Estimation of additive and dominance genetic variances for - CGIL ...

Ž .
Aquaculture 204 2002 383–392
www.elsevier.comrlocateraqua-online
Estimation of additive and dominance genetic
variances for body weight at harvest in rainbow
trout, Oncorhynchus mykiss
Ma. Josefa R. Pante a,b,) , Bjarne Gjerde a , Ian McMillan c ,
Ignacy Misztal d
a ˚
AKVAFORSK ( Institute of Aquaculture Research Ltd. ) , N-1432 As, Norway
b
Marine Science Institute, UniÕersity of the Philippines, Diliman, Quezon City, Philippines
c
Department of Animal and Poultry Science, UniÕersity of Guelph, Guelph, ON, Canada, N1G 2W1
d
Department of Animal and Dairy Science, UniÕersity of Georgia, Athens, GA 30605, USA
Abstract
Additive genetic, dominance genetic, and common environmental variance components were
estimated for body weight at harvest for three populations of rainbow trout under selection for six
generations in Norway. Six different models were studied by including all or different subsets of
the following effects in an animal model: additive genetic Ž A . , parental dominance Ž D . , common
environmental due to full-sibs Ž CE. and inbreeding coefficient Ž F. as a covariate. Variance
components were estimated using the Average Information Restricted Maximum Likelihood
Ž AIREML. method. In general, the results showed that estimates of additive genetic variance were
inflated under the simple models Ž A. and Ž AqF . , and decreased remarkably under the more
complex models such as Ž AqCE . , Ž AqCEqF . , Ž AqDqF . , and Ž AqDqCEqF . . The
magnitude of the dominance variance ranged from 0 to 22% and the common environmental
variance from 0% to 6% of the total phenotypic variance. The study confirmed the presence of a
significant dominance genetic variance for harvest body weight in rainbow trout. However, the
results indicate that the dominance and common environmental effects may be confounded in the
present data. q 2002 Elsevier Science B.V. All rights reserved.
Keywords: Rainbow trout; Body weight; Additive variance; Dominance variance; Common environmental
variance; Oncorhynchus mykiss
)
Corresponding author. Marine Science Institute, University of the Philippines, Diliman, Quezon City,
Philippines. Tel.: q63-2-922-3921; fax: q63-2-924-7678.
E-mail address: dosette.pante@upmsi.ph Ž M.J.R. Pante . .
0044-8486r02r$ - see front matter q 2002 Elsevier Science B.V. All rights reserved.
Ž .
PII: S0044-8486 01 00825-0

384
1. Introduction
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M.J.R. Pante et al.rAquaculture 204 2002 383–392
Breeding programs are designed to change the genetics of a population to improve its
productivity and profitability. In animal breeding, a considerable amount of genetic
progress has been achieved through the exploitation of the simple additive genetic
effects. Non-additive genetic components such as dominance and epistatic effects are
usually ignored because they tend to be confounded with the common maternal
environment; they have little practical application in selection Ž Mrode, 1996 . , and their
estimation would involve large computational requirements Ž Varona and Misztal, 1999 . .
However, accounting for non-additive genetic effects in genetic evaluation models is
important for obtaining accurate predictions of breeding values of animals, to obtain a
precise estimate of heritability and precise prediction of response to selection, and to
help in deciding which breeding strategy and selection method should be utilized. There
is a renewed interest in the estimation of non-additive genetic effects for important traits
in domesticated animal species. This was set off by the improvement in computing
facilities and availability of software ŽMeyer,
1989; Hoeschele and Van Raden, 1991;
Misztal, 1997. that permit estimation of non-additive genetic effects from large field
data sets. Evidence of non-additive genetic variation for important traits has been
reported in cattle ŽHoeschele,
1991; Tempelman and Burnside, 1991; Fuerst and
Solkner, 1994; Miglior et al., 1995; Rodriguez-Almeida et al., 1995; Misztal, 1997;
Misztal et al., 1997. and poultry ŽWei
and van der Werf, 1993; Misztal and Besbes,
2000 . .
In fish, salmonids in particular, several studies suggest a significant and important
influence of non-additive genetic effects on growth traits. In a majority of these studies,
the presence of non-additive genetic effects was based on the observation of a larger
dam than sire component of variance when estimated using a nested mating design
Ž Gjedrem, 1983; Gall and Huang, 1988; Gjerde and Schaeffer, 1989. or by the presence
of a significant sire by dam interaction Ž Gunnes and Gjedrem, 1981; McKay et al., 1986.
when estimated using a factorial design. However, the dam component in the above
studies may be inflated by effects common to full-sibs other than additive and
non-additive genetics, i.e. common environmental and maternal effects. Gall Ž 1975.
found evidence of non-additive genetic variation for post-spawning body weight among
crosses and backcrosses in two strains of rainbow trout. In rainbow trout, evidence of
non-additive genetic effects is also seen by a significant inbreeding depression on
growth Ž Pante et al., 2001a . , and significant heterosis when crossing inbred lines
Ž Gjerde, 1988 . . However, low heterosis was found when crosses were performed
between wild strains of Atlantic salmon Ž Gjerde and Refstie, 1984 . .
In studies that estimated the dominance genetic variance for important traits in fish,
results indicate that its magnitude is within the range of the additive genetic variance.
For example, in chinook salmon, the dominance variance for freshwater and saltwater
weights were 0.26 and 0.08, respectively Ž Winkelman and Peterson, 1994a . . For body
weight after 9 and 22 months of saltwater rearing, estimated dominance variance were
0.19 and 0.27, respectively Ž Winkelman and Peterson, 1994b . . In Atlantic salmon, the
dominance variance for body weight at harvest ranged from 0.02 to 0.18 depending on
the models utilized Ž Rye and Mao, 1998 . . These estimates imply that dominance is an

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M.J.R. Pante et al.rAquaculture 204 2002 383–392 385
important source of genetic variation for some growth traits in fish. Therefore, the
purpose of this study was to determine the magnitude of additive and dominance genetic
variances for body weight at harvest of rainbow trout and the common environmental
effect due to full-sib groups.
2. Materials and methods
Data were from three rainbow trout populations under selection for six generations
at the Aqua Gen AS in Norway from 1972 to 1992. Each population was established
separately in a different year Ž Table 1 . . The founding individuals for each population
were from different fish farms in Norway and Sweden and thus were assumed to be
from different gene pools. The pedigree data comprised seven generations Žgenerations
0–6 . . Individual growth was measured as body weight Ž kg. at harvest recorded after
16–18 months of rearing in floating net cages in the sea.
The data analyzed were from generations 2–6 for all three populations and comprise
a total of 15 year-classes Ž Table 1. and with a data structure as presented in Table 2. The
fish were offspring of broodstock selected mainly for fast growth rate, and the selection
method practiced was a combination of between-family and within-family selection. A
hierarchical mating design was applied where each sire is mated on average to two to
three dams. In all generations, full- and half-sib matings were avoided and matings that
would yield inbreeding coefficients of 12.5% or higher were restricted. Marking of
newly hatched larvae or fry is impossible; thus, each full-sib family was reared in
separate tanks until reaching the average tagging size of 20 g. This introduces an
environmental effect common to full-sib groups. To identify the families, a combination
of fin clipping and freeze-branding was used Ž Gunnes and Refstie, 1980 . . The individuals
selected as parents for the next generation were individually marked with operculum
tags.
Variance components for body weight at harvest were estimated for different effects
fitted to a single trait animal model using the AIREMLF90 program ŽTsuruta
and
Misztal, 2000 . . The algorithm uses the Average Information Ž AI. as second differentials
Table 1
The three separate populations analyzed in the study and the year-classes representing the time of hatching in
each population
Generation Population 1 Population 2 Population 3
0 1972 1973 1974
a 1 1975 1976 1977
2 1978 1979 1980
3 1981 1982 1983
4 1984 1985 1986
5 1987 1988 1989
6 1990 1991 1992
a The first generation where offspring were selected for fast growth rate.

386
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M.J.R. Pante et al.rAquaculture 204 2002 383–392
Table 2
Number of sires, dams, offspring and average body weight Ž kg. for the three populations of rainbow trout
Population Number Number Number of Average body s.d. Ž kg.
of sires of dams offspring weight Ž kg.
1 154 512 69,920 3.71 1.18
2 165 456 62,897 3.70 1.27
3 278 682 67,280 4.16 1.55
of the likelihood function Ž Jensen et al., 1996 . . Six different models were studied by
including all or different subsets of the following effects in the animal model: the
random additive genetic effect, the random parental dominance genetic effect, the
random common environmental effect due to full-sibs, and the inbreeding coefficient as
a covariate:
ysXhqZ 1aqe
Ž 1.
ysXhqbFqZ 1aqe
Ž 2.
ysXhqZ 1aqZ2cqe Ž 3.
ysXhqbFqZ 1aqZ2cqe Ž 4.
ysXhqbFqZ 1aqZ3dqe Ž 5.
ysXhqbFqZ 1aqZ2cqZ3dqe Ž 6.
where y is a vector of observations of animals; h is a vector of the fixed effects of
generation)location)cage)sex; a, d, c are random effects of direct additive genetic,
parental dominance interaction, and common environment due to full-sib groups,
respectively; b is the linear regression of y on inbreeding coefficients; F is the
coefficient of inbreeding; X, Z 1, Z 2, Z3 are the corresponding incidence matrices
relating the effects to y; and e is the vector of random residuals.
Eq. Ž. 1 is the simple additive genetic model Ž A . ; Eq. Ž. 2 is the Ž AqF . model with
additive genetic effects and the inbreeding coefficients as a linear covariate; Eq. Ž. 3 is
model Ž AqCE. with the additive genetic and common environment effects; Eq. Ž 4. is
model Ž AqCEqF . with the additive genetic and common environment effects and
with inbreeding coefficients as linear covariate; Eq. Ž. 5 is model Ž AqDqF . with
additive and dominance genetic effects and inbreeding coefficients as covariate; and Eq.
Ž. 6 is the full model Ž AqDqCEqF . , where all effects are fitted into the model. A
model where only the additive and dominance genetic effects Ž AqD . are present was
not included in the study because the inbreeding coefficient has to be fitted to obtain
proper estimates of the dominance genetic effects Ž Hoeschele and Van Raden, 1991 . .
The assumptions for the parameter means and variances were:
2
y X b
A sa 0 0 0
a
0
2
a
d
0 0.25Dsd 0 0
d 0
2
c 0 0 Isc 0
E s ;Var s ,
c
e
0
0
e
0 0 0 2 Ise

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M.J.R. Pante et al.rAquaculture 204 2002 383–392 387
where s 2 is the additive genetic variance, s 2 is the dominance genetic variance, s 2
a d c
is the common environment variance, s 2 is the error variance, A is the additive genetic
e
relationship matrix, D is the dominance genetic relationship matrix and I is an identity
matrix. Note that parental dominance variance is one-quarter of the offspring dominance
variance.
Following the algorithm of Hoeschele and Van Raden Ž 1991 . , inbreeding was
accounted for when inverting the A matrix but was ignored when inverting the D matrix.
However, with low levels of inbreeding, including the individual inbreeding coefficients
as a covariate in the model may be sufficient to account for ignoring inbreeding in
forming the inverse of the D relationship matrix Ž Hoeschele and Van Raden, 1991 . .
Moreover, the covariance between the additive and dominance genetic effects was also
ignored due to the large size of the data set.
The estimated variance components were expressed as ratios of the total phenotypic
Ž 2 . 2 2 2
variance s for each model: the additive genetic variance ratio as h ss rs , i.e.
t a t
the heritability; the dominance genetic variance ratio as d 2 ss 2rs 2 d t ; and the common
environmental variance ratio as c2 ss 2rs 2 c t .
Log likelihood ratio tests were carried out among the six models to determine the
most suitable of the six models. The likelihood ratio is LRsy2logwŽ rNz . rNz Ž .xs
y2wlogŽ rNz . yŽlogŽ Nz .x, where logŽ Nz . is the maximum of the likelihood function for
the full model and logŽ rNz . is the maximum of the likelihood function for the reduced
model subject to r number of constrained effects or parameters ŽLynch
and Walsh,
Table 3
Ž 2 . Ž 2 . Ž 2 Estimates of additive h , dominance d , and common environmental c . variances expressed as ratio of
Ž . Ž 2 total phenotypic variance with their corresponding standard errors s.e. , and the residual variance s . e for
each of the model for the three populations of rainbow trout
2 2 2 2
Population Model h "s.e. d "s.e c "s.e. s e
1 A 0.366"0.018 0.549
Aq F 0.354"0.018 0.554
AqCE 0.156"0.021 0.041"0.005 0.637
AqCEq F 0.158"0.021 0.038"0.004 0.637
Aq Dq F 0.162"0.023 0.144"0.005 0.635
Aq DqCEq F 0.158"0.020 0.000"0.000 0.038"0.004 0.637
2 A 0.365"0.019 0.559
Aq F 0.344"0.018 0.570
AqCE 0.087"0.018 0.062"0.006 0.681
AqCEq F 0.089"0.017 0.055"0.005 0.681
Aq Dq F 0.083"0.017 0.218"0.005 0.683
Aq DqCEq F 0.082"0.017 0.161"0.013 0.014"0.013 0.684
3 A 0.462"0.020 0.558
Aq F 0.441"0.019 0.572
AqCE 0.180"0.022 0.058"0.006 0.707
AqCEq F 0.185"0.022 0.053"0.005 0.705
Aq Dq F 0.167"0.022 0.216"0.005 0.713
Aq DqCEq F 0.167"0.012 0.215"0.004 0.000"0.000 0.714

388
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M.J.R. Pante et al.rAquaculture 204 2002 383–392
1997 . . An effect was considered to have a significant influence when its addition
resulted to a significant increase in the log likelihood Ž y2logL . , compared to the model
in which it was ignored. The LR test statistic is asymptotically distributed as x 2 , with r
r
degrees of freedom.
3. Results
Table 3 presents the estimates of variance components as proportions of the total
phenotypic variance for the different models and for all three populations of rainbow
trout. The results were fairly consistent across all three populations. In general, the
heritability estimates from models Ž A. and Ž AqF . were inflated compared with
estimates from the other models. Within a population, the heritability estimates were
nearly similar for models such as Ž AqCE . , Ž AqCEqF . , Ž AqDqF . , and ŽAqD
qCEqF . . With the simple additive genetic model Ž A . , the heritability ranged from
0.365 to 0.462, which were similar to heritability values for growth-related traits in other
salmonid species as estimated from sire components of variance Ž Gjedrem, 2000 . .
When fitting the inbreeding coefficient as a covariate in the model Ž AqF . , the
heritability decreased slightly by 0.01 to 0.02 when compared to model Ž A . . Also fitting
Table 4
Log likelihood values Ž y2logL. for the different models and the likelihood ratio Ž LR. when comparing each
of the models with model Ž A.
a
Population Model y2logL LR
1 A 689408.1
Aq F 689393.1 y15.02 )
AqCE 689357.2 y50.93 )
AqCEq F 689347.2 y60.94 )
Aq Dq F 689355.8 y52.33 )
Aq DqCEq F 689347.2 y60.94
2 A 622024.2
Aq F 621998.5 y25.68 )
AqCE 621953.9 y70.36 )
AqCEq F 621926.0 y98.24 )
Aq Dq F 621919.7 y104.50 )
Aq DqCEq F 621919.1 y105.07
3 A 672165.3
Aq F 672132.5 y32.83 )
AqCE 672063.2 y102.09 )
AqCEq F 672039.7 y125.58 )
Aq Dq F 672024.9 y140.43 )
Aq DqCEq F 672024.9 y140.42
a Ž .
LR is the difference between the y2logL for the specified model and model A ; a negative value
indicates improvement in the minimum of the likelihood.
) Significant difference at P -0.01.
)
)
)

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M.J.R. Pante et al.rAquaculture 204 2002 383–392 389
the common environmental Ž CE. effects Ž AqCE . , reduced the heritability by 0.21 to
Ž 2 0.28 and estimates of the CE variance ratio c . ranged from 0.04 to 0.06. For model
Ž . Ž . Ž 2 AqDqF the dominance D variance ratio d . ranged from 0.14 to 0.22, and
compared to model Ž AqCEqF . , the heritability slightly increased for population 1
while a slight decrease was observed for populations 2 and 3. In all three populations,
2 the estimate of d obtained from model Ž AqDqF . was close to four times the
2 estimate for c obtained from model Ž AqCEqF . indicating that the estimates of
these two effects might be confounded.
Ž . 2 2
With the complete model AqDqCEqF , the estimates of d and c were
reduced substantially compared to the estimates obtained from models Ž AqDqF . and
Ž . 2
AqCEqF , respectively. However, in population 1, the d estimate was zero and the
2 c estimate was identical to that obtained from the Ž AqCEqF . model, while in
population 3, the c2 estimate was zero and the d 2 estimate was almost identical to that
obtained from the Ž AqDqF . model, supporting that the estimated D and CE effects
might be confounded. This is also supported by the magnitude of the residual variance,
which in most cases, either increased marginally or remained the same when an effect
was added to the model Ž Table 3 . .
Table 4 presents the log likelihood values Ž y2logL. obtained for each model within a
population and the values of the likelihood ratio Ž LR. test statistics. Fitting the
inbreeding coefficient as a covariate or fitting, either the D or the CE effect always
increased the log likelihood significantly. However the log likelihood was almost
identical to that with the full model when the D effect was removed for population 1 or
when the CE effect was removed for populations 2 and 3.
4. Discussion
The magnitude of the heritability estimate for body weight at harvest from models
Ž A. and Ž AqF . were in agreement with previous heritability estimates for growth-related
traits in salmonid species. In general for models Ž A. and Ž AqF . , and for models
Ž AqCE. and Ž AqCEqF . , the inclusion of the inbreeding coefficients as a covariate
did not seem to greatly influence the heritability estimate. This may be due to the
relatively low average inbreeding in each population, which was estimated as less than
9% Ž Pante et al., 2001b . .
Fitting either the dominance genetic Ž D. or common environmental Ž CE. effects in
the model resulted in a remarkable decrease in the heritability estimate while the
residual variance either remained the same or increased slightly. This implies that a large
proportion of the D and CE variances are included in the estimated additive genetic
variance when these effects are ignored in the model and, as expected, were not lost to
the residual variance in the simple models. A substantial reduction in the additive
genetic variance for body weight at harvest when including the D genetic effect in the
model was likewise observed in Atlantic salmon, whereas the presence of a CE effect
only marginally influenced the additive genetic variance Ž Rye and Mao, 1998 . . In dairy
cattle studies, only a small decrease in the additive genetic variance was observed when
the D effect was included in the model Ž Miglior et al., 1995; Misztal et al., 1997 . , which

390
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M.J.R. Pante et al.rAquaculture 204 2002 383–392
is most likely due to a smaller number of dominance relationships among the animals
Ž Misztal et al., 1997 . . However, in fish populations, full-sib relationships dominate.
Ž 2 The magnitude of the estimated D variance ratio d . is similar to, and in some cases
much higher than, the heritability; ranging from 0% to 263% of the heritability estimate.
The extreme value is very high compared to the range from 12% to 147% for body
weight in Atlantic salmon Ž Rye and Mao, 1998 . , and 108% for body weight after 22
months in saltwater for chinook salmon Ž Winkelman and Peterson, 1994b . . The results
of this study along with the results from studies on other salmonid species indicate that
D may be an important source of genetic variation for growth in these species.
Ž 2 The estimated CE variance ratio c . ranging from 0 to 0.06 is in agreement with
previous estimates for growth related traits in Atlantic salmon ŽRefstie
and Steine, 1978;
Gjerde et al., 1994; Rye and Mao, 1998. but the maximum value is less than the 0.08
estimate for saltwater weight in chinook salmon Ž Winkelman and Peterson, 1994a. and
the 0.09 estimate for harvest body weight in rainbow trout ŽElvingson
and Johansson,
1993 . . Previous studies in salmonid species reported that the CE effects associated with
full-sibs for traits close to time of harvesting diminish over time ŽGunnes
and Gjedrem,
1978; Elvingson and Johansson, 1993; Gjerde et al., 1994; Winkelman and Peterson,
1994a . . However, the result from the present study suggests that the CE effect for body
weight, though small in magnitude, is still significant at harvest time and has an
influence on the estimate of the additive genetic variance. This result also calls attention
to the importance of at least including the CE effect in models for estimating
heritabilities and for predicting breeding values for growth-related traits in salmonids.
In the present data, the CE and D effects appear to be confounded. Confounding of
CE and D, seems to be complete in population 1, but not in populations 2 or 3. For both
effects, the design matrix is identical but the Ž co. variance structure differs. The average
size of each full-sib group was about 100, and with such a large group size, the
influence of the dominance relationship matrix on the prediction of dominance solutions
appeared to be minimal. Similar confounding was observed for egg traits of laying hens
Ž Misztal and Besbes, 2000 . . Separation of these two effects may require a different
mating design to obtain stronger dominance genetic connections among the animals in
the population. However, results obtained from Atlantic salmon with a similar data
structure as in this study did not indicate strong confounding between common
environmental and genetic effects Ž Rye and Mao, 1998 . .
Because of confounding between the CE and D effects, a model for the prediction of
breeding values should include both of these effects. Both effects are important and
cannot be partitioned with sufficient accuracy. The complete model, Ž AqDqCEqF .
is probably best for all future analyses of data sets involving a population structure more
suited to estimating and predicting all the effects investigated here and with all effects
being statistically significant.
For future work, a simulation study is warranted to determine whether the confounding
between the D and CE effects found in this study is due to methodological problems
or the design of the specific breeding scheme. If a breeding scheme can be found that
can provide simultaneously unbiased estimates of the D and CE effects, such a scheme
should be applied to obtain more reliable estimates of variance components for these
effects. Given a significant D genetic variance, studies should be undertaken to look

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M.J.R. Pante et al.rAquaculture 204 2002 383–392 391
into whether re-rankings of breeding values occur, particularly when the D effect is
either ignored or included in genetic evaluation models and to look at mating and
breeding schemes that can exploit both the additive and dominance genetic effects in the
breeding programs.
Acknowledgements
The authors would like to thank the Aqua Gen AS for providing the rainbow trout
data and the Research Council of Norway for funding part of the study through Project
No. 122859r122. The authors would also like to thank Dr. Larry Schaeffer for his
invaluable comments to the manuscript. This work is part of the PhD studies of MJRP at
the University of Guelph, Canada, that was funded by the International Development
Research Centre Ž IDRC . .
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