PRODUCTION, MODELING, AND EDUCATION
Growth curves for ostriches (Struthio camelus) in a Brazilian population
S. B. Ramos,* S. l. Caetano,* R. P. Savegnago,* B. N. Nunes,* A. A. Ramos,† and D. P. munari*1
*Departamento de Ciências Exatas, Faculdade de Ciências Agrárias e Veterinárias,
Universidade Estadual Paulista, 14884-900, Via de Acesso Prof. Paulo Donato Castellane s/n, Jaboticabal,
São Paulo, Brazil; and †Departamento de Produção e Exploração Animal, Faculdade de Medicina
Veterinária e Zootecnia, Universidade Estadual Paulista, 18618-970, Botucatu, São Paulo, Brazil
and the Akaike information criterion. The R2 calculated for the logistic growth model was 0.945 for hens and
0.928 for cockerels and for the Gompertz growth model,
0.938 for hens and 0.924 for cockerels. The third-order
polynomial fit gave R2 of 0.938 for hens and 0.924 for
cockerels. Among the Akaike information criterion calculations, the logistic growth model presented the lowest values in this study, both for hens and for cockerels.
Nonlinear models are more appropriate for describing
the sigmoid nature of ostrich growth.
ABSTRACT The objective of this study was to fit
growth curves using nonlinear and linear functions to
describe the growth of ostriches in a Brazilian population. The data set consisted of 112 animals with BW
measurements from hatching to 383 d of age. Two nonlinear growth functions (Gompertz and logistic) and
a third-order polynomial function were applied. The
parameters for the models were estimated using the
least-squares method and Gauss-Newton algorithm.
The goodness-of-fit of the models was assessed using R2
Key words: growth, nonlinear models, ostrich, Struthio camelus
2013 Poultry Science 92:277–282
http://dx.doi.org/10.3382/ps.2012-02380
INTRODUCTION
2005/2006). Despite the size of the national flock, no
studies describing its growth are available. The objective of this study was to fit growth curves using nonlinear and linear functions to describe the growth of
ostriches in the Brazilian population.
Growth can be defined as an increase in body size
per unit of time (Tompić et al., 2011). modeling growth
curves of animals is a necessary tool for optimizing
the management and efficiency of animal production
(Köhn et al., 2007). However, growth can only be attained under nonlimiting conditions. For example, food
needs to be available ad libitum; the nutrient content
must at least meet the required ratios in relation to
energy; intake must not be constrained by the bulk of
the food or the presence of toxins; and environmental
factors such as high temperature and disease must not
constrain intake (Emmans and Kyriazakis, 1999). An
animal’s genetic potential for growth can described in
terms of its growth curve (Emmans and Fisher, 1986).
The available literature on ostrich growth used data
from South African farms and modeled only the Gompertz growth function (du Preez et al., 1992; Cilliers et
al., 1995; Cooper, 2005). In Brazil, ostrich production
began in 1995 with the importation of the first animals
from Italy (Carrer et al., 2005). In 2006, the estimated
number of commercially farmed birds in the country
was 335,425, according to the Brazilian ostrich-Rearing Yearbook (Anuário da Estrutiocultura Brasileira,
MATERIALS AND METHODS
The data used for the growth analysis came from
commercial flocks and were provided by the Brazilian
ostrich Rearers’ Association (Associação dos Criadores
de Avestruz do Brasil), based in São Paulo, SP, Brazil.
This institute approved the use of this data to perform
this research. A total number of 441 BW records from
58 hens and 54 cockerels measured from hatching to 383
d of age were used. The animals were crossbreds from
the African Black, Red Neck, and Blue Neck breeds.
The exact proportions of these genetic groups within
each animal were unknown.
Figure 1 shows animals of the African Black breed.
Figure 1a shows a triplet consisting of 1 cockerel (at
the center) and 2 hens. They are 8-yr-old animals with
an approximate BW of 150 kg and approximate height
of 2.20 m. Figure 1b shows 8-mo-old male and female
chicks, with no visible sexual differentiation in plumage, with approximate BW and height of 75 kg and
1.80 m, respectively.
After the chicks had hatched, they were weighed,
tagged around the neck for identification, and trans-
©2013 Poultry Science Association Inc.
Received April 3, 2012.
Accepted September 8, 2012.
1 Corresponding author: [email protected]
277
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Ramos et al.
Figure 1. An African Black triplet consisting of one cockerel (at the center) and 2 hens (a); male and female African Black chicks (b). Photos
courtesy of Celso da Costa Carrer (Faculdade de Zootecnia e Engenharia de Alimentos, Universidade de São Paulo). Color version available in
the online PDF.
ferred to small pens. At night, they were housed in a
controlled environment with a minimum temperature
of 25°C. When the birds reached 3 mo of age, they were
moved to larger pens and were no longer housed. At 6
mo of age, the birds were transferred again to larger
pens. The birds’ diet was composed of pasture grass,
specific industrial food with added citric pulp, and water ad libitum.
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Table 1. Functions for modeling the growth curve and inflection points in the ostrich
Model
Equation1
ti2
A
Logistic
W=
Gompertz
W = Ae−e
Polynomial
W = d0 + d1t + d2t2 + d3t3
(
1 + Be(
−Ct)
ti =
)
(B−Ct)
yi3
(ln B)
C
B
C
−d2
ti =
3d3
ti =
Reference
yi =
A
2
Fekedulegn et al. (1999)
yi =
A
e
Wellock et al. (2004)
yi = 2d2
Tompić et al. (2011)
1W = predicted BW (kg) at age t; A = asymptotic final BW (kg); t = age in days; C = instantaneous relative
growth rate; B = function-specific parameters; e = base of natural logarithm (2.71828); d0 = intercept; and d1,
d2, and d3 = regression coefficients.
2t = age (d) at inflection point.
i
3y = BW (kg) at inflection point.
i
To estimate the BW at a certain age, two 3-parameter nonlinear growth functions and a polynomial
growth function were fitted to the ostrich BW data.
The equations for the growth models applied are given
in Table 1.
The model parameters were estimated and the statistical analysis was carried out using the R software
version 2.14.2 (R Development Core Team, 2012). The
nonlinear and linear modeling was carried out using the
NLS and LM procedures, respectively. The LM procedure used the least-squares method and the nonlinear
regression the Gauss-Newton algorithm. The initial values for the curve parameters were estimated from earlier reports (du Preez et al., 1992; Cilliers et al., 1995).
The goodness-of-fit of the functions was assessed using R2 and the Akaike information criterion (AIC).
The R2 is defined as the proportion of the total sum of
squares that is explained by the model. The range is 0
≤ R2 ≤ 1. Values closer to 1 indicate better fit (Faraway, 2004). The AIC is defined as
AIC = −2Lm + 2m,
where Lm is the maximized log-likelihood and m is the
number of parameters in the model. Lower AIC values
indicate the preferred model (Akaike, 1973).
The t-test was used to investigate whether the estimates were significantly different from zero and to compare nonlinear model parameter estimates for cockerels
and hens. The inflection points of the nonlinear functions and the third-order polynomial were calculated.
The equations for calculating the inflection points of
these functions are given in Table 1.
RESULTS
Table 2 shows the estimated fitting parameters, their
SE, R2, AIC, and inflection points of the Gompertz and
logistic functions. Parameter A of the nonlinear growth
curves, which can be interpreted as the asymptotic final
BW, was greater in the Gompertz function than in the
logistic function, both for cockerels and for hens (P <
0.05). Parameter C, which can be interpreted as the
instantaneous relative growth rate, was also greater in
the logistic function than in the Gompertz function,
both for cockerels and for hens (P < 0.05). There were
no significant differences in mature weights and instantaneous relative growth rates between cockerels and
hens, for either of the nonlinear growth functions. The
logistic curve showed higher R2 values both for hens
and for cockerels.
According to the nonlinear functions, the hens
reached the inflection point at an earlier age than the
cockerels. However, the third-order polynomial function
showed the opposite. Both of the nonlinear functions
showed that the cockerels had greater BW at the inflection point.
Table 3 shows the estimated fitting parameters, their
SE, R2, AIC, and inflection points of the third-order
polynomial fit. The intercept (d0) can be interpreted
as the mean BW at hatching. The estimate of d0 was
negative but not significantly different from zero. The
Table 2. Estimated parameters, SE, inflection point, R2, and Akaike information criterion (AIC) for 2 nonlinear growth curves
Model parameter1,2
Model
Logistic
 
Gompertz
 
a,bMeans
Sex
A
Female
Male
Female
Male
(2.124)a
(2.815)a
(5.441)b
(7.174)b
101.7
103.7
120.4
124.9
Point of inflection3
B
34.99 (4.269)
28.09 (3.860)
1.55 (0.063)
1.465 (0.066)
C
0.019
0.018
0.009
0.008
(0.001)a
(0.001)a
(0.001)b
(0.001)b
ti
yi
R2
AIC
185.060
188.743
169.656
173.842
50.85
51.83
44.28
45.97
0.945
0.928
0.938
0.924
1,576
1,560
1,605
1,571
within a column with different superscripts differ significantly (P < 0.05).
= asymptotic final BW (kg); B = function-specific parameter; C = instantaneous relative growth rate.
2Standard errors are between parentheses.
3t = age (d) at point of inflection; y = BW (kg) at point of inflection.
i
i
1A
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Ramos et al.
Table 3. Estimated parameters, SE, inflection point,
model
R2,
and Akaike information criterion (AIC) for third-order polynomial growth
Model parameter1,2
Sex
Female
Male
d0
d1
d2
d3
ti
yi
R2
AIC
1.768 (1.049)
1.622 (1.255)
−0.040 (0.030)
0.005 (0.038)
2.000 (0.300)
2.000 (0.300)
−5.000 (0.500)
4.000 (0.600)
3.85
2.70
0.005
0.004
0.938
0.924
1,598
1,568
1d = intercept; d = regression coefficient; d =
0
1
2
2Standard errors are shown between parentheses.
3t
i
Point of inflection3
regression coefficient (×10−3); d3 = regression coefficient (×10−6).
= age (d × 10−9) at point of inflection; yi = BW (kg) at point of inflection.
estimate of the regression coefficient of the first power
term (d1) was also not significantly different from zero.
Among the polynomial and nonlinear functions, the
logistic curve showed the highest R2 and lowest AIC
values, both for hens and for cockerels. Except for the
third-order polynomial parameters with estimates not
significantly different from zero, all the models showed
small SE, thus indicating accurate estimates of the parameters.
Figures 2 and 3 show the results from all the models
applied to the hens and cockerels, respectively. Visually, all 3 growth models showed similar fits from the
start to the end of the growth period. The third-order
polynomial showed a slightly decrease in BW at the
end of the growth period. The Gompertz model suggested that growth had not stopped at the end of the
period. The logistic model showed the best fit of all the
models.
DISCUSSION
Growth is an important attribute of organisms and
the efforts to predict it that have been made can be
seen in the large number of functions that have been
Figure 2. Growth curves of females. Observed data are shown as circles; lines are modeled curves using the estimated parameters of each of
the following functions: (a) logistic, (b) Gompertz, and (c) third-order polynomial. y = predicted BW (kg) at age t (d).
PRODUCTION, MODELING, AND EDUCATION
281
Figure 3. Growth curves of males. Observed data are shown as circles; lines are modeled curves using the estimated parameters of each of the
following functions: (a) logistic, (b) Gompertz, and (c) third-order polynomial. y = predicted BW (kg) at age t (d).
created (Fekedulegn et al., 1999; Wellock et al., 2004).
Among the nonlinear functions, the logistic and Gompertz functions were chosen for this study because of
their economy of parameters and ability to describe
relative growth rate as a simple function of size. They
can also describe continuous growth, sigmoid forms, asymptotes, inflection points, and parameters with biological interpretations. All these properties are desirable in nonlinear growth models (Wellock et al., 2004).
The third-order polynomial was chosen because of its
resemblance to nonlinear growth functions.
The R2 values calculated for all the models were
very similar, but the logistic growth function showed a
slightly higher value. The logistic growth function also
showed the smallest calculated AIC value. The R2 measures linear associations and is therefore a goodnessof-fit measurement that is more appropriate for linear
models. The AIC is a more appropriate goodness-of-fit
measurement for use in comparisons between linear and
nonlinear models and functions with different numbers
of parameters.
The estimates for the parameters A and C, which
can be interpreted as mature BW and instantaneous
relative growth rate, respectively, were similar to those
found in previous studies on ostrich growth. du Preez
et al. (1992) found mature BW estimates of 102.1 ±
3.72 kg for cockerels and 98.4 ± 4.2 kg for hens and
instantaneous relative growth rate estimates of 9.7 ±
0.43 (×10−3) for cockerels and 9.0 ± 0.44 (×10−3) for
hens. Cilliers et al. (1995) found mature BW estimates
of 119.22 ± 2.48 kg for cockerels and 122.30 ± 3.47 kg
for hens and instantaneous relative growth rate estimates of 9.10 ± 0.28 (×10−3) for cockerels and 8.50 ±
0.41 (×10−3) for hens.
The values for inflection points relating to age that
were found in this study (Tables 2 and 3) were also
similar to what has been reported in the literature. du
Preez et al. (1992) found an inflection point for age,
which was interpreted as the age at maximum weight
gain, of 163 d for cockerels and 175 d for hens. Cilliers
et al. (1995) found inflection points for age of 180.83 d
for cockerels and 199.20 d for hens.
The Gompertz model suggested that growth had not
stopped at the end of the period. This may be an indication that the birds in this study were not fully matured at the end of the period.
282
Ramos et al.
R2
According to
and the AIC, the third-order polynomial showed a good fit. Tompić et al. (2011) found
a similar result. Compared with the nonlinear models,
linear models lack parameters with biological interpretation, but such models can be linearized and their parameters estimated by means of linear regression.
Further studies are needed to understand ostrich
growth in Brazil. Ideally, study data sets should contain
a large number of birds, each with the same number of
BW records, collected at regular intervals that are not
too close, so that the measurements are neither correlated nor too distant, such that there are not enough
classes. The present study suggests that the logistic
model is appropriate for describing ostrich growth,
both for cockerels and for hens.
ACKNOWLEDGMENTS
We thank ACAB (Associação dos Criadores de
Avestruzes do Brasil, São Paulo, SP, Brazil) for the
data set and Celso da Costa Carrer, from Faculdade de
Zootecnia e Engenharia de Alimentos, Universidade de
São Paulo, for photos. Financial support was provided
by FAPESP (Fundação de Amparo a Pesquisa do Estado de São Paulo, Brazil), CAPES (Coordenação de
Aperfeiçoamento de Pessoal de Nível Superior, Brasília,
DF, Brazil), and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brasília, DF, Brazil). S. B. Ramos and B. N. Nunes were granted scholarships from CAPES–Programa de Pós-graduação em
Genética e Melhoramento Animal, Curso Doutorado,
FCAV/UNESP. S. B. Ramos, R. P. Savegnago, and S.
L. Caetano received scholarships from FAPESP. D. P.
Munari was the recipient of a fellowship from CNPq
(Conselho Nacional de Desenvolvimento Científico e
Tecnológico).
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