Comparison of Gompertz and nEural Network Models of Broiler Growth

Abstract

Neural networks offer an alternative to regression analysis for biological growth modeling. Very little research has been conducted to model animal growth using artificial neural networks. Twenty-five male chicks (Ross x Ross 308) were raised in an environmental chamber. Body weights were determined daily and feed and water were provided ad libitum. The birds were fed a starter diet (23% CP and 3,200 kcal of ME/kg) from 0 to 21 d, and a grower diet (20% CP and 3,200 kcal of ME/ kg) from 22 to 70 d. Dead and female birds were not included in the study. Average BW of 18 birds were used as the data points for the growth curve to be modeled. Training data consisted of alternate-day weights starting with the first day. Validation data consisted of BW at all other age periods. Comparison was made between the modeling by the Gompertz nonlinear regression equation and neural network modeling. Neural network models were developed with the Neuroshell Predictor. Accuracy of the models was determined by mean square error (MSE), mean absolute deviation (MAD), mean absolute percentage error (MAPE), and bias. The Gompertz equation was fit for the data. Forecasting error measurements were based on the difference between the model and the observed values. For the training data, the lowest MSE, MAD, MAPE, and bias were noted for the neural-developed neural network. For the validation data, the lowest MSE and MAD were noted with the genetic algorithm-developed neural network. Lowest bias was for the neural-developed network. As measured by bias, the Gompertz equation underestimated the values whereas the neural- and genetic-developed neural networks produced little or no overestimation of the observed BW responses. Past studies have attempted to interpret the biological significance of the estimates of the parameters of an equation. However, it may be more practical to ignore the relevance of parameter estimates and focus on the ability to predict responses.

Modelación del crecimiento de pollitas Lohmann LSL con redes neuronales y modelos de regresión no lineal

“…En comparación con los otros modelos, la RNA presentó mayor facilidad de programación y ejecución, ya que solo es necesaria la variación heurística en el número de neuronas ocultas para lograr el ajuste, mientras que para MNL y MNLM son cuatro (β 0 , β 1 , β 2 y ε) y (β 0 , β 1 , β 2 , b 0 ,b 2 , rho y ε) siete parámetros respectivamente, con los que el investigador debe probar de forma consecutiva hasta lograr el ajuste del modelo; por lo que la velocidad y facilidad de ajuste del MNL y MNLM dependen directamente de la calidad de los parámetros iniciales, aspecto también expresado por Roush et al (14).…”

“…En tal sentido, para la descripción ajuste y predicción de la curva de crecimiento en aves se han utilizado las funciones de Brody (8), Gompertz (9), Logística (10), Richards (11), Von Bertalanffy (12), modelos con la inclusión de algoritmos genéticos (13) y las RNA (14), entre otros.…”

“…Autores como Ahmadi et al (16) y Roush (14) han comparado la capacidad de ajuste de las RNA con otros modelos usando datos de crecimiento de pollos de engorde, encontrando que las RNA son más fáciles de usar y más eficientes; además como no tienen una ecuación prediseñada tienen la posibilidad de trabajar con datos que tengan "ruido" y así maximizar su poder de ajuste. En otra evaluación Yee (17), modelando el crecimiento de ovejas, afirmó que las RNA fueron menos influenciada por la variabilidad longitudinal en los datos lo que le da superioridad ante otros modelos por combinar la exactitud y precisión en el ajuste de la curva.…”

A hybrid model of uniform design and artificial neural network for the optimization of dietary metabolizable energy, digestible lysine, and methionine in quail chicks

“…The 100 data lines were randomly divided into 2 sets of training (70 data lines) and testing (30 data lines). All data were imported into the Statistica Neural Network software version 8.0 (StatSoft, 2008) to develop the models and the goodness-of-fit of the ANN models was evaluated using R 2 , mean absolute deviation (MAD), mean square error (MSE), mean absolute percentage error (MAPE), and bias (Roush et al, 2006).…”

“…Artificial neural networks (ANN) have been employed to analyze data in poultry experiments Ahmadi & Golian, 2010a;Ahmadi and Golian, 2010b;Ahmadi & Golian, 2011;Mehri, 2012;Roush et al, 2006). Central composite design (CCD) has been successfully used to optimize dietary nutrients using response surface methodology and ANN approach (Ahmadi & Golian, 2011;Mehri, 2012).…”