Vol.3, No.4, 305-310 (2013) Open Journal of Animal Sciences
http://dx.doi.org/10.4236/ojas.2013.34045
Mathematical modeling of the native Mexican
turkey’s growth
E. Pérez-Lara1, M. A. Camacho-Escobar2*, J. C. García-López3, S. Machorro-Samano4,
N. Y. Ávila-Serrano2, J. Arroyo-Ledezma2
1Independent Consultant, Domicilio Conocido, Bajos de Chila, San Pedro Mixtepec, Mexico
2Cuerpo Académico Ciencias Agropecuarias, Universidad del Mar Campus Puerto Escondido, Puerto Escondido, México;
*Corresponding Author: marcama@zicate la. umar.mx
3Instituto de Investigación de Zonas Desérticas, Universidad Autónoma de San Luis Potosí, San Luis Potosí, México
4Instituto de Industrias, Universidad del Mar Campus Puerto Escondido, Puerto Escondido, México
Received 16 August 2013; revised 25 September 2013; accepted 15 October 2013
Copyright © 2013 E. Pérez-Lara et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
Little is known about the productive perfor-
mance of Mexican turkey, so the objective of the
present study was to characterize growth per-
formance curves of backyard turkey under a
confined system. Forty fertile eggs were artifi-
cially incubated and turkey weight was recorded
at hatch. During growth performance weekly
weight was measured until 385 days of age. Tur-
key commercial feed and water were offered ad
libitum. To characterize growth curves, a fourth
degree polynomial model regression and a Rich -
ards biological model were used, which were
compared by determination coefficient (r2), to
reach the best fit model. The best fit model was
the fourth degree polynomial regression model
from a mathematical standpoint of view. It was
found that maximum tom grow th was reached at
15.7 weeks with a weight gain of 259.3 g/week
and in hens at 12.4 weeks with a weight gain of
112.0 g/week. Body weight reached by toms at
40 weeks was 6 kg an d hens at 35 weeks with 3.6
kg.
Keywords: Age to Slaughter; Growth Curves;
Guajolotes; Maximum Weight; Slow G rowth Turkeys
1. INTRODUCTION
Growth curves models can describe and summarize
quantitative changes that birds experiment through their
lives, they are useful to select Creole birds according to
the producer request and to program feeding phases, fo-
cusing a large amount of nutrients on the fast growth
phases, to know the optimal age to slaughter, effects of
gene selection on curve components, and weight gain on
a certain age [1-3].
In addition, growth curve parameters can be used in-
dividually or as a whole to predict growth rates, and
other animal husbandry traits [4]. To Knízetová et al. [5],
the forms that obtain the growth curves are the result of a
growth index and changes during ontogenesis.
Animal growth is defined as an increase of cell enlar-
gement or hypertrophy and also includes the increase in
number of cell hyperplasia [6,7]. Postnatal growth of
domestic animals, which parameters are described as
biological constant interpreted under the form of a ma-
thematical equation that generally can be plotted as a sig-
moid curve [8], starts with a fixed point (weight at birth)
and with a slow initial growth, where the inferior asymp-
totic is the start of growth [9], the higher asymptotic is
the mature size and the point of inflection is the maxi-
mum growt h p oi nt [10].
The sigmoid growth curve extends from conception to
maturity. After hatch and for some time there is fast
growing phase during which, growth rhythm is almost
constant, during the last periods of muscle, bones and
vital organs growing, start to gradually decay, and the
inflection point appears. The last period is characterized
for fat accumulation; and possible maximum weight is
achieved, growth stops (maturity phase), finally with the
old age corporal volume decreases (declination phase)
and muscular mass is lost.
The use of growth sigmoid curv e is useful to study the
animal development, make comparisons between species,
within animals of the same breed [11]. Considering the
animal husbandry and economic importance of some
characteristics like body weight, weight gain, mature age
and highest weight, several models that express growth

E. Pérez-Lara et al. / Open Journal of Animal Sciences 3 (2013) 305-310
306
have been proposed: polynomials, nonlinear and linear
mix.
For the case of birds, the absolute growth ratio meas-
ures the development of each unit time and represents an
index of how much does the bird grow by a selected unit
time. Relative growth ratio represents the increase by
presenting weight unit, and it’s an index of the effort re-
alized by the bird to increase its biomass [1].
Knízetová et al. [5] reported that the most appropri-
ated function to estimate growth curves in poultry is the
Richards sigmoid model. This biological model has had
such a great importance in the poultry growth paradigm,
that three growth biological aspects have been described:
1) size, higher limit or asymptotic; 2) the index, a meas-
ure to specify the time requested of the growth increase;
and 3) shape, a quantitative measure that describe the
path of the grow th process [12].
Slow growth Mexican bronze turkeys raised in the
backyard have characteristics that make them favorable
for organic meat production which has a high demand on
Europe, USA and Asia [13]; however, information about
these turkeys is scarce [14]. This situation turns out to be
difficult to establish the right market time. It has not been
established the optimal age where maximum growth is
achieved, therefore, the objective of the present study was
to characterize, through mathematical models, the growth
curve and to estimate optimal weight and age to market
slow growth bronze turkeys reared on intensive conditions.
2. MATERIALS AND METHODS
Forty fertile eggs were collected from slow growth
bronze turkeys in two rural communities from Tututepec
and San Pedro Mixtepec from the region of Oaxaca coast,
México.
Eggs were weighed with a balance Ohaus PA 3102,
eggs were marked and set into an automatic incubator
Brinsea Octagon 40, and were incubated for 28 days at
37.7˚C. Previous to incubation, the incubator was disin-
fected with 5% sodium hypochlorite solution.
At hatch, each poult was weighed and marked with
color plastic tags attached in the head, each tag had a
number to identify each turkey [15]. Each poult was
raised individually and was considered as an experimen-
tal unit. Raising period was realized in the Universidad
del Mar (UMAR) facilities in th e Campus Puerto Escon-
dido, Oaxaca, Mexico, with artificial temperature and
lasted four weeks, moreover heat source was removed
and poults were allocated to the UMAR experimental
field on individual cement cages.
During raising period, poults were vaccinated and de-
wormed following the sanitary program of the region
[16]. Hatching time was considerate as week zero, vari-
ables were recorded for 55 week s.
A commercial feed program for turkeys was used in
two phases: for growth crumble presentation, and for
finalization period pellet. Feed and water were offered ad
libitum.
Right after poults hatch, th e following productiv e vari-
ables were recorded on a weekly basis: feed intake,
weight gain and feed conversion ratio. When turkeys
reached two kg body weight, and electronic scale Torrey,
model EQB 1007/200, with 50 kg capacity was used for
the rest of the experiment.
A dispersion diagram was plotted with weight gain
means of males and females, and the mathematical mod-
els proposed by Richards were used to estimate constant
values of variables; in addition a fourth order polyno mial
regression model was applied


[17].0yixnxn    
Then, a correlation coefficient was calculated which is
the confidence mathematical model index [10] and growth
was estimated per each sex.
Agudelo-Gómez et al. [18] described Richards’s equa-
tion as:


2
01
1t
e
W





where:
W: Is the weight at any moment
β0: Is the higher asymptotic that correspond to maxi-
mum stable weight
β1: Fit parameter established for the initial values of w
and β2: mature ratio
μ: Mature grade referred as the point of inflection
To find the best fit determination coefficients were cal-
culated. Comparison of such coefficients a best fit model
for the studied phenomenon can be established.
The determination coefficient of a nonlinear model is
obtained as:

22
2
rimie im wwww ww 

2
where:
r2: Determination coefficient
wi: Weight real value at certain moment
we: Estimated weight with the model at certain mo-
ment
m
w: A verage weight
Average growth rate it’s defined by the change of
weight at a certain interval of time:


grams week
m
DWW t 
If it is wanted to find the velocity of weight increase of
an animal respect to the time at any moment, then it
would be instant growth rate:


0
limgrams week
t
DWW t



E. Pérez-Lara et al. / Open Journal of Animal Sciences 3 (2013) 305-310 307
In other words:


grams weekDWdW dt
Means and analysis of variance were performed by
SAS statistical software [19]. Growth curve graphics
were elaborated by Graph software package [20].
3. RESULTS AND DISCUSSION
Tab le 1 shows body weight means for males and fe-
males respectively from hatch to 55 weeks old. Esti-
mated equations and determination coefficients are shown
in Table 2.
Table 1. Means and standard deviation of egg weight before
incubation and bronze turkeys slow-growing Mexican males and
females after hatching and during 55 weeks.
Males Female s
Producti on st age/age (g)
Egg to hatching 69.2 (±3.2) 69.0 (±2.4)
Hatching 46.7 (±6.5) 43.0 (±4.3)
5 weeks 318.0 (±31.2) 309.5 (±43.5)
10 weeks 1 212.0 (±65.2) 1 090.7 (±81.7)
15 weeks 2 346.0 (±88.5) 1 801.0 (±82.0)
20 weeks 2 563.5 (±82.0) 2 563.5 (±56.0)
25 weeks 5 082.0 (±155.0) 3 1 12. 4 (±140.1)
30 weeks 5 565.0 (±193.1) 3 512.5 (±93.6)
35 weeks 5 827.5 (±177.1) 3 487.5 (±93.6)
40 weeks 5 825.0 (±108.0) 3 247.5 (±93.6)
45 weeks 5 592.1 (±124.9) 3 015.0 (±124.9)
50 weeks 5 667.5 (±99.6) 3 052.5 (±99.6)
55 weeks 5 422.4 (±201.6) 2 446.4 (±58.0)
Ta ble 2. Estimated equations, coefficients of determination (r2)
obtained in the models studied.
Models Equations r2
Males
Polynomial
43
0.0057 0.7023 24.62.37
83.0818 148.6012
Wt t
t


It was observed that polynomial regression equation
that included the fourth degree, showed a good fit, in
females with values of r2 = 0.991 and in males 0.995,
while the Richards (β2 variable) nonlinear model showed
a lower fit with 0.959 for femal es and 0. 981 for males.
The Richards (β2 constant) model showed a lower fit
to the original data, with a determination constant of
0.978 for males, and 0.793 for males which are not ac-
ceptable for the application of the present study. The
fourth degree polynomial model curves for male and fe-
male are shown in Figur es 1 and 2, respectively.
Figures 3 and 4 are showing the Richards (constant)
biological model curves for bronze male and female tur-
keys; and the Figures 5 and 6 are the Richards models
(variable).
Brisbin et al. [22] mentioned that Richards model or
any other biological model trends to change because in
the equation a large number of biological parameters are
evaluated; or can be affected by environment factors as
changes in the temperature or diet.
Other limitations found in the use of polynomial models
Figure 1. Fourth-order polynomial model for growth of native
male turkey slow growth phenotype bronze.
2
t
0.995
Richards (β2 variable)


1.3551
0.0031 0.2991
5990 134.95tt We


 0.981
Richards (β2 constant)

1.3551
0.2122
5990 134.95t We




0.978
Females
Polynomial
43
0.00380.4195 12.1218
24.1287 16.6680
Wt t
t


2
t
0.991
Richards (β2 variable)


1.096
0.005166 0.3663
3750 157.84tt We


 0.959
Richards (β2 constant) 
1.096
0.2216
3750 157.84t We



Figure 2. Fourth-order polynomial model for growth of native
female turkey slow growth phenotype bronze.

0.793

E. Pérez-Lara et al. / Open Journal of Animal Sciences 3 (2013) 305-310
308
Figure 3. Growth curve with Richards model (constant) native
male turkey slow growth phenotype bronze.
Figure 4. Growth curve with Richards model (constant) native
female turkey slow growth phenotype bronze.
Figure 5. Growth curve with Richards model (variable) native
male turkey slow growth phenotype bronze.
in comparison with biological models like the Richards,
are that they exhibit multicollinearity along the curve and
dependence of the function of high concentration point
areas [18].
Figure 6. Growth curve model with variable Richards native
female turkey slow growth phenotype bronze.
It is acknowledged that the polynomial model impor-
tance is given by its application. It’s easy to obtain;
however, the calculations are slow and demanding from a
computational standpoint.
Despite the latest, the linear and quadratic answers are
easy to interpret biologically [23]. In the present study,
the female body weight at 20 weeks old was 75% for the
male body weight at the same age, this is in agreement
with Juárez and Fraga [24], due to the sexual dimor-
phism in turkey that is considerable, where the mature
female weight is 50% to 85% less than the one in males.
Fast growth bronze turkey phenotype reaches their com-
plete development at 22 - 26 weeks, with average weight
of 9 - 11.5 kg for males and 6.5 - 7.8 kg for females [25];
however, it was observed in the present study that, due to
the slow growth of the genetic line used, growth is ex-
tended until 35 weeks for females and 40 weeks for
males, that’s where the maximum weight is reached. The
male presented the maximum instant growth three weeks
later than the female and with a gain weight capacity
over twofold (Fi gures 7 and 8).
This is useful information to determine the feeding
programs for this genetic line, and because of the differ-
ences in growth, it’s recommended to separate by sex the
raising changing the feed formula at 12 weeks for fe-
males and 15 weeks for males.
The idea is confirmed when observing the maximum
estimated weight, where the males can reach 2.4 kg more
than the females with five more weeks of fattening. The
latest is useful to make productive decisions, because the
market optimal age for females is at 35 weeks, while the
male is 40 weeks where their maximum body weight is
reached.
The weight for Mexican male mature turkeys, without
specific line or genotype, is reported variable and ranks
from 5.0 - 6.8 kg, and for females 2.0 - 6.0 kg [26-29].
These weights are in agreement with the ones estimated

E. Pérez-Lara et al. / Open Journal of Animal Sciences 3 (2013) 305-310 309
Figure 7. Growth rate in female native turkey slow growth
phenotype bronze.
Figure 8. Growth rate in male native turkey slow growth phe-
notype bronze.
in the present study; however, the maximum weights re-
ported in other studies for males ar e 8.9 and 20.0 kg and
for females 3.0 - 17.0 kg [14,27,30]. This difference in
weight can be due to the fact that the maximum weights
are considered that the bird can reach along their entire
life, when the bird stops growing and starts fat deposits,
while the present study estimated the adequate market
weight, or they may be heavy fast growth genetic lines
different from the bronze turkey.
Based on the present results, it is concluded that the
fourth degree polynomial model is the most adequate to
estimate the slow growth bronze turkey growth, which
has the maximum instant growth rate at 12 - 15 weeks.
The age and weight for slaughter were of 35 weeks
and 3.6 kg for females and 40 weeks old and weight of
6.0 kg for males. It is important to characterize other
phenotypes, because they are less studied and they rep-
resent an important zoo genetic resource adapted to or-
ganic production conditions.
4. ACKNOWLEDGEMENTS
The authors thank UMAR facilities to carry out the present study,
and workers in Experimental Field Bajos de Chila for their help during
the experimental phase.
REFERENCES
[1] Valencia, N.F., Muñoz, L.L.J.E. and Ramírez, L.M. (2003)
Caracterización de la curva de crecimiento en cuatro tipos
de gallina criolla. Acta Agronómica, 52, 85-92.
[2] Ahmad, H. and Mottaghitalab, M. (2007) Hyperbolastic
models as a new poweful tool to describe broiler growth
kinetics. Poultry Science, 86, 2461-2465.
http://dx.doi.org/10.3382/ps.2007-00086
[3] Keskin, I., Dag, B., Sariye, V. and Gokmen, V. (2009)
Estimation of growth curve parameters. In: Konya Me-
rino sheep. South African Journal of Animal Science, 39,
163-168. http://dx.doi.org/10.4314/sajas.v39i2.44390
[4] Malhado, C.H.M., Ramos, A.A., Carneiro, P.L.S., Souza,
J.C., Wechsler, F.S., Eler, J.P, Azevêdo, D.M.M.R. and
Sereno, J.R.B. (2008) Modelo no lienales para describir el
crecimiento de bufalinos de la raza Murrah. Archivos de
Zootecnia, 57, 497-503.
[5] Knízetová, H., Hyánek, J., Hyánková, L. and Belícek, P.
(1995) Comparative study of growth curves in poultry.
Genetics Selection Evolution, 27, 365-375.
http://dx.doi.org/10.1186/1297-9686-27-4-365
[6] Cañas, Á.J., Ramírez, T.J., Arboleda, A.O., Ochoa, S.J.,
Vergara, G.O., and Cerón, M.M. (2007) Estimación de
parámetros genéticos para peso al destete en ganado
blanco orejinegro (BON) en el noroccidente colombiano.
Revista MVZ Córdoba, 13, 1138-1145.
[7] Chambers, J.R. (1993) Poultry Breeding and Genetics:
Genetics of growth and meat production in chickens. In:
Crawford, R.D. Ed., Poultry Breeding and Genetics, El-
sevier, The Netherlands, 599-643.
[8] Ersoy, E.I., Mendes, M. and Aktan, S. (2006) Growth
curve establishment for American Bronze turkeys. Archiv
Tierzucht, 49, 293-299.
[9] Takma, Ç., Özkan, S. and Akbas, Y. (2004) Describing
growth curve of turkey toms using Gompertz model.
Proceedings of XXII World’s Poultry Congress, Istanbul.
[10] Herrera-Martínez, M., Machorro-Samano S., Arcos-Gar-
cía, J.L. and Mendoza-Martínez, G.M. (2008) Regresión
polinomial de la longitud total en la iguana negra
(Ctenosaura pectinata) en relación con el tiempo.
Memorias del XI Reunión Nacional de Iguanas. Puebla,
21-23.
[11] Nuñez, G.F.A. (2009) Fundamentos de crecimiento y
evaluación animal, Barcelona, España, Ed. Trafford Pub-
lishing, pp. 21-30.
[12] Brisbin, L. Jr., Collins, C.T., White, C.G. and Mccallum,
C.A. (2009) A New Paradigm for the Analysis and Inter-
pretation of Growth Data: The Shape of Things to Come.
The Auk, 104, 552-554.
http://dx.doi.org/10.2307/4087567
[13] Camacho-Escobar, M.A., Pérez-Lara, E., García-López,
J.C., Ávila-Serrano, N.Y., Rodríguez-Delatorre, M. and
Arroyo-Ledezma, J. (2011) Rendimiento de canal en
guajolotes bronceados nativos de lento crecimiento ali-

E. Pérez-Lara et al. / Open Journal of Animal Sciences 3 (2013) 305-310
310
mentados con diferentes dietas tradicionales. In:
Universidad Autónoma del Estado de Morelos (ed), 1era.
Reunión de la Investigación Agropecuaria 2011 Libro de
resúmenes en extenso. [In CD]. Cuernavaca, 12-21.
[14] Camacho-Escobar, M.A., Hernandez-Sanchez, V., Rami-
rez-Cancino, L., Sánchez-Bernal, E.I., and Arroyo-Lede-
zma, J. (2008) Characterization of backyard guajolotes
(Meleagris gallopavo gallopavo) in tropical zones of Me-
xico. Livestock Research for Rural Development, 20,
April 7, 2008.
http://www.cipav.org.co/lrrd/lrrd20/4/cama20050.htm
[15] Morales-Salud, T. (2001) Sistema de marcaje, problema
de identidad o simple requisito. Memorias del Cuarto
Taller Nacional sobre Manejo de Iguanas en Cautiverio
(Puerto Ángel, Oaxaca). Consultado el 28 de marzo de
2010.
http://www.subcomitedeiguanas.org/PDF%B4s/taller4.pd
f
[16] Camacho-Escobar, M.A., Arroyo-Ledezma, J., Pérez-Lara,
E., Sánchez-Bernal, E.I. and García-López, J.C. (2009-
2010) Enfermedades y parasitosis asociadas a una explo-
tación intensiva de guajolotes nativos. Revista Ciencias
Agrícolas Informa, 19, 56-61.
[17] Sánchez-Ramírez, E. (1999) Comportamiento en creci-
miento de avestruces alimentadas con diferentes dietas.
Ms. Sci. Thesis. Universidad de Colima, Mexico.
[18] Agudelo-Gómez, D.A., Cerón-Muñoz, M.F. and Restre-
po-Betancur, L.F. (2008) Modelación de las funciones de
crecimiento aplicadas a la producción animal. Revista
Colombiana de Ciencias Pecuarias, 21, 39-51.
[19] SAS/STAT (1999) User’s Guide. 4th Edition, SAS Insti-
tute. Inc., Cary.
[20] Graph. (2009) Licensed Company. Version 4.7, USA.
http://www.padowan.dk/
[21] Aggrey, S.E. (2002) Comparison of three nonlinear and
spline regression models for describing chicken growth
curves. Poultry Science, 81, 1782-1788.
[22] Brisbin, I.L. Jr., White, G.C. and Bush, P.B. (1986) PCB
intake and the growth of waterfowl: Multivariate analyses
based on a reparameterized Richards sigmoid model.
Growth, 50, 1-11.
[23] Delgado, C., Valera, M., Molina, A., Jiménez, J.M. and
Rodero, A. (2000) Circunferencia escrotal como predictor
de la capacidad reproductiva en razas de vacuno de carne
autóctono: curvas de crecimiento en el vacuno retinto.
Archivos de Zootecnia, 49, 229-240.
[24] Juárez, A. and Fraga, M. (2002) Nota preliminar de
indicadores productivos de pavos mexicanos en condi-
ciones de confinamiento. Revista Cubana de Ciencia Ag-
rícola, 36, 65-68.
[25] Schopflocher, R. (1994) Avicultura lucrativa, Argentina,
Ed., Albatros, 402.
[26] López-Zavala, R., Monterrubio-Rico, T., Cano-Camacho,
H., Chassin-Noria, O., Aguilera-Reyes, U. and Zavala-
Páramo, M.G. (2008) Native turkey (Meleagris gallopavo
gallopavo) backyard production sistems’ characterization
in the physiographic regions of the State of Michoacan,
Mexico. Técnica Pecuaria México, 46, 303-316.
[27] Losada, H., Rivera, J., Cortés, J., Castillo, A., González,
R.O. and Herrera, J. (2006) Un análisis de sistemas de
producción de guajolotes (Meleagridis gallipavo) en el
espacio suburbano de la delegación de Xochimilco al sur
de la Ciudad de México. Livestock Research for Rural
Development, 18, June 8, 2006.
http://www.cipav.org.co/lrrd/lrrd18/4/losa18052.htm
[28] Mallia G. (1998) Indigenous domestic turkeys of Oaxaca
and Quintana Roo, Mexico. Animal Genetic Resources
Information, 23, 69-78.
http://dx.doi.org/10.1017/S1014233900001085
[29] National Research Council (1991) Microlivestock: Little
known small animals with a promising economic future.
The National Academic Press, Washington DC, October
11, 2006.
http://nap/edu/openbook/030904295X/html/157.html
[30] Hernández J.S., Oviedo, M.R., Martínez, A.S., Carreón,
L.L., Reséndiz, M.R., Romero, B.J., Ríos, M.J., Zamitiz,
G.J. and Vargas, S. (2005) Situación del guajolote común
en la comunidad de Santa Úrsula (Puebla, México). In:
Universidad Autónoma de Chiapas, Eds., VI Simposio
Iberoamericano sobre conservación y utilización de
recursos zoogenéticos. San Cristóbal de las Casas, Chia-
pas, México, 277-281.