Choice of animal models for estimation of genetic
parameters of reproductive, growth and slaughter traits of Californian and New
Zealand rabbits raised under tropical conditions
J B S Ferraz and J P Eler
University of Sao Paulo/FZEA/ZAB,
Cx. Postal 23, 13630-970, Pirassununga SP Brazil
jbferraz@spider.usp.br
Abstract
In order to compare different animal models, the methodology
of mixed models under animal models was used to predict (co)variance components
of 23 traits related to reproduction traits of 1,456 litters and growth and
slaughter traits of 3,845 Californian and New Zealand White rabbits raised in
southeastern Brazil. The (co)variance components, obtained by four different
models in single trait analysis, were used to estimate genetic parameters. The
four animal models considered as random effects only the animal direct genetic
effects (model 1), the animal direct and permanent effects of litters or common
effects of does as permanent environment effects (model 2), the animal direct
and maternal genetic effects, uncorrelated to each other, and permanent
environmental effects (model 3), and as in model 3, but with correlated animal
direct and maternal effects (model 4). All the models considered the fixed
effects of contemporary groups, parity, sex and the covariates - level of
inbreeding of litters or rabbits, and litter sizes, where these were applied.
The models were compared based on likelihood test and the "best" model
is proposed for each trait. Permanent environmental effects were important for
all traits and should be considered in animal models that analyze reproductive,
growth and slaughter traits of rabbits of these two breeds. The magnitude of the
c² term varied from 0 to 0.39. Maternal genetic effects were not important for
reproductive traits, but significantly affected growth and slaughter traits, and
were more important for New Zealand White than for Californian rabbits. Maternal
heritabilities varied from 0.03 to 0.14. As models 1, 2, 3 and 4 gave different
estimates for genetic parameters, total heritabilities were calculated for all
traits. Total heritabilities were low for reproductive traits (from 0 to 0.14),
and moderate for growth (from 0.03 to 0.36) and slaughter traits (0.02 to 0.23).
Although New Zealand White and Californian rabbits perform similarly, the
results showed that the genetic parameters for these two breeds are different
and should not be analyzed together. The models chosen for each trait serve as
guides for proposition of animal models in single or multi trait analysis of
rabbit data.
Key words: Rabbits, genetic parameters, New Zealand White, Californian
Introduction
As rabbits can be fed with forages and do not compete
directly with humans for grains, they can be a very important source of high
quality animal protein in developing countries. However the knowledge of
genetics of rabbit breeds , including two of the most used ones, New Zealand
White and Californian, under tropical conditions is not well established and
more studies are needed (Lukefahr and Cheeke 1991; Lukefahr et al 1992;
Ferraz 1993; Ferraz et al1994).
In selection programs applied to rabbit production,
reproductive, growth and slaughter traits can be considered. However, the larger
the number of traits, the smaller the genetic gain obtained in each trait. The
decision about which trait should be considered depends not only on the
economics involved, but also on genetic parameters of the traits and the
"practical" importance of the trait. The definition is taken by the
geneticist and the breeder, always considering market reasons.
Studies on genetic parameters of several traits of rabbits
have been made by some authors. Khalil et al (1986) made an important review
article on this subject. However, the studies of parameters estimated for
populations raised under tropical or subtropical conditions are not very many.
Among such studies can be placed those of Nunes and Polastre (1988), Baselga and
Camacho (1990), Camacho and Baselga (1990), Ferraz et al (1991a,b), Moura et al
(1991a,b), Polastre et al (1991), Santacreu and Blasco (1991), Baselga et al
(1992), Ferraz et al (1992), Lukefahr et al (1992), Ferraz et al (1994),
Lukefahr et al (1994), Rochambeau et al(1994) and Ayyat et al. (1995), using
different models, including animal models.
Genetic parameters are ratios of variances and covariances,
so these estimates are needed for the complete genetic knowledge of populations.
The estimation of variance and covariance components evolved from Henderson’s
Methods I and III (Henderson 1953), through maximum likelihood
(Hartley and Rao 1967), iterative maximum likelihood (Cunningham and
Henderson 1968; Thompson 1969), MINQUE (Rao 1970; LaMotte 1970), Restricted
Maximum Likelihood - REML (Patterson and Thompson 1971) and MIVQUE
(Rao 1971). Best Linear Unbiased Predictors - BLUP (Henderson 1949; Henderson et
al 1959), using methodology of mixed models is becoming the preferred method of
estimation for animal breeders (Henderson 1988). REML co(variance) component
estimation is also becoming the most commonly used algorithm in such
estimations.
The objectives of this study were to compare different animal
models used to estimate genetic parameters of eight reproductive, nine growth
and six slaughter traits of Californian and New Zealand White rabbits raised
under subtropical conditions in southeastern Brazil, using single trait analysis
with mixed models methodology. The aim was not only to have a better knowledge
of genetics of those breeds in sub-tropics but also to try to choose the
"best" models for each one of the traits that can be used as selection
criteria.
Material and Methods
Data came from records of 1,456 litters (for reproductive
traits), 3,845 rabbits (for growth traits) and 2,195 carcasses (for slaughter
traits) of Californian and New Zealand White rabbits, born between 1988 and
1992. Table 1 shows the distribution of data between the breeds.
The animals had been raised at the Rabbit farm on the
Campus of the University of Sao Paulo, located in Pirassununga (22ºS and 47ºW,
750 m above sea level). Average temperatures were around 22.5ºC from January to
March, 19ºC from April to June (decreasing each month) and from July to
September (increasing each month) and 22ºC from October to December. Sunlight
hours had similar trends to temperature. The rabbits were housed in metal cages
and fed a commercial pelleted feed (18% crude protein and 17% fibre).
Reproduction started after reaching 130 days of age.
|
Table 1:
Distribution of data used for estimation of genetic parameters, between
Californian and New Zealand White breeds. |
![]() |
|
Item
|
Californian
|
New
Zealand White
|
![]() |
|
Reproductive
traits (litters)
|
662
|
794
|
|
Growth
traits (rabbits)
|
2,010
|
1,835
|
|
Slaughter
traits (rabbits)
|
1,149
|
1,046
|
|
Number
of sires
|
42
|
56
|
|
Number
of dams
|
161
|
180
|
|
Number
of animal with pedigree for reproductive traits
|
744
|
746
|
|
Number
of animals with pedigree for growth and slaughter traits
|
2,138
|
1,968
|
![]() |
Traits that were analyzed were:
Reproduction data for each doe and parturition were recorded:
litter size at birth total (LSB) and alive (LSBA), litter size at 21 days of age
(LS21), litter size at weaning (LSW), litter weights at birth (LWB), 21 days
(LW21) and weaning (LWW) and mortality from birth to weaning (MORT).
The rabbits were weekly weighed from weaning to 11 weeks, and
the traits were: weaning weight (WW), weights at 5, 6, 7, 8, 9, 10 and 11 weeks
(W5, W6, W7, W8, W9, W10, W11), besides average daily gain (ADG).
At slaughter, each animal was individually weighed before and
after slaughter, giving the traits: weight at slaughter (WS), carcass weight
(CW), viscera weight (VW), head weight (HEAD), skin weight (SKIN) and carcass
yield (CY).
Inbreeding coefficients for litters and does were calculated
using a modification of K. Meyer’s program DFNRM, made by Van Vleck (1991,
personal communication). Pedigree information was used as far it existed. Data
were analyzed by mixed model methodology for animal models, in single trait
analysis. using the software DFREML (Meyer 1988, 1989), modified by Boldman and
Van Vleck (1991) for use of Sparspak, a sparse matrix solver, according to
suggested procedures described by Ferraz (1992). Parameters estimated were
heritability for direct and maternal effects, total heritability (as proposed by
Dickerson 1947, 1970), besides the c² term (ratio between the variance due to
permanent environment and phenotypic variance). Phenotypic variance was also
estimated.
Analyseswere done according to the general model:
y = X$ + Za + Zm +Zc
+ e, where:
y =vector of dependent variable, the observations;
X = incidence matrix of fixed effects;
$ = vector of
fixed effects, including sex (for growth and slaughter traits), parity, year and
trimester (for reproductive traits), contemporary groups (for growth and
slaughter traits), linear and quadratic effects of covariable level of
inbreeding of does and rabbits, linear effects of covariable age at weaning (for
weaning traits), linear and quadratic effects of litter size at weaning and
linear effects of age at slaughter (for slaughter traits);
Z = incidence matrix for random effects;
a = vector of random animal direct genetic effects;
m = vector of random animal maternal genetic effects;
c = vector of random permanent environmental effects of
does (for reproductive traits) or common effects of litters (for growth and
slaughter traits);
e = vector of random errors, NID (0, F²).
The differences among the models refers to the number of
random effects considered. Model 1 considered only the animal direct
genetic effect, Model 2 the animal direct genetic effect and the
permanent environmental effect of doe or common effect of litters, Model 3
also considered the effects included in Model 2 plus the animal maternal
genetic effect, uncorrelated with the direct effect and Model 4
considered all the effects included in Model 3, but in this case the
animal direct and maternal genetic effects were considered correlated.
To compare animal models, it was assumed that the higher the
likelihood function, the more the model explained the data. Likelihood function
is higher when new parameters are included in the model. So, to go from model
1 to model 2, model 2 to model 3 and model 3 to model
4, one parameter was added each time. To compare the difference between the
values of the likelihood function of two models, the methodology used was that
described by Rao (1973) and Mood et al (1974). This method is based on the fact
that that the difference -2[log7i
- log7i’]
has Qui squared distribution, where 7i
and 7i’ are the values
of likelihood function, after the convergence criteria of the iterative process
has been reached (in this case the variance of the function in the last 5
evaluations should not be larger than 1 x 10-9) in the different
models. The number of degrees of freedom of this comparison is equal to the
number of parameters that were added to the model (one in the case of the
comparisons made here). Significance was tested not only at level of P<0.05,
but also a "practical" significance, based on variation of values of
genetic parameters was considered in the choice of the "best" model.
Results and Discussion
The definition of the correct model is important, because the
more complex the model, the larger the time needed for solution. This is even
more important in multi-trait analysis, because CPU time is a function of n3,
where n is the number of variance and covariance components to be estimated. If
you go from a Model 1 to Model 4 in a single trait analysis, the
number of parameters to be estimated goes from one ( the variance component for
the animal direct genetic effect) to three (animal direct and maternal genetic
effect and the covariance between them), and CPU time will be close to 9 times
larger. In a two-trait analysis, the number of variance components goes from
three (both direct effects and their covariance) to nine and CPU time will be
increased in the order of 93/33 or 27 times larger. This
"rule" is only a guide to estimate the processing time, but it depends
of course on several factors, like the genetic relationship among animals,
established in A matrix (the relationship matrix) and it’s inverse, A-1,
The case will be even worse for three or four-trait analysis. With the right
models defined in single-trait analysis, a great waste of time can be avoid.
The Qui-squared value and it’s significance for the
likelihood test for each trait is given in Table 2. The analysis shows that the
models affect the results differently, depending on whether the traits are
reproductive or growth and slaughter.
|
Table
2: Qui-squared value (1 degree of freedom) for likelihood test used to
compare different animal models used for (co)variance components
estimation in 23 traits of rabbits
|
![]() |
|
|
Californian
Comparison
between Models
|
New
Zealand White
Comparison
between Models
|
|
Trait
|
2-1
|
3-2
|
4-3
|
2-1
|
3-2
|
4-3
|
![]() |
|
LSB
|
3.42
|
65.7*
|
1.50
|
4.8*
|
0.72
|
0.13
|
|
LSBA
|
5.6*
|
69.9*
|
0.68
|
2.07
|
1.79
|
0.10
|
|
LS21
|
3.76
|
0.00
|
0.40
|
0.68
|
0.00
|
0.18
|
|
LSW
|
3.46
|
0.00
|
0.62
|
1.59
|
0.00
|
0.11
|
|
LWB
|
1.04
|
0.16
|
0.04
|
5.1*
|
0.17
|
0.27
|
|
LW21
|
0.98
|
0.36
|
0.00
|
1.41
|
0.00
|
0.00
|
|
LWW
|
0.10
|
0.04
|
1.48
|
1.72
|
0.00
|
-0.13
|
|
MORT
|
4.66*
|
0.40
|
-0.16
|
4.7*
|
0.00
|
-0.84
|
|
WW
|
317.8*
|
5.2*
|
0.28
|
391.5*
|
4.7*
|
0.15
|
|
W5
|
257.5*
|
3.58
|
0.22
|
285.5*
|
6.5*
|
0.17
|
|
W6
|
49.3*
|
1.82
|
-1.04
|
183.4*
|
6.7*
|
0.22
|
|
W7
|
179.6*
|
0.00
|
0.22
|
163.0*
|
4.7*
|
0.22
|
|
W8
|
161.6*
|
0.04
|
0.62
|
83.3*
|
8.1*
|
2.12
|
|
W9
|
112.1*
|
0.00
|
0.54
|
128.0*
|
7.9*
|
0.14
|
|
W10
|
57.0*
|
0.06
|
0.70
|
61.3*
|
8.4*
|
0.38
|
|
W11
|
26.0*
|
0.00
|
0.46
|
84.2*
|
4.9*
|
1.44
|
|
ADG
|
3.8*
|
0.00
|
0.08
|
30.8*
|
1.64
|
0.06
|
|
WS
|
50.0*
|
0.10
|
0.58
|
49.5*
|
4.7*
|
2.58
|
|
CW
|
54.32*
|
0.02
|
0.66
|
48.6*
|
8.1*
|
0.42
|
|
VW
|
1471.2*
|
0.00
|
0.52
|
26.5*
|
4.6*
|
0.86
|
|
HEAD
|
15.1*
|
0.00
|
0.18
|
15.4*
|
0.00
|
-0.16
|
|
SKIN
|
40.1*
|
0.00
|
0.70
|
53.9*
|
2.44
|
0.56
|
|
CY
|
13.9*
|
4.1*
|
0.10
|
14.0*
|
1.48
|
-0.72
|
![]() |
| *
Stat5istically significant at P<0.05 |
|
For both breeds, the common environmental effects of litters
strongly affected the estimation of (co)variance components for growth and
slaughter traits, but very few reproductive traits were affected by permanent
environmental effects of does. That can be explained by the age of animals when
measurements were made. Rabbits are animals that grow very fast and there is an
interval of only around 50 days between weaning and slaughter, and in this
interval the effects of litters still exist. These results show that is very
important to include permanent environmental effects when (co)variances are
estimated with rabbit data.
When comparing Model 3 with Model 2 (the latter
includes maternal genetic effects), only LSB and LSBA for reproductive traits,
and WW and CY were influenced by this source of variation in Californian
rabbits. However, no reproductive traits and all growth traits (except ADG) and
WS, CW, VW were affected by genetic maternal effects in New Zealand White
rabbits. This is very important, because the inclusion of genetic maternal
effects sometimes is confounded with permanent environmental effects of does and
hard to separate or explain. In Californian rabbits, maternal effects can be
excluded from the animal models in the majority of traits. The differences
between Models 4 and 3 (includes the correlation between direct
and maternal genetic effects) were not detected in any one of the 23 traits
analyzed in both Californian and New Zealand White rabbits, which is also an
important finding so as to avoid wasting CPU time.
Table 3 presents the values of total heritability, which
considers heritabilities for direct and maternal effects and also their
correlation. These values are very important in the choice of "best"
models, because if no statistical difference has been detected by the likelihood
test, but total heritability changes in what can be considered a
"practical" difference, a more complex model can be considered
"better" than the one detected by the statistical test.
|
Table
3: Total heritabilities for 23 reproductive, growth and slaughter
traits of Californian and New Zealand White rabbits, estimated by four
different animal models.
|
![]() |
|
|
Californian
Models
|
New
Zealand White
Models
|
|
Trait
|
1
|
2
|
3
|
4
|
1
|
2
|
3
|
4
|
|
![]() |
|
LSB
|
.222
|
.077
|
.098
|
.072
|
.240
|
.083
|
.027
|
.033
|
|
|
LSBA
|
.303
|
.110
|
.120
|
.094
|
.207
|
.098
|
.036
|
.052
|
|
|
LS21
|
.148
|
.000
|
.000
|
.013
|
.197
|
.119
|
.118
|
.115
|
|
|
LSW
|
.146
|
.000
|
.002
|
.023
|
.226
|
.100
|
.100
|
.095
|
|
|
LWB
|
.124
|
.057
|
.058
|
.059
|
.129
|
.000
|
.010
|
.002
|
|
|
LW21
|
.311
|
.130
|
.082
|
.095
|
.167
|
.080
|
.079
|
.082
|
|
|
LWW
|
.103
|
.083
|
.079
|
.048
|
.293
|
.126
|
.126
|
.145
|
|
|
MORT
|
.181
|
.000
|
.014
|
.000
|
.190
|
.001
|
.000
|
.039
|
|
|
WW
|
.608
|
.030
|
.093
|
.136
|
.554
|
.117
|
.109
|
.116
|
|
|
W5
|
.583
|
.090
|
.110
|
.155
|
.532
|
.076
|
.068
|
.090
|
|
|
W6
|
.324
|
.000
|
.033
|
.045
|
.516
|
.170
|
.134
|
.158
|
|
|
W7
|
.558
|
.209
|
.209
|
.249
|
.533
|
.170
|
.137
|
.153
|
|
|
W8
|
.554
|
.194
|
.187
|
.212
|
.434
|
.133
|
.116
|
.170
|
|
|
W9
|
.467
|
.187
|
.186
|
.203
|
.516
|
.203
|
.164
|
.184
|
|
|
W10
|
.398
|
.241
|
.236
|
.244
|
.516
|
.309
|
.220
|
.243
|
|
|
W11
|
.412
|
.264
|
.264
|
.275
|
.541
|
.261
|
.212
|
.245
|
|
|
ADG
|
.439
|
.358
|