Livestock Research for Rural Development 20 (12) 2008  Guide for preparation of papers  LRRD News  Citation of this paper 
In order to study the interest of substituting raw materials in concentrate diets, the effects of different prices of corn and soybean meal as well as the variation of crude protein (CP) content in soybean meal were studied.
Our results showed that substituting raw materials could be classified according to their minimum prices (MP), to the price variations of corn and soybean meal and to the rate of CP in soybean meal. In addition, if we consider the price variations of corn and soybean meal, it’s possible to establish predictive equations for the values of MP different substituting raw materials, for different animal species and group of species. The integration of the rate of CP from soybean meal in the models, improved (P <0.01) the significance level of the predictive equations.
Keywords: concentrate, raw materials, substitution, animal feeding, Tunisia
For a long time, concentrate feeds manufacturing in Tunisia was based on a limited number of raw materials, mainly corn, soybean meal, barley and wheat bran. During the last years some trials to substitute partially these raw materials, mainly soybean and corn in animal concentrate feeds were carried out in order to reduce the feeding cost. The increase of soybean and corn prices in the international markets and the availability of other raw materials at lower prices resulted in a growing interest given to the study of the opportunities and the conditions of substitution of basic raw materials, and to enlarge the range of them used in animal concentrate feed manufacturing (Lapierre and Huard 1996; Lapierre and Pressenda 2000; Sauvant et al 2003; Gerfault 2003). The current work aimed to study the interest of some raw materials of substitution at different prices of corn and soybean meal, and to establish predictive models for the minimum price of these raw materials, according to the variation of corn and soybean prices. The effects of some other variation sources of MP, such as CP content in soybean were also analysed.
Material and methods
Optimisation methods
The study of the interest of the raw materials of substitution was carried out through optimisation using linear programming method (Bernot 1979; Capon 1979). The study was based on the analysis of the optimisation results obtained from a linear model solved using simplex method (software LIBRA). Concentrate composition was optimised using corn and soybean meal 48 for monogastric species, and soybean meal 44, barley, dehydrated Lucerne and wheat bran for ruminants. At first, optimisation used market prices of raw materials during the period of the study. Then, simulating variations (20%, 10%, +10% et +20%) of corn price and soybean meal 44 and 48 average prices (210 and 463 or 410 Tunisian Dinars DT, respectively, DT = 1.3 $US) were tested. Another optimisation was carried out by including variations of CP content of soybean 48 for layers feed (45.3%, 45.8%, 46.3%, 46.8% and 47.3%). At last, we optimised layers and dairy cow feeds considering a variation of corn and soybean meal prices in a range from –20 to + 20%. The different row materials and limits of their incorporation are presented in table 1.
Table 1. Raw materials and limits of their incorporation 

Feed 
Dairy cows 
Ovine 
Growing broiler 
Layers 
Turkey 

min 
Max 
min 
Max 
min 
Max 
min 
Max 
min 
Max 

Corn 

 

 

 

 

 
Soybean 

 

 

 

 

 
Barley 

 

 

 

 

 
Dehydrated alfa alfa 

 

 

 

 

 
Wheat bran 

30 

45 

 

 

 
Mineral and vitamin supplement 
0.5 
0.5 
0.5 
0.5 
0.5 
0.5 
0.5 
0.5 
0.5 
0.5 
Crude Protein, g/kg 
180 

140 

196 

160 

160 

PDIE, g/kg 
110 

90 

 

 

 

PDIN, g/kg 
120 

90 

 

 

 

UFL, /kg 
0.95 

0.8 

 

 

 

ME : Metabolisable Energy, kcal/kg 
 

 

2900 

2800 

2900 

DE : Digestible Energy, kcal/kg 
 

 

 

 

 

Lysin, g/Kg 
 

 

9.8 

8.5 

8.6 

Methionin + cystein, g/kg 
 

 

7.5 

6.5 

5.4 

Calcium, g/kg 
10 

10 

9 

33 

9.3 

Phosphorus, g/kg 
6 
 
2.1 
4.1 






PDIN Protein digestible in the intestine when nitrogen is the limiting factor in the rumen ; PDIE : Protein digestible in the intestine when energy the limiting factor in the rumen; UFL: unite fourragère lait (net energy for milk product 
Data analyses
Rresults from the second optimisation were used to establish predictive equations of the MP of substituting raw materials were established using linear and nonlinear regressions procedures. For each raw material, models resulting in the highest correlation coefficient and the lowest residual standard deviations were retained. The used models are presented in table 2.
Table 2. Models used for prediction 

Linear models 
Nonlinear models 
Y = b_{0} + bx + e_{i} Y = b_{0} + b_{1} x_{1} + b_{2} x_{2} +…+ b_{i} x_{i} +e_{i} 
Y = b_{0} + b_{1} x_{1} + b_{2} x_{2} + b_{3}(x_{3})^{2 }+…+ b_{i} (x_{i})^{ p} +e_{i} Y = b_{0} + b_{1} x_{1} + b_{2} 1/x_{1} + b_{3}(x_{3})^{2 }+…+ b_{i} (x_{i})^{ p }+e_{i} Y = b_{0} + b_{1} x_{1} + b_{2} 1/x_{1} + …+ b_{i} x_{i} +e_{i} Y = b_{0} + b_{1} x_{1} + b_{2} 1/x_{1} + b_{3}(x_{3})^{2 }+ ln (x_{1}) +…+ b_{i} (x_{i})^{ p }+e_{i} 
Y = the value of the response; b0 constant of the model; X: value of the variables of prediction; X 1: corn price; X 2: soybean price; X 3: square of corn or soybean price; b_{0}, b_{1}, b_{2} ,bi: estimated variation of the average response Y for every oneunit of the value of the corresponding predictor X (Tomassone et al 1983). 
Results and discussion
The simultaneous increases of the prices of corn and the soybean meal respectively from 168 to 252 DT and 370 to 555 DT, resulted in an increase of the MP of all the alternative raw materials, except manioc, soybean, rapeseed meal and sunflower meal. This result concerns all the studied animal feeds, except layer feed. Only the MP of sorghum, faba bean and soybean varied. This could be explained by the fact that only these raw materials may cover the requirements of this species. The calculation of global correlations for all the concentrates showed that the MP of the sorghum, tritical and fodder wheat are positively correlated to the price of corn (R = 0.45^{***}, R = 0.83^{***}, R = 0.81^{***, } respectively). However, no relationship between the price of soybean and those of sorghum, tritical and fodder wheat were observed. The minimum prices of faba bean, corn gluten feed (CGF), pea and dried distiller grain and soluble (DDGS) are positively correlated with the price of soybean (R = 0.30 ^{***}, R = 0.41 ^{***}, R = 0.52 ^{***}, R = 0.50 ^{***}, respectively), but we didn’t found any relationship between the price of corn and those of faba bean, CGF, pea and dried distiller DDGS. These results confirmed those reported by Grant (1995), leading to differentiate two types of raw materials on the basis of protein or energy, which are respectively very influenced by price variations of soybean and corn.
The increase of corn prices and the decrease of soybean respectively of 10 % and 20% resulted in an increase in the MP of manioc. This latter changed from 100 D/T to 170 D/T and from 150 D/T to190 D/T when corn prices increases by 84 DT and which of soybean decreases by 185 DT. For all the formulated concentrate feeds, the determination of the global correlation indicated that the MP of manioc is positively correlated with which of corn (R = 0.71***) and negatively correlated with which of soybean (R =  0.40***). In the same way, the MP of the sunflower meal increased respectively from 200 to 240 DT and 260 to 300 DT when which of soybean increased by 95 D/T. For the same variations of the MP of sunflower meal, the price of corn decreased by 40 DT. For the rapeseed meal, the MP increases by 50 DT when which of soybean increased from 370 to 460 DT. This price decreased by 10 DT when the price of corn decreased from 231 to 210 D/T. For the oil cakes and soya bean the MP vary in the same trend as the price of the protein row material. The dependence on energetic raw material prices is variable.
A reduction in the various MP of the studied raw materials was observed when the protein rate of the soybean 48 increased by 5% and 10%. This variation depends on the raw materials, it is more important for the protein sources energy ones. Indeed, the MP of CGF remains relatively constant when the protein rate in soybean increased from 45.3% to 46.3%. In contrast, the MP of pea and rapeseed meal increased respectively from 268 DT to 288 DT and from 357 DT to 367 DT for the same variations of the protein rate. These variations could be explained by the nature of the raw material. The CGF is both an energy and nitrogen source; consequently it’s lower dependant on the variations of the protein content in soybean (Schroeder 1997, Becart et al 2000, Blasi et al 2001). While pea and rapeseed meal are protein sources for which the minimum prices and the rate of incorporation depend closely on soybean characteristics. (Prolea 2001, Prolea 2005).
The determination coefficients of the regression models of the substituting raw materials between PM and price variations of corn and soybean vary from 70.1 to 98.2% (Table 3).
Table 3. Prediction equation of MP in broilers according to protein rate variation. 

Raw material 
Equations 
R ^{2}, % 
CGF 
MP = 165  0.224 Pc^{***} + 0.246 Psb^{***} MP = 296  0.224 Pc^{***} + 0.246Psb^{***}  2.83 CP^{*} 
70.1^{***} 70.8^{***} 
pea 
MP = 56.1 + 0.322 Pc^{***} + 0.316 Psb^{***} MP = 207 + 0.322 Pc^{***} + 0.316 Psb^{*** } 3.26 CP^{***} 
94^{***} 95^{***} 
Colza oil cake 
(1’) MP = 90.6  0.150 Pc^{***} + 0.651 Psb^{***} (2’) MP = 330  0.150 Pc^{***} + 0.651 Psb^{*** } 5.18CP^{***} 
97.5^{***} 98.2^{***} 
MP: minimum price; Pc: price of corn, Psb: price of soybean, CP: crude protein. ***: P<0.001 
The linear models used did not allow always the prediction of the MP of the concerned feeds. The quadratic, reciprocal and logarithmic connection forms allowed to better describe the variations of the data and to improve the correlation coefficients in 7,3% of the cases. The analysis of these coefficients indicated that till the significance level of 5% and 1%, respectively 97% and 95% of these coefficients are significant. The high significant correlation coefficients allowed suggesting that the variations of corn and soybean prices could be used as the main predictors of minimum prices in the different substituting raw materials. These different results confirmed those reported by UCAAB (1981), Grasser et al (1995) and Gerfault (2003).
The regression coefficients associated to the predictors are positive and significant for 44.6% of the cases, of opposite sign and significant in 31.1% of the cases, while significant in 24% of the equations. These variations of the sign and the statistical significance are also related to type of the substituting materials (energy or protein source of both of them). These results confirmed those of UCAAB (1981) according to which the variations of the signs of the regression coefficients are dependent on the type of the raw material.
The significance of the regression coefficients depends also on the optimised formula. This may be related to the relative weight of energy or protein constraint in the different formulas, and consequently to concerned animal requirements. Grasser et al (1995) reported similar results.
The regrouping of the prediction equations relative to MP by pool of formulas resulted in an improvement of the significance of the regression coefficients of the models. The determination coefficient (R^{2}) increased averagely by 3%. This could result in a better practical utilisation of the regression models.
Including the protein rate in the prediction equations of the MP of CGF, pea and the rapeseed meel (Table 3) resulted in improved R^{2} of these models. For the MP of CGF, R^{2} increased from 70.1% to 70.8%. In the cases of pea and rapeseed meal, R^{2} increased respectively from 94% to 95% and 97.5% to 98.2%. These results showed that MP of CGF are lower related to the variations of protein rate of soybean oil than which of pea and rapeseed meal. Consequently, the prediction of the MP could be limited only to the variations of minimum prices of corn and soybean for protein and energy sources and those providing simultaneously energy and proteins. Including the variation of protein rate in MP predictingmodels for protein sources could result in improved significance levels in these models.
Validation of the models
In order to be able to use of the previous models for different economic situations of prices, it was seemed necessary to validate them. In connection with this, we established the relations between the minimum prices of the raw materials determined by the regression equations (MP predicted MP) and their real MP calculated by optimization using linear programming method (calculated MP), for prices of corn and soybean meal situated outside of the already studied intervals. This validation was carried out for the concentrate formulas for dairy cows and broilers. The results (Figure 1a, b) showed a highly significant correlation between the calculated MP and predicted ones using the models relative to dairy cows and broilers concentrates.



b) chicken broiler 

Minimum price (equation)
Consequently, it's possible to recommend the use of the established predictive models in economic situations in ranges situated apart from the minimum and the maximum limits of the studied prices for the corn and the soybean meal.
The regression equations relating to these two adjustments are as follows:
 Dairy cows: MP equation = 4.492 + 0.991 MP calculated (R2 = 91.2%)
 Chicken: MP equation = 5.163 + 1.013 MP calculated (R2 = 96.1%)
It should be noted that the precision of the adjustment was better in chicken concentrate.
In the light of the found results, it was concluded that the analysis of the variations of the MP in the different studied raw materials in relation with the variation of the prices of corn and the soybean showed that it is possible to estimate with high precision the minimum prices of the different raw materials according to these two parameters.
Including the variation of the protein rate of soybean in the models of regression resulted mainly in an improvement of their precision for the materials sources of proteins.
The different results obtained varied according to concentrate formula and to concerned animal species. The regrouping of the regression equation by group of species facilitated their practical application while preserving a high level of prediction precision.
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Received 3 August 2008; Accepted 9 October 2008; Published 5 December 2008