DOI: 10.1111/jpn.12235
ORIGINAL ARTICLE
Modelling broilers’ abdominal fat in response to dietary treatments A. Salarpour1, E. Rahmatnejad1 and H. Khotanlou2 1 Young Researchers & Elite Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran, and 2 ISIP Lab, Computer Engineering Department, Bu-Ali Sina University, Hamedan, Iran
Summary Neural networks are capable of modelling any complex function and can be used in poultry production. Dietary crude fibre (CF) and exogenous enzymes (exEn) extensively affected abdominal fat (AF) of broilers. Current methods to study AF and its correlation with dietary CF levels and exEn supplements are costly, laborious and time-consuming. The purpose of this study was to develop an artificial neural network–genetic algorithm (ANNGA) to model data on the response of broiler chickens (AF) to CF and exEn from 0 to 42 days of age. A data set containing eight treatments was divided to the train, validation, and test data set of the ANN models. The information about feeding eight diets at two periods [starter (0–21 days of age) and grower (22–42 days of age)] were used to estimate AF of broilers by ANN-GA. A multilayer feed-forward neural network with different structures was developed using MATLAB software, and optimal values for the ANN weights were obtained using the genetic algorithm (GA). Crude fibre, and exEn were used as input variables and AF of broilers was output variable. The best model of ANN-GA was determined based on the train root mean square error (RMSE). The best selected ANN-GA showed desirable results, RMSE, 0.1286% and R2 coefficient, 0.876 for test data. Keywords neural network, crude fibre, exogenous enzyme Correspondence A. Salarpour, Young Researchers & Elite Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran. Tel: +98 9133413051; Fax: +98 8138292631; E-mail: [email protected] Received: 26 April 2013; accepted: 8 July 2014
The primary goal of broiler breeding is to improve profitability of broiler meat production (Zerehdaran et al., 2004). The gainfulness of broiler production is largely determined by the possibility of increasing the proportion of prime parts in the carcass, mainly breast meat, and by reducing fat (Le Bihan-Duval et al., 1999). The abdominal fat pad represents one of the main regions of fat deposition in chickens, and it seems to be mainly related to total carcass fat (Becker et al., 1981). Excessive fat is one of the main problems faced by the broiler industry nowadays, because it does not just reduce carcass yield and feed efficiency, but also cause rejection of the meat by the consumers and difficulties in processing. A great volume of information exists on the AF of broilers. The effects of some factors, including dietary CF (Rahmatnejad et al., 2011), energy (Jackson et al., 1982; Sizemore and Siegel, 1993), protein (Jackson et al., 1982; Sizemore and Siegel, 1993; Kamran et al., 2008), energy to protein ratio (Sizemore and Siegel,
1993; Kamran et al., 2008; Zhao et al., 2009), exEn supplements (Nahas and Lefrancois, 2001; Mushtaq et al., 2009; Rahmatnejad et al., 2011), age (Fortin et al., 1983; Kamran et al., 2008), strain (Fortin et al., 1983; Zhao et al., 2009), sex (Fortin et al., 1983; Sizemore and Siegel, 1993) and the applied response model on carcarss quality (e.g., AF) of meat birds have been studied. Neural networks are capable of modelling any complex function and can be used in the poultry and animal production areas. In recent years, the softcomputing methods like artificial neural network (ANN) have been applied in the field of poultry nutrition (Ahmadi et al., 2008; Chen et al., 2009; Ahmadi and Golian, 2010; Savegnago et al., 2011). Artificial neural networks are computational modelling tools that have recently emerged and found extensive acceptance in many disciplines for modelling complex real-world problems. Artificial neural networks may be defined as structures comprised of densely interconnected adaptive simple processing elements (called artificial neurons or nodes) that are capable of
Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
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Introduction
Modelling in broilers
performing massively parallel computations for data processing and knowledge representation. Although ANNs are drastic abstractions of the biological counterparts, the idea of ANNs is not to replicate the operation of the biological systems, but to make use of what is known about the functionality of the biological networks for solving complex problems. The attractiveness of ANNs comes from the remarkable information processing characteristics of the biological system such as non-linearity, high parallelism, robustness, fault and failure tolerance, learning, ability to handle imprecise and fuzzy information and their capability to generalize. Neural networks are being used in areas of prediction and classification, areas where regression models and other related statistical techniques have traditionally been used (Paliwal and Kumar, 2009). The objective of this study was to develop ANN-GA models to predict the published data from the response of broiler chickens (AF) to CF levels and exEn supplements in diets.
A. Salarpour, E. Rahmatnejad and H. Khotanlou
main activity is xylanase and b-glucanase, are obtained by fermentation with Penicillium funiculosum. As shown in Table 1, diets were formulated according to NRC (NRC, 1994). To measure broilers’ AF, at 42 days of age, two birds per replicate pen cage (n = 8/treatment) were randomly selected, weighed, and killed using thiopental sodium and bleeding of the carotid artery. Percentage of broilers’ AF (% of carcass weights) was measured at the end of experiment. A completely randomized design with a factorial arrangement was used. Artificial neural network–genetic algorithm (ANN-GA) Artificial neural network construction
Two hundred fifty-six-day-old male broiler chicks (Ross 308) were randomly assigned to eight treatments with four replicates, and eight chicks per each replicate pen in a 6 weeks study. The birds were kept in floor pens (2 9 1 m). Throughout the study, birds were housed in an environmentally controlled room. Temperature of room was maintained at 33 °C during the first 3 days of life and then was reduced gradually according to age until reaching to 24 °C at 21 days. The RH was maintained at 55–65% throughout the rearing period. Chicks received a 23 h/day of light programme and had free access to feed in mash form and water throughout the trial. Procedures for bird management and care were approved by the Animal Care Committee of Ramin Agricultural and Natural Resources University. In the weeks 1, 2 and 3 (starter period), birds fed eight diets including diet 1, control (3.8% CF); diets 2, 3 and 4, 5.4%, 7.3% and 8.6% CF respectively; diet 5, diet 1 plus enzyme; diet 6, diet 2 plus enzyme; diet 7, diet 3 plus enzyme and diet 8, diet 4 plus enzyme. Subsequently, at weeks 4, 5 and 6 (grower period), birds fed other eight diets, including diet 1, control (3.7% CF); diets 2, 3 and 4, 5.2%, 6.7% and 8.4% CF respectively; diet 5, diet 1 plus enzyme; diet 6, diet 2 plus enzyme; diet 7, diet 3 plus enzyme and diet 4, diet 4 plus enzyme. The enzyme used in this study was Rovabioâ Excel AP (Adisseo, Asia Pacific Pte, Singapore) at 0.5 g/kg of feed. This enzyme is a powder concentrated enzyme, whose
An ANN consists of a number of interconnected neurons, which are positioned in at least three layers, that is one input layer of source neurons, at least one hidden layer and an output layer of computational neurons. Each neuron in the hidden layer of the network can generally be considered as a simple processing element taking one or more input(s) and giving one and more output(s). In each neuron, a related weight is assigned to an input through which the power of each input is adjusted. The neuron can, thereby, combine all the inputs and calculate an output. Multilayer perceptron, used in this study, can be regarded as the most widely accepted structure of neural networks, applied to model the physical phenomena (Basheer and Hajmeer, 2000). Regarding the interconnections within the ANN structure, feedforward networks, whose response paths are processed forward and do not return to the previous layers, were considered. Training the ANN is adjusting the weight of the neuron, so that the network’s output will converge to the desired output. In this study, training artificial neural networks were performed based on the supervised learning method using error back propagation learning algorithm. A network receives a set of inputs and corresponding output examples, applies these examples to learn and determines the relationship between the inputs and the output. The networks process the inputs and compare theirs resulting output against the expected output. Afterwards, errors are propagated backward through the structure, leading the networks to gradually modify the weights until the desired output is created (Basheer and Hajmeer, 2000). In this study, 70% of data set was used randomly to train the networks, 15% reserved for validation and 15% to test the networks. Training the networks continues until the number of certain epochs (100) is passed or the error variations of network estimation in
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Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
Materials and methods Data
Modelling in broilers
A. Salarpour, E. Rahmatnejad and H. Khotanlou
Table 1 Diet formulation and composition (%)* Ingredient
Strater (0–21 days)
Grower (22–42 days)
DTP† Corn Soybean meal Wheat bran Fish meal DCP‡ Oyster shell Salt Sodium bicarbonate Soybean oil DL-Met§ L-Lysine HCL Coccidioacetate Vit & Min¶ Calculated ME**, MJ/kg CP††,% CF‡‡,% Ca§§,% AP¶¶,% Lys***,% Met††† + Cys‡‡‡,%
0.00 57.29 29.94 5.00 3.00 1.30 1.06 0.13 0.08 1.25 0.16 0.29 0.00 0.50
8.00 56.48 28.44 0.00 2.60 1.10 1.20 0.18 0.17 1.00 0.16 0.17 0.00 0.50
16.00 50.56 25.39 0.00 2.79 0.93 1.10 0.20 0.19 2.00 0.20 0.14 0.00 0.50
24.00 49.19 14.30 0.00 8.02 0.73 1.10 0.20 0.05 1.70 0.19 0.02 0.00 0.50
0.00 60.00 27.71 5.00 1.20 1.00 1.30 0.18 0.26 2.50 0.10 0.20 0.05 0.50
8.00 60.00 26.57 0.00 1.00 0.39 0.86 0.20 0.15 2.00 0.12 0.16 0.05 0.50
16.00 58.20 15.98 0.00 5.40 0.17 1.40 0.20 0.12 1.80 0.12 0.06 0.05 0.50
24.00 51.90 13.61 0.00 5.20 0.00 1.40 0.19 0.01 2.90 0.16 0.09 0.05 0.50
11.93 20.48 3.88 0.90 0.45 1.29 0.82
11.93 20.48 5.40 0.90 0.45 1.29 0.82
11.93 20.48 7.30 0.90 0.45 1.29 0.82
11.93 20.48 8.60 0.90 0.45 1.29 0.82
12.35 18.44 3.70 0.90 0.35 1.10 0.70
12.35 18.44 5.20 0.90 0.35 1.10 0.70
12.35 18.44 6.70 0.90 0.35 1.10 0.70
12.35 18.44 8.60 0.90 0.35 1.20 0.70
*To evaluate the effect of enzyme, phytase (1000 UFT/kg) was added to diets. †Dried tomato pomace. ‡Dicalcium phosphate. §DL-methionine. ¶Vitamin and Mineral premix, provided per kilogram: vitamin A, 360,000 IU; vitamin D3, 800,000 ICU; vitamin E, 7,200 IU; vitamin K3, 800 mg; vitamin B1, 720 mg; vitamin B9, 400 mg; vitamin H2, 40 mg; vitamin B2, 2,640 mg, vitamin B3, 4,000 mg; vitamin B5, 12,000 mg; vitamin B6, 1,200 mg; vitamin B12, 6 mg; choline chloride, 200,000 mg, manganese, 40,000 mg, iron, 20,000 mg; zinc, 40,000 mg, copper, 4,000 mg; iodine, 400 mg; selenium, 80 mg. **Metabolizable Energy. ††Crude Protein. ‡‡Crude Fibre. §§Calcium. ¶¶Available phosphorus. ***Lysine. †††Methionine. ‡‡‡Cysteine.
Genetic algorithm (GA) is a parallel searching algorithm depending on best natural selection and Darwin
evolution theory. GA combined selection operators, generation, crossover and mutation for identifying the best solution for the problem. The solution of the problem is named chromosome. The chromosome consists of a collection of genes that easily optimize parameters of ANN. GA produces an initial population (a collection of chromosomes) and then evaluates the population by training an ANN for every chromosome and evolves the population by multiple generations (using GA operators) in finding the best parameters of the network. The main difference between this method and other searching methods is that the GA deals with a population of coded points instead of focusing on finding values of total points, which may form the collection of solution (Goldberg, 1989).
Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
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a mentioned epoch are minimized. In addition, principal component analysis (PCA) was used to process the input features into new component without correlation to achieve the simple interpretation of information. In this study, neural networks have at least one hidden layer with the number of neurons from 1 to 40 and at most two, three and four hidden layers with the same number of neurons between 1 and 20 (Haykin, 1994; Bishop, 1995, 2006; Abu-Mostafa et al., 2012). The networks were developed in MATLAB software 7.14 (R2012a) (Demuth and Beale, 2002). Genetic algorithm
Modelling in broilers
A. Salarpour, E. Rahmatnejad and H. Khotanlou
The learning algorithm of the networks determines the initial values of weights randomly and then calculates the set of connected weight values to the least error through error optimization method of gradient descent. The random initial value of connected weights is important in network performance. Therefore, random search and evolution methods such as genetic algorithm are used to determine the optimal values for the initial weights of neural networks (Fiszelew et al., 2007). In this study, weight values of the networks comprise the real chromosome genes such that each gene could be a real number. The evolutionary process of this chromosome took place in 100 generations under standard combination and mutation. We use 100 generations because it is good trade of between precision and velocity. After 100th generation, there is not salient improve per each new generation, it choose experimental. Finally, the best response in 100 generations was recorded. For this purpose, the genetic algorithm program along with MATLAB software was used. Artificial neural network– genetic algorithm selected variables for the inputs of ANN are CFs and exEn. And AF was elicited as a result of each ANN-GA.
Results and discussion To attain the AF estimation technique in broilers, an ANN with the different structures was developed. The results showed that estimation errors of all different structures of ANN-GA were in acceptable level with a 0.08% average for train data and 0.22% for test data. Based on the findings, network structure with three hidden layers and 20 neurons exhibited the highest level of accuracy. In general, prediction errors in the training phase of the developed different estimation techniques were lower than the test phase. Comparison of different structures RMSE and R2 of ANN-GAs in the train and the test stages presented in Fig. 1 and Fig. 2, respectively. Networks number 1–40 related to
Train RMSE
Test RMSE
0.4 0.35 0.3
RMSE
Combination of ANN and GA
0.25 0.2 0.15 0.1 0.05 0
Statistical evaluation criteria
1
RMSE ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP un 2 u ðTj Yj Þ tj¼1 n
P ðTj Yj Þ2 P 2 R2 ¼ 1 P ð Tj Þ Tj2 n
8
15 22 29 36 43 50 57 64 71 78 85 92 99
Number of networks Fig. 1 Root mean square error values for all different structure of artificial neural networks (ANNs) in train and test phases. Networks number 1–40 related to one layer ANN, 41–60 related to two layers ANN, 61–80 is for three layers, and 81–100 is for four layers ANN; the best RMSE is belonging to Network number 80 with three hidden layers and 20 neurons in each.
TrainR2
R2
Root mean square error (RMSE) and coefficient of determination (R2) are commonly used to assess the performance of prediction techniques. These criteria determine the differences between estimated values and real values of the subject (Paliwal and Kumar, 2009). R2 is used to show the similarity between the model tendency and the measured data, with higher R2 values representing greater similarities. Furthermore, RMSE indicates the estimation accuracy. Lower RMSE values represent more accurate estimations. The RMSE and R2 criteria can be formulated as follows:
Test R2
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1
8
15 22 29 36 43 50 57 64 71 78 85 92 99
Number of networks
where Tj and Yj are the measured and the predicted values of data j respectively; and n represents the number of measurements.
Fig. 2 R2 values for all different structure of Artificial neural networks (ANNs) in train and test phases. Networks number 1–40 related to one layer ANN, 41–60 related to two layers ANN, 61–80 is for three layers, and 81–100 is for four layers ANN; the best R2 belongs to Network number 80 with three hidden layers and 20 neurons in each.
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Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
Modelling in broilers
•
•
Real data
Estimated data
2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 1
5
9
13
17
Train&Validation samples Fig. 3 Comparison of real data with estimated data for train and validation phase.
Abdominal Fat (% of carcass weight)
one layer ANN, 41–60 related to two layers ANN; 61– 80 is for three layers ANN and 81–100 belonged to four layers ANN. Some useful information about all configures of ANN-GAs was gathered at table 2. The best network with (1-20-20-20-1 structure) was selected. We use the least and most boundary for the number of layers and number of neurons based on experiment and the number of ANN features that we used (Bishop, 2006). In all examined ANN-GAs for two periods, we used below characteristics: Network Transfer function = ‘tansig’ Network training function = ‘traingdx’ Weight/bias learning function = ‘learngdm’ Performance function = ‘mse’ Divide function = ‘dividerand’ Epochs = ‘1000 Train goal = ‘0.010 Genetic Generation = ‘1000 Combination of mutation = ‘standard’ Selecting should be experimentally to reach acceptable precision and avoid overfitting that was proven in previous works (Bishop, 1995; Abu-Mostafa et al., 2012). The plots of measured values of AF in comparison with estimated values by the best shape of ANN-GA consist of three hidden layers with 20 neurons for the train, the validation and the test phase are presented in Fig. 3 and Fig. 4, respectively. All achieved information is shown in Table 3. Neural networks are capable of modelling any complex function and can be used in the poultry and animal production areas. In recent years, the softcomputing methods resembling ANN has been applied in the field of poultry nutrition (Ahmadi
Abdominal Fat (% of carcass weight)
A. Salarpour, E. Rahmatnejad and H. Khotanlou
Real data
Estimated data
3 2.5 2 1.5 1 0.5 0 1
2
3
4
Test samples Fig. 4 Comparison of real data with estimated data for test phase.
et al., 2008; Chen et al., 2009; Ahmadi and Golian, 2010; Savegnago et al., 2011). The profitability of broiler production is largely determined by the possibility of increasing the proportion of prime parts in the carcass, mainly breast meat, and by reducing fat (Le Bihan-Duval et al., 1999). The abdominal fat pad represents one of the main regions of fat deposition
Table 2 Data acquired from 100 different structures of ANN-GA that was trained for broilers abdominal fat output Training phase
The Best ANN-GA with 1 layer The MEAN ANN-GA with 1 layer The Best ANN-GA with 2 layers The MEAN ANN-GA with 2 layers The Best ANN-GA with 3 layers The MEAN ANN-GA with 3 layers The Best ANN-GA with 4 layers The MEAN ANN-GA with 4 layers
Testing phase
ANN structure
RMSE
R
1 hidden layer with 33 neurons – 2 hidden layer with 16 neurons – 3 hidden layer with 20 neurons – 4 hidden layer with 14 neurons –
0.0553 0.0750 0.0505 0.0830 0.0487 0.0818 0.0520 0.0939
0.887 0.792 0.896 0.757 0.913 0.743 0.873 0.722
2
RMSE
R2
0.1811 0.2253 0.1774 0.2819 0.1286 0.1972 0.3069 1.1523
0.813 0.758 0.725 0.699 0.876 0.698 0.826 0.680
ANN: artificial neural networks, ANN-GA: artificial neural networks–genetic algorithm, RMSE: root mean square error, R2: coefficient of determination, inf: infinity.
Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
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Modelling in broilers
A. Salarpour, E. Rahmatnejad and H. Khotanlou
ANN structure
ANN Parameters
Total
Train
Test
ANN-GA RMSE
1-20-20-20-1
0.1472
0.0487
0.1286
ANN-GA R2
1-20-20-20-1
Epochs = ‘6’ Time = ‘inf ‘ Goal = ‘0.1’ Min_grad = ‘1e-05’ Max_fail = ‘6’ Mu = ‘0.001’
0.883
0.913
0.876
Table 3 Attributes and results of the best structure selected for broiler abdominal fat
ANN: artificial neural networks, ANN-GA: artificial neural networks–genetic algorithm, RMSE: root mean square error, R2: coefficient of determination, inf: infinity.
in chickens, and it seems to be directly related to total fat (Becker et al., 1981). Excessive fat is one of the main problems faced by the broiler industry nowadays, because it does not just reduce carcass yield and feed efficiency, but also cause rejection of the meat by the consumers and difficulties in processing. Some factors, including nutrients’ density of diets, exEn supplements, age, strain, sex and the applied response model may influence carcass quality of meat birds. The analysis of the results of performance criteria showed that feed-forward multilayer neural networks could accurately estimate the AF. The estimation error by the developed ANNs techniques was in the acceptable range. Therefore, if the ANNs used properly, then it seems to be an ideal technique for estimating the AF in achieving the precision grade of accuracy. One of the most important applications of estimation models with this grade of accuracy can be defined for determining the effectiveness of various solutions of a dietary programme at different times. This demonstrates that the soft-computing system can be a good tool for minimizing the uncertainties in the AF estimation approaches. To attain the networks with optimal performance, structural, activation function and learning algorithms were chosen in accordance with the nature of the phenomenon of study. In addition, the best networks were chosen using trial and error in terms of the number of hidden layers and their neurons (Fig. 3 and Fig. 4). The estimation error of networks with one hidden layer showed a descending trend with the increase of the number of neurons, which can be due to using more non-linear features and better learning of the networks. On the other hand, if the networks have too many hidden layers and neuron numbers, they will follow the AF in the observations due to overfitting, resulting n too weak generalization for untrained data. One practical way is to begin with a small number of hidden layers and increase on as needed to
achieve the expected model accuracy. Using the genetic algorithm to determine the optimal structural of the networks has been proposed as a suitable approach. In this study, genetic algorithm could improve the performance of the networks through determining the optimal values of the initial weights. The results confirmed the high capabilities of artificial intelligence approach to estimate the AF. The main cause of estimation error in the AF estimation techniques may be due to the measuring selected features for modelling. In real situations, there are many other parameters that can influence the AF level; however, all of them cannot be incorporated in the model.Because neural networks are the data-oriented methods, the type of features and the number of observations and preparing them correctly to improve the networks with optimal performance are important. Observations to be used for training ANNs should be large enough to cover the possible known variations in the subject domain.
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Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
Conclusion The results of the current study have shown that the ANN-GA could satisfactorily estimatie and predict broiler AF. Selection of a suitable model might change based on the fibre and enzyme amounts in the diets of broiler chickens. The best selected ANN-GA showed pleasing results (RMSE, 0.1286% and R2 coefficient, 0.876 for test data). The estimation error by the developed ANN techniques was in the acceptable range to estimate AF of broiler at different ages. Using artificial intelligence approaches to develop a valid manner of AF estimation and prediction based on real data can improve the efficacy of broiler husbandry programs and may provide suitable information for breeders and poultry nutritionists. Therefore, the ANNs, if used properly, seem to be an ideal technique for the purpose of estimating the AF in achieving the grade of accuracy.
Modelling in broilers
A. Salarpour, E. Rahmatnejad and H. Khotanlou
References Abu-Mostafa, Y. S.; Magdon-Ismail, M.; Lin, H.-T., 2012: Learning From Data. AMLBook. http://www.AMLbook.com Ahmadi, H.; Golian, A., 2010: The integration of broiler chicken threonine responses data into neural network models. Poultry Science 89, 2535–2541. Ahmadi, H.; Golian, A.; Mottaghitalab, M.; Nariman-Zadeh, N., 2008: Prediction model for true metabolizable energy of feather meal and poultry offal meal using group method of data handlingtype neural network. Poultry Science 87, 1909–1912. Basheer, I. A.; Hajmeer, M., 2000: Artificial neural networks: fundamentals, computing, design, and application. Journal of Microbiological Methods 43, 3–31. Becker, W. A.; Spencer, J. V.; Mirosh, L. W.; Verstrate, J. A., 1981: Abdominal and carcass fat in five broiler strains. Poultry Science 60, 693–697. Bishop, C. M., 1995: Neural Networks for Pattern Recognition. Oxford university press, New York. Bishop, C. M., 2006: Pattern Recognition and Machine Learning. Springer, New York. Chen, L. J.; Xing, L.; Han, L. J., 2009: Quantitative determination of nutrient content in poultry manure by near infrared spectroscopy based on artificial neural networks. Poultry Science 88, 2496–2503. Demuth, H.; Beale, M., 2002: Neural Network Toolbox User’s Guide for use with MATLAB, The MathWorks, Inc., Natick, MA. Fiszelew, A.; Britos, P.; Ochoa, A.; Merlino, H.; Fernandez, E.; Garcia-Martinez, R., 2007: Finding optimal neural network architecture using genetic algorithms. Advances in Computer Science and
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or without enzyme addition and whole wheat on broiler performance and carcass traits. Poultry Science 80, 195–202. NRC, 1994: Nutrient Requirements of Poultry. National Academies Press, Washington, DC. Paliwal, M.; Kumar, U. A., 2009: Neural networks and statistical techniques: a review of applications. Expert Systems with Applications 36, 2–17. Rahmatnejad, E.; Bojarpour, M.; Mamuei, M.; Mirzadeh, K.; Perai, A. H., 2011: The effects of dried tomato pomace and a multipleenzyme mixture supplementation (Rovabio ExcelTM) on performance and carcass quality of broiler chickens. African Journal of Biotechnology 10, 9207–9212. Savegnago, R. P.; Nunes, B. N.; Caetano, S. L.; Ferraudo, A. S.; Schmidt, G. S.; Ledur, M. C.; Munari, D. P., 2011: Comparison of logistic and neural network models to fit to the egg production curve of White Leghorn hens. Poultry Science 90, 705–711. Sizemore, F. G.; Siegel, H. S., 1993: Growth, feed conversion, and carcass composition in females of four broiler crosses fed starter diets with different energy levels and energy to protein ratios. Poultry Science 72, 2216–2228. Zerehdaran, S.; Vereijken, A.; van Arendonk, J.; van der Waaijt, E., 2004: Estimation of genetic parameters for fat deposition and carcass traits in broilers. Poultry Science 83, 521–525. Zhao, J. P.; Chen, J. L.; Zhao, G. P.; Zheng, M. Q.; Jiang, R. R.; Wen, J., 2009: Live performance, carcass composition, and blood metabolite responses to dietary nutrient density in two distinct broiler breeds of male chickens1. Poultry Science 88, 2575–2584.
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ORIGINAL ARTICLE
Modelling broilers’ abdominal fat in response to dietary treatments A. Salarpour1, E. Rahmatnejad1 and H. Khotanlou2 1 Young Researchers & Elite Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran, and 2 ISIP Lab, Computer Engineering Department, Bu-Ali Sina University, Hamedan, Iran
Summary Neural networks are capable of modelling any complex function and can be used in poultry production. Dietary crude fibre (CF) and exogenous enzymes (exEn) extensively affected abdominal fat (AF) of broilers. Current methods to study AF and its correlation with dietary CF levels and exEn supplements are costly, laborious and time-consuming. The purpose of this study was to develop an artificial neural network–genetic algorithm (ANNGA) to model data on the response of broiler chickens (AF) to CF and exEn from 0 to 42 days of age. A data set containing eight treatments was divided to the train, validation, and test data set of the ANN models. The information about feeding eight diets at two periods [starter (0–21 days of age) and grower (22–42 days of age)] were used to estimate AF of broilers by ANN-GA. A multilayer feed-forward neural network with different structures was developed using MATLAB software, and optimal values for the ANN weights were obtained using the genetic algorithm (GA). Crude fibre, and exEn were used as input variables and AF of broilers was output variable. The best model of ANN-GA was determined based on the train root mean square error (RMSE). The best selected ANN-GA showed desirable results, RMSE, 0.1286% and R2 coefficient, 0.876 for test data. Keywords neural network, crude fibre, exogenous enzyme Correspondence A. Salarpour, Young Researchers & Elite Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran. Tel: +98 9133413051; Fax: +98 8138292631; E-mail: [email protected] Received: 26 April 2013; accepted: 8 July 2014
The primary goal of broiler breeding is to improve profitability of broiler meat production (Zerehdaran et al., 2004). The gainfulness of broiler production is largely determined by the possibility of increasing the proportion of prime parts in the carcass, mainly breast meat, and by reducing fat (Le Bihan-Duval et al., 1999). The abdominal fat pad represents one of the main regions of fat deposition in chickens, and it seems to be mainly related to total carcass fat (Becker et al., 1981). Excessive fat is one of the main problems faced by the broiler industry nowadays, because it does not just reduce carcass yield and feed efficiency, but also cause rejection of the meat by the consumers and difficulties in processing. A great volume of information exists on the AF of broilers. The effects of some factors, including dietary CF (Rahmatnejad et al., 2011), energy (Jackson et al., 1982; Sizemore and Siegel, 1993), protein (Jackson et al., 1982; Sizemore and Siegel, 1993; Kamran et al., 2008), energy to protein ratio (Sizemore and Siegel,
1993; Kamran et al., 2008; Zhao et al., 2009), exEn supplements (Nahas and Lefrancois, 2001; Mushtaq et al., 2009; Rahmatnejad et al., 2011), age (Fortin et al., 1983; Kamran et al., 2008), strain (Fortin et al., 1983; Zhao et al., 2009), sex (Fortin et al., 1983; Sizemore and Siegel, 1993) and the applied response model on carcarss quality (e.g., AF) of meat birds have been studied. Neural networks are capable of modelling any complex function and can be used in the poultry and animal production areas. In recent years, the softcomputing methods like artificial neural network (ANN) have been applied in the field of poultry nutrition (Ahmadi et al., 2008; Chen et al., 2009; Ahmadi and Golian, 2010; Savegnago et al., 2011). Artificial neural networks are computational modelling tools that have recently emerged and found extensive acceptance in many disciplines for modelling complex real-world problems. Artificial neural networks may be defined as structures comprised of densely interconnected adaptive simple processing elements (called artificial neurons or nodes) that are capable of
Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
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Introduction
Modelling in broilers
performing massively parallel computations for data processing and knowledge representation. Although ANNs are drastic abstractions of the biological counterparts, the idea of ANNs is not to replicate the operation of the biological systems, but to make use of what is known about the functionality of the biological networks for solving complex problems. The attractiveness of ANNs comes from the remarkable information processing characteristics of the biological system such as non-linearity, high parallelism, robustness, fault and failure tolerance, learning, ability to handle imprecise and fuzzy information and their capability to generalize. Neural networks are being used in areas of prediction and classification, areas where regression models and other related statistical techniques have traditionally been used (Paliwal and Kumar, 2009). The objective of this study was to develop ANN-GA models to predict the published data from the response of broiler chickens (AF) to CF levels and exEn supplements in diets.
A. Salarpour, E. Rahmatnejad and H. Khotanlou
main activity is xylanase and b-glucanase, are obtained by fermentation with Penicillium funiculosum. As shown in Table 1, diets were formulated according to NRC (NRC, 1994). To measure broilers’ AF, at 42 days of age, two birds per replicate pen cage (n = 8/treatment) were randomly selected, weighed, and killed using thiopental sodium and bleeding of the carotid artery. Percentage of broilers’ AF (% of carcass weights) was measured at the end of experiment. A completely randomized design with a factorial arrangement was used. Artificial neural network–genetic algorithm (ANN-GA) Artificial neural network construction
Two hundred fifty-six-day-old male broiler chicks (Ross 308) were randomly assigned to eight treatments with four replicates, and eight chicks per each replicate pen in a 6 weeks study. The birds were kept in floor pens (2 9 1 m). Throughout the study, birds were housed in an environmentally controlled room. Temperature of room was maintained at 33 °C during the first 3 days of life and then was reduced gradually according to age until reaching to 24 °C at 21 days. The RH was maintained at 55–65% throughout the rearing period. Chicks received a 23 h/day of light programme and had free access to feed in mash form and water throughout the trial. Procedures for bird management and care were approved by the Animal Care Committee of Ramin Agricultural and Natural Resources University. In the weeks 1, 2 and 3 (starter period), birds fed eight diets including diet 1, control (3.8% CF); diets 2, 3 and 4, 5.4%, 7.3% and 8.6% CF respectively; diet 5, diet 1 plus enzyme; diet 6, diet 2 plus enzyme; diet 7, diet 3 plus enzyme and diet 8, diet 4 plus enzyme. Subsequently, at weeks 4, 5 and 6 (grower period), birds fed other eight diets, including diet 1, control (3.7% CF); diets 2, 3 and 4, 5.2%, 6.7% and 8.4% CF respectively; diet 5, diet 1 plus enzyme; diet 6, diet 2 plus enzyme; diet 7, diet 3 plus enzyme and diet 4, diet 4 plus enzyme. The enzyme used in this study was Rovabioâ Excel AP (Adisseo, Asia Pacific Pte, Singapore) at 0.5 g/kg of feed. This enzyme is a powder concentrated enzyme, whose
An ANN consists of a number of interconnected neurons, which are positioned in at least three layers, that is one input layer of source neurons, at least one hidden layer and an output layer of computational neurons. Each neuron in the hidden layer of the network can generally be considered as a simple processing element taking one or more input(s) and giving one and more output(s). In each neuron, a related weight is assigned to an input through which the power of each input is adjusted. The neuron can, thereby, combine all the inputs and calculate an output. Multilayer perceptron, used in this study, can be regarded as the most widely accepted structure of neural networks, applied to model the physical phenomena (Basheer and Hajmeer, 2000). Regarding the interconnections within the ANN structure, feedforward networks, whose response paths are processed forward and do not return to the previous layers, were considered. Training the ANN is adjusting the weight of the neuron, so that the network’s output will converge to the desired output. In this study, training artificial neural networks were performed based on the supervised learning method using error back propagation learning algorithm. A network receives a set of inputs and corresponding output examples, applies these examples to learn and determines the relationship between the inputs and the output. The networks process the inputs and compare theirs resulting output against the expected output. Afterwards, errors are propagated backward through the structure, leading the networks to gradually modify the weights until the desired output is created (Basheer and Hajmeer, 2000). In this study, 70% of data set was used randomly to train the networks, 15% reserved for validation and 15% to test the networks. Training the networks continues until the number of certain epochs (100) is passed or the error variations of network estimation in
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Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
Materials and methods Data
Modelling in broilers
A. Salarpour, E. Rahmatnejad and H. Khotanlou
Table 1 Diet formulation and composition (%)* Ingredient
Strater (0–21 days)
Grower (22–42 days)
DTP† Corn Soybean meal Wheat bran Fish meal DCP‡ Oyster shell Salt Sodium bicarbonate Soybean oil DL-Met§ L-Lysine HCL Coccidioacetate Vit & Min¶ Calculated ME**, MJ/kg CP††,% CF‡‡,% Ca§§,% AP¶¶,% Lys***,% Met††† + Cys‡‡‡,%
0.00 57.29 29.94 5.00 3.00 1.30 1.06 0.13 0.08 1.25 0.16 0.29 0.00 0.50
8.00 56.48 28.44 0.00 2.60 1.10 1.20 0.18 0.17 1.00 0.16 0.17 0.00 0.50
16.00 50.56 25.39 0.00 2.79 0.93 1.10 0.20 0.19 2.00 0.20 0.14 0.00 0.50
24.00 49.19 14.30 0.00 8.02 0.73 1.10 0.20 0.05 1.70 0.19 0.02 0.00 0.50
0.00 60.00 27.71 5.00 1.20 1.00 1.30 0.18 0.26 2.50 0.10 0.20 0.05 0.50
8.00 60.00 26.57 0.00 1.00 0.39 0.86 0.20 0.15 2.00 0.12 0.16 0.05 0.50
16.00 58.20 15.98 0.00 5.40 0.17 1.40 0.20 0.12 1.80 0.12 0.06 0.05 0.50
24.00 51.90 13.61 0.00 5.20 0.00 1.40 0.19 0.01 2.90 0.16 0.09 0.05 0.50
11.93 20.48 3.88 0.90 0.45 1.29 0.82
11.93 20.48 5.40 0.90 0.45 1.29 0.82
11.93 20.48 7.30 0.90 0.45 1.29 0.82
11.93 20.48 8.60 0.90 0.45 1.29 0.82
12.35 18.44 3.70 0.90 0.35 1.10 0.70
12.35 18.44 5.20 0.90 0.35 1.10 0.70
12.35 18.44 6.70 0.90 0.35 1.10 0.70
12.35 18.44 8.60 0.90 0.35 1.20 0.70
*To evaluate the effect of enzyme, phytase (1000 UFT/kg) was added to diets. †Dried tomato pomace. ‡Dicalcium phosphate. §DL-methionine. ¶Vitamin and Mineral premix, provided per kilogram: vitamin A, 360,000 IU; vitamin D3, 800,000 ICU; vitamin E, 7,200 IU; vitamin K3, 800 mg; vitamin B1, 720 mg; vitamin B9, 400 mg; vitamin H2, 40 mg; vitamin B2, 2,640 mg, vitamin B3, 4,000 mg; vitamin B5, 12,000 mg; vitamin B6, 1,200 mg; vitamin B12, 6 mg; choline chloride, 200,000 mg, manganese, 40,000 mg, iron, 20,000 mg; zinc, 40,000 mg, copper, 4,000 mg; iodine, 400 mg; selenium, 80 mg. **Metabolizable Energy. ††Crude Protein. ‡‡Crude Fibre. §§Calcium. ¶¶Available phosphorus. ***Lysine. †††Methionine. ‡‡‡Cysteine.
Genetic algorithm (GA) is a parallel searching algorithm depending on best natural selection and Darwin
evolution theory. GA combined selection operators, generation, crossover and mutation for identifying the best solution for the problem. The solution of the problem is named chromosome. The chromosome consists of a collection of genes that easily optimize parameters of ANN. GA produces an initial population (a collection of chromosomes) and then evaluates the population by training an ANN for every chromosome and evolves the population by multiple generations (using GA operators) in finding the best parameters of the network. The main difference between this method and other searching methods is that the GA deals with a population of coded points instead of focusing on finding values of total points, which may form the collection of solution (Goldberg, 1989).
Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
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a mentioned epoch are minimized. In addition, principal component analysis (PCA) was used to process the input features into new component without correlation to achieve the simple interpretation of information. In this study, neural networks have at least one hidden layer with the number of neurons from 1 to 40 and at most two, three and four hidden layers with the same number of neurons between 1 and 20 (Haykin, 1994; Bishop, 1995, 2006; Abu-Mostafa et al., 2012). The networks were developed in MATLAB software 7.14 (R2012a) (Demuth and Beale, 2002). Genetic algorithm
Modelling in broilers
A. Salarpour, E. Rahmatnejad and H. Khotanlou
The learning algorithm of the networks determines the initial values of weights randomly and then calculates the set of connected weight values to the least error through error optimization method of gradient descent. The random initial value of connected weights is important in network performance. Therefore, random search and evolution methods such as genetic algorithm are used to determine the optimal values for the initial weights of neural networks (Fiszelew et al., 2007). In this study, weight values of the networks comprise the real chromosome genes such that each gene could be a real number. The evolutionary process of this chromosome took place in 100 generations under standard combination and mutation. We use 100 generations because it is good trade of between precision and velocity. After 100th generation, there is not salient improve per each new generation, it choose experimental. Finally, the best response in 100 generations was recorded. For this purpose, the genetic algorithm program along with MATLAB software was used. Artificial neural network– genetic algorithm selected variables for the inputs of ANN are CFs and exEn. And AF was elicited as a result of each ANN-GA.
Results and discussion To attain the AF estimation technique in broilers, an ANN with the different structures was developed. The results showed that estimation errors of all different structures of ANN-GA were in acceptable level with a 0.08% average for train data and 0.22% for test data. Based on the findings, network structure with three hidden layers and 20 neurons exhibited the highest level of accuracy. In general, prediction errors in the training phase of the developed different estimation techniques were lower than the test phase. Comparison of different structures RMSE and R2 of ANN-GAs in the train and the test stages presented in Fig. 1 and Fig. 2, respectively. Networks number 1–40 related to
Train RMSE
Test RMSE
0.4 0.35 0.3
RMSE
Combination of ANN and GA
0.25 0.2 0.15 0.1 0.05 0
Statistical evaluation criteria
1
RMSE ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP un 2 u ðTj Yj Þ tj¼1 n
P ðTj Yj Þ2 P 2 R2 ¼ 1 P ð Tj Þ Tj2 n
8
15 22 29 36 43 50 57 64 71 78 85 92 99
Number of networks Fig. 1 Root mean square error values for all different structure of artificial neural networks (ANNs) in train and test phases. Networks number 1–40 related to one layer ANN, 41–60 related to two layers ANN, 61–80 is for three layers, and 81–100 is for four layers ANN; the best RMSE is belonging to Network number 80 with three hidden layers and 20 neurons in each.
TrainR2
R2
Root mean square error (RMSE) and coefficient of determination (R2) are commonly used to assess the performance of prediction techniques. These criteria determine the differences between estimated values and real values of the subject (Paliwal and Kumar, 2009). R2 is used to show the similarity between the model tendency and the measured data, with higher R2 values representing greater similarities. Furthermore, RMSE indicates the estimation accuracy. Lower RMSE values represent more accurate estimations. The RMSE and R2 criteria can be formulated as follows:
Test R2
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1
8
15 22 29 36 43 50 57 64 71 78 85 92 99
Number of networks
where Tj and Yj are the measured and the predicted values of data j respectively; and n represents the number of measurements.
Fig. 2 R2 values for all different structure of Artificial neural networks (ANNs) in train and test phases. Networks number 1–40 related to one layer ANN, 41–60 related to two layers ANN, 61–80 is for three layers, and 81–100 is for four layers ANN; the best R2 belongs to Network number 80 with three hidden layers and 20 neurons in each.
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Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
Modelling in broilers
•
•
Real data
Estimated data
2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 1
5
9
13
17
Train&Validation samples Fig. 3 Comparison of real data with estimated data for train and validation phase.
Abdominal Fat (% of carcass weight)
one layer ANN, 41–60 related to two layers ANN; 61– 80 is for three layers ANN and 81–100 belonged to four layers ANN. Some useful information about all configures of ANN-GAs was gathered at table 2. The best network with (1-20-20-20-1 structure) was selected. We use the least and most boundary for the number of layers and number of neurons based on experiment and the number of ANN features that we used (Bishop, 2006). In all examined ANN-GAs for two periods, we used below characteristics: Network Transfer function = ‘tansig’ Network training function = ‘traingdx’ Weight/bias learning function = ‘learngdm’ Performance function = ‘mse’ Divide function = ‘dividerand’ Epochs = ‘1000 Train goal = ‘0.010 Genetic Generation = ‘1000 Combination of mutation = ‘standard’ Selecting should be experimentally to reach acceptable precision and avoid overfitting that was proven in previous works (Bishop, 1995; Abu-Mostafa et al., 2012). The plots of measured values of AF in comparison with estimated values by the best shape of ANN-GA consist of three hidden layers with 20 neurons for the train, the validation and the test phase are presented in Fig. 3 and Fig. 4, respectively. All achieved information is shown in Table 3. Neural networks are capable of modelling any complex function and can be used in the poultry and animal production areas. In recent years, the softcomputing methods resembling ANN has been applied in the field of poultry nutrition (Ahmadi
Abdominal Fat (% of carcass weight)
A. Salarpour, E. Rahmatnejad and H. Khotanlou
Real data
Estimated data
3 2.5 2 1.5 1 0.5 0 1
2
3
4
Test samples Fig. 4 Comparison of real data with estimated data for test phase.
et al., 2008; Chen et al., 2009; Ahmadi and Golian, 2010; Savegnago et al., 2011). The profitability of broiler production is largely determined by the possibility of increasing the proportion of prime parts in the carcass, mainly breast meat, and by reducing fat (Le Bihan-Duval et al., 1999). The abdominal fat pad represents one of the main regions of fat deposition
Table 2 Data acquired from 100 different structures of ANN-GA that was trained for broilers abdominal fat output Training phase
The Best ANN-GA with 1 layer The MEAN ANN-GA with 1 layer The Best ANN-GA with 2 layers The MEAN ANN-GA with 2 layers The Best ANN-GA with 3 layers The MEAN ANN-GA with 3 layers The Best ANN-GA with 4 layers The MEAN ANN-GA with 4 layers
Testing phase
ANN structure
RMSE
R
1 hidden layer with 33 neurons – 2 hidden layer with 16 neurons – 3 hidden layer with 20 neurons – 4 hidden layer with 14 neurons –
0.0553 0.0750 0.0505 0.0830 0.0487 0.0818 0.0520 0.0939
0.887 0.792 0.896 0.757 0.913 0.743 0.873 0.722
2
RMSE
R2
0.1811 0.2253 0.1774 0.2819 0.1286 0.1972 0.3069 1.1523
0.813 0.758 0.725 0.699 0.876 0.698 0.826 0.680
ANN: artificial neural networks, ANN-GA: artificial neural networks–genetic algorithm, RMSE: root mean square error, R2: coefficient of determination, inf: infinity.
Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
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Modelling in broilers
A. Salarpour, E. Rahmatnejad and H. Khotanlou
ANN structure
ANN Parameters
Total
Train
Test
ANN-GA RMSE
1-20-20-20-1
0.1472
0.0487
0.1286
ANN-GA R2
1-20-20-20-1
Epochs = ‘6’ Time = ‘inf ‘ Goal = ‘0.1’ Min_grad = ‘1e-05’ Max_fail = ‘6’ Mu = ‘0.001’
0.883
0.913
0.876
Table 3 Attributes and results of the best structure selected for broiler abdominal fat
ANN: artificial neural networks, ANN-GA: artificial neural networks–genetic algorithm, RMSE: root mean square error, R2: coefficient of determination, inf: infinity.
in chickens, and it seems to be directly related to total fat (Becker et al., 1981). Excessive fat is one of the main problems faced by the broiler industry nowadays, because it does not just reduce carcass yield and feed efficiency, but also cause rejection of the meat by the consumers and difficulties in processing. Some factors, including nutrients’ density of diets, exEn supplements, age, strain, sex and the applied response model may influence carcass quality of meat birds. The analysis of the results of performance criteria showed that feed-forward multilayer neural networks could accurately estimate the AF. The estimation error by the developed ANNs techniques was in the acceptable range. Therefore, if the ANNs used properly, then it seems to be an ideal technique for estimating the AF in achieving the precision grade of accuracy. One of the most important applications of estimation models with this grade of accuracy can be defined for determining the effectiveness of various solutions of a dietary programme at different times. This demonstrates that the soft-computing system can be a good tool for minimizing the uncertainties in the AF estimation approaches. To attain the networks with optimal performance, structural, activation function and learning algorithms were chosen in accordance with the nature of the phenomenon of study. In addition, the best networks were chosen using trial and error in terms of the number of hidden layers and their neurons (Fig. 3 and Fig. 4). The estimation error of networks with one hidden layer showed a descending trend with the increase of the number of neurons, which can be due to using more non-linear features and better learning of the networks. On the other hand, if the networks have too many hidden layers and neuron numbers, they will follow the AF in the observations due to overfitting, resulting n too weak generalization for untrained data. One practical way is to begin with a small number of hidden layers and increase on as needed to
achieve the expected model accuracy. Using the genetic algorithm to determine the optimal structural of the networks has been proposed as a suitable approach. In this study, genetic algorithm could improve the performance of the networks through determining the optimal values of the initial weights. The results confirmed the high capabilities of artificial intelligence approach to estimate the AF. The main cause of estimation error in the AF estimation techniques may be due to the measuring selected features for modelling. In real situations, there are many other parameters that can influence the AF level; however, all of them cannot be incorporated in the model.Because neural networks are the data-oriented methods, the type of features and the number of observations and preparing them correctly to improve the networks with optimal performance are important. Observations to be used for training ANNs should be large enough to cover the possible known variations in the subject domain.
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Journal of Animal Physiology and Animal Nutrition © 2014 Blackwell Verlag GmbH
Conclusion The results of the current study have shown that the ANN-GA could satisfactorily estimatie and predict broiler AF. Selection of a suitable model might change based on the fibre and enzyme amounts in the diets of broiler chickens. The best selected ANN-GA showed pleasing results (RMSE, 0.1286% and R2 coefficient, 0.876 for test data). The estimation error by the developed ANN techniques was in the acceptable range to estimate AF of broiler at different ages. Using artificial intelligence approaches to develop a valid manner of AF estimation and prediction based on real data can improve the efficacy of broiler husbandry programs and may provide suitable information for breeders and poultry nutritionists. Therefore, the ANNs, if used properly, seem to be an ideal technique for the purpose of estimating the AF in achieving the grade of accuracy.
Modelling in broilers
A. Salarpour, E. Rahmatnejad and H. Khotanlou
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