Nonlinear equations to determine the growth curve of immunocastrated pigs

The objective of this work was to compare the performance of the nonlinear Gompertz, logistic, and von Bertalanffy equations, to describe the growth curve of immunocastrated male pigs from birth until reaching 140 kg body weight. Standard error, number of iterations, mean square of the error, and coefficient of determination were compared between the models. The logistic and von Bertalanffy equations do not accurately estimate the initial and slaughter weights. The Gompertz equation shows the highest reliability and is, therefore, the most suitable one to describe the growth curve of immunocastrated pigs from birth until 140 kg body weight is reached.

Index terms:
Gompertz; growth rate; logistic equation; von Bertalanffy

Authorship

Marcos Speroni Ceron ^**Corresponding author: marcossperoni@gmail.com

Universidade José do Rosário Vellano, Departamento de Agronomia, Rodovia MG-179, Km 0, s/no, CEP 37132-440 Alfenas, MG, Brazil. E-mail: marcossperoni@gmail.com, natyelynunespieve@yahoo.com.br, nhayandra_dias@yahoo.com.brUniversidade José do Rosário VellanoBrazilAlfenas, MG, Brazil Universidade José do Rosário Vellano, Departamento de Agronomia, Rodovia MG-179, Km 0, s/no, CEP 37132-440 Alfenas, MG, Brazil. E-mail: marcossperoni@gmail.com, natyelynunespieve@yahoo.com.br, nhayandra_dias@yahoo.com.br

http://orcid.org/0000-0003-1510-7188

Vladimir de Oliveira

Universidade Federal de Santa Maria, Departamento de Zootecnia, Centro de Ciências Rurais, Avenida Roraima, no 1.000, CEP 97159-000 Santa Maria, RS, Brazil. E-mail: vladimir.oliveira@ufsm.br, henriquecmmuniz@hotmail.comUniversidade Federal de Santa MariaBrazilSanta Maria, RS, Brazil Universidade Federal de Santa Maria, Departamento de Zootecnia, Centro de Ciências Rurais, Avenida Roraima, no 1.000, CEP 97159-000 Santa Maria, RS, Brazil. E-mail: vladimir.oliveira@ufsm.br, henriquecmmuniz@hotmail.com

http://orcid.org/0000-0002-9292-8943

Natielei Alexandre Nunes Novais Pieve

http://orcid.org/0000-0003-0692-3490

Nhayandra Christina Dias e Silva

http://orcid.org/0000-0003-1804-8312

Carlos Augusto Rigon Rossi

Universidade Federal de Santa Maria, Departamento de Clínica de Grandes Animais, Centro de Ciências Rurais, Avenida Roraima, no 1.000, CEP 97105-900 Santa Maria, RS, Brazil. E-mail: carlos.rossi.mv@gmail.comUniversidade Federal de Santa MariaBrazilSanta Maria, RS, Brazil Universidade Federal de Santa Maria, Departamento de Clínica de Grandes Animais, Centro de Ciências Rurais, Avenida Roraima, no 1.000, CEP 97105-900 Santa Maria, RS, Brazil. E-mail: carlos.rossi.mv@gmail.com

http://orcid.org/0000-0001-7314-8602

Bruno Neutzling Fraga

Universidade Federal do Pampa, Campus Itaqui, Rua Joaquim de Sá Britto, s/no, CEP 3432-1850 Itaqui, RS, Brazil. E-mail: bnfraga@gmail.comUniversidade Federal do PampaBrazilItaqui, RS, Brazil Universidade Federal do Pampa, Campus Itaqui, Rua Joaquim de Sá Britto, s/no, CEP 3432-1850 Itaqui, RS, Brazil. E-mail: bnfraga@gmail.com

http://orcid.org/0000-0002-1652-7179

Henrique da Costa Mendes Muniz

http://orcid.org/0000-0002-4512-4424

Alexandre de Mello Kessler

Universidade Federal do Rio Grande do Sul, Departamento de Zootecnia, Faculdade de Agronomia, Avenida Bento Gonçalves, no 7.712. CEP 91540-000 Porto Alegre, RS, Brazil. E-mail: akessler@ufrgs.brUniversidade Federal do Rio Grande do SulBrazilPorto Alegre, RS, Brazil Universidade Federal do Rio Grande do Sul, Departamento de Zootecnia, Faculdade de Agronomia, Avenida Bento Gonçalves, no 7.712. CEP 91540-000 Porto Alegre, RS, Brazil. E-mail: akessler@ufrgs.br

http://orcid.org/0000-0002-7626-5588

*Corresponding author: marcossperoni@gmail.com

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (1)
Tables (1)

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Figure 1.
Mean of observed weights, predicted weights by age (black lines), and growth rates (gray lines), estimated by derivatives of Gompertz, logistic, and von Bertalanffy equations of immunocastrated pigs, from birth until 140 kg body weight was reached (age of slaughter, 174 days).

Thumbnail

Table 1.
Parameterization of the nonlinear equations to estimate the growth curve of immunocastrated male piglets (Sus scrofa domesticus) (Agroceres x Danbred) from birth until 140 kg body weight.

Figure 1. Mean of observed weights, predicted weights by age (black lines), and growth rates (gray lines), estimated by derivatives of Gompertz, logistic, and von Bertalanffy equations of immunocastrated pigs, from birth until 140 kg body weight was reached (age of slaughter, 174 days).

Table 1. Parameterization of the nonlinear equations to estimate the growth curve of immunocastrated male piglets (Sus scrofa domesticus) (Agroceres x Danbred) from birth until 140 kg body weight.

Model	Equations	Weight IP	Age IP
Gompertz	Y = Aexp(-exp(-K(t-C)))	= A/e	= C
Logistic	Y = A/(1+B exp -K*t)	= A/2	= (ln(B))/K
von Bertalanffy	Y = A(1-B exp -Kt)^3	= (8*A)/27	= log(e)(3B)/K
	Growth rate of nonlinear equations (first derivative)
Gompertz	Y=AKexp(-K(t-C)-exp(-K(t-C)))
Logistic	Y = (ABKexp(Kt))/((B+exp(K*t))^2)
von Bertalanffy	Y = 3ABKexp(-3Kt)(B-exp(Kt))^2
Parameters	Gompertz	Logistic	von Bertalanffy
A (kg per BW)	255.7	169.0	398.8
B	-	31.747	0.902
K (kg per day)	0.012	0.027	0.006
C (day)	138.4	-	-
Weight IP (kg per BW)	94.09	84.52	118.1
Age IP (days)	138	128	196
Iterations	5	6	5
MSE	68.8944	70.6139	68.9213
S	8.30027	8.40321	8.30189
R²	0.9994	0.9977	0.9996

IP, inflection point of the sigmoidal curve; e, base of the Neperian logarithm (e, 2.71828); Y, body weight at age t; A, weight at maturity; B, constant integration; C, age at which the maximum growth rate is reached, which is the inflection point of the sigmoidal curve; K, growth rate; MSE, mean squared error; S, standard error; R², determination coefficient.

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Nonlinear equations to determine the growth curve of immunocastrated pigs

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[1] *Corresponding author: marcossperoni@gmail.com