CHAPTER THREE:
FISH FEED FORMULATION

mohammed, chado isah

3.1        GENERAL INTRODUCTIONS

The quality of fish feed used in fish production have high effect on the quality of fish product. How cheap one is able to produce the fish feed will give both the feed producer and fish producer a better maximum economic return (MER), which may be passed on to the consumers (users) or added to the ‘personal effort’ when calculating the economic return. The nutritionists have been concerned with development of feed that result in better growth and food conversion factor. Now the attention is on least cost and the next target would be how to improve the organoleptic properties of the product.

Feed formulation is the calculation for the combination ratio of feed ingredient to meet the specification of targeted feed to be consumed. The ingredients and their composition are represented by two letter e.g. rice bran (RB), maize germ (MG), fish meal (FM), soybean meal (SM), wheat middling (WM), CP for crude protein etc. and the content of nutrients are represented as percentage or gram per weight (i.e. numeric symbols). From the calculation (i.e. formulation) the ratio of combination is known to meet the constraints. This may include crude protein, energy, percentage amino acids, lipid content, percentage fatty acid, percentage mineral and vitamin, total fiber content etc. Thus feed formulation can be defined as a mathematical modeling where letters represent names and numerical figures represent content of feed ingredients and feed to be composed. There has been evolution of method used in feed formulation due to the variation in the interest of the feed user. Pearson’s square, is an arithmetic method first used which was developed into Trial and Error and to Equational method to take care of more than two specifications (Sadiku, 2001). To meet the multi constraint feed requirement and give cost a place, many constraints are considered, giving rise to many equations and many ingredients are required giving rise to many variables (unknowns). These two factors makes the equation generation too many and so lengthy thereby consuming much time when the equation method is to be used.


 

3.2        TECNIQUES OF FEED FORMULATION

There are four conventional methods used for feed formulation, (1) Pearson (2) Trial and Error (3) Equational methods. (Algebraic method) (4)Linear programming (Computer software)

3.2.1   PEARSON SQUARE FORMULATION

Pearson square uses Arithmetic ‘trick’ to formulate feed. This trick is equivalent to quantitative aptitude. For example to formulate 30% crude protein using maize germ and cottonseed is as follow: maize germ meal  20% crude protein and cottonseed meal 54% crude protein are available to formulate a 30% crude protein supplement feed.

Example 1:

Cottonseed 54%                                     30-20=10/(10+24) x 100%=29.41

 

Maize germ 20%                                    54-30=24/(10+24) x 100%=70.59

 

That is 29.41% cottonseed + 70.59% maize germ would give 30% crude protein diet.

For more than two protein sources, Pearson Square cannot give the actual amount of each ingredient required because the ingredients have to be grouped into two, those with crude protein greater than 30% and those with crude less than 30%. For example: using soybean meal 48%crude protein, cottonseed meal 54% crude protein, maize meal 20% crude protein and rice polishing 14% crude protein to formulate 30% crude diet. The ingredients have to be premixed so as to have just two components before they can be used in Pearson method. At the end, the percentage required for each group is known. The other problem of this Square method is that it cannot solve for more than one specification likes protein, lipid and energy.

Example 2:

Formulation of 30% crude diet using soybean meal 48%crude protein, cottonseed meal 54% crude protein, maize meal 20% crude protein and rice polishing 14% crude protein.

Premix of ingredients 50/50, w/w

Soybean meal and Cottonseed meal 51% crude protein

Maize meal and rice polishing 17% crude protein

Soybean+Cottonseed 51%                                     30-17=13/(13+21) x 100%=38.24%

 

Maize meal+rice polishing 17%                             51-30=21/(13+21) x 100%=61.76%

Thus, 38.24% Soybean and Cottonseed + 61.76% Maize meal+Rice polishing would give 30% crude protein diet.

3.2.2   THE TRIAL AND ERROR METHOD

New (1987) developed the Pearson Square method into Trial-and-error method e.g. to formulate a diet 26% crude protein and 7%lipid from fish meal, groundnut, maize and soybean using table 3.1 as ingredient file.

Table 3.1 Ingredient file to formulate 26% crude protein and 7% lipid.

Ingredients name

Lipid content

Protein

Cost (N)

Fish Meal

6.0

55.0

600

Groundnut

13.7

34.5

350

Soybean Meal

1.3

46.8

490

Rice Bran

2.4

13.3

150

Maize Germ

4.5

9.8

180

Source: Modified from New (1987)

If we assumed that experiment set a minimum fish meal level of 10% supplying 0.6% lipid, 5.5% protein and costing N60 per t. Thus, we need two other feed stuff, one high in protein and one low in protein level. Since square can solve for one specification, Square is used to solve protein and lipid levels are calculated for all possible combination of the remaining ingredients.

As fish meal contributes 5.5% protein, we will have 26% -5.5% to find from 90% of the diet. Therefore what we are looking for now is 90% diet having 20.5%X (100/90) = 22.78% protein.

Square for each possible 2 ingredient combination are:

a.       Soybean 46.8                                                   13/(13+24) x 100=35.1x90/100=31.62%

                                             22.8

Maize germ 9.8                                               24/(13+24) x 100=64.9 x90/100=58.38%

 

b.      Soybean 46.8                                                  9.5/(9.5+24) x 100=28.36x90/100=25.52%

      22.8

Rice 13.3                                                        24/(9.5+24) x 100=71.64 x90/100=64.48%

 

c.       Groundnut 34.5                                              13/(13+11.7) x 100=52.6x90/100=47.37%

     22.8

Maize germ 9.8                                              11.7/(11.7+13) x 100=47.4x90/100=42.63%

 

d.      Groundnut 34.5                                                     9.5/(9.5+11.7) x 100=44.8 x90/100=40.3%

    22.8

Rice 13.3                                                       11.7/(9.5+11.7) x 100=55.2 x90/100=49.7%

Each of these protein base calculations matches up the desired lipid level and their effect on prize can be checked in the diet formulation worksheet in table 3.2 below

Table 3.2 : Diet formulation worksheet

 

Ingredient

Inclusion

rate

Inclusion

cost (Nt-1)

Lipid

contribution

Protein

contribution

A

Fish meal

10.00

60.00

0.60

5.50

Maize meal

58.40

105.12

2.63

5.72

Soybean meal

31.60

154.84

0.41

14.79

 

100.00

319.96

03.64

26.01

B

Fish meal

10.00

60.00

0.60

5.50

Rice meal

64.50

96.75

1.55

8.58

Soybean meal

25.50

124.95

0.61

11.93

 

100.00

281.70

2.76

26.01

C

Fish meal

10.00

60.00

0.60

5.50

Maize meal

42.60

76.68

1.92

4.17

Groundnut meal

47.40

165.90

6.49

16.35

 

100.00

302.58

9.01

26.03

D

Fish meal

10.00

60.00

0.60

5.50

Rice meal

49.70

74.55

1.19

6.61

Groundnut meal

40.30

141.05

5.52

13.90

 

100.00

275.60

7.31

26.01

The Trial and Error is a technique in which all the possible formulations are worked out and the one that is most preferred is selected. In this case, the requirements 7% lipid, 26% protein and cost of ingredients were considered. The last formulation is closest to the requirements and accidentally the cheapest, costing N275.60, having 7.31% lipid and 26.01% protein.

The problems of this method include choice of ingredient to be used, the requirements are not accurately met, all possible combinations must be worked out one after the other and least cost may be arrived at, accidentally.

Formulation by Trial and Error is time consuming and less precise which does not fit into the current situation in which formulation is a frequent exercise because of factors that affect fish feed requirements, which does not give room for resource wasting as a result of Trial and Error technique.

3.2.3   EQUATIONAL METHOD

It has not been understood that there is a linear relationship between mixing of ingredients to meet the targeted requirement. Thus, the limited reliability of Trial and Error method while formulating for more than one specification has led to the search for a definite method with 100 percent degree of precision, where all the specification are met. In addition, all the possible and impossible combination of ingredients that ordinarily are not visible as in Pearson Square and cannot be conjured by mere mental arithmetic can be arrive at through algebraic methods. Sadiku (2000) concluded that this is a great advancement in feed formulation-a major break through such that formulation becomes a matter of mere imagination.

The number of equations generated is equal to the number of specifications and the number of unknown equals number of ingredients. For two specifications using two ingredient, a simple simultaneous equation with two unknown is desired. For three specifications with three ingredients, a set of three simultaneous equations with three unknown is desired and so on. For example: To formulate a 100g diet of 30% crude protein and 300kcalg-1 energy from soybean meal, wheat middling and fish oil using table 3.3 as ingredient file.

Table 3.3 Ingredient file for formulating 30% crude protein and 300kcalg-1 energy diet.

Ingredient

Percent crude protein

Energy kcalg-1

Soybean meal

48.00

3.22

Wheat middling

17.00

1.67

Fish oil

0.00

8.0

Source: Sadiku (2000)

Computation file for formulating 30% protein and 300kcalg-1 energy diet

SM + WM + FO = 100……………………………….equation 1

0.48SM + 0.1WM + 0FO = 30………………………equation 2

3.22SM + 1.6WM + 8.00FO = 300…………………..equation 3

Solve equation1          and     equation3

SM+WM+FO=100…………..equation1

3.22SM + 1.67WM + 8.00FO=300……………….equation.3

To eliminate FO then multiply 8.00 by                       equation1

8.00SM + 8.00WM + 8.00FO=800…………equation4

3.22SM + 1.67WM + 8.00FO=300……….equation3

4.78SM + 6.33WM + 0=500

Subtract                    equation3   from         equation4

4.78SM + 6.33WM + 0=500………….equation5

Solve       quation2      and          equation 5

0.48SM + 0.17WM=30…….equation 2

4.78SM + 6.33WM=500…….equation 5

To eliminate SM multiply equation2   by       4.78 and         equation5        by 0.48

2.29SM + 0.81WM = 143                   …………….equation6

2.29SM + 3.04WM = 240                   …………….equation7

Subtract equation 7fro equation6

         -2.23WM= -97               …………….equation 8

Divide the both side by -2.23

WM = -2.23/-2.23 -97/-2.23=

WM =43.5

Substitute value of WM in   equation2

0.48SM + 0.17(43.5) + 0FO=30

0.48SM + 7.4 = 30

0.48SM = 30-7.4 = 22.6

0.48SM = 22.6

SM = 22.6/0.48 = 47.08

SM = 47.08

Insert value of SM & WM in   equation3

3.22(47.08) + 1.67(43.5) + 8FO = 300

151.6 + 72.65 + 8FO = 300

224.25 + 8FO = 300

8FO = 300 - 224.25

8FO = 75.75

FO = 75.75/8 = 9.47

Table: 4 production file for formulation of 30% crude protein and 300kcal energy diet.

Ingredient

*Including rate

%Crude protein

**Crude protein contribution

Energy (Kcal/g)

**Energy Contribution (kcal/g)

Soybean

47.08

48.8

23

3.22

151.6

Wheat

43.50

17.0

7

1.67

72.6

Fish

9.47

0.0

0

8.00

75.8

 

100

 

30

 

300.00

Key      *Calculated                         **Checked

The problem with this technique is that it does not optimize and cannot take more than 3 equation, 3 unknowns.