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AbstractIn this study, feed formulation software REFS3000 was applied to design dietary formula for blackfeather Muscovy duck at different growth stages, which provided the basic information for dietary combination in further feeding experiment, aiming at improving the targeted feeding level of duck in China.
Key wordsMuscovy duck; Feed formulation software; Dietary formula; Design; Application
Received: September 25, 2018Accepted: December 12, 2018
Kai Zhang (1988- ), female, P. R. China, assistant veterinarian, devoted to disease control and prevention in intensive livestock and poultry farms.
*Corresponding author. Email: [email protected].
At present, there are three common methods for designing dietary formula: Manual trial and error method, Excel method, and feed formulation software method［1］. The manual trial and error method requires cumbersome calculation process in which few feed ingredients and nutritional indicators are considered, and it is difficult to calculate a suitable formula. Excel method requires the operator to be familiar with the solver tool, otherwise there may be no solution. Although feed formulation software is expensive, it is easy to calculate with relatively strong flexibility, and multiple factors can be considered［2］. Since feed formulation software REFS3000 was developed in 1996, it has become the most commonly used feed formula design management system in China. Based on the above analysis, feed formulation software REFS3000 was used for designing dietary formula to obtain the optimal feed composition for blackfeather Muscovy duck at different nutrient levels and at different feeding stages, aiming at providing the basis for further nutrition research and scientific breeding of blackfeather Muscovy duck.
Materials and Methods
Experimental design
Maize, rice bran, wheat bran, soybean meal, cottonseed meal, soybean oil, rock powder, calcium hydrogen phosphate, salt, and 1% premix were selected as feed ingredients to design dietary formula. In nutritional requirement test, metabolic energy (ME), crude protein (CP), calcium (Ca), and available phosphorus (AP) were employed as experimental factors, each of which was set at three levels. On the basis of previous studies, the nutritional goals for blackfeather Muscovy duck at various growth stages were determined. At the first stage (0-21 days of age), metabolic energy levels were 11.52, 11.92 and 12.32 MJ/kg, respectively; crude protein levels were 18%, 20% and 22%, respectively; calcium levels were 0.6%, 0.8% and 1.0%, respectively; available phosphorus levels were 0.30%, 0.45% and 0.60%, respectively. At the second stage (22-42 days of age), metabolic energy levels were 11.92, 12.32 and 12.72 MJ/kg, respectively; crude protein levels were 16%, 18% and 20%, respectively; calcium levels were 0.6%, 0.8% and 1.0%, respectively; available phosphorus levels were 0.30%, 0.45% and 0.60%, respectively. At the third stage (43-91 days of age), metabolic energy levels were 12.32, 12.72 and 13.12 MJ/kg, respectively; crude protein levels were 14%, 16% and 18%, respectively; calcium levels were 0.6%, 0.8% and 1.0%, respectively; available phosphorus levels were 0.30%, 0.45% and 0.60%, respectively. An L9(34) orthogonal array experimental design, consisting of four parameters, each with three levels, was employed to identify nine different nutritional goals for blackfeather Muscovy duck at three growth stages (Table 1). Based on the abovementioned nutritional goals and feed ingredients selected, a total of 27 dietary formulas for blackfeather Muscovy duck at three stages were designed using feed formulation software REFS3000［3］. Design Procedures
Establishing a formula factory
Add a formula factory under the "Formula Factory Management Operation" in "System Management" module, which is named "Blackfeather Muscovy Duck Formula Factory (code: HYFYSLC)", input the factory name, save and exit.
Factory data preparation
Click "Factory Data Preparation" in "Formula Production" module, click "Select the Current Formula Operation Factory", select "Blackfeather Muscovy Duck Formula Factory" which was just input. In the "Copy Factory Formula Data from the System Library" column, copy the variety of feed ingredients used in the factory from the system library according to the feed ingredients selected by the factory. Copy the nutritional standards according to the type of formula required by the factory. For in stance, if the factory needs to produce feed for blackfeather Muscovy duck, the nutritional standards for the duck and the use limit of feed ingredients in each nutritional standard can be copied to the factory library at one time.
Dietary formula design
Click "New Single Formula Design Plan" in "Single Formula Preparation" module, input "Plan Name" (such as "Dietary formula for blackfeather Muscovy duck"), temporarily select "Meattype duckling formula (China)" as the "Nutritional Standard", and click "Confirm". The next window "Plan Management" consists of "Nutritional Standard", "Feed Ingredient", "Feed Ingredient Limit" and "Formula Result". Click "Nutritional Standard", select four nutrients (metabolic energy, crude protein, calcium, and available phosphorus) required for designing the dietary formula in the "Nutrient Name" column in the upperright corner, click "Nutrient Storage", modify the upper and lower limits of each nutrient to make it conform to the designed nutritional goal, and click "Nutritional Standard Storage". In this case, there are 27 kinds of nutritional levels in the formula design for blackfeather Muscovy duck (Table 1), which are selected and modified in turn.
Click the "Feed Ingredient" column in the upperleft corner, click the upperright window to input the ingredients of the formula, click the green arrow between the upperright window and the lower window to transfer feed ingredients to the lower display window, and click "Feed Ingredient Data Storage" to activate the operation. Assume that maize, wheat bran, rice bran, soybean meal, soybean oil, cottonseed meal, rock powder, calcium hydrogen phosphate, salt, and 1% premix are the feed ingredients in the factory, when these feed ingredients are selected, the price and nutritional content will be displayed in the lower part as a table. It is necessary to notice whether the nutrient data of various feed ingredients are consistent with the actual data of the feed ingredients in the factory, and the data should be modified according to the actual content if there are changes. Click the "Feed Ingredient Limit" column in the upperleft corner, set the upper and lower limits of various feed ingredients in the lower window, and click "Feed Ingredient Limit Storage" to activate the operation. For instance, the upper and lower limits of premix in the formula should be set to 1%. However, due to the high price of soybean oil, the formula may not be adopted without setting the lower limit. Operation and output
Click the "Linear Plan Calculation" and "Clear the Last Calculation Result" to complete the operation. The result output report is displayed (Fig. 1).
Table 1Nutritional goals for blackfeather Muscovy duck at various growth stages
Growth stageGroupMetabolic energy∥MJ/kgCrude protein∥%Calcium∥%Available phosphorus∥%
First stage (0-21 days of age)A1 11.5218 0.6 0.30
A2 11.52 20 0.8 0.45
A3 11.52 22 1.0 0.60
A4 11.92 18 0.80.60
A5 11.92 20 1.0 0.30
A6 11.92 22 0.6 0.45
A712.32 18 1.0 0.45
A8 12.3220 0.6 0.60
A9 12.32 22 0.8 0.30
Second stage (22-42 days of age)B1 11.92 16 0.6 0.30
B2 11.92 18 0.8 0.45
B3 11.92 20 1.0 0.60
B4 12.32 16 0.8 0.60
B5 12.32 18 1.0 0.30
B6 12.32 20 0.6 0.45
B7 12.72 16 1.0 0.45
B8 12.72 180.6 0.60
B9 12.72 20 0.8 0.30
Third stage (43-91 days of age)C1 12.32 14 0.6 0.30
C2 12.32 16 0.8 0.45
C3 12.32 18 1.0 0.60
C4 12.72 14 0.8 0.60
C5 12.72 16 1.0 0.30
C6 12.72 180.6 0.45
C713.22 14 1.0 0.45
C813.22 16 0.6 0.60
C9 13.22 18 0.80.30
Results and Analysis
Through the above specific steps, nutritional goals of 27 kinds of diets for blackfeather Muscovy duck at three stages were selected in turn. By using the selected feed ingredients, nine formulas for blackfeather Muscovy duck at various stages were designed (Table 2-Table 4).
Fig. 1Result output of feed formulation
Kai Zhang. Design and Application of Dietary Formula for Muscovy Duck at Different Growth Stages
Table 2Dietary formula for blackfeather Muscovy duck at 0-21 days of age
ItemA1A2A3A4A5A6A7A8A9
Feed compositionMaize∥%43.1253.4249.6448.0155.7250.4059.5340.0047.92
Wheat bran∥%1.001.001.0013.891.001.001.0013.631.00
Rice bran∥%25.976.201.001.001.001.001.001.001.00
Soybean meal∥%20.8529.4636.4422.7530.6636.3025.3024.9436.76
Cottonseed meal∥%5.005.005.005.005.005.005.009.005.00
Soybean oil∥%1.001.002.145.002.522.993.627.674.87
Rock powder∥%0.890.930.930.502.060.401.500.001.47
Calcium hydrogen phosphate∥%0.871.692.552.550.741.611.752.460.68
Salt∥%0.300.300.300.300.300.300.300.300.30
Premix∥%1.001.001.001.001.001.001.001.001.00
Nutritional levelMetabolic energy∥MJ/kg11.5211.5211.5211.9211.9211.9212.3212.3212.32 Crude protein∥%18.0020.0022.0018.0020.0022.0018.0020.0022.00
Calcium∥%0.600.801.000.821.000.621.000.620.80
Available phosphorus∥%0.300.450.600.600.300.450.450.570.30
Table 3Dietary formula for blackfeather Muscovy duck at 22-42 days of age
ItemB1B2B3B4B5B6B7B8B9
Feed compositionMaize∥%58.1862.7854.1166.5560.1954.8864.0041.9650.70
Wheat bran∥%1.001.001.001.001.001.001.0015.032.00
Rice bran∥%14.831.001.001.001.001.001.002.001.00
Soybean meal∥%16.6624.5830.8419.2225.0630.7019.7019.0827.16
Cottonseed meal∥%5.005.005.005.005.005.005.009.009.00
Soybean oil∥%1.001.463.002.573.383.854.479.006.41
Rock powder∥%0.920.940.930.402.070.401.510.001.49
Calcium hydrogen phosphate∥%0.911.742.622.750.811.681.832.430.75
(Continued)
(Table 3)
ItemB1B2B3B4B5B6B7B8B9
Salt∥%0.500.500.500.500.500.500.500.500.50
Premix∥%1.001.001.001.001.001.001.001.001.00
Nutritional levelMetabolic energy∥MJ/kg11.9211.9211.9212.3212.3212.3212.7212.7212.72
Crude protein∥%16.0018.0020.0016.0018.0020.0016.0018.0020.00
Calcium ∥%0.600.801.000.811.000.621.000.620.80
Available phosphorus∥%0.300.450.600.600.300.450.450.570.30
Table 4Dietary formula for blackfeather Muscovy duck at 43-91 days of age
ItemC1 C2 C3 C4 C5 C6 C7 C8 C9
Feed compositionMaize∥%73.25 67.25 58.77 71.03 64.85 59.55 67.55 52.20 52.20
Wheat bran∥%1.001.00 1.00 1.00 1.00 1.00 1.00 10.22 5.00
Rice bran∥%3.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Soybean meal∥%12.3819.1825.4013.8219.4625.1010.3514.6525.40
Cottonseed meal∥%5.095.044.895.055.255.059.059.054.55
Soybean oil∥%1.002.423.763.424.134.606.088.908.00
Rock powder∥%0.950.950.940.401.970.401.620.001.59
Calcium hydrogen phosphate∥%0.941.712.792.830.891.851.902.530.81
Salt∥%0.450.450.450.450.450.450.450.450.45
Premix∥%1.001.001.001.001.001.001.001.001.00
Nutritional levelMetabolic energy∥MJ/kg12.3212.3212.3212.7212.7212.7213.1213.1213.12
Crude protein∥%14.0016.0018.0014.0016.0018.0014.0016.0018.00
Calcium ∥%0.600.801.000.811.000.611.000.620.80
Available phosphorus∥%0.300.450.600.600.300.450.450.570.30
The 27 kinds of diets designed by feed formulation software REFS3000 have reached the expected nutritional levels in Table 1. The contents of metabolic energy, crude protein, calcium and available phosphorus meet the nutritional needs of blackfeather Muscovy duck at 0-21 days of age, 22-42 days of age and 43-91 days of age, respectively. Discussions
The rational use of feed formulation software lies in the establishment of optimized formula model, complete feed ingredient database and outstanding formula design technique. These three factors directly affect the practicality of formulation software and the effectiveness of dietary formula［4］.
Optimizing the dietary formula model
Linear programming and target programming are used for designing dietary formula with feed formulation software REFS3000. Because of the single goal, linear programming has limitations and exhibits low flexibility in dealing with multiple problems at the same time, which may cause lack of solution due to the contradiction between restrictive conditions and actual conditions. In addition, nutritional specifications determine formula cost, whereas it is impossible to determine relatively reasonable nutritional specifications based on requirements of formula cost. Aiming at overcoming the defects of linear programming, target programming has been developed. There is a close relationship between these two methods. Linear programming is not only the basis of target programming, but also a special case. Under the same feed ingredients, nutrients and constraints, linear programming and target programming may lead to the same results.
Most of the solutions of linear programming are singledetermined and strongly adoptive, whereas the results of target programming are often affected by the weight of the target, thus leading to extremely significant changes in the rationality of the solution. Linear programming is easy to learn and easy to use, which has been widely applied, whereas target programming has high requirements for professional knowledge and practical experience, which is difficult to master. Moreover, target programming limits costs in designing formulas, which is a prominent advantage, whereas it is not easy to limits costs in linear programming［4-6］. In the present study, both linear programming and target programming were used, which not only effectively overcomes the unsolvable problem of linear programming, but also ensures the rationality of the dietary formula.
Improving the ingredient database
The construction of a large database is an important symbol of the information age. In order to optimize the local or even national feed resources and promote the scientific production of the livestock industry, it is imperative to establish a perfect database of feed ingredients and nutritional value. The reference value of the feed ingredient database is also an important factor affecting the quality of the formulation result. However, there are remarkable differences in the nutritional value of feed ingredients between different regions. Even feed ingredients from the same source may vary in nutrients due to the influence of multiple factors such as storage processing method. Therefore, data in feed nutritional value table and dietary formula system database are conditional and variable, and it is necessary to take into account the nutrient content in feed ingredients［7］. In the present study, nutrients in feed ingredients such as rice bran and wheat bran were accurately determined before designing dietary formula, to ensure the accuracy and reliability of the data used.
Highlighting the formula design technique
The use limit of feed ingredients should be set reasonably during the designing process of dietary formula. Some ingredients may be used in large quantities, while some other ingredients may not be used. In most cases, this is associated with the set limit of feed ingredients［7］. Feed ingredients without setting an upper use limit can be used in large quantities due to lower prices, whereas some feed ingredients without setting a lower use limit are not used due to higher prices. During the designing process of dietary formula, it is better not to preset the upper and lower use limits of feed ingredients. The upper and lower limits can be set and adjusted as appropriate after obtaining the result of dietary formula.
Cottonseed meal contains antinutritional factors such as free gossypol with unbalanced amino acid composition. Therefore, the addition of cottonseed meal should be limited in livestock and poultry diet. In the present study, the amount of cottonseed meal in dietary formula for blackfeather Muscovy duck is 5%-9%. In addition, the amount of premix and salt can be set to a regular ratio. In the present study, the amount of premix and salt is 1% and 0.5%, respectively. For feed ingredients to be used, the lower use limit should be set. For instance, soybean oil without setting the lower use limit may not be used because of its high price, and excessive use of such ingredients may increase the feed cost［7-8］.
The dietary formula can be adjusted and optimized based on the shadow price. The shadow price of the feed ingredient refers to as the increased cost of dietary formula after increasing the use of a certain ingredient in the formula by one unit. In general, when the shadow price of the feed ingredient is negative or positive, formula cost can be reduced by accordingly increasing or declining the use of the ingredient during the designing process of dietary formula. However, the shadow price of each ingredient is not fixed during the designing process. When there are changes in the price, nutrient content, use limit and nutritional goal of each ingredient involved in the designing of dietary formula, the shadow price of various ingredients may also vary［9］. References
［1］ ZHOU M. Capriccio during feed formula design［J］. Feed Industry, 2016, 37(16):1-5.(in Chinese)
［2］ DING YF. Making feed formulation checking table using EXCEL［J］. China Animal Industry, 2016, (2):73-74.(in Chinese)
［3］ ZHANG YY, HE X, LIU GM, et al. Parallel design with multipleformulas: A new method of formulating diets for livestock and poultry［J］. Acta Zoonutrimenta Sinica, 2016, 28(7):2191-2203.(in Chinese)
［4］ LIU JB, LIU GL, DONG WC, et al. A summary of feed formulation software in dairy cows［J］. China Dairy Cattle, 2014(8):54-57.(in Chinese)
［5］ ZHU L, SUN L. Comparison of stochastic programming and linear programming application in animal feed formulation［J］. Journal of Anhui Agricultural Sciences, 2006, 34(9): 1778-1779, 1784.(in Chinese)
［6］ LIU GL, SUN J, WANG BW. Computer feed formulation technique［J］. Shandong Poultry, 2004, (12):38-39.(in Chinese)
［7］ HUANG CH, GUO DS. Problems and solutions in feed formulation designed by professional formula software［J］. Journal of Anhui Agricultural Sciences, 2012, 40(5):2706-2707.(in Chinese)
［8］ LIU SJ, CHEN JS, YAO K, et al. Nutritional composition of cottonseed meal and its application in poultry and animal production［J］. Animal Husbandry and Feed Science, 2016, 37(9):45-49.(in Chinese)
［9］ WANG JH, DONG EQ. Shadow price in feed formulation design［J］. Swine Industry Science, 2012, 29(12):44-47.(in Chinese)
Key wordsMuscovy duck; Feed formulation software; Dietary formula; Design; Application
Received: September 25, 2018Accepted: December 12, 2018
Kai Zhang (1988- ), female, P. R. China, assistant veterinarian, devoted to disease control and prevention in intensive livestock and poultry farms.
*Corresponding author. Email: [email protected].
At present, there are three common methods for designing dietary formula: Manual trial and error method, Excel method, and feed formulation software method［1］. The manual trial and error method requires cumbersome calculation process in which few feed ingredients and nutritional indicators are considered, and it is difficult to calculate a suitable formula. Excel method requires the operator to be familiar with the solver tool, otherwise there may be no solution. Although feed formulation software is expensive, it is easy to calculate with relatively strong flexibility, and multiple factors can be considered［2］. Since feed formulation software REFS3000 was developed in 1996, it has become the most commonly used feed formula design management system in China. Based on the above analysis, feed formulation software REFS3000 was used for designing dietary formula to obtain the optimal feed composition for blackfeather Muscovy duck at different nutrient levels and at different feeding stages, aiming at providing the basis for further nutrition research and scientific breeding of blackfeather Muscovy duck.
Materials and Methods
Experimental design
Maize, rice bran, wheat bran, soybean meal, cottonseed meal, soybean oil, rock powder, calcium hydrogen phosphate, salt, and 1% premix were selected as feed ingredients to design dietary formula. In nutritional requirement test, metabolic energy (ME), crude protein (CP), calcium (Ca), and available phosphorus (AP) were employed as experimental factors, each of which was set at three levels. On the basis of previous studies, the nutritional goals for blackfeather Muscovy duck at various growth stages were determined. At the first stage (0-21 days of age), metabolic energy levels were 11.52, 11.92 and 12.32 MJ/kg, respectively; crude protein levels were 18%, 20% and 22%, respectively; calcium levels were 0.6%, 0.8% and 1.0%, respectively; available phosphorus levels were 0.30%, 0.45% and 0.60%, respectively. At the second stage (22-42 days of age), metabolic energy levels were 11.92, 12.32 and 12.72 MJ/kg, respectively; crude protein levels were 16%, 18% and 20%, respectively; calcium levels were 0.6%, 0.8% and 1.0%, respectively; available phosphorus levels were 0.30%, 0.45% and 0.60%, respectively. At the third stage (43-91 days of age), metabolic energy levels were 12.32, 12.72 and 13.12 MJ/kg, respectively; crude protein levels were 14%, 16% and 18%, respectively; calcium levels were 0.6%, 0.8% and 1.0%, respectively; available phosphorus levels were 0.30%, 0.45% and 0.60%, respectively. An L9(34) orthogonal array experimental design, consisting of four parameters, each with three levels, was employed to identify nine different nutritional goals for blackfeather Muscovy duck at three growth stages (Table 1). Based on the abovementioned nutritional goals and feed ingredients selected, a total of 27 dietary formulas for blackfeather Muscovy duck at three stages were designed using feed formulation software REFS3000［3］. Design Procedures
Establishing a formula factory
Add a formula factory under the "Formula Factory Management Operation" in "System Management" module, which is named "Blackfeather Muscovy Duck Formula Factory (code: HYFYSLC)", input the factory name, save and exit.
Factory data preparation
Click "Factory Data Preparation" in "Formula Production" module, click "Select the Current Formula Operation Factory", select "Blackfeather Muscovy Duck Formula Factory" which was just input. In the "Copy Factory Formula Data from the System Library" column, copy the variety of feed ingredients used in the factory from the system library according to the feed ingredients selected by the factory. Copy the nutritional standards according to the type of formula required by the factory. For in stance, if the factory needs to produce feed for blackfeather Muscovy duck, the nutritional standards for the duck and the use limit of feed ingredients in each nutritional standard can be copied to the factory library at one time.
Dietary formula design
Click "New Single Formula Design Plan" in "Single Formula Preparation" module, input "Plan Name" (such as "Dietary formula for blackfeather Muscovy duck"), temporarily select "Meattype duckling formula (China)" as the "Nutritional Standard", and click "Confirm". The next window "Plan Management" consists of "Nutritional Standard", "Feed Ingredient", "Feed Ingredient Limit" and "Formula Result". Click "Nutritional Standard", select four nutrients (metabolic energy, crude protein, calcium, and available phosphorus) required for designing the dietary formula in the "Nutrient Name" column in the upperright corner, click "Nutrient Storage", modify the upper and lower limits of each nutrient to make it conform to the designed nutritional goal, and click "Nutritional Standard Storage". In this case, there are 27 kinds of nutritional levels in the formula design for blackfeather Muscovy duck (Table 1), which are selected and modified in turn.
Click the "Feed Ingredient" column in the upperleft corner, click the upperright window to input the ingredients of the formula, click the green arrow between the upperright window and the lower window to transfer feed ingredients to the lower display window, and click "Feed Ingredient Data Storage" to activate the operation. Assume that maize, wheat bran, rice bran, soybean meal, soybean oil, cottonseed meal, rock powder, calcium hydrogen phosphate, salt, and 1% premix are the feed ingredients in the factory, when these feed ingredients are selected, the price and nutritional content will be displayed in the lower part as a table. It is necessary to notice whether the nutrient data of various feed ingredients are consistent with the actual data of the feed ingredients in the factory, and the data should be modified according to the actual content if there are changes. Click the "Feed Ingredient Limit" column in the upperleft corner, set the upper and lower limits of various feed ingredients in the lower window, and click "Feed Ingredient Limit Storage" to activate the operation. For instance, the upper and lower limits of premix in the formula should be set to 1%. However, due to the high price of soybean oil, the formula may not be adopted without setting the lower limit. Operation and output
Click the "Linear Plan Calculation" and "Clear the Last Calculation Result" to complete the operation. The result output report is displayed (Fig. 1).
Table 1Nutritional goals for blackfeather Muscovy duck at various growth stages
Growth stageGroupMetabolic energy∥MJ/kgCrude protein∥%Calcium∥%Available phosphorus∥%
First stage (0-21 days of age)A1 11.5218 0.6 0.30
A2 11.52 20 0.8 0.45
A3 11.52 22 1.0 0.60
A4 11.92 18 0.80.60
A5 11.92 20 1.0 0.30
A6 11.92 22 0.6 0.45
A712.32 18 1.0 0.45
A8 12.3220 0.6 0.60
A9 12.32 22 0.8 0.30
Second stage (22-42 days of age)B1 11.92 16 0.6 0.30
B2 11.92 18 0.8 0.45
B3 11.92 20 1.0 0.60
B4 12.32 16 0.8 0.60
B5 12.32 18 1.0 0.30
B6 12.32 20 0.6 0.45
B7 12.72 16 1.0 0.45
B8 12.72 180.6 0.60
B9 12.72 20 0.8 0.30
Third stage (43-91 days of age)C1 12.32 14 0.6 0.30
C2 12.32 16 0.8 0.45
C3 12.32 18 1.0 0.60
C4 12.72 14 0.8 0.60
C5 12.72 16 1.0 0.30
C6 12.72 180.6 0.45
C713.22 14 1.0 0.45
C813.22 16 0.6 0.60
C9 13.22 18 0.80.30
Results and Analysis
Through the above specific steps, nutritional goals of 27 kinds of diets for blackfeather Muscovy duck at three stages were selected in turn. By using the selected feed ingredients, nine formulas for blackfeather Muscovy duck at various stages were designed (Table 2-Table 4).
Fig. 1Result output of feed formulation
Kai Zhang. Design and Application of Dietary Formula for Muscovy Duck at Different Growth Stages
Table 2Dietary formula for blackfeather Muscovy duck at 0-21 days of age
ItemA1A2A3A4A5A6A7A8A9
Feed compositionMaize∥%43.1253.4249.6448.0155.7250.4059.5340.0047.92
Wheat bran∥%1.001.001.0013.891.001.001.0013.631.00
Rice bran∥%25.976.201.001.001.001.001.001.001.00
Soybean meal∥%20.8529.4636.4422.7530.6636.3025.3024.9436.76
Cottonseed meal∥%5.005.005.005.005.005.005.009.005.00
Soybean oil∥%1.001.002.145.002.522.993.627.674.87
Rock powder∥%0.890.930.930.502.060.401.500.001.47
Calcium hydrogen phosphate∥%0.871.692.552.550.741.611.752.460.68
Salt∥%0.300.300.300.300.300.300.300.300.30
Premix∥%1.001.001.001.001.001.001.001.001.00
Nutritional levelMetabolic energy∥MJ/kg11.5211.5211.5211.9211.9211.9212.3212.3212.32 Crude protein∥%18.0020.0022.0018.0020.0022.0018.0020.0022.00
Calcium∥%0.600.801.000.821.000.621.000.620.80
Available phosphorus∥%0.300.450.600.600.300.450.450.570.30
Table 3Dietary formula for blackfeather Muscovy duck at 22-42 days of age
ItemB1B2B3B4B5B6B7B8B9
Feed compositionMaize∥%58.1862.7854.1166.5560.1954.8864.0041.9650.70
Wheat bran∥%1.001.001.001.001.001.001.0015.032.00
Rice bran∥%14.831.001.001.001.001.001.002.001.00
Soybean meal∥%16.6624.5830.8419.2225.0630.7019.7019.0827.16
Cottonseed meal∥%5.005.005.005.005.005.005.009.009.00
Soybean oil∥%1.001.463.002.573.383.854.479.006.41
Rock powder∥%0.920.940.930.402.070.401.510.001.49
Calcium hydrogen phosphate∥%0.911.742.622.750.811.681.832.430.75
(Continued)
(Table 3)
ItemB1B2B3B4B5B6B7B8B9
Salt∥%0.500.500.500.500.500.500.500.500.50
Premix∥%1.001.001.001.001.001.001.001.001.00
Nutritional levelMetabolic energy∥MJ/kg11.9211.9211.9212.3212.3212.3212.7212.7212.72
Crude protein∥%16.0018.0020.0016.0018.0020.0016.0018.0020.00
Calcium ∥%0.600.801.000.811.000.621.000.620.80
Available phosphorus∥%0.300.450.600.600.300.450.450.570.30
Table 4Dietary formula for blackfeather Muscovy duck at 43-91 days of age
ItemC1 C2 C3 C4 C5 C6 C7 C8 C9
Feed compositionMaize∥%73.25 67.25 58.77 71.03 64.85 59.55 67.55 52.20 52.20
Wheat bran∥%1.001.00 1.00 1.00 1.00 1.00 1.00 10.22 5.00
Rice bran∥%3.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Soybean meal∥%12.3819.1825.4013.8219.4625.1010.3514.6525.40
Cottonseed meal∥%5.095.044.895.055.255.059.059.054.55
Soybean oil∥%1.002.423.763.424.134.606.088.908.00
Rock powder∥%0.950.950.940.401.970.401.620.001.59
Calcium hydrogen phosphate∥%0.941.712.792.830.891.851.902.530.81
Salt∥%0.450.450.450.450.450.450.450.450.45
Premix∥%1.001.001.001.001.001.001.001.001.00
Nutritional levelMetabolic energy∥MJ/kg12.3212.3212.3212.7212.7212.7213.1213.1213.12
Crude protein∥%14.0016.0018.0014.0016.0018.0014.0016.0018.00
Calcium ∥%0.600.801.000.811.000.611.000.620.80
Available phosphorus∥%0.300.450.600.600.300.450.450.570.30
The 27 kinds of diets designed by feed formulation software REFS3000 have reached the expected nutritional levels in Table 1. The contents of metabolic energy, crude protein, calcium and available phosphorus meet the nutritional needs of blackfeather Muscovy duck at 0-21 days of age, 22-42 days of age and 43-91 days of age, respectively. Discussions
The rational use of feed formulation software lies in the establishment of optimized formula model, complete feed ingredient database and outstanding formula design technique. These three factors directly affect the practicality of formulation software and the effectiveness of dietary formula［4］.
Optimizing the dietary formula model
Linear programming and target programming are used for designing dietary formula with feed formulation software REFS3000. Because of the single goal, linear programming has limitations and exhibits low flexibility in dealing with multiple problems at the same time, which may cause lack of solution due to the contradiction between restrictive conditions and actual conditions. In addition, nutritional specifications determine formula cost, whereas it is impossible to determine relatively reasonable nutritional specifications based on requirements of formula cost. Aiming at overcoming the defects of linear programming, target programming has been developed. There is a close relationship between these two methods. Linear programming is not only the basis of target programming, but also a special case. Under the same feed ingredients, nutrients and constraints, linear programming and target programming may lead to the same results.
Most of the solutions of linear programming are singledetermined and strongly adoptive, whereas the results of target programming are often affected by the weight of the target, thus leading to extremely significant changes in the rationality of the solution. Linear programming is easy to learn and easy to use, which has been widely applied, whereas target programming has high requirements for professional knowledge and practical experience, which is difficult to master. Moreover, target programming limits costs in designing formulas, which is a prominent advantage, whereas it is not easy to limits costs in linear programming［4-6］. In the present study, both linear programming and target programming were used, which not only effectively overcomes the unsolvable problem of linear programming, but also ensures the rationality of the dietary formula.
Improving the ingredient database
The construction of a large database is an important symbol of the information age. In order to optimize the local or even national feed resources and promote the scientific production of the livestock industry, it is imperative to establish a perfect database of feed ingredients and nutritional value. The reference value of the feed ingredient database is also an important factor affecting the quality of the formulation result. However, there are remarkable differences in the nutritional value of feed ingredients between different regions. Even feed ingredients from the same source may vary in nutrients due to the influence of multiple factors such as storage processing method. Therefore, data in feed nutritional value table and dietary formula system database are conditional and variable, and it is necessary to take into account the nutrient content in feed ingredients［7］. In the present study, nutrients in feed ingredients such as rice bran and wheat bran were accurately determined before designing dietary formula, to ensure the accuracy and reliability of the data used.
Highlighting the formula design technique
The use limit of feed ingredients should be set reasonably during the designing process of dietary formula. Some ingredients may be used in large quantities, while some other ingredients may not be used. In most cases, this is associated with the set limit of feed ingredients［7］. Feed ingredients without setting an upper use limit can be used in large quantities due to lower prices, whereas some feed ingredients without setting a lower use limit are not used due to higher prices. During the designing process of dietary formula, it is better not to preset the upper and lower use limits of feed ingredients. The upper and lower limits can be set and adjusted as appropriate after obtaining the result of dietary formula.
Cottonseed meal contains antinutritional factors such as free gossypol with unbalanced amino acid composition. Therefore, the addition of cottonseed meal should be limited in livestock and poultry diet. In the present study, the amount of cottonseed meal in dietary formula for blackfeather Muscovy duck is 5%-9%. In addition, the amount of premix and salt can be set to a regular ratio. In the present study, the amount of premix and salt is 1% and 0.5%, respectively. For feed ingredients to be used, the lower use limit should be set. For instance, soybean oil without setting the lower use limit may not be used because of its high price, and excessive use of such ingredients may increase the feed cost［7-8］.
The dietary formula can be adjusted and optimized based on the shadow price. The shadow price of the feed ingredient refers to as the increased cost of dietary formula after increasing the use of a certain ingredient in the formula by one unit. In general, when the shadow price of the feed ingredient is negative or positive, formula cost can be reduced by accordingly increasing or declining the use of the ingredient during the designing process of dietary formula. However, the shadow price of each ingredient is not fixed during the designing process. When there are changes in the price, nutrient content, use limit and nutritional goal of each ingredient involved in the designing of dietary formula, the shadow price of various ingredients may also vary［9］. References
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