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

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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