Artificial neural network models offer an alternative to linear regression analysis for predicting the amino acid content of feeds from their chemical composition. A group method of data handling-type neural network (GMDH-type NN), with an evolutionary method of genetic algorithm, was used to predict methionine (Met) and lysine (Lys) contents of soybean meal (SBM) and fish meal (FM) from their proximate analyses (

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 (^{2} values (<0.50) in certain cases (^{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

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

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 (

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.

Data were taken from published literature (

Detailed descriptions of GMDH-type NN terminology, development, application, and examples have been previously reported by several researchers (

The predictive performance of the models developed was assessed using several measures of precision and bias between estimated (predicted) and observed (actual) values for each response variable. Two measures of precision were used: 1) the proportion of variance accounted for by the model (^{2}), and 2) the mean square prediction error (MSPE), calculated as:

where _{i}_{i}

Concordance correlation coefficient (CCC) was calculated to evaluate the precision and accuracy of predicted vs. observed values for the models (

The range of values for the input and predicted (Met and Lys) variables, and the pair-wise correlation matrices are shown in

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:

Met in FM:

Met in SBM:

Lys in FM:

Lys in SBM:

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 ^{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

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 ^{2}=0.77) and limited for Lys (^{2}=0.58). On the contrary, ^{2} values for digestible Met and Lys in feeds of animal origin and medium to low ^{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 (

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.