom SE Resid SE
Reduced 896.61 16.9 - 2174.53 5.9
Full 480.96 26.1 523.30 29.2 2125.10 6.5

 

59

Table 11a : 100% animals in full-sib families with simulated values, VA = 950,
VD =50, VE = 2000.

 

 

Model Add SE Dom SE Resid SE
Reduced 1009.88 15.3 - 2010.44 5.0
Full 948.06 17.6 66.81 15.7 2006.39 5.0

 

Table 11b : 100% animals in full-sib families with simulated values,VA = 800,
VD = 200, VE = 2000.

 

 

Model Add SE Dom SE Resid SE
Reduced 993.49 14.4 - 2052.18 4.7
Full 809.65 27.9 216.98 28.3 2034.58 4.7

 

Table 11c : 100% animals in full-sib families with simulated values,VA = 500,
VD = 500, VE = 2000.

 

 

Model Add SE Dom SE Resid SE
Reduced 905.28 13.5 - 2181.52 4.7
Full 476.92 23.9 501.42 26.5 2141.57 4.7

 

Table 12 : Summary table for estimates of additive variance under reduced

60

and full models.

 

 

Percent animals firllsib Reduced Model Full Model
families A B C A B C
O 951 790 508 950 790 508
2 979 830 557 949 800 497
10 1048’ 920" 652” 959 837 485
20 995' 921” 826" 945 784 543
50 1012" 955" 896" 943 788 480
100 1010" 993" 905” 948 809 476

 

Bias significant at P < .05
" Bias significant at P < .01

A : Additive Variance = 950, Dominance Variance = 50

B : Additive Variance = 800, Dominance Variance = 200
C : Additive Variance = 500, Dominance Variance = 500

61

Estimates of heritability

Estimates of heritability in the narrow sense under various population structures
and magnitudes of dominance genetic variance are presented in Tables 13 to 17. The
heritabilities are presented under reduced and full models.

Presented in Table 13 are the estimates of heritability with 2% of animals in full-
sib families. In the population with simulated heritability value of 0.317, the estimate of
heritability under the reduced model was 0.321 which is slightly higher than the
simulated heritability value. Under the full model, the estimate was 0.312. In a
population with simulated heritability value of 0.267, the estimate of heritability under
the reduced model was 0.275 and this estimate under the full model was 0.266. These
estimates were found not to be significantly different. Estimates of heritabilities under a
population with simulated heritability value of 0.167 were also found not to be
significantly different. The estimate of heritability under the reduced model was 0.183
and the estimate under the firll model was 0.165. Heritabilities under reduced and full
models are not significantly different in populations with a small number of animals in
full-sib families (2%).

Presented in Table 14 are the estimates of heritability under reduced and full
models in populations with 10% of animals in full-sib families. In the population with a
simulated heritability value of 0.317, the estimate of heritability obtained in this
population under the reduced model was higher than the estimate of 0.318 obtained
under the full model. Under the full model, the estimate of heritability corresponds well

with the simulated heritability value. In a population with simulated heritability value of

62

0.267, the estimate of heritability obtained in this population under the reduced model
was 0.303 which is higher than the estimate of 0.276 obtained under the full model. In
the population with a simulated heritability value of 0.167, the estimate of heritability
obtained under the reduced model was 0.214 which is higher than the estimate of 0.161
obtained under the full model. Under the full model, the estimates of heritability
correspond well with the simulated heritability values.

Presented in Table 15 are the estimates of heritability under reduced and full
models in populations with 20% of animals in full-sib families. In the population with
simulated heritability value of 0.317, the estimate of heritability obtained under the
reduced model was 0.329, which is larger than the estimate in the full model. In the
population with a simulated heritability value of 0.267, the estimate of heritability under
the reduced model was 0.304 and this estimate was larger than the estimate obtained
under the full model. The estimate of heritability under the reduced model was 0.268 and
the estimate under the full model was 0.161 for the population with heritability simulated
at 0.167. As the number of animals in full-sib families increase, the estimates of
heritability under reduced models become increasingly overestimated. Under the full
model, the estimates of heritability are estimated with increased accuracy. It is also
apparent that as the magnitude of dominance increases, the estimates of heritability
become increasingly biased upwards. The overestimation of heritability in the narrow
sense when only additive effects were included in the model, suggests that simultaneous
inclusion of non-additive genetic effects explained part of the genetic variance that would
otherwise be allocated with the additive genetic component (Miglior et al, 1995; Fuerst

and Solkner, 1994).

63

Presented in Table 16 are the estimates of heritability under reduced and full
models in populations with 50% of animals in full-sib families. In the population with a
simulated heritability value of .317, the estimate of heritability obtained in this population
under the reduced model was .335, which is higher than the estimate of 0.314 obtained
under the full model. Under the full model, the estimate of the heritability corresponds
well with the simulated value. In a population with simulated heritability value of .267,
the estimate of heritability obtained in this population under the reduced model was .315,
which is higher than the estimate of .261 obtained under the full model. In the population
with a simulated genetic value of .167 for the heritability value, the estimate of
heritability obtained in this population under the reduced model was .289, which is higher
than the estimate obtained under the full model. Heritability in the narrow sense has been
found to be over-estimated in numerous studies when dominance genetic effects are not
considered in the model (Wei and Vanderwerf, 1993; Rye and Mao, 1996; Fuerst and
Solkner, 1994).

Presented in Table 17 are heritability estimates in populations with all animals in
full-sib families. The heritability estimates under the reduced model in these populations
are even more biased than in the previous populations. The estimate of heritability
obtained under the reduced model was .334, which is higher than the estimate of .313
obtained under the full model for the population with simulated heritability value of .317.
In a population with simulated heritability value of .267, the estimate of heritability
obtained in this population under the reduced model was .325, which is much higher than
the estimate of .268 obtained under the full model. In the population with a simulated

heritability value was .167, the estimate of heritability obtained in this population under

64

the reduced model was .293 which is much higher than the estimate obtained under the
full model.

The number of animals with dominance genetic relationships and the magnitude
of the dominance genetic variance both affect the estimates of heritability. Predictions of
heritability are unbiased when the full model is used. Biases seem to increase with the
increase in the number of animals in full-sib families and with the increase in the
magnitude of dominance genetic effects. When dominance genetic effects are included in
the model, it has been observed that changes in breeding values are more pronounced in
animals with a large proportion of their information coming from animals with

dominance genetic relationships.

65

Table 13 : Estimated heritabilities (hz) under reduced and full models - 2% animals in

full-sib families.

 

 

Reduced Model Full Model
True h2 Estimated h2 SE Estimated h2 SE
0.317 0.321 0.014 0.312 0.014
0.267 0.275 0.008 0.266 0.009
0.167 0.183 0.008 0.165 0.007

 

66

Table 14 : Estimated heritabilities (hz) under reduced and full models - 10%

animals in full-sib families.

 

 

Reduced Model Full Model
True h2 Estimated h2 SE Estimated h2 SE
0.317 0.345 0.01 0.318 0.01
0.267 0.303 0.01 0.276 0.01
0.167 0.214 0.007 0.161 0.007

 

67

Table 15 : Estimated heritabilities (hz) under reduced and full models - 20%

animals in full-sib families.

 

 

Reduced Model Full Model
True h2 Estimated h2 SE Estimated h2 SE
0.317 0.329 0.006 0.313 0.007
0.267 0.304 0.007 0.257 0.009
0.167 0.268 0.007 0.161 0.007

 

68

Table 16 : Estimated heritabilities (hz) under reduced and full models - 50%

animals in full-sib families.

 

 

Reduced Model Full Model
True h2 Estimated h2 SE Estimated h2 SE
0.317 0.335 0.005 0.314 0.007
0.267 0.315 0.005 0.261 0.01
0.167 0.289 0.005 0.159 0.009

 

69

Table 17 : Estimated heritabilities (hz) under reduced and full models - 100%

animals in full-sib families.

 

 

Reduced Model Full Model
True h2 Estimated h2 SE Estimated h2 SE
0.317 0.334 0.004 0.313 0.004
0.267 0.325 0.004 0.268 0.007
0.167 0.293 0.004 0.158 0.007

 

70

CHAPTER 4

CONCLUSIONS

Current genetic evaluations and estimation of genetic parameters are based on the
additive genetic models. Considerable amount of genetic improvement has been
achieved through the utilization of these models, however, it is possible to increase the
accuracy of genetic evaluations by including nonadditive genetic effects. The choice of
efficient breeding programs for the genetic improvement of livestock is dependent upon
knowledge of the relative magnitude of the components of total genetic variance,
additive, dominance, epistasis, for the trait in which improvement is sought (Miller et al,
1963). The study examined the effect of population structure and magnitude of
dominance genetic effects on the estimation of dominance genetic variance. The impact
on the estimates of additive effects when dominance effects are considered and ignored in
the models was also investigated. The study revealed that given appropriate family
structure, it is possible to estimate dominance genetic variance. The size of full-sib
relationships and the magnitude of dominance genetic effects have substantial effect on
the estimation of dominance genetic variance. It can also be concluded from the study
that there is a strong bias in the estimation of additive genetic variance under an additive
genetic model.

The increase in the use of embryo transfer by farmers has allowed proliferation of
animals with non-additive genetic relationships. Multiple ovulation and embryo transfer,

MOET, has the potential for further increasing these genetic relationships. Further

71

propagation of dominance genetic relationships resulting fi'om other reproductive
technologies such as in-vitro fertilization and maturation, embryo splitting and cloning
may seriously bias genetic evaluations under an additive model if dominance genetic
effects are important. The change in the population structures due to these new
reproductive technologies will require a re-evaluation of the importance of dominance
genetic effects in the livestock populations. Data in current populations (dairy, beef) may
still be sparse with respect to the number and size of dominance coefficients. However,
species such as swine are populations that have a large number of non-additive genetic
relationships and therefore there is need for immediate exploration of the significance of
non-additive genetic effects in traits of economic importance. The knowledge of the
magnitude of these effects for important traits is needed before it could be recommended
that non-additive genetic effects be used in derivation of selection criteria.

The new reproductive technologies are likely to increase inbreeding with a
resultant increase in inbreeding depression (Tempelman, 1989). Inbreeding depression is
significantly underestimated under an additive genetic model (Maki-Tanila and Kennedy,
1986). To account for this increased inbreeding more accurately, dominance genetic
effects should be considered in the genetic evaluation models.

The expression of heterosis in crossbred populations points to the existence of
dominance genetic effects. In some livestock species such as beef, swine and poultry, the
commercial offspring if often a cross of two or more breeds taking advantage of heterotic
effects. Genetic variance in these populations is usually estimated from within breed
variance with predictions of random effects being adjusted for fixed breed-group effects

(Van der Werf and de Boer, 1989, Miller and Goddard, 1998). Estimates of heritability

72

for milk production traits in crossbred populations using mixed models with breed-group
effects have been found higher than published values for pure breeds (Van der Werf and
de Boer, 1989). Nonadditive effects have been attributed to this increase in the
heritability estimates. It seems desirable that in crossbreeding systems, genetic
evaluations predict the performance of potential crossbred progeny accounting for
nonadditive genetic effects.

It is important that crossbreeding should be balanced appropriately with selection
(Swan and Kinghom, 1992). Selection operates at the level of the individual animal and
thus if crossbreeding and selection are to be considered simultaneously, crossbreeding
effects should be handled at the same level as selection. This can be achieved by
incorporating the crossbreeding effects into the selection index framework and applying a
mating algorithm that finds the overall population mating sets, to maximize predicted
genetic merit of progeny (Swan and Kinghom, 1992).

Dominance genetic effects have been found to be important in traits that are lowly
heritable such as traits related to fitness, disease resistance. It is particularly important to
study dominance genetic variation in such traits. Studies on non-additive genetic effects
in dairy cattle for-instance have concentrated mostly on production traits such as milk
production. It would be ideal to study the non-additive effects on all traits that contribute
to the animal’s total economic merit.

For those traits that non-additive genetic variance is important, appropriate
models and algorithms should be developed to predict the transmitting ability for
individuals and breeding value for families. Breeding programs should be designed to

use breeding values for both individuals and families. Future corrective mating programs

73

should consider dominance for traits having significant dominance variation
(Tempehnan, 1989). Tempelman, (1989) pointed out that breeders could strategically
concentrate on additive genetic effects when selecting individual sires and dams for their
breeding program and then subsequently mate for total genetic merit for traits of choice.
In many cases, dairy producers using AI rely primarily upon the superiority of AI sires
rather than intraherd selection to improve the herd with the main objective being to obtain
maximum producing ability (Henderson, 1989). When non-additive genetic effects are
significant, this could be achieved by selecting a specific sire to mate to the daughter of a
particular AI sire.

It may be desirable to study the importance of other non-additive genetic effects
such as epistatic effects particularly additive x additive effects for possible confounding
with additive genetic effects. Large estimates of additive x additive genetic effects have
been associated with reduced estimates of additive genetic variance (Miglior et al, 1995 ;
Fuerst et al, 1996). Expected merit of an offspring is highly dependent on the
relationship between mates when additive x additive genetic effects exist (Chang, 1988).
Optimum mating plans should therefore be carefully researched whenever significant

epistasis genetic effects are detected.

74

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