Arch.Geflügelk., 70 (4). S. 181–186, 2006, ISSN 0003-9098. © Verlag Eugen Ulmer, Stuttgart
Growth curve analysis using nonlinear mixed model in divergently
selected Japanese quails
Analyse der Wachstumskurven von in entgegen gesetzter Richtung selektierten japanischen Wachtellinien mittels eines nicht linearen gemischten Modells
K. Kızılkaya1, M.S. Balcıo g lu2, H.İ. Yolcu2, K. Karaba g 2 and I.H. Genc3
Manuskript eingegangen am 10. Februar 2005, angenommen am 23. April 2005
Introduction
Growth, a trait of prime interest to the animal industry, is
a complex physiological process. Mathematical models
have the potential to represent the entire growth phase of
the chicken and the parameters in the models have biological meaning. Growth curves, which are the graphical illustration of the mathematical functions, are generally used
to describe the increase in body weight of an individual or
the average growth of population over time, and are also
utilized to define the effects of selection on growth or body
weight at any stage of life (BLASKO and GOMEZ, 1993). Many
studies have been carried out to determine the growth pattern of chicken (TZENG and BECKER, 1981; ANTHONY et al.,
1991b; AGGREY, 2002), turkey (BUFFINGTON et al., 1973; ANTHONY et al., 1991a, 1991b), Japanese quail (MARKS, 1978;
ANTHONY et al., 1986; ANTHONY et al., 1991b), swine
(SCHINCKEL and CRAIG, 2001) and cattle (CHO et al., 2002)
by fitting the most common non-linear growth curve functions such as Gompertz, Logistic, Bertalanffy, Brody and
Richards models to the time-body weight information.
The parameters of non-linear growth curve models are
estimated by iterative procedures minimizing the error
variance or maximizing the likelihood by assuming that
the residuals are independently distributed. However,
growth curves are built up based on repeated live body
weight measurements on the same experimental unit.
These serial data usually have underlying relationships or
correlations among the serial body weight observations.
Therefore, heavier animals at birth or hatch usually have a
competitive advantage and remain heavier than the other
animals of the group in the later age stages. Also, the variation among the animals for live body weight increases as
age increases. This typical result contradicts the assumption that the residual values are independent and have a
constant variance at each age (SCHINCKEL and CRAIG, 2001).
Random effects of experimental units or individuals
would stem from repeated measurements on the same animal over time. A mixed model is one that incorporates
both fixed and random effects simultaneously (PEEK et al.,
2002). Therefore, the objective of this study is first to com-
pare non-linear fixed and mixed models and then to determine the effect of short-term divergent selection for
5-week body weights on growth characteristics of Japanese quail by comparing with those of the control line.
Materials and Methods
Material
High (HL) and low (LL) Japanese quail lines were established by applying the individual selection with 10% and
40% selection intensity on males and females, respectively,
for increased or decreased 5-week body weights through 5
generations. Quail chicks (351, 272 and 619) in HL, LL,
and control line (CL), respectively were hatched,
wing-banded and placed in separate brooder batteries. The
birds were sexed at 5-week of age according to their plumage color pattern. Random mating between selected parents was taken place within divergently selected lines. All
Japanese quail had ad-libitum access to a 24% crude protein and 2400 kcal ME/kg of diet and to water. For all the
three lines, hatch weight and thereafter weekly-body
weights were collected from progeny of generation 5 until
8-week of age.
Method
The nonlinear model for growth data from the animal i can
be expressed as:
BW ij = f ( θ i ,t ij ) + e ij
i = 1,..., N and j = 1,...,n i
where f is the nonlinear function relating the response variable (BWij) to time (tij), and θ i is a vector including the parameters of the non-linear function.
Japanese quail growth data were fit to the Richards fixed
effect function (RICHARDS, 1959),
BW it = A ( 1 + Bexp { – Kt } )
1Adnan
Menderes University, Faculty of Agriculture, Department of Animal
Science, Aydın-Turkey
2Akdeniz University, Faculty of Agriculture, Department of Animal Science,
Antalya-Turkey
3University of Idaho, Statistics, College of Science, Moscow, Idaho-USA
Arch.Geflügelk. 4/2006
(1)
1
 ---- m
+ e it
(2)
A > 0 , K > 0 and exp = 2.7818
where BWit is the body weight of Japanese quail at age
(week) t; A is the asymptotic weight or an estimation of
182
Kizilkaya et al.: Growth curve analysis in Japanese quails
mature weight as age approaches infinity; K is the rate of
maturing and refers to growth rate relative to mature
weight; m is the shape parameter determining the position
of the inflection point at which the auto acceleration
growth phase passes into the auto retardation phase; B is
the integration constant defining the degree of maturity at
t=0. The θ i vector in equation (1) includes fixed parameters A, B and Kei is the residuals with the assumption of
2
2
ei~N(0, δ Ii) where δ Ii is the residual variance structure
for all subjects, assuming that no covariance structure exists between the residuals of the model. However, a model
with some covariance structure could be also proposed to
incorporate the heteroskedasticity and correlation of the
residuals over all ages.
From equation (2) the absolute or instantaneous growth
rate (AGRit) and the relative growth rate (RGRit) in the Richards function were estimated as follows:
KB exp – Kt
AGR it = BW it -------------------------------------------------------------- and
m1 + B exp – Kt
(3)
KB exp { – Kt }
RGR it = ------------------------------------------------------------------------------m ( 1 + B exp { – Kt } )
The age (tinf) and weight (Winf) at the inflection point
were calculated below:
m
-1n  ------
 B
t inf = ---------------------------K
and
W inf = A ( m + 1 )
1
 ---- m
BW it = ( A + a i ) ( 1 + B exp { – ( K + k i )t } )
+ e it
(5)
where ai and ki are the random effects for the ith Japanese
quail. Thus, the θ i = [β, ui] includes a fixed component, β =
[A, B, K], common to all subjects, and a random component, ui =m [α, k] specific to each subject. Based on the
parametric inference approach, it is assumed that the distribution is ui ~N(0, G)where ui is independent of ei and
2
δA δ AK
G =
δ AK δ 2
K
and
(6)
( K + k i )B exp { ( – K + k i )t }
RGR it = ------------------------------------------------------------------------------------------------------m ( 1 + B exp { – ( K + k i ) t } )
The age (tinf) and weight (Winf) were found as follows:
m
-1n  ------
 B
t inf = ----------------------------( K + ki )
Model choice is an important issue both in animal and
plant science and also in other fields. However, breeders
and researchers in animal breeding have not shown a serious interest for statistical model choice criteria until recent
years (SORENSEN et al., 1995; KİZİLKAYA et al., 2003). The
most obvious fact is that the simple models are preferred to
more complicated ones. Significant advancements in computing power and statistical software now make possible to
use the more complicated models. The two most popular
model selection criteria to select the better fit model
among candidate ones are the Akaike Information Criteria
(AIC),
AIC = – 2f ( θ̂ ) + 2d
(8)
BIC = – 2f ( θ̂ ) + d ln ( n )
(9)
where f( θ̂ )denotes the maximum value of the (possibly restricted) log likelihood, θ̂ the vector of parameter estimates, d the dimension of the model, and n the number of
effective observations (BOZDOGAN, 1987; WOLFINGER, 1993).
They analytically measure how well different models fit
the data. Equations (8) and (9) indicate that AIC and BIC
reward descriptive accuracy via the maximum likelihood
by penalizing lack of parsimony according to the number
of free parameters. Therefore, the lowest values of AIC and
BIC determine the better fit model among candidate models for the observed data.
Results and Discussion
is the variance-covariance matrix of the random effects.
Genetic relationship between individuals was also ignored
in the analysis.
Thus, the absolute growth rate (AGRit) and the relative
growth rate (RGRit) from the mixed effects model were:
( K + k i )B exp { ( – K + k i )t }
AGR it = BW it ------------------------------------------------------------------------------------------------------m ( 1 + B exp { – ( K + k i ) t } )
Model Comparison
and the Bayesian Information Criteria (BIC),
(4)
The mixed effects model is:
1
 ---- m
non-linear growth curves in this study. In order to apply
non-linear mixed effects model to divergently selected Japanese quail growth curves, we used the procedure of
NLMIXED available SAS package (SAS, 2000). Initial values for each parameter were obtained from the results of
Richards fixed effects model which was run by using PROC
NLIN in SAS, and then the PROC NLMIXED used an iterative approach based on these initial values to generate a solution that properly account for individual animal effect on
repeated body weight measures.
and W inf = ( A + a i ) ( m + 1 )
1
 ---- m
(7)
The advantages of a mixed effect model analysis were
combined with the straightforward interpretability of
The observed growth curves for Japanese quail lines (HL,
LL and CL) within sex are shown in Figure 1. Live body
weights of male and female quails within lines were found
to be similar from hatch to 5-week of age, and thereafter females were significantly heavier than the males (P<0.05).
Also, divergence of selected lines from control occurred
immediately after hatching. The estimates of parameters
(A, K and m) for the Richards fixed and mixed effects models, the weight (Winf) and age (tinf) at inflection point, and
correlation coefficients (rAK) between mature weight and
rate of maturing are given in Table 1. As shown in Table 1,
parameter estimates from non-linear fixed and mixed effect models are not identical. Although there were not significant differences between the estimates of A and tinf for
both models, the estimates of K and Winf between models
were determined to be significantly different from each
other (p<0.05). In addition, the shape parameter (m) estimates from mixed effects model were found to be lower
than those from fixed effects model. Correlation coefficient
estimates (rAK) for male quails within HL and for females
within LL also indicated that mixed effects model produced non-similar results with fixed effects model.
Arch.Geflügelk. 4/2006
Kizilkaya et al.: Growth curve analysis in Japanese quails
300
200
150
100
50
b)
LL
HL
CL
250
B ody W eight (g)
B ody W eight (g)
250
300
a)
LL
HL
CL
200
Figure 1. Observed growth curves
of Japanese quail lines divergently
selected for 8-week body weight
and their control (a males, b females)
Beobachtete Wachstumskurven von
japanischen Wachteln, die auf das
8-Wochengewicht selektiert wurden, und der Kontrolllinie (a Hähne,
b Hennen)
150
100
50
0
0
0
1
2
3
4
5
6
7
8
9
183
0
1
2
3
A ge (week)
4
5
6
7
8
9
A ge (week)
The information criteria used to select the better fit
model are given in Table 2. These AIC and BIC values
showed that the non-linear mixed effect model resulted in
the smaller AIC and BIC than the non-linear fixed effect
model. Therefore, it was concluded that the non-linear
mixed effect model fitted better to observed growth data
from divergently selected Japanese quails, and non-linear
mixed effect model results were discussed in this study.
The live body weights of Japanese quails increase towards mature weights. As seen in Figure 1 and given in
Table 1, male and female quails within HL, LL and CL do
not have identical growth patterns, a phenomenon known
as sexual dimorphism. The studies of AGGREY and CHENG
(1994), DU PREEZ and SALES (1997), HYANKOVA et al. (2001),
AGGREY et al. (2003) exhibited the sexual dimorphism in
Japanese quail. Therefore, the Richards mixed growth
model was fit separately to live body weights from quail
lines for each sex.
Growth curves have four characteristics: an accelerating
growth phase following hatch, a point of inflection coinci-
dent with maximum growth rate, a decelerating growth
phase, and a limiting mature weight which is approached
asymptotically (CRAWFORD, 1990). The parameters of
growth curves have been used to quantify the differences
in growth patterns between sexes and between selected
lines. The estimates of parameter A for divergently selected
lines and controls were found significantly higher for females 291.51, 200.58 and 213.31 g (p<0.05) than for
males 228.71, 160.94 and 175.18 g, respectively (Table 1).
There was also a significant line-sex interaction for parameter A (p<0.05). Mature weight of HL and LL quails deviated differently from the controls. Therefore, it increased by
about 37% and 31% in HL; but, declined by only about 6%
and 8% in LL for females and males, respectively. The effects of sex and divergent selection on the estimates of parameter A in Japanese quails were also reported by AKBAŞ
and O g UZ (1998), HYANKOVA et al. (2001) and AGGREY at al.
(2003). Sex differences were also found in random-bred
Japanese quails (AKBAŞ and YAYLAK, 2000; KİZİLKAYA et al.,
2005) and in European quail (DU PREEZ and SALES, 1997).
Table 1. Estimates of Richards growth curve parameters by fixed and mixed effects models
Schätzwerte der Richard’s Wachstumskurvenparameter für das fixe und das gemischte Modell
Parameters
High Line
Female
N=171
Low Line
Female
N=134
Male
N=180
Control Line
Female
N=296
Male
N=138
Male
N=323
Fixed effects model
A
B
K
tinf
Winf
m
rAK
291.78
1.47
0.63
3.22
122.63
0.44
-0.573
±
±
±
±
±
±
3.20
0.71
0.02
0.05
1.32
0.05
-0.573
228.21
4.76
0.88
2.87
106.00
0.81
-0.542
±
±
±
±
±
±
1.63
1.39
0.02
0.04
0.94
0.06
-0.542
200.82
3.78
0.75
3.35
90.17
0.75
-0.519
±
±
±
±
±
±
2.30
1.32
0.04
0.05
1.05
0.09
-0.519
162.14
10.81
1.00
3.04
79.91
1.10
-0.408
±
±
±
±
±
±
1.41
3.25
0.03
0.05
0.85
0.08
-0.408
218.51
15.79
0.97
3.71
110.06
1.42
-0.594
±
±
±
±
±
±
1.95
4.26
0.03
0.04
0.90
0.08
-0.594
177.12
22.55
1.12
3.30
92.83
1.56
-0.604
±
±
±
±
±
±
1.09
5.00
0.03
0.03
0.61
0.07
-0.604
±
±
±
±
±
±
2.422
0.28
0.01
0.04
1.00
0.04
-0.666
228.71
5.52
0.79
2.83
104.46
0.60
-0.324
±
±
±
±
±
±
1.41
0.59
0.01
0.03
0.64
0.03
-0.324
200.58
3.67
0.63
3.31
88.34
0.47
-0.738
±
±
±
±
±
±
1.57
0.66
0.01
0.04
0.69
0.05
-0.738
160.94
14.23
0.92
3.03
79.22
0.92
-0.502
±
±
±
±
±
±
0.97
1.83
0.01
0.04
0.48
0.05
-0.502
213.31
20.92
0.82
3.67
108.08
1.07
-0.533
±
±
±
±
±
±
1.22
3.21
0.01
0.02
0.62
0.06
-0.533
175.18
30.81
0.98
3.27
91.84
1.27
-0.520
±
±
±
±
±
±
0.83
3.64
0.01
0.02
0.44
0.05
-0.520
Mixed effects model
A
B
K
tinf
Winf
m
rAK
291.51
1.53
0.56
3.17
120.30
0.27
-0.666
Arch.Geflügelk. 4/2006
184
Kizilkaya et al.: Growth curve analysis in Japanese quails
60
a)
A bsolute Growth R ate (g/week)
A bsolute Growth R ate (g/week)
60
50
40
30
20
LL
HL
CL
10
0
0
1
b)
50
40
30
20
LL
HL
CL
10
0
2
3
4
5
6
7
8
9
0
1
2
3
A ge (week)
6
7
8
1,00
a)
R elative Growth R ate (%/week)
R elative Growth R ate (%/week)
5
9
A ge (week)
1,00
0,75
0,50
0,25
4
LL
HL
CL
0,00
b)
0,75
0,50
0,25
LL
HL
CL
0,00
0
1
2
3
4
5
6
7
8
Figure 2. Estimated
absolute
growth rate of Japanese quail lines
divergently selected for 8-week
body weight and their control (a
males, b females)
Geschätzte absolute Wachstumsrate von japanischen Wachteln, die
auf das 8-Wochengewicht selektiert
wurden, und der Kontrolllinie (a
Hähne, b Hennen)
9
0
1
2
3
A ge (week)
4
5
6
7
8
9
A ge (week)
The parameter of growth rate and the rate of maturing
is another variable that describes the growth of Japanese
quails. These parameter changes as it moves towards its
mature weight. These changes give the quail a growth
curve that has a characteristic S shape in Figure 1 (ROSE,
1997). Parameter K of growth rate was significantly higher
in males (p<0.05) than females in all the lines (HL, LL and
CL) indicating that male quails grew faster than female
quails and reached their weight at point of inflection and
asymptotic weight at younger age. The effect of sex on the
parameter of growth rate and the rate of maturing has also
been determined in Japanese quails which were selected
for increased or decreased 4-week body weight for 30 generations (AGGREY, 2003; AGGREY et al., 2003); for relative
gain between 11 and 28 days of age (HYANKVA et al., 2001);
and for higher 4-week body weight for five generations
(AKBAŞ and O g UZ, 1998); and in European quail (DU PREEZ
and SALES, 1997). In addition, there was a significant decrease in the parameter of growth rate and the rate of maturing of the HL (32% and 19%) and LL (23% and 6%)
over the CL for females and males, respectively. It ap-
Figure 3. Estimated
relative
growth rate of Japanese quail lines
divergently selected for 8-week
body weight and their control (a
males, b females)
Geschätzte relative Wachstumsrate
von japanischen Wachteln, die auf
das 8-Wochengewicht selektiert
wurden, und der Kontrolllinie (a
Hähne, b Hennen)
peared that selection for increased and decreased 5-week
body weight resulted in a decline in the parameter of
growth rate and the rate of maturing for both sexes. The estimates of correlation between parameters A and K showed
that there was a moderately negative relationship between
maturation rate and asymptotic weight (Table 1). This antagonistic association indicates that early maturing quails
tend to attain smaller mature weight, and high mature
weight is strongly related with long growth period or quails
with lighter asymptotic weight reached that weight at
younger age (AKBAŞ and O g uz, 1998; KNIZETOVA et al.,
1991). Also, the divergent selection resulted in significant
correlation coefficient difference between male and female
within lines, compared to controls. The maximum maturation rate and weights (Winf) (120.30, 104.46, 88.34 and
79.22 g) indicated by the ages (3.17, 2.83, 3.31 and 3.03
weeks) at the inflection point (tinf) were also given for female and male quails within HL and LL lines (Table 1). Results showed that male quails reached the inflection point
significantly earlier than female quails. For LL quails, the
age at maximum growth was about 2.5 days later, suggest-
Table 2. AIC and BIC values for non-linear fixed and mixed effects models
AIC und BIC Werte für das nicht-lineare fixe und das gemischte Modell
High Line
Model
Fixed
Mixed
Female
Low Line
Male
Female
Control
Male
Female
Male
AIC
BIC
AIC
BIC
AIC
BIC
AIC
BIC
AIC
BIC
AIC
BIC
13697
11697
13723
11722
13683
11401
13710
11427
8999
8076
9024
8099
9342
7970
9368
7993
22624
20647
22654
20677
23121
20631
23150
20661
Arch.Geflügelk. 4/2006
Kizilkaya et al.: Growth curve analysis in Japanese quails
ing a prolonged growing period. Also, significant sex and
line effects were found on the weight at inflection point.
Divergence selection for 5-week body weight in this study
altered the Winf of HL and LL quails compared to controls
because of the positive correlation between asymptotic
weight and weight at inflection point (KNIZETOVA et al.,
1991).
The shape of growth curve, which has a variable point of
inflection for the Richards mixed effects model, is defined
by the shape or growth trajectory parameter m (AGRREY et
al., 2003). However, popular growth models, such as the
Gompertz and Logistic models have fixed growth shapes
with inflection point at 37% and 50% of the asymptote, respectively. When the values of m are close to 0 or 1, the Richards model corresponds to the Gompertz or Logistic
growth curve models (BRISBIN et al., 1987). Although both
females and males of CL had growth curve shapes of Logistic model, the selection for increased and decreased
5-week body weight resulted in the decline in the values of
m, which were 0.27, 0.60 in HL and 0.47, 0.92 in LL for
both sexes. Therefore, the shape of the growth curve of females in HL resembles more the Gompertz growth curve;
however, others still were equivalent to the logistic model.
The estimated absolute and relative growth rates by line
and sex were presented in Figure 2 and Figure 3. As seen in
Figure 2, all lines for absolute growth rate increased until
about week 3 which is the age of maximum accumulation;
and thereafter a rapid decline occurred. Females produced
significantly larger absolute growth rates than males
(p<0.05) within all ages. For both sexes, the absolute
growth rates were found significantly higher in HL than LL
and CL through growth period; however, the differences
between lines got smaller after the age of maximum
growth rate. In addition to the asymmetric response for absolute growth rate to divergent selection, Figure 3 indicated that selection resulted in significantly higher relative
growth rate for HL and LL in the first two weeks compared
to the CL within sexes. The lower birth weight at hatch in
line LL could result in larger relative growth rate in LL than
line CL. Initial advantage of quails from HL diminished
with age. So, LL and CL quails maintained a slightly higher
relative growth rate over the HL until week 5. MARKS
(1979, 1980) indicated that selection for high 8-week body
weight in chicken resulted in an increase in relative growth
in the first two weeks. AGGREY (2003) studied Japanese
quail lines divergently selected for 4-week body weight,
suggested that the initial spurt in the relative growth rates
in the first few weeks may determine the asymptotic body
weight and this being the case, relative growth may decline
by a factor proportional to the amount of the remaining
growth.
Acknowledgements
This study was supported by The Scientific Research
Projects Unit of Akdeniz University (pr.no:21.01.0121.30).
Summary
This study was undertaken to apply non-linear mixed effects model to examine the effect of short-term selection
for 8-week body weight on growth parameters in divergently selected lines of Japanese quail and their controls.
The parameters of Richards models were utilized to describe growth pattern of Japanese quails from the generation 5 including growth curves; and absolute and relative
growth rates.
Arch.Geflügelk. 4/2006
185
Growth parameter estimates were significantly different
in mixed model from in fixed effects model for all lines by
sexes, except asymptotic weight and age of inflection
point. There was a significant increase and decrease in maturing weights of divergently selected lines over the control
for both females and males. However, growth rates and
ages of maximum growth rate for lines decreased significantly compared to control. Although Richards model is
equivalent to the Logistic model for both females and
males of control line, the selection for increased and decreased 8-week body weight resulted in the decline in the
values of the growth curve for both sexes. Therefore, the
trajectory of the growth curve of females in high line resembles more of the Gompertz growth curve; however, the
selection did not alter the shape of growth curves in males
of high line and in females and males of low line. Absolute
and relative growth rates were also affected by the divergence selection. The high line quails showed significant absolute growth rate through growth period and relative
growth rates were found significantly higher for lines compared to control in the first two weeks.
Key words
Japanese quail, non-linear mixed model, divergence selection, growth curve, Richard’s model
Zusammenfassung
Analyse der Wachstumskurven von in entgegen gesetzter Richtung selektierten japanischen Wachtellinien mittels eines nicht linearen gemischten
Modells
In der vorliegenden Studie wurde ein nicht-lineares gemischtes Modell zur Untersuchung des Einflusses einer
kurzzeitigen Selektion auf die Wachstumsparameter von
Japanischen Wachteln, die in entgegen gesetzter Richtung
auf das 8-Wochengewicht selektiert wurden, und deren
Kontrolllinien verwendet. Zur Beschreibung der Wachstumsparameter (Wachstumskurven, absolute und relative
Wachstumsraten) für die japanischen Wachteln aus der
Generation 5 wurden die Parameter des Richard’s Modells
herangezogen.
Die Schätzwerte für die Wachstumsparameter waren für
alle Linien und Geschlechter mit Ausnahme des asymptotischen Gewichts und des Wendepunkts zwischen dem gemischten Modell und dem fixen Modell unterschiedlich.
Die Gewichte zur Geschlechtsreife nahmen in den entgegen gesetzt selektierten Linien gegenüber der Kontrolle sowohl für die Hennen als auch für die Hähne signifikant zu
bzw. ab. Demgegenüber nahmen die Wachstumsrate und
das Alter beim maximalen Wachstum in den Selektionslinien im Vergleich zur Kontrolle signifikant ab. Obwohl das
Richard’s Modell in der Kontrolllinie sowohl für die Hennen als auch für die Hähne äquivalente Ergebnisse zum logistischen Modell erbrachte, führte die Selektion auf höheres bzw. geringeres 8-Wochengewicht zu einer Abnahme
der Werte der Wachstumskurve für beide Geschlechter.
Der Verlauf der Wachstumskurve entsprach daher bei den
Hennen bei einer Selektion auf hohes 8-Wochengewicht
eher der Gompertz Funktion. Demgegenüber führte die Selektion bei den Hähnen in der ‚Aufwärts-Linie’ sowie bei
den Hennen und Hähnen in der ‚Abwärts-Linie’ zu keiner
Veränderung des Verlaufs der Wachstumskurven. Die absoluten und relativen Wachstumsraten wurden ebenfalls
durch die entgegen gesetzte Selektion beeinflusst. Die
186
Kizilkaya et al.: Growth curve analysis in Japanese quails
Wachteln der ‚Aufwärts-Linie’ zeigten eine signifikant höhere absolute Wachstumsrate über die gesamte Wachstumsperiode. In den ersten 2 Lebenswochen waren die relativen Wachstumsraten in den Selektionslinien generell höher als in der Kontrolllinie.
Stichworte
Japanische Wachtel, nicht lineares gemischtes Modell, entgegen gesetzte Selektion, Wachstumskurve, Richard’s Modell
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Correspondence: Dr. Kadir Kızılkaya, Dept. of Animal Science, Faculty of Agriculture, Adnan Menderes University, Aydın-Turkey; e-mail:
[email protected] or [email protected]
Arch.Geflügelk. 4/2006