PRODUCTION, MODELING, AND EDUCATION Response surface and neural network models for performance of broiler chicks fed diets varying in digestible protein and critical amino acids from 11 to 17 days of age H. Ahmadi1 and A. Golian Center of Excellence in the Animal Sciences Department, Ferdowsi University of Mashhad, Mashhad, Iran, 91775-1163 ABSTRACT Central composite design (CCD; 5 levels and 4 factors), response surface methodology (RSM), and artificial neural network-genetic algorithm (ANNGA) were used to evaluate the response of broiler chicks [ADG and feed conversion ratio (FCR)] to dietary standardized ileal digestible protein (dP), lysine (dLys), total sulfur amino acids (dTSAA), and threonine (dThr). A total of 84 battery brooder units of 5 birds each were assigned to 28 diets of CCD containing 5 levels of dP (18–22%), dLys (1.06–1.30%), dTSAA (0.81–1.01%), and dThr (0.66–0.86%) from 11 to 17 d of age. The experimental results of CCD were fitted with the quadratic and artificial neural network models. A ridge analysis (for RSM models) and a genetic algorithm (for ANN-GA models) were used to compute the optimal response for ADG and FCR. For both ADG and FCR, the goodness of fit in terms of R2 and MS error corresponding to ANN-GA and RSM models showed a substantially higher accuracy of prediction for ANN models (ADG model: R2 = 0.99; FCR model: R2
= 0.97) compared with RSM models (ADG model: R2 = 0.70; FCR model: R2 = 0.71). The ridge maximum analysis on ADG and minimum analysis on FCR models revealed that the maximum ADG may be obtained with 18.5, 1.10, 0.89, and 0.73% dP, dLys, dTSAA, and dThr, respectively, in diet, and minimum FCR may be obtained with 19.44, 1.18, 0.90, and 0.75% of dP, dLys, dTSAA, and dThr, respectively, in diet. The optimization results of ANN-GA models showed the maximum ADG may be achieved with 19.93, 1.06, 0.90, and 0.76% of dP, dLys, dTSAA, and dThr, respectively, in diet, and minimum FCR may be achieved with 18.63, 1.26, 0.84, and 0.69% of dP, dLys, dTSAA, and dThr, respectively, in diet. The results of this study revealed that the platform of CCD (for conducting growth trials with minimum treatments), RSM model, and ANNGA (for experimental data modeling and optimization) may be used to describe the relationship between dietary nutrient concentrations and broiler performance to achieve the optimal target.
Key words: design of experiment, response surface method, neural network model, digestible protein and amino acid, chick performance 2011 Poultry Science 90:2085–2096 doi:10.3382/ps.2011-01367
INTRODUCTION The significant effects on chicken performance of diets based on standardized ileal digestible protein rather than total protein and critical amino acids have been reported (Lemme et al., 2004). However, the weight of nutrients on the response of chickens usually depends on the applied experimental design and statistical or mathematical methods. Appropriate mathematical or statistical models are necessary to extract appropriate
©2011 Poultry Science Association Inc. Received January 18, 2011. Accepted May 1, 2011. 1 Corresponding author:
[email protected]
conclusions with regard to the responses of chickens to dietary nutrient concentrations (Pesti, 2009; Ahmadi and Golian, 2010b). The recommended nutrient concentrations (dietary protein and critical amino acids) and optimization practices for feed formulation are mostly empirical and statistical. Many studies have been conducted to develop diets for optimization of growth in broiler chickens. Although several approaches such as general linear model (Pesti, 2009), polynomial linear regression model (Dozier et al., 2008), nonlinear mathematical model (Rosa and Pesti, 2001), and restricted maximum likelihood (Barkley and Wallis, 2001) were used to describe chicken response to dietary protein and amino acids, the description and optimization of performance is still controversial. The problem is partly attributable to the nonlinearity of growth responses to dietary nutrients and statistical and math-
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ematical techniques used for data analyses (MacLeod, 2000). The experiments are usually designed in a manner to determine 1 or 2 nutrient requirements at a time. All nutrients are maintained at or above the requirements except the test nutrient, which is used at the graded levels. This conventional “one factor at a time” approach is laborious and time consuming and may not warrant the determination of optimal conditions (Hanrahan and Lu, 2006). The limitations of a singlevariable optimization process can be overcome by using empirical methods of modeling such as statistics-based and new soft computing-based approaches (Desai et al., 2008). Response surface methodology (RSM) as a statistics-based approach has been extensively used in biological system optimization. The RSM is a collection of statistical and mathematical techniques for designing experiments, building models, evaluating the effects of input variables, and searching for the optimal conditions of output(s) (Box et al., 1987). It is based on design of experiment (DOE), in which several factors are simultaneously investigated. The experimental data obtained from DOE in the RSM is often fitted to a quadratic function. The central composite design (CCD) is the most common DOE used in the response surface modeling, in which the inputs take on 3 or 5 different levels, but not all combinations of these values appear in the factorial design. Thus, it requires fewer experimental runs (e.g., dietary treatments) and may conserve resources. The successful application of RSM for the purpose of modeling and optimization was reported in biological science (Hanrahan and Lu, 2006) and in poultry research (Roush et al., 1979). Alternatively, soft computing-based approaches such as artificial neural network (ANN) and genetic algorithm (GA) have appeared as attractive tools for nonlinear multivariate modeling and optimization (Dayhoff and DeLeo, 2001; Jong, 2009). The ANN is considered to be an alternative to the polynomial regression method. This methodology is quite flexible in regard to the number and form of experimental data, which makes it possible to use more informal experimental designs than with statistical approaches. In recent years, the ANN has been applied in the field of poultry nutrition for different purposes such as prediction of poultry performance given dietary nutrients (Ahmadi et al., 2007, 2008b; Mottaghitalab et al., 2010), modeling true ME of feedstuffs (Ahmadi et al., 2008a; Perai et al., 2010), growth and body composition analysis of chickens (Ahmadi and Golian, 2010a), and analyses of chicken threonine responses (Ahmadi and Golian, 2010b). The usual optimization methods may not be used for optimizing the input space of an ANN model. Thus, GA as an artificial intelligence-based stochastic optimization method is often used to optimize the input space of an ANN model. The hybrid methodology of ANN with GA has come up as one of the most efficient methods for empirical modeling and optimization, especially for nonlinear systems (Desai et al., 2008; Gulati et al., 2010).
The purposes of this study were to 1) conduct an optimal CCD experiment with diets containing 4 nutrients of 5 levels each to feed broiler chicks from 11 to 17 d of age; 2) develop the RSM and ANN-GA models to analyze the response of chicks to digestible protein and amino acids obtained from the CCD experiment; 3) apply the developed models to rank the relative importance of dietary nutrients on ADG and feed conversion ratio (FCR); and 4) find the optimal dietary nutrients for ADG maximization and FCR minimization through model optimization in broiler chicks.
MATERIALS AND METHODS Experimental Design A 5-level, 4-factor CCD with 28 experimental runs (i.e., dietary treatments) was used in this study. This fractional factorial design comprised 24 factorial points and 4 center points with 3 replications for all runs (Box et al., 1987).
Birds and Diets Experimental procedures and care of the birds were carried out according to FASS (2010) guidelines. A total of 420 male broiler chicks (Ross 308, 1 d old) were obtained from a commercial hatchery after being vaccinated against Marek’s disease (d 18 via in ovo administration), Newcastle disease, and infectious bronchitis (via coarse spray at hatch). Chicks were equally grouped and randomly distributed across 84 battery brooder units. A standard diet (Leeson and Summers, 2005) containing 3,025 kcal/kg of ME, 21% standardized ileal digestible protein (dP), 1.27% lysine (dLys), 0.94% total sulfur amino acids (dTSAA), and 0.83% threonine (dThr) was fed to all birds from arrival until d 11 of age. According to the scheme produced by 5-level, 4-factor CCD, 84 units of 5 birds each were assigned to 28 diets containing 5 levels of dP (18, 19, 20, 21, and 22%), dLys (1.06, 1.12, 1.18, 1.24, and 1.30%), dTSAA (0.81, 0.86, 0.91, 0.96, and 1.01%), and dThr (0.66, 0.71, 0.76, 0.81, and 0.86%) from 11 to 17 d of age (Tables 1 and 2). The main ingredients used in all diets were corn (9.3% CP), soybean meal (45.2% CP), and corn gluten meal (48.6% CP). Protein and amino acid analyses were performed for these ingredients before diet formulation by Degussa AG (Hanau-Wolfgang, Germany). All diets were formulated to maintain 3,050 kcal/kg of ME and maintain all other essential nutrients (amino acids, Ca, P, Na) at or above recommended levels (Leeson and Summers, 2005) with the exception of dP, dLys, dTSAA, and dThr, which were provided as suggested by the CCD. Feed and water were provided ad libitum. Temperature was maintained at 31°C for wk 1 and approximately 28°C thereafter. The house was artificially ventilated and incandescent light was provided 24 h/d throughout the experiment.
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MODELS OF CHICK PERFORMANCE Table 1. Dietary nutrient concentrations used in central composite design response surface methodology to feed broiler chicks from 11 to 17 d of age Level Item (% of diet) Digestible Digestible Digestible Digestible
protein lysine total sulfur amino acids threonine
−2
−1
0
1
2
18 1.06 0.81 0.66
19 1.12 0.86 0.71
20 1.18 0.91 0.76
21 1.24 0.96 0.81
22 1.30 1.01 0.86
Measurements of Growth and FCR
Statistical and Computational Analyses
The group weight of birds in every unit was recorded at the initiation and termination of the experiment. The ADG was calculated from the weight gain of birds in each unit. Feed intake was calculated by subtracting remaining feed from offered feed in each unit during the experiment. Mortality was recorded daily. Feed conversion was corrected for mortality and represented as grams of feed consumed by all birds divided by grams of BW gain, plus the BW gain of dead birds in each unit. After conducting a growth experiment through CCD, a data set consisting of 84 data lines was produced and subjected to statistical and computational analyses in which the average of inputs (dP, dLys, dTSAA, and dThr) and outputs (ADG and FCR) was used as the experimental unit for all analyses.
RSM Model. The most commonly used model in RSM analysis is the following second-order polynomial equation (Box et al., 1987):
k
k
y = β0 + ∑ βi x i +∑ ∑ βij x i x j +∑ βii x i2 + ε, i =1
i
