Mathematical Model for Pigs Nutrition

Transcription

1 Bulletin UASVM Animal Science and Biotechnologies, 66 (1-)/009 int ISSN ; Electronic ISSN X Mathematical Model for Pigs Nutrition Radu BURLACU Faculty of Engineering and Land Improvement Environment, University of Agronomic Science and Veterinary Medicine, 59 Marasesti Bv., Bucharest, Romania; Abstract. The paper presents a mathematical model to calculate the energy and protein requirements of the growing and fattening pigs. I used the functions and parameters cited in the literature (Whittemore, 199; Kyriazakis and Emmans, 199), as well as own experimental results (Burlacu et al., 1996). Based on this model, the paper also presents a procedure to calculate the diet formulations. Keywords: mathematical modelling, Gompertz-type equation, metabolisable energy, pigs nutrition NORMS FOR GROWING AND FATTENING PIGS A) Evaluation of the body weight and body chemical composition The body weight [kg], function of the age, is calculated with a Gompertz-type equation: B t-t x e G = A e [kg] (1) where: A = body weight at maturity B = growth coefficient t = age in days t x = inflexion point, i.e. the time in days when imum gain is achieved The net weight, Gn can be estimated with the formula: Gn = G/1,05 [kg] () and the net weight gain Gn is the sum of (retained protein), (retrained lipids), Cen r (retained ash) and Ar (retained water). The values of, were calculated with the following formula: Pt = B Pt In [kg] () Pt where Pt, kg is given by the formula: B t-t x e Pt = Pt ˆ e [kg] (4) The daily lipid gain was calculated from / ratio. = / [kg] (5) where / has been calculated differently for the males, females and castrated pigs, according to their age (Burlacu et al., 1996):

2 For growing boars: -0,95-0,088t + 0,00086t -0, t + 0, t / = e (6) For gilts: -,6+ 0,08t -0,0014t + 0, t 4-0, t + 0, t / = e (7) For the castrated pigs: -,074+ 0,0664t -0,00117t + 0, t 4 + 0, t + 0, t / = e (8) where The daily retained water and ash () are calculated with the formula: Ar Cenr = + [kg] (9) has the following values: For growing boars and castrated pigs: = e For gilts: = 7,4 e,79 0,044t + 0,00041t 0, t t 10,70 + 4,154 e t 744,84 (10) (11) The net weight Gn, ([Kg] at the age t + 1) = Gn + ( Gn at moment t), where initial t = 5 days, and initial Gn = 9.5 Kg for all sexes and categories. B) Estimation of EM norms EM = EMm + E + E + Q' [MJ/day] (1) For the calculation of: EMm = requirement of metabolisable energy for maintenance [MJ/day] E = requirement of metabolisable energy for body protein synthesis [MJ/ day] E = requirement of metabolisable energy for body lipids synthesis [MJ/ day] The following formlas are to be used: 0,75 EMm = 1,75 Pt [MJ/ day] (1) E = 54,6 [MJ/ day] (14) E = 5,, [MJ/ day] (15) where: (lipid gain in kg.) = C) Estimation of the norms for available protein and limiting amino acids = Pm + : 0.81 [kg] (16) where: Pm (net protein for maintenance) Pm = 0,04 x Pt, [kg] (17) P r = gain of body protein [kg] 0.81 is the output of use for 6

3 - requirement of lysine = x 70, [g] (18) - requirement of met. + cys. = x 40, [g] (19) - requirement of triptophan = x 15, [g] (0) - requirement of threonine = x 45, [g] (1) RTICULAR CASES OF DIET CALCULATION We are often confronted in practice with situations when feeding is limited. In this situation (restricted feeding) we use a different way of calculation; following is the procedure for energy and amino acid requirement calculation: Input data: Body age: G [kg] Average daily gain: G [kg] Age: t [days] Parameters: B, Pt,, t * - with the values and significance shown above. Stage I: Calculation of the requirement for metabolisable energy and protein corresponding to the minimal / ratio. The value of b min =a + - t-c 1+ e d min ratio was calculated on the basis of the experimental results: where for the castrated pigs we used the values: a = 0.677; b = 1.95; c = 148; d =.6 The amount of retained protein is given in this case by: G = [kg] 1,05 1+ min + where: G - average daily gain [kg] Ar +Cenr The above formulas are to be used for Pt, Pm,, EMm, E,, E, EM, LizD, M+CD, TRID, TREONINAD. REMARK 1: Obviously, the important measures in determining the requirement of energy and protein, with this system of calculation, are: the metabolisable energy EM and the available protein. The two stages of calculation presented above show one more fact, maybe striking at first sight, but perfectly justified physiologically: for restricted feeding and weight gains lower than the imal ones the existence of variable values for / ratio. min; Involves the existence of norms belonging to intervals: EM [ EMmin; EM ] [ ; ] min () 6

4 In other words, for a fixed daily weight gain, for each value of norm of energy and protein. The graphic presentation of Observation 1 is as follows: there is a distinct G - fixed A min B EM EM min EM Fig. 1 Any pair EM, from segment AB represent pertinent values allowing achieving the set weight gain. Obviously, each time the quality indicator given by the / ratio will be different. REMARK : It may be readily observed that the protein norms evaluated with the system presented here eliminate the value of the digestible protein. However, diet optimization involves the essential use of an equation with PBD (digestible crude protein). The connection between PBD and is given by the biological value of the diet: VB = PBD =, 0 < VB < 1 PBD VB As VB can not be known beforehand, it results that the norm of PBD depends on the nature and structure of the raw diet ingredients; since the value of PBD is no longer unique, it can no longer be used traditionally in the tables of norms even though diet optimisation is still done at the level of the digestible nutrients. Stage II. Calculation of the requirement for metabolisable energy and protein, corresponding to the imal / ratio. We calculate the imum intake of metabolisable energy: G EM = - 0, e [MJ] We calculate the imum amount of retained protein with the formula: Pt = B Pt ln Pt 64

5 With the formula E = 54,6 [MJ/day] we compute the energy required to retain the protein corresponding to. We calculate the energy required to retain the lipids: E = EM - EM - E - Q, [MJ] m Hence the imal amount of retained lipids: E = [kg] 5, Thus, we obtained the imal ratio retained lipids to retained protein: = Further, we use the same procedure as in stage I starting with the calculation of inclusive. Figure shows the dependence of PBD requirement function of the biological value of the diet. - given PBD C PBD min D VB VB VB min Fig. Figure shows the dependence of PBD requirement function of the available protein. PBD PBD O P N PBD min M min Fig. 65

6 Figure 4 shows the relation between EM and PBD. PBD E G - fixed H F VB min G VB PBD EM EM min EM parameters Fig. 4 Any point on EFGH trapezium is a norm expressed in EM, PBD for the set G. The existence of an area EFGH for the requirement of EM and PBD is due to the two min, and VB [VBmin, VB]. REMARK : For simplification, the tables may show the average values for EM and (and therefore for the amino acids too). EM + EM min EM = tabel tabel = + min REFERENCES 1. Burlacu Gh., Burlacu R., Cavache A, (00). PotenŃialul productiv al nutreńurilor şi utilizarea lor. Bucureşti: Editura CERES.. Kyriazakis J., G.C. Emmans (199). The effects of varying protein and energy intakes on the growth and body composition of pigs British J. Nutr. 68(0): Whittemore C. (199). The Science and actice of Pig oductions. London: Longmane Scientific and Technical. 66