Achieving appropriate nutritional and physical characteristics of animal feed is very important for animal health and growth. Once the nutrient requirements of the animals were established, a correct balanced diet can be formulated if the accurate nutrient composition of feedstuffs is known (Čolović et al., 2010; Dale and Batal, 2002). Energy value of diets is of great importance for animal feed manufacturers and end users. The amount of available energy in feeds is described either by its metabolizable energy (ME) or by organic matter digestibility (OMD), (Palić and Leeuw, 2009; Pojić et al., 2008). ME determination of diets requires the use of live animals, appropriate sample collection, ME assay trial, and determination of energy content of feed ingredients and collected excreta (Elkin, 1987; Mohamed, 1984).

In vivo determination of ME can be expensive in terms of time and resources, thus it is important to develop rapid, inexpensive, and accurate methods for ME prediction which could be helpful to manufacturers and nutritionists in monitoring of animal feed quality. There has been a considerable and continuous interest to develop equations for prediction of ME (Perai et al., 2010; Robbins and Firman, 2005; Zhang et al., 1994).

The aim of this study was to develop equations for rapid prediction of metabolizable energy of diets for poultry.

Twenty one complete diets for broilers were used in this study. Dry matter, crude protein, crude fat, crude fibre and ash of the diets were determined according to AOAC official methods (AOAC, 2000). A modified method of Boisen and Fernandez (1997) for estimating the enzymatic digestibility of organic matter (EDOM) was used. For determination of in vivo TMEn, a method of Fisher and McNab (1987) was followed.

Regression analysis was used to generate mathematical models for prediction of response value of true metabolizable energy (TMEn (MJ/Kg DM)). Independent variables in models were: in vitro digestibility (%, x1), crude protein (%, x2), crude fat (%, x3), crude fibre (%, x4) and ash content (%, x5). The response was related to selected variables by secondorder polynomial model. The generalized model proposed for the response is given in equation below:

where Y represents the experimental response, b0, bi, bii, and bij are constants and regression coefficients of the model, and xi and xj are uncoded values of independent variables. STATISTICA software version 9 (Statsoft, Tulsa, OK, USA) was used for regression analysis of experimental data. The software generated regression coefficients for each of the combinations of the independent variables and their significances were determined using the p-values generated through the t‑tests. Adequacy of predicted model was evaluated by coefficient of determination (R2) and magnitude of root mean square (RMS):

where Yexp and Ypred are the experimental and predicted values of the response (TMEn (MJ/Kg DM)) and N is the number of experimental values.

The chemical composition of complete diets used in this study is shown in Table 1.
The six polynomial equations are proposed in this study. Each equation is describing individual and interaction effects of three factors on the TMEn. In vitro digestibility was taken into account in all equations. Regression equation coefficients are presented in Table 3. Subscript numbers of the coefficients are denoting factors to whom they are related. The significance of the coefficients is evaluated by Student’s t-test and p-values. Bold numbers denote values significant at 95% level.
Equation 1 (in vitro digestibility, crude protein and crude fat) shows that linear and quadratic effect of in vitro digestibility on TMEn is significant (p ≤ 0,05). Equations 2 (in vitro digestibility, crude protein and crude fibre) and 3 (in vitro digestibility, crude protein and crude fibre) are not having significant regression coefficients. All three equations are having relatively low coefficient of determination (R2 < 0,8). Equation 4 (in vitro digestibility, crude fat and crude fibre) indicated that linear and quadratic influence of crude fat and crude fibre was significant, as well as the interaction of all three factors. Obtained coefficient of determination was relatively higher in comparison with equations 1, 2 and 3. Equation 5 (in vitro digestibility, crude fat and ash) is showing significant linear and quadratic influence of in vitro digestibility, with high coefficient of determination (R2 = 0,93). Linear and quadratic influence of in vitro digestibility in equation 6 (in vitro digestibility, crude fibre and ash), likewise in equations 1 and 5, was significant.
Coefficient of determination of equation 6 was R2 = 0,87. The EDOM and TMEn values of complete poultry diets are shown in Table 2.

The RMS of equations 1, 2, 3, 4 and 6 was lower than 4%, showing that those equations had very good prediction of experimental results. The RMS value of equation 5 was very high due to big discrepancy between experimental and predicted results.

Equations with crude protein as one of independent variables had low fit of experimental data, indicating that crude protein did not have strong influence on TMEn. On the other hand, in most of equations in vitro digestibility had significant linear, quadratic or interactional effect on TMEn with relatively good fit of data.

Each of six proposed equations describe individual and interactional effects of three independent variables, and was evaluated by several quality criteria. This could be helpful in choosing appropriate model depending on chosen variable, or quality criteria. The root mean square of most of equations was very low, showing good prediction of experimental data. The polynomial equations proposed in this study could be successfully used for accurate and rapid prediction of TMEn.

This paper is a result of the research within the project III046012 “Istraživanje savremenih biotehnoloških postupaka u proizvodnji hrane za životinje u cilju povećanja konkurentnosti, kvaliteta i bezbednosti hrane za životinje (Study of modern biotechnological methods in the production of animal feed in order to increase competitiveness, quality and safety of the feed)”, financed by the Ministry of Science and Technological Development, Republic of Serbia. This study was also supported by the Ministry of Agriculture, Republic of South Africa.