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Accuracy of Nonlinear Formulation of Broiler Diets: Maximizing Profits

Abstract

Nutritionists need to make commercial decisions about the optimal nutrient content broiler feeds. In order to demonstrate that broiler prices may influence dietary nutrient density, this study developed quadratic feed intake and weight gain equations, according to broiler sex and feeding phase, to be applied in a nonlinear feed formulation model. Four hundred and eighty Cobb broilers were allotted to a completely randomized experimental with six treatments, each with four replicates of 10 birds each, from 1 to 56 days old. Treatments consisted of diets containing 2800, 2900, 3000, 3100, 3200, or 3300 kcal metabolizable energy (ME)/kg and constant nutrient to ME ratio. A nonlinear version of the PPFR feed formulation software (http://www.fmva.unesp.br/ppfr) was developed with the objective of optimizing energy density and bird performance. According to the results, when the models are applied in the PPFR nonlinear spreadsheet, the most favorable nutrient density content is defined by mathematical models, as optimized by the Excel Solver tool by means of cost/benefit comparisons and as a function of rearing phase (starter, grower, and finisher) and sex. This contradicts the recommendations of genetic company manuals and published requirement tables, whose goal is to maximize weight gain and do not necessarily guarantee maximum economic efficiency.

Energy; excel; mathematical modeling; nutrition; response surface


INTRODUCTION

Broiler nutritionists usually use least cost formulation programs to formulate feeds. However, this method does not optimize commercial broiler production profits (Guevara, 2004Guevara VR. Use of Nonlinear Programming to Optimize Performance Response to Energy Density in Broiler Feed Formulation. Poultry Science 2004;83:147-151.). In fact, in order to obtain the greatest economic benefits, broiler companies should apply optimization methodologies to determine the nutritional requirements, because live performance directly depend on feed intake (nutritional levels). In addition, broiler production is influenced by fluctuations in feed costs, broiler market prices, and consumer's demand for birds of different sizes (Cerrate & Waldroup, 2009aCerrate S, Waldroup P. Maximum profit feed formulation of broilers: 1. Development of a feeding program model to predict profitability using non linear programming. International Journal of Poultry Science 2009a;8:205-215.).

Studies have shown that increasing dietary energy density promotes broiler growth and feed efficiency (Saleh et al., 2004Saleh EA, Watkins SE, Waldroup AL, Waldroup PW. Effects of dietary nutrient density on performance and carcass quality of male broilers grown for further processing. International Journal of Poultry Science 2004;3:1-10.). However, increasing energy levels result in higher production costs. In addition, considering the current rise in the price of energy sources, it is essential to review the energy levels of broiler diets.

Feed formulation using nonlinear programming takes into account practical issues. The concept of feeding by using economically optimal concentrations of nutrients is based on the law of diminishing returns (Almquist, 1953Almquist HJ. Interpretation of amino acid requirement data according to the law of diminishing returns. Archives of Biochemistry and Biophysics 1953;44:245-247.) and many different biologic and economic situations are considered in nonlinear formulation.

Aiming at addressing those challenges, mathematical models were developed in the present study to estimate broiler performance according to sex, age, and dietary energy density in order to develop a nonlinear version of the feeding formulation program PPFR (Garcia-Neto, 2012Garcia-Neto M. PPFR: programa prático para formulação e otimização de ração frangos de corte programação não linear [cited 2012 Fev 15].Available from:: https://sites.google.com/site/ppfrprogramforfeedformulation/ .
https://sites.google.com/site/ppfrprogra...
), which uses the Guevara (2004)Guevara VR. Use of Nonlinear Programming to Optimize Performance Response to Energy Density in Broiler Feed Formulation. Poultry Science 2004;83:147-151. model, thereby allowing to obtain the parameters of the objective function that maximizes profits.

MATERIAL AND METHODS

In this trial, 480 Cobb broilers chicks were reared between 1 and 56 days of age in a conventional broiler house, which was environmentally controlled to maintain the thermal comfort of the birds. On day 1, birds were separated by sex, weighed, and allotted to six treatments, with four replicates of ten birds each. Replicates were equally distributed into 48 pens, each measuring 1.4x3m, with concrete floor covered with wood-shavings litter. A continuous lighting program, with 23 hours of light daily, was applied throughout the experiment.

Diets were formulated according to the recommendations of Rostagno et al. (2005)Rostagno HS, Albino LFT, Donzele JL, Gomes PC, Oliveira RF, Lopes DC, et al. Tabelas brasileiras para aves e suínos: composição de alimentos e exigências nutricionais. 2ªed. Viçosa: UFV; 2005. 186p. for each sex and rearing period (starter: 1 to 21 days, grower: 22 to 42 days, and finisher: 43 to 56 days), using the feed formulation program PPFR (Garcia-Neto, 2012Garcia-Neto M. PPFR: programa prático para formulação e otimização de ração frangos de corte programação não linear [cited 2012 Fev 15].Available from:: https://sites.google.com/site/ppfrprogramforfeedformulation/ .
https://sites.google.com/site/ppfrprogra...
). The six experimental diets were based on corn-soybean meal and contained 2800, 2900, 3000, 3100, 3200, or 3300 kcal metabolizable energy (ME)/kg. The ratio of all essential nutrients to dietary energy was maintained constant. The diets are presented in Table 1 (females) and Table 2 (males). Crumbled feed and water were offered ad libitum throughout the trial.

Table 2.
Ingredients and nutritional composition of male diets, according to rearing phase.
Table 1.
Ingredients and nutritional composition of female diets, according to rearing phase.

Live weight, feed intake, feed:energy ratio (feed intake/dietary energy content) and feed conversion ratio (feed intake/weight gain) were determined on days 21, 35, 42, 49, and 56. Mortality was daily checked for the adjustment of feed intake.

Carcass quality was evaluated on days 35, 42, 49 and 56. One bird per pen, which body weight was close to the average weight of the replicate, was selected and submitted to feed fasting for nine hours, but were offered water ad libitum. Birds were then weighed, slaughtered according to official procedures (Brasil, 1997Brasil. Decreto n°. 2244, de 5 de junho de 1997. Estabelece regulamentação da inspeção industrial e sanitária de produtos de origem animal. Diário oficial [da] República Federativa do Brasil, poder Executivo, Brasília, DF, 4 jun.1997. Seção 1I, p. 204.; 1998Brasil. Ministério da Agricultura, Pecuária e Abastecimento. Portaria n° 210, de 10 de novembro de 1998. Aprova o regulamento técnico da inspeção tecnológica e higiênico-sanitária de carne de aves. Diário oficial [da] República Federativa do Brasil, poder Executivo, Brasília, DF, 26 nov. 1998. Seção 1, p. 226.), de-feathered, eviscerated, and chilled by immersion in cold water, after which the abdominal fat pad was manually removed and the carcasses were weighed.

Results were submitted to analysis of variance to check the effects of treatments and to obtain information on the robustness of the binomial age and nutrient density. The results were considered significant at p<0.05. A response surface was built to determine and quantify synergistic and antagonistic effects among treatments (Rodrigues & Iemma, 2009Rodrigues MS, Iemma AF. Planejamento de experimentos e otimização de processos. 2ª ed. Campinas: Casa do Espírito Amigo Fraternidade Fé e Amor; 2009. 358p.) using the PROC GLM of SAS statistical package (SAS Institute, 2009SAS Institute. SAS user´s guide: statistics. version five edition. Cary, NC; 2009.).

A nonlinear programming version of the PPFR software was developed with the objective of optimizing dietary energy density and bird performance. The steps of this feed formulation model that uses Excel Workbook was detailed by Guevara (2004)Guevara VR. Use of Nonlinear Programming to Optimize Performance Response to Energy Density in Broiler Feed Formulation. Poultry Science 2004;83:147-151.. However, in our experiment, response surface data were used to obtain the equations according to age, sex, and dietary nutrient density in order to optimize gross profit margin in broiler feed formulation (Maximum Profit Ration), both as a nutritional strategy and as a mathematical modeling tool for broiler production. Therefore, broiler production response always requires two inputs to define the quadratic function, according to the equation:

Y = f (D,E) = β0 + β1D + β2E + β3D2 + β4E2 + β5D*E,

Where, in this study, Y is the "output", i.e. the average output result (body weight, feed intake, energy consumption, feed conversion ratio, abdominal fat weight, and carcass weight); D is bird age (days); and E is dietary energy content (Mcal ME/kg of diet).

The linear (β1D and β2E) and the quadratic (β3D2 and β4E2) responses and the possible effects of the interactions (β5D*E) follow the law of diminishing returns for age and energy content ("Inputs").

According to the procedure of Guevara (2004)Guevara VR. Use of Nonlinear Programming to Optimize Performance Response to Energy Density in Broiler Feed Formulation. Poultry Science 2004;83:147-151., the model identifies which is the best fit of parameters to maximize profits and to promote the best animal performance (source of income). However, it does not necessarily maximize their potential weight gain because it takes into account product price (price per kilogram of live broiler paid by the market) and cost (feed expenses), and therefore, the diets will contain the nutrient and energy levels that are the most appropriate in each specific scenario.

RESULTS AND DISCUSSION

Dietary energy content is the most important item in broiler feed formulation, and makes up 70% of the total diet (Guevara, 2004Guevara VR. Use of Nonlinear Programming to Optimize Performance Response to Energy Density in Broiler Feed Formulation. Poultry Science 2004;83:147-151.; Saleh et al., 2004Saleh EA, Watkins SE, Waldroup AL, Waldroup PW. Effects of dietary nutrient density on performance and carcass quality of male broilers grown for further processing. International Journal of Poultry Science 2004;3:1-10.). Therefore, this study aimed at understanding and determining the optimal energy content required to accelerate broiler growth, without, however, compromising maximum economic return.

Live weight and feed intake results of male and female broilers are presented separately for the periods of 1 to 20 days of age and 21 to 56 days of age. This strategy was adopted to allow a better fit to the growth curve of broilers, which is typically sigmoidal.

There were significant interactions between age and dietary metabolizable energy content for live weight and feed intake of both males and females (Table 3). Therefore, in order to determine the best market age to obtain the greatest profit, diet nutrient density must be considered, and it depends on bird age.

Table 3.
Probability, coefficient of variation (CV), coefficient of determination (R2) and analysis of variance of live weight (LW) and feed intake (FI) of female and male broilers between 1to 20 days of age and 21 to 56 days of age.

The effects of age and nutrient density (independent variables) on the dependent variables (e.g. body weight) are complex and cannot be explained by a simple linear function. The models developed in the present study were shown to be biologically realistic and capable of explaining the results, as demonstrated by the obtained coefficients of determination (R2), which were extremely high (>0.95). Moreover, the coefficients of variation (CV) indicate that the instability of responses was very low, except for abdominal fat weight (Table 4), which is known to be very unstable (Sampaio, 2007Sampaio IBM. Estatística aplicada à experimentação animal. 3ªed. Belo Horizonte: Fundação de Estudo e Pesquisa em Medicina Veterinária e Zootecnia; 2007. 264 p.).

Table 4.
Probability, coefficient of variation (CV), coefficient of determination (R2) and analysis of variance for energy consumption, feed conversion, abdominal fat weight and carcass weight responses of female and male broilers.

The analysis of variance (Table 3 and 4) of the evaluated parameters as function of age and dietary metabolizable energy content show that the mathematical models were highly significant (p <0.0001) for all studied parameters, indicating that the experimental data fully fit the models.

Therefore, the analysis of the response surface allows defining an optimal region of dietary nutrient density according to broiler age and sex instead of a best-value point, as in the case of linear formulation. As a practical application, it allows reducing dietary nutrient density without compromising broiler performance when weight gain and feed intake are considered, and this is precisely what promotes the economic viability of the nonlinear principle.

The females, which have lower genetic potential for muscle accretion than males, presented higher abdominal fat content (Figure 3) and it almost doubled between the two evaluated periods (1-42 and 1-56 days old). The excessive abdominal fat deposition shows that there was a waste of energy. Therefore, the efficiency of energy utilization of females is poor after 40 days, as shown by the significantly lower carcass yield and greater deposition of abdominal fat compared with males. Consequently, females should be slaughtered at an earlier age for economic reasons. In addition, the results show that the influence of dietary nutrient density on live weight is reduced as broilers age (Figure 2), as demonstrated by the steeper slope of the body weight curve when broilers are younger. This indicates that the optimal slaughter weight depends on bird sex (higher profits for males), justifying the earlier slaughter of females. Also, the interaction between age and nutrient density shows that targeting only weight gain in feed formulation (least cost formulation) is costly, contradicting the law of diminishing returns. Therefore, in order to minimize costs and time and to maximize economic returns, it is essential to apply the nonlinear principle as a tool for formulation.

Figure 1.
Response Surface of feed intake (g) of females (a) and males (b), according to age (days) and dietary energy density (kcal ME/kg).

Figure 2.
Response Surface of body weight (g) of females (a) and males (b), according to age (days) and dietary energy density (kcal ME/kg).

Figure 3.
Response Surface of abdominal fat weight (g) of females (a) and males (b), according to age (days) and dietary energy density (kcal ME/kg).

The simulations obtained with calibration of the current model, using specific PPFR spreadsheets for males and females, were more consistent when compared with previous studies that considered only a single diet for both sexes (Miller et al., 1986Miller BR, Arraes RA, Pesti GM. Formulation of broiler finishing ratios by quadratic programming. Southern Journal of Agricultural Economics 1986;18(1):141-150.; Guevara 2004Guevara VR. Use of Nonlinear Programming to Optimize Performance Response to Energy Density in Broiler Feed Formulation. Poultry Science 2004;83:147-151.). When a single diet is applied, the performance of females fed on diets formulated for males is not compromised, but there are economic losses. On the other hand, the performance of males fed on female diets is reduced, also leading to economic losses. In addition, considering carcass quality, the ratio between energy and nutrients must be maintained constant so that body composition does not change as body weight increases, thereby maintaining carcass quality (Saleh et al., 2004Saleh EA, Watkins SE, Waldroup AL, Waldroup PW. Effects of dietary nutrient density on performance and carcass quality of male broilers grown for further processing. International Journal of Poultry Science 2004;3:1-10.; Cerrate & Waldroup, 2009aCerrate S, Waldroup P. Maximum profit feed formulation of broilers: 1. Development of a feeding program model to predict profitability using non linear programming. International Journal of Poultry Science 2009a;8:205-215.; 2009bCerrate S, Waldroup P. Maximum Profit Feed Formulation of Broilers: 2. Comparison among Different Nutritional Models. International Journal of Poultry Science 2009b;8:216-228.). That is the reason why the model "energy to nutrient" ratio is considered the best method for nonlinear feed formulation (Cerrate & Waldroup, 2009aCerrate S, Waldroup P. Maximum profit feed formulation of broilers: 1. Development of a feeding program model to predict profitability using non linear programming. International Journal of Poultry Science 2009a;8:205-215.; 2009bCerrate S, Waldroup P. Maximum Profit Feed Formulation of Broilers: 2. Comparison among Different Nutritional Models. International Journal of Poultry Science 2009b;8:216-228.), and also because metabolizable energy is the main factor that affects feed intake, inducing an increase or reduction of the intake of the other nutrients (Leeson et al., 1996Leeson S, Caston L, Summers JD. Broiler response to energy diet. Poultry Science 1996;75:529-535.).

It is also observed (Table 4) that the energy consumption (ME*ME) response was curvilinear. Therefore, the model must be nonlinear to ensure the maximization of economic efficiency (Guevara, 2004Guevara VR. Use of Nonlinear Programming to Optimize Performance Response to Energy Density in Broiler Feed Formulation. Poultry Science 2004;83:147-151.; Cerrate & Waldroup, 2009aCerrate S, Waldroup P. Maximum profit feed formulation of broilers: 1. Development of a feeding program model to predict profitability using non linear programming. International Journal of Poultry Science 2009a;8:205-215.; Eila et al., 2012Eila N, Lavvaf A, Farahvash T. A model for obtaining more economic diets for laying hen. African Journal of Agricultural Research 2012;7(8):1302-1306.). Consequently, the most favorable nutrient density content, when nonlinear PPFR formulation is applied, will be defined by mathematical models optimized by the Excel Solver tool, using cost/benefit comparisons according to rearing phase (starter, grower, and finisher) and sex. This contradicts the recommendations of the genetic line manuals and published requirement tables, whose goal is to maximize weight gain and do not necessarily ensure maximum economic efficiency.

The results of the present study obtained by applying the models to the nonlinear PPFR spreadsheet answer the questions mentioned above and proved to be reliable within the range of values based on which the equations were generated (1-56 days old). Moreover, when feedstuff and chicken prices change, the model seeks to maintain the most favorable nutrient density to achieve maximum profit by relocating the other ingredients available (Guevara, 2004Guevara VR. Use of Nonlinear Programming to Optimize Performance Response to Energy Density in Broiler Feed Formulation. Poultry Science 2004;83:147-151.; Renz, 2005Renz SV. Comparação de sistemas de formulação lineares e não lineares para frangos de corte [dissertação]. Porto Alegre (RS): Universidade Federal do Rio Grande do Sul; 2005.).

This economic fit is very dependent on how narrow or broad is the energy to nutrient ratio, i.e., because pre-starter and starter diets typically have very close ratios (e.g., energy to protein ratio of 140:1; Tables 1 and 2), they do not allow extensive optimization manipulations by the Solver. However, because feed intake is still low during those phases (Figure 1), such limitation does not cause significant damage. In addition, as birds age and energy to protein ratios in the formulation increase (to 171:1 in the grower phase and 197:1 in the finisher phase; Tables 1 and 2, respectively), nonlinear programming of more flexible ratios, allows adjustements precisely as feed intake becomes increasingly relevant, having direct impact on costs.

The obtained results clearly show the importance of developing mathematical models and applying new feed formulation principles that take into account the current knowledge on nutrient utilization and tissue deposition in modern broilers, particularly of protein and energy, aiming at optimizing nutrient carcass deposition (Lopez et al., 2007Lopez G, Lange K, Leeson S. Partitioning of retained energy in broilers and birds with intermediate growth rate. Poultry Science 2007;86:2162-2171.). Therefore, mathematical modeling presents an opportunity for the broiler industry to produce better-quality carcasses for increasingly demanding consumers, who seek low-fat food products (Meinerz et al., 2001Meinerz C, Ribeiro AML, Penz-Junior AM, Kessler AM. Níveis de energia e peletização no desempenho e rendimento de carcaça de frangos de corte com oferta alimentar equalizada. Revista Brasileira de Zootecnia 2001;30:2026-2032.), and at the same time, to balance the cost-benefit ratio.

CONCLUSIONS

The results of this study suggest that, when applying the concept of precision feeding for broilers, nonlinear feed formulation provides better results compared with linear feed formulation because the requirements of all nutrients are automatically adjusted by the mathematical model, resulting in optimal dietary energy supply, in addition to estimating the most profitable weight gain.

ACKNOWLEDGEMENTS

To the São Paulo Research Foundation (FAPESP) by financial support and CAPES Foundation for the master scholarship granted to the first author.

REFERENCES

  • Almquist HJ. Interpretation of amino acid requirement data according to the law of diminishing returns. Archives of Biochemistry and Biophysics 1953;44:245-247.
  • Brasil. Ministério da Agricultura, Pecuária e Abastecimento. Portaria n° 210, de 10 de novembro de 1998. Aprova o regulamento técnico da inspeção tecnológica e higiênico-sanitária de carne de aves. Diário oficial [da] República Federativa do Brasil, poder Executivo, Brasília, DF, 26 nov. 1998. Seção 1, p. 226.
  • Brasil. Decreto n°. 2244, de 5 de junho de 1997. Estabelece regulamentação da inspeção industrial e sanitária de produtos de origem animal. Diário oficial [da] República Federativa do Brasil, poder Executivo, Brasília, DF, 4 jun.1997. Seção 1I, p. 204.
  • Cerrate S, Waldroup P. Maximum profit feed formulation of broilers: 1. Development of a feeding program model to predict profitability using non linear programming. International Journal of Poultry Science 2009a;8:205-215.
  • Cerrate S, Waldroup P. Maximum Profit Feed Formulation of Broilers: 2. Comparison among Different Nutritional Models. International Journal of Poultry Science 2009b;8:216-228.
  • Eila N, Lavvaf A, Farahvash T. A model for obtaining more economic diets for laying hen. African Journal of Agricultural Research 2012;7(8):1302-1306.
  • Garcia-Neto M. PPFR: programa prático para formulação e otimização de ração frangos de corte programação não linear [cited 2012 Fev 15].Available from:: https://sites.google.com/site/ppfrprogramforfeedformulation/ .
    » https://sites.google.com/site/ppfrprogramforfeedformulation/
  • Guevara VR. Use of Nonlinear Programming to Optimize Performance Response to Energy Density in Broiler Feed Formulation. Poultry Science 2004;83:147-151.
  • Kessler AM, Snizek Júnior PN, Brugalli I. Manipulação da quantidade de gordura na carcaça de frango. Anais da Conferência Apinco 2000 de Ciência e Tecnologia Avícolas; 2000; Santos, São Paulo. Brasil. Campinas: FACTA; 2000. v. 1, p. 107-134.
  • Leeson S, Caston L, Summers JD. Broiler response to energy diet. Poultry Science 1996;75:529-535.
  • Lopez G, Lange K, Leeson S. Partitioning of retained energy in broilers and birds with intermediate growth rate. Poultry Science 2007;86:2162-2171.
  • Meinerz C, Ribeiro AML, Penz-Junior AM, Kessler AM. Níveis de energia e peletização no desempenho e rendimento de carcaça de frangos de corte com oferta alimentar equalizada. Revista Brasileira de Zootecnia 2001;30:2026-2032.
  • Miller BR, Arraes RA, Pesti GM. Formulation of broiler finishing ratios by quadratic programming. Southern Journal of Agricultural Economics 1986;18(1):141-150.
  • Renz SV. Comparação de sistemas de formulação lineares e não lineares para frangos de corte [dissertação]. Porto Alegre (RS): Universidade Federal do Rio Grande do Sul; 2005.
  • Rodrigues MS, Iemma AF. Planejamento de experimentos e otimização de processos. 2ª ed. Campinas: Casa do Espírito Amigo Fraternidade Fé e Amor; 2009. 358p.
  • Rostagno HS, Albino LFT, Donzele JL, Gomes PC, Oliveira RF, Lopes DC, et al. Tabelas brasileiras para aves e suínos: composição de alimentos e exigências nutricionais. 2ªed. Viçosa: UFV; 2005. 186p.
  • Saleh EA, Watkins SE, Waldroup AL, Waldroup PW. Effects of dietary nutrient density on performance and carcass quality of male broilers grown for further processing. International Journal of Poultry Science 2004;3:1-10.
  • Sampaio IBM. Estatística aplicada à experimentação animal. 3ªed. Belo Horizonte: Fundação de Estudo e Pesquisa em Medicina Veterinária e Zootecnia; 2007. 264 p.
  • SAS Institute. SAS user´s guide: statistics. version five edition. Cary, NC; 2009.
  • Erratum

    In the article entitled Litter Accuracy of Nonlinear Formulation of Broiler Diets: Maximizing Profits published in the Revista Brasileira de Ciência Avícolas/Brazilian Journal of Poultry Science, v17 (2):173-180, in page 173 where it was written
    Author(s)
    Gonçalves CAI
    Almeida MA deI
    Faria-Júnior JAII
    Pinto MFII
    Garcia-Neto MII
    the correct form is
    Author(s)
    Gonçalves CAI
    Almeida MA deI
    Faria-Júnior MJAII
    Pinto MFII
    Garcia-Neto MII

Publication Dates

  • Publication in this collection
    Apr-Jun 2015

History

  • Received
    Feb 2013
  • Accepted
    Nov 2014
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