Methionine (Met) and lysine (Lys) are the two most limiting amino acids (AA) in broiler diets based on corn and soybean meal (SBM). Supplementation of broiler feeds with these AA in synthetic forms is very common in the poultry industry to improve dietary protein, reduce nitrogen excretion, and minimise the cost of feed. More profitable production systems and better carcass yields can be achieved by an adjustment of dietary protein levels. Such adjustment requires information on the levels of AA, particularly Met and Lys, in feed ingredients (Mendes et al., 1997). For poultry and pigs, accurate estimation of Lys is necessary because it is the reference essential AA in ideal protein (Baker & Han, 1994). Conventional methods for the separation and analysis of Met and Lys in feedstuffs (AOAC, 1990) are slow, expensive, cumbersome, and time-consuming. These disadvantages have prompted a search for alternative methods based on the prediction of AA content from other chemical fractions or from near-infrared spectra (Kovalenko et al., 2006). Both predictive approaches require similar computational methodologies. Two quantitative methods of predicting AA levels in feed ingredients have been developed using linear regression, with an input of either crude protein (CP) (Degussa Corporation, 1990) or proximate chemical constituents of feed ingredients (Monsanto, 1986a,b,c). The National Research Council (NRC, 1994) has accepted these regression approaches for predicting AA composition. However, some of the AA prediction equations show divergence and lead to low R ² values (<0.50) in certain cases (Degussa Corporation, 1990; Monsanto, 1986a,b,c). Since the R ² value reflects the amount of input variability explained by the equation, a more definitive method of AA prediction is desirable.

Artificial neural networks (ANN) reflect effectively the complex relationship between ingredient composition (inputs) and nutrient levels (outputs). The ANN are applied in many fields to model and predict the behaviour of unknown systems or systems with complexity (or both) based on given input-output data. Using ANN does not require an a priori equation or model. This characteristic is potentially advantageous in modelling biological processes (Dayhoff & De Leo, 2001). The ANN predictions usually result in a closer fit to the data than is accomplished with regression analysis. As a result, this better fit usually leads to more accurate predictions (Ward Systems Group, 1993).

One ANN sub-model is the group method of data handling-type neural network (GMDH-type NN). It is a self-organizing approach by which gradually more complicated models are generated based on the evaluation of their performance on a set of multi-input, single output data pairs. The GMDH was first developed by Ivakhnenko (1971) as a multivariate analysis method for modelling and identification of complex systems. The GMDH-type NN has been used to circumvent the difficulty of having prior knowledge of the mathematical model of the process being considered. In other words, GMDH-type NN can be used to model complex systems without having specific knowledge of the systems.

The main idea of GMDH is to build an analytical function in a feed-forward network based on a quadratic node transfer function whose coefficients are obtained using linear regression procedures (Farrow, 1984). The use of such self-organizing networks has led to their successful application in a broad range of areas in engineering, science, and economics (Seginer et al., 1994; Vallejo-Cordoba et al., 1995; Roush et al., 1996). The GMDH-type NNs have been used in poultry science for the prediction of broiler performance (Faridi et al., 2011; 2013b), turkey performance (Mottaghitalab et al., 2010), egg production of broiler breeder hens (Faridi et al., 2012; 2013a) and true metabolizable energy content in feather meal and poultry offal meal (Ahmadi et al., 2008).

The present study was conducted to examine the capability of GMDH-type NNs in predicting Met and Lys contents of SBM and fish meal (FM) based on their proximate chemical composition.

The range of values for the input and predicted (Met and Lys) variables, and the pair-wise correlation matrices are shown in Table 1 for FM and SBM. In both meals, Met and Lys were positively correlated with CP. The AA contents were negatively correlated with ash in FM, and with crude fibre in SBM.

The optimal structures of the evolved two hidden layer GMDH-type NNs suggested by the genetic algorithm were found with five hidden neurons for Met and Lys in FM and for Met in SBM, and with six hidden neurons for Lys in SBM. The corresponding polynomial equations obtained are:

where CP, FAT, ASH, CF and MST represent the input variables: crude protein, crude fat, ash, crude fibre and moisture, respectively. The observed and predicted values of Met and Lys for the training and validation sets are depicted in Figs. 1 and 2, and relevant statistical information is given in Table 2. High R ² and low MSPE (RMSPE was always less than 5% of the observed mean) values indicate a high degree of precision in the predictions. The high CCC values and low contribution of ER to MSPE provide measures of a close agreement (accuracy) between observed and predicted values, with a coefficient of regression (slope) between both variables that was in all cases close to unity. Finally, all the statistics related to bias in the predictions show a small deviation without substantial over- or under-estimation of the observed (reference) values.

ANN models offer an alternative to linear regression analysis for investigating biological systems. The advantage of using an ANN to predict an output from several input variables is that it does not require an equation or model a priori to construct the relationship between the variables, as is the case with regression analysis (Roush & Cravener, 1997). The potential of GMDH-type NNs to predict the behaviour of unknown systems has been demonstrated in relation to poultry production (Faridi et al., 2013a,b; Mottaghitalab et al., 2010). In this study, the validity of this type of ANN model was examined using a genetic algorithm method to predict Met and Lys content of SBM and FM based on their proximate analysis. It is clearly evident from Figs. 1 and 2 that the evolved networks in terms of simple polynomial equations could successfully predict the output validation data, which were not used during the training process. The resultant statistical tests revealed very close agreement between observed and predicted Met and Lys values, although accuracy of prediction was higher for SBM.

Acceptance of all input variables (the five nutritional fractions) by the networks shows that the five selected input variables have some influence on the AA levels in the feed ingredients. This finding is similar to that reported by Cravener & Roush (1999) who compared three types of ANN with linear regression to predict AA levels in feed ingredients, and observed that a general regression ANN was superior to linear regression in predicting the AA contents of a number of feed ingredients. Cravener & Roush (2001) showed that genetic algorithm calibration of NN was superior to linear regression and to other ANN calibration approaches in predicting the Met and Lys contents of feeds. There are significant differences in the number of neurons in the hidden layers between our models and those proposed by Roush & Cravener (1997) and Cravener & Roush (1999, 2001), 5 to 6 vs. 160 to 181 neurons, depending on AA and feed ingredients. Other approaches, such as near-infrared reflectance spectroscopy (NIRS) have been used for the prediction of AA content of feedingstuffs. Accuracy of the prediction of the amount of AA added to compound feedingstuffs for different animal species (Pérez Marín et al., 2004) was medium for Met (R ²=0.77) and limited for Lys (R ²=0.58). On the contrary, Fontaine et al. (2001) observed an excellent performance of NIRS to predict the essential AA content of protein-rich feed ingredients, with relative mean deviations below 5%. The prediction of true ileal digestible AA content of protein concentrates was tested by van Kempen & Bodin (1998), with high R ² values for digestible Met and Lys in feeds of animal origin and medium to low R ² values for the prediction of the same AA in soybean meal.

The number of neurons in the hidden layers of an ANN model is subject to input variables and network structure. Using too many neurons in the hidden layers can result in several problems. First, it may result in over-fitting and the ANN has so much information processing capacity that the limited amount of information contained in the training set is not enough to train all the neurons in the hidden layers. A second problem can occur even when the training data are sufficient. An inordinately large number of neurons in the hidden layers may increase the time it takes to train the network. The amount of training time can increase to the point that it is impossible to train the ANN adequately (Heaton, 2008).

The AA composition of FM and SMB can be predicted from chemical composition using ANN. It is expected that this method could be also suitable to predict the content of truly digestible AA for poultry, although this analysis could not be performed due to the limited data available.

In conclusion, results of this study can be considered as a basis for accepting the validity of GMDH-type NN models to estimate the AA composition of poultry feed ingredients from their corresponding chemical composition with suitable performance.