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Animal Science
 
Growth curve of broiler chicken submitted the cassava meal diet
 

iDL. R. R. Lucena*✉:

iDM. A. C. Holanda

iDM. C. R. Holanda

 

Universidade Federal Rural de Pernambuco, Unidade Acadêmica de Serra Talhada, Serra Talhada, PE, CEP: 56909-535, Brasil.

 

Abstract

Achieve success in broiler chickens creation is necessary to provide a diet rich in essential nutrients to maximize poultry performance. In this context, cassava stands out, source rich in carbohydrates and can provide great weight gain and decrease the cost of production. Current success in genetic improvement in birds has caused changes in the growth curve, however the objective was to model the weight growth of broiler chickens fed diets containing cassava. A total of 450 male broiler chickens of Cobb lineage were used. The experimental design was completely randomized with five treatments (0, 25, 50, 75 and 100% inclusion of cassava meal) and five repetitions, each experimental unit was composed of 18 birds. To evaluate the weight performance according to age and the inclusion of cassava in the animals' diet, adjustments of regression models were proposed. Power, hyperbolic tangent and gamma models presented the best results for estimating broiler chickens weight. Power model was the most adequate for estimating the weight of broiler chickens as it presents the best criteria (R²=99.7%; SSR=0.09 and AIC=-82.34). The adoption of the power model provides information on the best level of inclusion of cassava meal (100%) and the best time for slaughtering (42 days) birds maximizing the weight in 3,295 g.

Keywords: 
alternative feeding; chicks; growth curve; weight performance; power model.
 
 
 

Poultry farming is one of the most developed animal production sectors in recent years, especially in the chicken meat production sector (Henrique et al. 2017Henrique, C.S., Oliveira, A.F.G., Ferreira, T.S., Silva, E.S., Mello, B.F.F.R., Andrade, A.F., Martins, V.S.F., Paula, F.O., Garcia, E.R.M. & Bruno, L.D.G. 2017. "Effect of stocking density on performance, carcass yield, productivity, and bone development in broiler chickens Cobb 500". Semina: Ciências Agrárias, 38(4): 2705-2718, ISSN: 1679-0359, DOI: http://dx.doi.org/10.5433/1679-0359.2017v38n4Supl1p2705. and Nogueira et al. 2019Nogueira, B.R.P., Reis, M.P., Carvalho, A.C., Mendoza, E.A.C., Oliveira, B.L., Silva, V.A. & Bertechini, A.G. 2019. "Performance, growth curves and carcass yield of four strains of broiler chicken". Brazilian Journal of Poultry Science, 21(4): 1-8, ISSN: 1806-9061, DOI: https://doi.org/10.1590/1806-9061-2018-0866.). To achieve success in a broiler chickens breeding system, is necessary to provide a balanced diet, provide a favorable environment, and perform management suitable (Pires et al. 2019Pires, G.A., Cordeiro, M.B., Freitas, H.J., Rodrigues, S.F.C. & Nascimento, A.M. 2019. "Desempenho zootécnico e rendimento de carcaça de linhagens de frangos de corte criadas sob condições ambientais da Amazônia ocidental". Enciclopédia Biosfera, 16(29): 633-645, ISSN: 2317-2606, DOI: https://doi.org/10.18677/EnciBio_2019A48.). Balanced diet is rich in essential nutrients for maximum performance of the animal species that you work with, in this context, the use of cassava stands out as an ingredient rich in carbohydrates, dietary fiber, starch, proteins, lipids and ashes (Holanda et al. 2015Holanda, M.A.C., Holanda, M.C.R., Vigoderes, R.B., Dutra Jr., W.M. & Albino, L.F.T. 2015. "Desempenho de frangos caipiras alimentados com farelo integral de mandioca". Revista Brasileira de Saúde e Produção Animal, 16(1): 106-117, ISSN: 1519-9940, DOI: http://dx.doi.org/10.1590/S1519-99402015000100012.), being able to compose diets capable of providing optimum weight gain and contributing to reducing the production cost of broiler chickens.

Current success in genetic improvement in birds has caused changes in the growth curve, increasing feed efficiency and consequently its genetic potential, causing birds to be slaughtered increasingly precocious.The knowledge of the growth curves of a species provides very useful information in the production and management of natural populations and enables the viability of production by the growth rate (Lucena et al. 2017Lucena, L.R.R., Holanda, M.A.C., Holanda, M.C.R. & Sousa, A.A. 2017. "Ajuste de modelos de regressão lineares, não lineares e sigmoidal no ganho de peso simulado de frangos de corte". Agrarian Academy, 4(8): 34-45, ISSN: 2357-9951, DOI: https://doi.org/10.18677/Agrarian_Academy_2017b4.). The curve that describes a sequence of measurements of a particular characteristic of a species or individual as a function of time, usually weight, height, diameter, length is called growth curve (Lucena et al. 2019Lucena L.R.R., Holanda, M.A.C., Holanda, M.C.R. & Anjos, M.L. 2019. Adjusting weight growth curve of male quails Coturnix Japonica reared in the semi-arid region of the state of Pernambuco". Acta Scientiarum Animal Sciences, 41: 1-8, ISSN: 1806-2636, DOI: https://doi.org/10.4025/actascianimsci.v41i1.42563 ).In poultry farming have been proposed several models to explain the biological growth of broiler chickens as a function of life time reported by Sakomura et al. (2011)Sakomura, N.K., Gous, R.M., Marcato, S.M. & Fernandes, J.B.K. 2011. "A description of the growth of the major body componentes of 2 broiler chicken strains". Poultry Science, 90(12): 2888-2896, ISSN: 1525-3171, DOI: https://doi.org/10.3382/ps.2011-01602., Rizzi et al. (2013)Rizzi, C., Contiero, B. & Cassandro, M. 2013. "Growth patterns of Italian local chicken populations". Poultry Science, 92(8): 2226-2235, ISSN: 1525-3171, DOI: https://doi.org/10.3382/ps.2012-02825., Al-Samarai (2015)Al-Samarai, F.R. 2015. "Growth curve of commercial broiler as predicted by different nonlinear functions". American Journal of Applied Scientific Research, 1(2): 6-9, ISSN: 2471-9730, DOI: https://doi.org/ 10.11648/j.ajasr.20150102.11., Zhao et al. (2015)Zhao, Z., Li, S., Huang, H., Li, C., Wang, Q. & Xue, L. 2015. "Comparative study on growth and developmental model of indigenous chicken breeds in China". Open Journal of Animal Sciences, 5(2): 219-223, ISSN: 2161-7597, DOI: https://doi.org/10.4236/ojas.2015.52024. and Michalczuk et al. (2016)Michalczuk, M., Damaziak, K. & Goryl, A. 2016. "Sigmoid models for the growth curves in medium-growing meat type chickens, raised under semi-confined conditions". Annals of Animal Science, 16(1): 65-77, ISSN: 2300-8733, DOI: https://doi.org/10.1515/aoas-2015-0061..

Although there are reports of several studies with growth curves in broiler chickens, no reports were found in the literature of growth curve adjustment in broiler chickens fed the cassava diet, thus aimed to model the growth of the weight of broilers fed different diets containing cassava.

Materials and Methods

The research was in the aviary of Fazenda São João, located in the district of Santa Rita, municipality of Serra Talhada-PE, in the micro region of the Sertão do Pajeú, mesoregion of the Sertão de Pernambuco, under license number 127/2019 of the ethics committee on the use of animals of the Federal Rural University of Pernambuco.

Were used 450 male broiler chickens of the Cobb lineage, with one day life, starting weight of 42 grams, vaccinated on the first day still in the hatchery, against Mareck, Newcastle, Gumboro and revaccinated at 14 days against Newcastle and Gumboro.

The birds were housed in an aviary built in masonry, with ceramic tiles and concrete floors, lined with bed of inert material (rice husk) at a height of 15 cm, keypad with galvanized wire screen and curtain to prevent drafts and control the environment temperature.

During the first 14 days of life, a 150 watt incandescent lamp was used with heat source for broiler chickens. Aviary was divided in 25 experimental plots, each measuring 2 m², with a density of 9 birds/m².

Experimental design was completely randomized with five treatments and five replications, where each experimental unit was composed of 18 birds.The treatments consisted of a control diet based on corn and soybean meal, and four test diets containing 25, 50, 75 and 100 % inclusion of integral meal of cassava roots supplemented with endogenous enzymes, in the quantity of 500 grams per ton of feed.

Cassava roots were acquired in the municipality of Araripina-PE, posteriorly the roots were processed and dehydrated in the sun for five days until they lost maximum moisture to obtain dry meal. A sample was collected and taken to the laboratory for chemical analysis that presented the following results:88.56% dry matter, 2.54% crude protein, 0.62% lipids, 5.32% crude fiber, 10.84% neutral detergent fiber (NDF), 3.96% acid detergent fiber (ADF), 84.92 % organic matter, 3.52 % ash, 0.18 % calcium and 0.09% phosphorus. The gross energy of 4,123 kcal/kg was determined in the IKA 200 calorimeter.

The result of the chemical composition was used to formulate the experimental diets together with the metabolizable energy of 12,502 MJ/kg (determined in a metabolism experiment carried out previously with chicks, this experiment was carried out before formulating the diets).The multi-enzyme complex was composed of galactosidase 35 U/g, galactomannanase 110 U/g, xylanase 1,500 U/g, β-glucanase 1,100 U/g, and was mixed to the premix in a Y-type mixer for mixing low level ingredients in the diets and used in the proportion of 500 grams per ton of feed for the test diets, for greater availability of nutrients contained in whole cassava meal.

From the first day of life the birds received experimental diets according to the treatments, following the nutritional recommendations of Rostagno et al. (2017)Rostagno, H.S., Teixeira, L.F., Hannas, M.I., Lopes, J., Kazue, N., Guilherme, F., Saraiva, A., Texeira, M.L., Borges, P., de Oliveira, R.F., de Toledo, S.L. & de Oliveira, C. 2017. Tablas Brasileñas para Aves y Cerdos - Composición de Alimentos y Requerimientos Nutricionales. Ed. Departamento de Zootecnia, Universidad Federal de Viçosa, Viçosa, Brasil, p. 403-404, ISBN: 978-85-8179-122-7. (table1, 2, 3 and 4).

 
Table 1.  Chemical composition and calculated of the experimental diets for broiler chickens from 1 to 7 days of age as a function of the levels cassava meal
IngredientsLevels of cassava inclusion (%)
0255075100
Corn (kg)46.54334.90723.27111.6350.000
Soybean meal (45%)46.12947.74349.36050.97752.594
Cassava meal (kg)0.0008.88817.77726.66535.554
Dicalcium phosphate1.9302.2392.5492.8593.169
Calcitic Limestone0.9410.7050.4700.2350.000
Vegetable oil3.3304.3905.4516.5127.573
NaCl0.4560.4500.4450.4390.434
L-lysine HCl (78%)0.1330.1110.0880.0660.044
DL-methionine (99%)0.3280.3480.3680.3880.408
L-threonine (98%)0.0100.0170.0250.0320.040
Multienzyme complex0.0000.0120.0250.0370.050
Choline chloride (60%)0.1000.1000.1000.1000.100
Premix mineral/vitamin10.1000.1000.1000.1000.100
Calculated Composition (%)
Crude protein 25.31 25.31 25.31 25.31 25.31
Metabolizable energy (MJ/kg)12,54012,54012,54012,54012,540
Calcium 1.0111.0111.0111.0111.011
Phosphorus available 0.4820.4820.4820.4820.482
Digestible lysine 1.3641.3641.3641.3641.364
Digestible methionine 0.6690.6800.6920.7030.715
Digestible met+cys 0.9890.9890.9890.9890.989
Digestible threonine 0.7730.7730.7730.7730.773
Digestible tryptophan 0.2960.3040.3120.3200.328
Sodium 0.2270.2270.2270.2270.227
Fat 5.6425.7815.9216.0606.200

1Premix vitamin/kg: Folic Acid 106.00 mg; Pantothenic 2,490 mg; Antifungal 5,000 mg; Antioxidant 200 mg; Biotin 21mg; Coccidiostatic 15,000 mg; Choline 118,750 mg; Vitamin K3 525.20 mg; niacin 7,840 mg; Pyridoxine 210 mg; Riboflavine 1,660 mg; Thiamine 360 mg; Vitamin A 2,090,000 UI; Vitamin B12 123,750 mcg; Vitamin D3 525,000 UI; Vitamin E 4,175 mg. Cu 2,000 mg; I 190 mg; Mn 18,750 mg; Se 75 mg; Zn 12,500 mg.

 

 
Table 2.  Chemical composition and calculated of the experimental diets for broiler chickens from 8 to 21 days of age as a function of the levels cassava meal
IngredientsLevels of cassava inclusion (%)
0255075100
Corn 48.08036.06024.04012.0200.000
Soybean meal (45%)43.60045.23546.87048.50550.141
Cassava meal 0.0009.35518.71028.06537.420
Dicalcium phosphate1.6791.6991.7191.7391.760
Calcitic Limestone1.0170.9670.9180.8690.820
Vegetable oil4.5105.5476.5857.6228.660
NaCl0.4440.4380.4320.4260.420
L-lysine HCl (78%)0.1360.1130.0910.0690.047
DL-methionine (99%)0.3270.3480.3690.3900.412
L-threonine (98%)0.0120.0410.0710.1000.130
Multienzyme complex0.0000.0120.0250.0370.050
Choline chloride (60%)0.1000.1000.1000.1000.100
Premix mineral/vitamin0.1000.1000.1000.1000.100
Calculated Composition (%)
Crude protein 24.3024.3024.3024.3024.30
Metabolizable energy (MJ/kg)12,95812,95812,95812,95812,958
Calcium 0.9700.9700.9700.9700.970
Phosphorus available 0.4320.4320.4320.4320.432
Digestible lysine 1.3061.3061.3061.3061.306
Digestible methionine 0.6570.6690.6810.6930.705
Digestible met+cys 0.9660.9660.9660.9660.966
Digestible threonine 0.8160.8050.7940.7830.773
Digestible tryptophan 0.2820.2690.2570.2440.232
Sodium 0.2210.2210.2210.2210.221
Fat 6.8206.9907.1607.3307.500

1Premix vitamin/kg: Folic Acid 106.00 mg; Pantothenic 2,490 mg; Antifungal 5,000 mg; Antioxidant 200 mg; Biotin 21mg; Coccidiostatic 15,000 mg; Choline 118,750 mg; Vitamin K3 525.20 mg; niacin 7,840 mg; Pyridoxine 210 mg; Riboflavine 1,660 mg; Thiamine 360 mg; Vitamin A 2,090,000 UI; Vitamin B12 123,750 mcg; Vitamin D3 525,000 UI; Vitamin E 4,175 mg. Cu 2,000 mg; I 190 mg; Mn 18,750 mg; Se 75 mg; Zn 12,500 mg.

 

 
Table 3.  Chemical composition and calculated of the experimental diets for broiler chickens from 22 to 35 days of age as a function of the levels cassava meal
IngredientsLevels of cassava inclusion (%)
0255075100
Corn (kg)60.88045.66030.44015.2200.000
Soybean meal (45%)32.81434.82536.83738.84840.860
Cassava meal (kg)0.00012.56025.13537.70250.270
Dicalcium phosphate1.4201.4451.4701.4951.520
Calcitic Limestone0.7180.6550.5890.5240.460
Vegetable oil3.0843.7214.3584.9955.663
NaCl0.4220.4130.4050.3960.388
L-lysine HCl (78%)0.2200.1940.1680.1420.116
DL-methionine (99%)0.2720.2990.3270.3640.394
L-threonine (98%)0.0000.0270.0550.0820.110
Multienzyme complex 0.000.0120.0250.0370.050
Choline chloride (60%)0.1000.1000.1000.1000.100
Premix mineral/vitamin10.1000.1000.1000.1000.100
Calculated Composition (%)
Crude protein 20.58 20.58 20.58 20.58 20.58
Metabolizable energy (MJ/kg)13,16713,16713,16713,16713,167
Calcium 0.7580.7580.7580.7580.758
phosphorus available 0.3740.3740.3740.3740.374
Digestible lysine 1.1241.1241.1241.1241.124
Digestible methionine 0.5570.5720.5880.6030.619
Digestible met+cys 0.8320.8320.8320.8320.832
Digestible threonine 0.7730.7730.7730.7730.773
Digestible tryptophan 0.2250.2290.2330.2370.241
Sodium 0.2240.2240.2240.2240.224
Fat 5.6806.2856.8907.4958.100

1Premix vitamin/kg: Folic Acid 106.00 mg; Pantothenic 2,490 mg; Antifungal 5,000 mg; Antioxidant 200 mg; Biotin 21mg; Coccidiostatic 15,000 mg; Choline 118,750 mg; Vitamin K3 525.20 mg; niacin 7,840 mg; Pyridoxine 210 mg; Riboflavine 1,660 mg; Thiamine 360 mg; Vitamin A 2,090,000 UI; Vitamin B12 123,750 mcg; Vitamin D3 525,000 UI; Vitamin E 4,175 mg. Cu 2,000 mg; I 190 mg; Mn 18,750 mg; Se 75 mg; Zn 12,500 mg.

 

 
Table 4.  Chemical composition and calculated of the experimental diets for broiler chickens from 36 to 42 days of age as a function of the levels cassava meal
IngredientsLevels of cassava inclusion (%)
0255075100
Corn (kg)62.72246.97631.32115.6750.000
Soybean meal (45%)30.21732.28234.34836.41438.500
Cassava meal (kg)0.00012.97325.94638.91951.892
Dicalcium phosphate1.0891.1141.1391.1641.190
Calcitic Limestone0.7010.6340.5680.5010.435
Vegetable oil4.2184.8565.4946.1326.770
NaCl0.4070.3980.3900.3810.373
L-lysine HCl (78%)0.2260.1990.1730.1460.120
DL-methionine (99%)0.2530.2810.3090.3370.366
L-threonine (98%)0.0640.0750.0870.0980.110
Multienzyme complex0.0000.0120.0250.0370.050
Choline chloride (60%)0.1000.1000.1000.1000.100
Premix mineral/vitamin10.1000.1000.1000.1000.100
Calculated Composition (%)
Crude protein 19.54 19.54 19.54 19.5419.54
Metabolizable energy (MJ/kg)13,58513,58513,58513,58513,585
Calcium 0.6610.6610.6610.6610.661
phosphorus available 0.3090.3090.3090.3090.309
Digestible lysine 1.0671.0671.0671.0671.067
Digestible methionine 0.5250.5410.5570.5730.589
Digestible met+cys 0.7900.7900.7900.7900.790
Sodium 0.2010.2010.2010.2010.201
Digestible threonine 0.7040.7040.7040.7040.704
Fat 6.7606.9227.0857.2477.410

1Premix vitamin/kg: Folic Acid 106.00 mg; Pantothenic 2,490 mg; Antifungal 5,000 mg; Antioxidant 200 mg; Biotin 21mg; Coccidiostatic 15,000 mg; Choline 118,750 mg; Vitamin K3 525.20 mg; niacin 7,840 mg; Pyridoxine 210 mg; Riboflavine 1,660 mg; Thiamine 360 mg; Vitamin A 2,090,000 UI; Vitamin B12 123,750 mcg; Vitamin D3 525,000 UI; Vitamin E 4,175 mg. Cu 2,000 mg; I 190 mg; Mn 18,750 mg; Se 75 mg; Zn 12,500 mg.

 

To evaluate the performance of broiler chickens weight according to age and inclusion of cassava meal, regression model adjustments were proposed: exponential, Weibull, logistic, Gompertz, power, hyperbolic tangent, and gamma (table 5).

 
Table 5.  Regression models evaluated
Regression ModelsEquation
Exponential Yi=w exp(β0+β1Ti+β2Mandi )εi
Weibull Yi=exp(β0+β1Ti+β2Mandi)exp(εi)
Logistic Yi= w1+exp(β0+β1Ti+β2Mandi )+εi
Gompertz Yi=w exp(exp(β0+β1Ti+β2Mandi))+εi
Power Yi=β0Tiβ1Mandiβ2εi
Hyperbolic Tangent Yi=w tanh(β0Tiβ1Mandiβ2εi)
Gamma Yi=(β0+β1Ti+β2Mandi )2+εi

where, Yiis the observed weight of the i-th broiler chickens after birth; Tiis the i-th evaluation day; Mandiis the percentage of cassava added to the diet of the i-th broiler chickens after birth and εiis the i-th error associated with weight, where presents exponential parameter distribution α to exponential model, Weibull distribution of parameters α and γ, normal distribution of mean 0 and constant variance σ² to logistic, Gompertz, power and hyperbolic tangente and Gamma distribution of parameters α and β. The metrics ω, β0, β1 and β2are the parameters associated with the model.

 

The following criteria evaluated the models: Coefficient of Determination of the Model (R²), Akaike's Information Criterion (AIC) and Sum of Square of Residuals (SSR).

Let Y^i the values of the i-th broiler chickens weight after model adjustment and Y¯ mean broiler chickens weight, define SSR for this study by the following expression:

 
SSRc =i=17(Yi-Y^i)²  
 

The coefficient of model determination is expressed by:

 
R2=1- i=17(Yi-Y^i)²i=17(Yi-Y-)²  
 

The Akaike information criteria (AIC), as defined by Akaike (1974)Akaike, H. 1974. "A new look at the statistical model identification". IEEE Transactions on Automatic Control, 19(6): 716-723, ISSN: 1558-2523, DOI: https://doi.org/10.1109/TAC.1974.1100705., are given by:

 
AIC= -2lnLx\θ^+2p  
 

where, L(x\ θ^) is the maximum likelihood function, defined as the production of density function and p is the number of model parameters.

Cluster analysis using the Ward method was used to verify which models are most similar to their adequacy criteria. Posteriorly, residue analysis was performed to validate the quality of the model that best adjusted to the weight growth of the broiler chickens according to age and the different levels of inclusion of cassava meal in their diet.Validation of the model was performed through studentized residues, analysis of leverage and influential points and quantile-quantile plot of distribution normal.

Let hat matrix (H),

 
H=X(X'X)-1X  
 

and,

 
rankH= i=1nhii =p  
 

where, hii are the diagonal elements of matrix H. Assume that any observation that exceeds twice the average ( hii>2p/n ) is remote enough from the rest of the data to be considered a leverage point.

Studentized resisuals defined by:

 
ri= eiSSRn-p(1-hii)  
 

where, ei is the residue of the i-th observation of the model (difference between the observed and adjusted weight).

To detect a point of influence we use Cook’s distance, defined by:

 
Di= ri2phii(1-hii)  
 

if Di>2pn , denoted influential point.

The R-project version 2.13.1 for windows software was used to perform the analyzes.

Results and Discussion

Mean weight of the birds in relation to the lifetime and the different diets with cassava meal are shown in table 6. For all evaluation periods, verified that there was not difference (p-value> 0.05) in the broiler chickens weight in relation to the different levels of cassava meal in diet (table 6).

 
Table 6.  Broiler chickens weight according to lifetime and inclusion of cassava meal in diet
lifetime (days)Broiler chickens weight (g) in inclusion of cassava meal p-value
0%25%50%75%100%
7158.8±11.1161.4±10.1170.9±6.4166.8±6.3159.2±15.20.309
14457.2±22.5475.8±10.9470.9±21.2458.6±24.4456.8±25.50.514
21978.8±35.5993.2±42.7978.1±67.4965.1±58.4962.0±46.20.878
281,787.4±36.61,778.9±80.21,771.5±96.41,725.2±153.51,729.5±57.70.751
352,443.2±76.02,448.4±117.22,450.5±146.92,408.4±184.92,408.4±75.00.964
423,193.7±64.43,286.3±171.43,314.7±159.43,342.1±214.13,320.0±59.40.552
 

The results of this study corroborate with findings of Sousa et al. (2012)Souza, J.P.L., Rodrigues, K.F., Albino, L.F.T., Santos-Neta, E.R., Vaz, R.G.M.V., Parente, I.P., Silva, G.F. & Amorim, A.F. 2012. "Bagaço de mandioca em dietas de frangos de corte". Revista Brasileira de Saúde e Produção Animal, 13(4): 1044-1053, ISSN: 1519-9940, DOI: https://doi.org/10.1590/S1519-99402012000400012. that verified a difference in the weight gain of broiler chickens fed up to 20% of cassava meal in the initial phase (1-21 days), while in the final phase (22-40 days) there was not difference in the weight gain. Carrijo et al. (2010)Carrijo, A.S., Fascina, V.B., Souza, K.M.R., Ribeiro, S.S., Allaman, I.B., Garcia, A.M. A. & Higa, J.A. 2010. "Níveis de farelo da raiz integral de mandioca em dietas para fêmeas de frangos caipiras". Revista Brasileira de Saúde e Produção Animal, 11(1): 131-139, ISSN: 1519-9940., Souza et al. (2011)Souza, K.M.R., Carrijo, A.S., Kiefer, C., Fascina, V.B., Falco, A.L., Manvailer, G.V. & García, A.M.L. 2011. "Farelo da raiz integral de mandioca em dietas de frangos de corte tipo caipira". Archivos de Zootecnia, 60(231): 489-499, ISSN: 1885-4494. and Holanda et al. (2015)Holanda, M.A.C., Holanda, M.C.R., Vigoderes, R.B., Dutra Jr., W.M. & Albino, L.F.T. 2015. "Desempenho de frangos caipiras alimentados com farelo integral de mandioca". Revista Brasileira de Saúde e Produção Animal, 16(1): 106-117, ISSN: 1519-9940, DOI: http://dx.doi.org/10.1590/S1519-99402015000100012., found no difference in the weight gain of free-range broiler chickens fed different levels of cassava meal.

Table 7 shows that the models exponential, Weibull, logistic and Gompertz presented explanatory power of less than 0.90, in addition to presenting the largest sums of squares of the residues, indicating a poor adequacy of these models to explain the broiler chickens weight as a function of age and percentage of cassava meal introduced in their diet.

 
Table 7.  Adjusted regression models and model adequacy criteria to growth broiler chickens weight fed with levels of cassava meal in the diet
Regression ModelsRegression EquationSSRAIC
Exponential Y^i=exp(-2.003+0.0835T-0.00013Mand) 0.7857.84 56.2
Weibull Y^i=exp(-1.862+0.0815T-0.00027Mand) 0.70810.618.4
Logistic Y^i=3.3421+exp(4.61-0.18T-0.0016Mand) 0.8921.7766.32
Gompertz Y^i= 3.342 exp(-exp(2.63-0.129T-0.0015Mand)) 0.8884.0775.19
Power Y^i= 0.0056T1.705Mand0.001 0.9970.09-82.34
Hyperbolic T. Y^i= 3.342 tanh(0.0008T2.03Mand0.0046) 0.9750.90 8.46
Gamma Y^i= (0.113+0.042T-0.00002Mand)2 0.9940.24-93.82

R²- model determination coefficient; SSR-sum of squares of residues; AIC- Akaike information criterion; Y^i is the adjusted weight of model of the i-th broiler chickens after birth; T is the lifetime; Mand is the percentage of cassava

 

Table 8 shows the estimates of the parameters of the models with their respective standard errors, test statistics and p-value, showing the significance of each parameter.

 
Table 8.  Estimative, standard error, t value and p-value of parameters models
EstimateStd. errort valuep-value
Exponential
β0 -2.003 0.523 13.83<0.0001
β1 0.0835 0.017 4.91<0.0001
β2 -0.00013 0.00005 -5.93<0.0001
Weibull
β0 -1.862 0.14 -13.26<0.0001
β1 0.0815 0.005 15.96<0.0001
β2 -0.00027 0.0001 10.26<0.0001
Logistic
β0 4.61 0.353.16<0.0001
β1 -0.18 0.0116.31<0.0001
β2 -0.0016 0.00031.58<0.0001
Gompertz
β0 2.63 0.416.45<0.0001
β0 -0.129 0.013-9.96<0.0001
β2 -0.0015 0.0004-6.36<0.0001
Power
β0 0.0056 0.0014-95.788<0.0001
β1 1.705 0.01799.84<0.0001
β2 0.001 0.000497.35<0.0001
Hyperbolic Tangent
β0 0.00080.00002-28.63<0.0001
β1 2.03 0.07925.51<0.0001
β2 0.0046 0.0018 24.10<0.0001
Gamma
β0 0.113 0.0073 15.57<0.0001
β1 0.042 0.0004 116.89<0.0001
β2 -0.000020.000009 18.53<0.0001
 

Lucena et al. (2017)Lucena, L.R.R., Holanda, M.A.C., Holanda, M.C.R. & Sousa, A.A. 2017. "Ajuste de modelos de regressão lineares, não lineares e sigmoidal no ganho de peso simulado de frangos de corte". Agrarian Academy, 4(8): 34-45, ISSN: 2357-9951, DOI: https://doi.org/10.18677/Agrarian_Academy_2017b4. verified that the exponential, Weibull and Gompertz models presented explanatory power of 0.993, 0.916 and 0.948, respectively. Rizzi et al. (2013)Rizzi, C., Contiero, B. & Cassandro, M. 2013. "Growth patterns of Italian local chicken populations". Poultry Science, 92(8): 2226-2235, ISSN: 1525-3171, DOI: https://doi.org/10.3382/ps.2012-02825. observed that the Gompertz model was the most adequate to explain the growth of broiler chickens with explanatory power greater than 99%, these divergent results of this research, what can be explained by the introduction of increasing levels of cassava in the diet of the broiler chickens causing a loss of yield of these models, as these authors only evaluated weight growth as a function of the birds lifetime.

The hyperbolic tangent model presented explanatory power of 0.975 and sums of residual squares of 0.90.These criteria classify these models with good precision in estimating of the broiler chickens weight, however, these results are inferior to those presented by the power and gamma models, (table 7). Michalczuk et al. (2016)Michalczuk, M., Damaziak, K. & Goryl, A. 2016. "Sigmoid models for the growth curves in medium-growing meat type chickens, raised under semi-confined conditions". Annals of Animal Science, 16(1): 65-77, ISSN: 2300-8733, DOI: https://doi.org/10.1515/aoas-2015-0061., Liu et al. (2015)Liu, X.H., Li, X.L., Li, J. & Lu, C.X. 2015. "Growth curve fitting of Bashang long-tail chicken during growth and development". Acta Agriculture Zhejiangensis, 27(5): 746-750, ISSN: 1004-1524, DOI: https://doi.org/10.3969/j.issn.1004-1524.2015.05.07., Zhao et al. (2015)Zhao, Z., Li, S., Huang, H., Li, C., Wang, Q. & Xue, L. 2015. "Comparative study on growth and developmental model of indigenous chicken breeds in China". Open Journal of Animal Sciences, 5(2): 219-223, ISSN: 2161-7597, DOI: https://doi.org/10.4236/ojas.2015.52024., Selvaggi et al. (2015)Selvaggi, M., Laudadio, V., Dario, C. & Tufarelli, V. 2015. "Modeling Growth Curves in a Nondescript Italian Chicken Breed: an Opportunity to Improve Genetic and Feeding Strategies". Japanese Poultry Science, 52(4): 288-294, ISSN: 0029-0254, DOI: https://doi.org/10.2141/jpsa.0150048. and Mohammed (2015)Mohammed, F.A. 2015. "Comparison of three nonlinear functions for describing chicken growth curves". Scientia Agriculturae, 9(3): 120-123, ISSN: 2310-953X, DOI: https://doi.org/10.15192/PSCP.SA.2015.9.3.120123 presented similar results for the logistic model, while the results for the hyperbolic tangent model corroborate with the describes by Lucena et al. (2017)Lucena, L.R.R., Holanda, M.A.C., Holanda, M.C.R. & Sousa, A.A. 2017. "Ajuste de modelos de regressão lineares, não lineares e sigmoidal no ganho de peso simulado de frangos de corte". Agrarian Academy, 4(8): 34-45, ISSN: 2357-9951, DOI: https://doi.org/10.18677/Agrarian_Academy_2017b4., that is, for all the researches reported, the weight behavior of the animals is similar when using these models.

Power and gamma models showed the highest model determination coefficients, lowest sums of squares of the residues and lowest Akaike information criteria, (table 7).These criteria indicate that these models are the most efficient to estimate the broiler chickens weight as a function of lifetime and introduction of cassava meal. Similar results were reported by Lucena et al. (2017)Lucena, L.R.R., Holanda, M.A.C., Holanda, M.C.R. & Sousa, A.A. 2017. "Ajuste de modelos de regressão lineares, não lineares e sigmoidal no ganho de peso simulado de frangos de corte". Agrarian Academy, 4(8): 34-45, ISSN: 2357-9951, DOI: https://doi.org/10.18677/Agrarian_Academy_2017b4. where they verified that the power model was the most adequate to explain the broiler chickens weight with precision of 0.997 followed by the gamma model with an explanatory power of 0.989.

Due to the different selection goals applied by geneticists in the last decades, growth parameters of broiler genotypes can differ in several characteristics, including those that affect the potential growth curves, with weight and maturation rates (Sakomura et al. 2011Sakomura, N.K., Gous, R.M., Marcato, S.M. & Fernandes, J.B.K. 2011. "A description of the growth of the major body componentes of 2 broiler chicken strains". Poultry Science, 90(12): 2888-2896, ISSN: 1525-3171, DOI: https://doi.org/10.3382/ps.2011-01602.).

The differences between the functions in the growth rate directly reflect on the behavior in the data adjustment. Nonlinear functions have been used extensively to represent changes in broiler chickens weight as a function of age, so that the genetic potential of animals can be valued (Kuhi et al. 2019Kuhi, H.D., López, S., France, J., Mohit, A., Shabanpour, A., Zadeh, N.G.H. & Falahi, S. 2019. "A sinusoidal equation as an alternative to classical growth functions to describe growth profiles in turkeys". Acta Scientiarum Animal Sciences, 41: 1-7, ISSN: 1806-2636, DOI: https://doi.org/10.4025/actascianimsci.v41i1.45990.).

Early estimation of weight at maturity and growth rate in relation to body size can be important for selection purposes, given its association with other characteristics and the economy of production (Kuhi et al. 2019Kuhi, H.D., López, S., France, J., Mohit, A., Shabanpour, A., Zadeh, N.G.H. & Falahi, S. 2019. "A sinusoidal equation as an alternative to classical growth functions to describe growth profiles in turkeys". Acta Scientiarum Animal Sciences, 41: 1-7, ISSN: 1806-2636, DOI: https://doi.org/10.4025/actascianimsci.v41i1.45990.). The exploration of these parameters in growth models by adjusting curves using age with live weight can positively improve economic returns (Salako 2014Salako, A.E. 2014. "Asymptotic nonlinear regression models for the growth of White Fulani and N'dama cattle in Nigeria". Livestock Research for Rural Development, 26(5), ISSN: 0121-3784, Available: <http://www.lrrd.org/lrrd26/5/sala26091.htm>.).

Success in studying the growth characteristics of broiler chickens will help to define more adequate diets to cover high nutritional requirements during the growth phase, from hatching to age at the point of slaughter.In addition, selecting the best function based on your ability to describe the relationship between live weight and age is the first step in developing a genetical improvement program (Selvaggi et al. 2015Selvaggi, M., Laudadio, V., Dario, C. & Tufarelli, V. 2015. "Modeling Growth Curves in a Nondescript Italian Chicken Breed: an Opportunity to Improve Genetic and Feeding Strategies". Japanese Poultry Science, 52(4): 288-294, ISSN: 0029-0254, DOI: https://doi.org/10.2141/jpsa.0150048.). Growth curve parameters provide an opportunity to plan selection strategies, modifying dietary practices or genetic makeup of the shape of the growth curve (Selvaggi et al. 2015Selvaggi, M., Laudadio, V., Dario, C. & Tufarelli, V. 2015. "Modeling Growth Curves in a Nondescript Italian Chicken Breed: an Opportunity to Improve Genetic and Feeding Strategies". Japanese Poultry Science, 52(4): 288-294, ISSN: 0029-0254, DOI: https://doi.org/10.2141/jpsa.0150048.).

Figure 1 shows that the power model presented better estimates of broiler chickens weights than the Gamma model, because the power model showed only a discrepant value from the observed weight of the chickens that occurred on the 28th day, while the Gamma model presented two weight discrepant occurrences (28th and 42nd day).

 
Figure 1.  Estimates of the broiler chickens weight in the power (a) and gamma (b) models
 

Through Ward cluster method using the metrics of model adequacy criteria, verified the formation of two groups of modelswhen using a cutting height greater 60, a group formed by the power and gamma models (models that presented higher R² and lower SSR and AIC), and the second formed by the others models (models that did not present criteria similar to the gamma and power models) (figure 2).

 
Figure 2.  Cluster of adjusted regression models to growth broiler chickens weight fed with levels of cassava meal in the diet
 

Evaluating the three criteria of adequacy of the model, the cluster analysis and the estimates of the broiler chickens weights, the power model was proposed with most adequate to explain the growth of broiler chickens as a function of the lifetime and the different percentages of cassava in their diet.

After defining the power model with most appropriate, the analysis of the residues was performed (figure 3).No discrepant residues were diagnosed (figure 3a),because none is outside the limits of [-2; 2],also no residual leverage or influence was detected (figure 3b and 3c) because no point exceeded the criteria defined by the dotted lines, the assumption of normality of the residues was diagnosed in the quantile-quantile graph of the normal distribution, where the residues are within the confidence bands (figure 3d).

 
Figure 3.  Analysis of residues of the power model in broilers that consume cassava meal
 

Cassava meal in the dietary supplementation of broiler chickens, in addition to promoting better zootechnical performance, decreases production costs, because for diets without inclusion of the cassava meal the production cost was higher because more corn was used ($0.27 per kg of feed for 0%; $0.26 per kg of feed for 25%; $0.24 per kg of feed for 50%; $0.23 per kg of feed for 75%; $0.21 per kg of feed for 100%),while the cost using 100% inclusion of cassava meal was lower because it used half quantity of corn for the control diet.

In many practical problems, such as parameter estimation, function values are uncertain or subject to variation. Therefore, a highly accurate solution is not necessary. In these situations, all you want is an improvement in the adjustement of the function, what can be observed in the use of the power model.

Weight growth of birds fed cassava meal can be estimated using the power regression model. The use of the power model provides information on the best level of inclusion of cassava meal (100%) and the best time for slaughtering birds (42 days) maximizing the weight in 3,295 g.

 
 
 

 

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Received: 05/05/2020

Accepted: 08/07/2020

 
 

Declaración de conflicto de intereses: Los autores declaran no presentar conflicto de intereses

Contribución de los autores: Los autores declaran presentar contribución igualitaria en la concepción de la investigación, obtención y procesamiento de los datos y redacción del documento

 

This is an open-access article distributed under the terms of the Creative Commons Attribution License


 
 
Ciencia Animal
 
Curva de crecimiento de pollos de ceba alimentados con dieta de harina de yuca
 

iDL. R. R. Lucena*✉:

iDM. A. C. Holanda

iDM. C. R. Holanda

 

Universidade Federal Rural de Pernambuco, Unidade Acadêmica de Serra Talhada, Serra Talhada, PE, CEP: 56909-535, Brasil.

 

Resumen

Paral lograr el éxito en la cría de pollos de ceba es necesario proporcionar una dieta rica en nutrientes esenciales para maximizar el rendimiento de las aves. En este contexto, se destaca la yuca, fuente rica en carbohidratos que puede proporcionar un gran aumento de peso y disminuir el costo de producción. El éxito actual en el mejoramiento genético de las aves ha provocado cambios en la curva de crecimiento; sin embargo, el objetivo fue modelar el crecimiento del peso de pollos de ceba alimentados con dietas que contienen yuca. Se utilizó un total de 450 pollos de ceba machos de linaje Cobb. El diseño experimental fue completamente al azar con cinco tratamientos (0, 25, 50, 75 y 100% de inclusión de harina de yuca) y cinco repeticiones, cada unidad experimental estuvo compuesta por 18 aves. Para evaluar el comportamiento del peso según la edad y la inclusión de la yuca en la dieta de los animales, se propusieron ajustes de modelos de regresión. Los modelos de potencia, tangente hiperbólica y gamma presentaron los mejores resultados para estimar el peso de los pollos de ceba. El modelo de potencia fue el más adecuado para estimar el peso de los pollos de ceba ya que presenta los mejores criterios (R² = 99,7%; SSR = 0,09 y AIC = -82,34). La adopción del modelo de potencia proporciona información sobre el mejor nivel de inclusión de harina de yuca (100%) y el mejor momento para el sacrificio de las aves (42 días) maximizando el peso en 3295 g.

Palabras clave: 
alimentación alternativa; pollos; curva de crecimiento; comportamiento del peso; modelo de potencia.
 
 
 
Introdución

La avicultura es uno de los sectores de producción animal más desarrollados en los últimos años, especialmente en el sector de producción de carne de pollo (Henrique et al. 2017Henrique, C.S., Oliveira, A.F.G., Ferreira, T.S., Silva, E.S., Mello, B.F.F.R., Andrade, A.F., Martins, V.S.F., Paula, F.O., Garcia, E.R.M. & Bruno, L.D.G. 2017. "Effect of stocking density on performance, carcass yield, productivity, and bone development in broiler chickens Cobb 500". Semina: Ciências Agrárias, 38(4): 2705-2718, ISSN: 1679-0359, DOI: http://dx.doi.org/10.5433/1679-0359.2017v38n4Supl1p2705. y Nogueira et al. 2019Nogueira, B.R.P., Reis, M.P., Carvalho, A.C., Mendoza, E.A.C., Oliveira, B.L., Silva, V.A. & Bertechini, A.G. 2019. "Performance, growth curves and carcass yield of four strains of broiler chicken". Brazilian Journal of Poultry Science, 21(4): 1-8, ISSN: 1806-9061, DOI: https://doi.org/10.1590/1806-9061-2018-0866.).

Para lograr el éxito en un sistema de cría de pollos de ceba, es necesario brindar una dieta balanceada, un ambiente favorable y realizar un manejo adecuado (Pires et al. 2019Pires, G.A., Cordeiro, M.B., Freitas, H.J., Rodrigues, S.F.C. & Nascimento, A.M. 2019. "Desempenho zootécnico e rendimento de carcaça de linhagens de frangos de corte criadas sob condições ambientais da Amazônia ocidental". Enciclopédia Biosfera, 16(29): 633-645, ISSN: 2317-2606, DOI: https://doi.org/10.18677/EnciBio_2019A48.).

La dieta balanceada es rica en nutrientes esenciales para el máximo rendimiento de las especies animales con las que se trabaja, en este contexto se destaca el uso de la yuca como ingrediente rico en carbohidratos, fibra dietética, almidón, proteínas, lípidos y cenizas (Holanda et al. 2015Holanda, M.A.C., Holanda, M.C.R., Vigoderes, R.B., Dutra Jr., W.M. & Albino, L.F.T. 2015. "Desempenho de frangos caipiras alimentados com farelo integral de mandioca". Revista Brasileira de Saúde e Produção Animal, 16(1): 106-117, ISSN: 1519-9940, DOI: http://dx.doi.org/10.1590/S1519-99402015000100012.), pudiendo componer dietas capaces de proporcionar óptimo aumento de peso y contribuir a reducir el costo de producción de pollos de ceba.

El éxito actual en el mejoramiento genético de las aves ha provocado cambios en la curva de crecimiento, aumentando la eficiencia alimentaria y en consecuencia su potencial genético, provocando que las aves sean sacrificadas cada vez más precoces. El conocimiento de las curvas de crecimiento de una especie proporciona información muy útil en la producción y manejo de poblaciones naturales y posibilita la viabilidad de la producción por la tasa de crecimiento (Lucena et al. 2017Lucena, L.R.R., Holanda, M.A.C., Holanda, M.C.R. & Sousa, A.A. 2017. "Ajuste de modelos de regressão lineares, não lineares e sigmoidal no ganho de peso simulado de frangos de corte". Agrarian Academy, 4(8): 34-45, ISSN: 2357-9951, DOI: https://doi.org/10.18677/Agrarian_Academy_2017b4.). La curva que describe una secuencia de medidas de una característica particular de una especie o individuo en función del tiempo, generalmente peso, altura, diámetro, longitud se denomina curva de crecimiento (Lucena et al. 2019Lucena L.R.R., Holanda, M.A.C., Holanda, M.C.R. & Anjos, M.L. 2019. Adjusting weight growth curve of male quails Coturnix Japonica reared in the semi-arid region of the state of Pernambuco". Acta Scientiarum Animal Sciences, 41: 1-8, ISSN: 1806-2636, DOI: https://doi.org/10.4025/actascianimsci.v41i1.42563 ). En avicultura se han propuesto varios modelos para explicar el crecimiento biológico de los pollos de ceba en función del tiempo de vida con lo informado por Sakomura et al. (2011)Sakomura, N.K., Gous, R.M., Marcato, S.M. & Fernandes, J.B.K. 2011. "A description of the growth of the major body componentes of 2 broiler chicken strains". Poultry Science, 90(12): 2888-2896, ISSN: 1525-3171, DOI: https://doi.org/10.3382/ps.2011-01602., Rizzi et.al (2013)Rizzi, C., Contiero, B. & Cassandro, M. 2013. "Growth patterns of Italian local chicken populations". Poultry Science, 92(8): 2226-2235, ISSN: 1525-3171, DOI: https://doi.org/10.3382/ps.2012-02825., Al-Samarai (2015Al-Samarai, F.R. 2015. "Growth curve of commercial broiler as predicted by different nonlinear functions". American Journal of Applied Scientific Research, 1(2): 6-9, ISSN: 2471-9730, DOI: https://doi.org/ 10.11648/j.ajasr.20150102.11.), Zhao et.al (2015)Zhao, Z., Li, S., Huang, H., Li, C., Wang, Q. & Xue, L. 2015. "Comparative study on growth and developmental model of indigenous chicken breeds in China". Open Journal of Animal Sciences, 5(2): 219-223, ISSN: 2161-7597, DOI: https://doi.org/10.4236/ojas.2015.52024. y Michalczuk et.al (2016)Michalczuk, M., Damaziak, K. & Goryl, A. 2016. "Sigmoid models for the growth curves in medium-growing meat type chickens, raised under semi-confined conditions". Annals of Animal Science, 16(1): 65-77, ISSN: 2300-8733, DOI: https://doi.org/10.1515/aoas-2015-0061..

Aunque hay informes de varios estudios con curvas de crecimiento en pollos de ceba, no se encontraron informes en la literatura de ajuste de la curva de crecimiento en pollos de ceba alimentados con la dieta de yuca, por lo que se utilizó como modelo el crecimiento del peso de los pollos de ceba alimentados con diferentes dietas que contienen yuca.

Materiales y Métodos

La investigación se realizó en el aviario de Fazenda São João, ubicado en el distrito de Santa Rita, municipio de Serra Talhada-PE, en la micro región del Sertão do Pajeú, mesorregión del Sertão de Pernambuco, bajo licencia número 127/2019 del comité de ética sobre el uso de animales de la Universidad Federal Rural de Pernambuco.

Se utilizaron 450 pollos de ceba machos del linaje Cobb, con un día de vida, peso inicial de 42 gramos, vacunados el primer día aún en la incubadora, contra Mareck, Newcastle, Gumboro y revacunados a los 14 días contra Newcastle y Gumboro.

Las aves fueron alojadas en un aviario construido en mampostería, con baldosas de cerámica y piso de concreto, revestido con lecho de material inerte (cascarilla de arroz) a una altura de 15 cm, cercado con alambre galvanizado y cortina para evitar corrientes de aire y controlar la temperatura ambiente.

Durante los primeros 14 días de vida se utilizó una lámpara incandescente de 150 watt con fuente de calor para pollos de ceba. El aviario se dividió en 25 parcelas experimentales de 2 m² cada una, con una densidad de 9 aves / m².

El diseño experimental fue completamente al azar con cinco tratamientos y cinco repeticiones, donde cada unidad experimental estuvo compuesta por 18 aves. Los tratamientos consistieron en una dieta control basada en harina de maíz y soja, y cuatro dietas de prueba que contenían 25, 50, 75 y 100 % de inclusión de harina integral de raíz de yuca suplementada con enzimas endógenas, en la cantidad de 500 gramos por tonelada de alimento.

Las raíces de yuca se adquirieron en el municipio de Araripina-PE, posteriormente las raíces fueron procesadas y deshidratadas al sol por cinco días hasta que perdieron la máxima humedad para obtener harina seca.Se tomó una muestra y se llevó al laboratorio para análisis químico que presentó los siguientes resultados: 88,56 % de materia seca, 2,54 % de proteína bruta, 0,62 % de lípidos, 5,32 % de fibra bruta, 10,84 % de fibra detergente neutra (FDN), 3,96 % fibra detergente ácido (FDA), 84,92 % de materia orgánica, 3,52 % de cenizas, 0,18 % de calcio y 0,09 % de fósforo. La energía bruta de 4.123 kcal/kg se determinó en el calorímetro IKA 200.

El resultado de la composición química se utilizó para formular las dietas experimentales junto con la energía metabolizable de 12.502 MJ/kg (determinada en un experimento de metabolismo realizado previamente con pollos, este experimento se realizó antes de formular las dietas). El complejo multienzimático estaba compuesto por galactosidasa 35 U/g, galactomananasa 110 U/g, xilanasa 1,500 U/g, β-glucanasa 1,100 U/g, y se mezcló con la premezcla en un mezclador tipo Y para mezclar bajo nivel ingredientes en las dietas y utilizarlos en la proporción de 500 gramos por tonelada de alimento para las dietas de prueba, para una mayor disponibilidad de los nutrientes contenidos en la harina de yuca entera.

Desde el primer día de vida las aves recibieron dietas experimentales según los tratamientos, siguiendo las recomendaciones nutricionales de Rostagno et. al (2017)Rostagno, H.S., Teixeira, L.F., Hannas, M.I., Lopes, J., Kazue, N., Guilherme, F., Saraiva, A., Texeira, M.L., Borges, P., de Oliveira, R.F., de Toledo, S.L. & de Oliveira, C. 2017. Tablas Brasileñas para Aves y Cerdos - Composición de Alimentos y Requerimientos Nutricionales. Ed. Departamento de Zootecnia, Universidad Federal de Viçosa, Viçosa, Brasil, p. 403-404, ISBN: 978-85-8179-122-7. (tabla 1, 2, 3 y 4).

 
Table 1.  Chemical composition and calculated of the experimental diets for broiler chickens from 1 to 7 days of age as a function of the levels cassava meal.
IngredientsLevels of cassava inclusion (%)
0255075100
Corn (kg)46.54334.90723.27111.6350.000
Soybean meal (45%)46.12947.74349.36050.97752.594
Cassava meal (kg)0.0008.88817.77726.66535.554
Dicalcium phosphate1.9302.2392.5492.8593.169
Calcitic Limestone0.9410.7050.4700.2350.000
Vegetable oil3.3304.3905.4516.5127.573
NaCl0.4560.4500.4450.4390.434
L-lysine HCl (78%)0.1330.1110.0880.0660.044
DL-methionine (99%)0.3280.3480.3680.3880.408
L-threonine (98%)0.0100.0170.0250.0320.040
Multienzyme complex0.0000.0120.0250.0370.050
Choline chloride (60%)0.1000.1000.1000.1000.100
Premix mineral/vitamin10.1000.1000.1000.1000.100
Calculated Composition (%)
Crude protein 25.31 25.31 25.31 25.31 25.31
Metabolizable energy (MJ/kg)12,54012,54012,54012,54012,540
Calcium 1.0111.0111.0111.0111.011
Phosphorus available 0.4820.4820.4820.4820.482
Digestible lysine 1.3641.3641.3641.3641.364
Digestible methionine 0.6690.6800.6920.7030.715
Digestible met+cys 0.9890.9890.9890.9890.989
Digestible threonine 0.7730.7730.7730.7730.773
Digestible tryptophan 0.2960.3040.3120.3200.328
Sodium 0.2270.2270.2270.2270.227
Fat 5.6425.7815.9216.0606.200

1Premix vitamin/kg: Folic Acid 106.00 mg; Pantothenic 2,490 mg; Antifungal 5,000 mg; Antioxidant 200 mg; Biotin 21mg; Coccidiostatic 15,000 mg; Choline 118,750 mg; Vitamin K3 525.20 mg; niacin 7,840 mg; Pyridoxine 210 mg; Riboflavina 1,660 mg; Thiamine 360 mg; Vitamin A 2,090,000 UI; Vitamin B12 123,750 mcg; Vitamin D3 525,000 UI; Vitamin E 4,175 mg. Cu 2,000 mg; I 190 mg; Mn 18,750 mg; Se 75 mg; Zn 12,500 mg.

 

 
Table 2.  Chemical composition and calculated of the experimental diets for broiler chickens from 8 to 21 days of age as a function of the levels cassava meal
IngredientsLevels of cassava inclusion (%)
0255075100
Corn 48.08036.06024.04012.0200.000
Soybean meal (45%)43.60045.23546.87048.50550.141
Cassava meal 0.0009.35518.71028.06537.420
Dicalcium phosphate1.6791.6991.7191.7391.760
Calcitic Limestone1.0170.9670.9180.8690.820
Vegetable oil4.5105.5476.5857.6228.660
NaCl0.4440.4380.4320.4260.420
L-lysine HCl (78%)0.1360.1130.0910.0690.047
DL-methionine (99%)0.3270.3480.3690.3900.412
L-threonine (98%)0.0120.0410.0710.1000.130
Multienzyme complex0.0000.0120.0250.0370.050
Choline chloride (60%)0.1000.1000.1000.1000.100
Premix mineral/vitamin0.1000.1000.1000.1000.100
Calculated Composition (%)
Crude protein 24.3024.3024.3024.3024.30
Metabolizable energy (MJ/kg)12,95812,95812,95812,95812,958
Calcium 0.9700.9700.9700.9700.970
Phosphorus available 0.4320.4320.4320.4320.432
Digestible lysine 1.3061.3061.3061.3061.306
Digestible methionine 0.6570.6690.6810.6930.705
Digestible met+cys 0.9660.9660.9660.9660.966
Digestible threonine 0.8160.8050.7940.7830.773
Digestible tryptophan 0.2820.2690.2570.2440.232
Sodium 0.2210.2210.2210.2210.221
Fat 6.8206.9907.1607.3307.500

1Premix vitamin/kg: Folic Acid 106.00 mg; Pantothenic 2,490 mg; Antifungal 5,000 mg; Antioxidant 200 mg; Biotin 21mg; Coccidiostatic 15,000 mg; Choline 118,750 mg; Vitamin K3 525.20 mg; niacin 7,840 mg; Pyridoxine 210 mg; Riboflavine 1,660 mg; Thiamine 360 mg; Vitamin A 2,090,000 UI; Vitamin B12 123,750 mcg; Vitamin D3 525,000 UI; Vitamin E 4,175 mg. Cu 2,000 mg; I 190 mg; Mn 18,750 mg; Se 75 mg; Zn 12,500 mg.

 

 
Table 3.  Chemical composition and calculated of the experimental diets for broiler chickens from 22 to 35 days of age as a function of the levels cassava meal
IngredientsLevels of cassava inclusion (%)
0255075100
Corn (kg)60.88045.66030.44015.2200.000
Soybean meal (45%)32.81434.82536.83738.84840.860
Cassava meal (kg)0.00012.56025.13537.70250.270
Dicalcium phosphate1.4201.4451.4701.4951.520
Calcitic Limestone0.7180.6550.5890.5240.460
Vegetable oil3.0843.7214.3584.9955.663
NaCl0.4220.4130.4050.3960.388
L-lysine HCl (78%)0.2200.1940.1680.1420.116
DL-methionine (99%)0.2720.2990.3270.3640.394
L-threonine (98%)0.0000.0270.0550.0820.110
Multienzyme complex 0.000.0120.0250.0370.050
Choline chloride (60%)0.1000.1000.1000.1000.100
Premix mineral/vitamin10.1000.1000.1000.1000.100
Calculated Composition (%)
Crude protein 20.58 20.58 20.58 20.58 20.58
Metabolizable energy (MJ/kg)13,16713,16713,16713,16713,167
Calcium 0.7580.7580.7580.7580.758
phosphorus available 0.3740.3740.3740.3740.374
Digestible lysine 1.1241.1241.1241.1241.124
Digestible methionine 0.5570.5720.5880.6030.619
Digestible met+cys 0.8320.8320.8320.8320.832
Digestible threonine 0.7730.7730.7730.7730.773
Digestible tryptophan 0.2250.2290.2330.2370.241
Sodium 0.2240.2240.2240.2240.224
Fat 5.6806.2856.8907.4958.100

1Premix vitamin/kg: Folic Acid 106.00 mg; Pantothenic 2,490 mg; Antifungal 5,000 mg; Antioxidant 200 mg; Biotin 21mg; Coccidiostatic 15,000 mg; Choline 118,750 mg; Vitamin K3 525.20 mg; niacin 7,840 mg; Pyridoxine 210 mg; Riboflavine 1,660 mg; Thiamine 360 mg; Vitamin A 2,090,000 UI; Vitamin B12 123,750 mcg; Vitamin D3 525,000 UI; Vitamin E 4,175 mg. Cu 2,000 mg; I 190 mg; Mn 18,750 mg; Se 75 mg; Zn 12,500 mg.

 

 
Table 4.  Chemical composition and calculated of the experimental diets for broiler chickens from 36 to 42 days of age as a function of the levels cassava meal
IngredientsLevels of cassava inclusion (%)
0255075100
Corn (kg)62.72246.97631.32115.6750.000
Soybean meal (45%)30.21732.28234.34836.41438.500
Cassava meal (kg)0.00012.97325.94638.91951.892
Dicalcium phosphate1.0891.1141.1391.1641.190
Calcitic Limestone0.7010.6340.5680.5010.435
Vegetable oil4.2184.8565.4946.1326.770
NaCl0.4070.3980.3900.3810.373
L-lysine HCl (78%)0.2260.1990.1730.1460.120
DL-methionine (99%)0.2530.2810.3090.3370.366
L-threonine (98%)0.0640.0750.0870.0980.110
Multienzyme complex0.0000.0120.0250.0370.050
Choline chloride (60%)0.1000.1000.1000.1000.100
Premix mineral/vitamin10.1000.1000.1000.1000.100
Calculated Composition (%)
Crude protein 19.54 19.54 19.54 19.5419.54
Metabolizable energy (MJ/kg)13,58513,58513,58513,58513,585
Calcium 0.6610.6610.6610.6610.661
phosphorus available 0.3090.3090.3090.3090.309
Digestible lysine 1.0671.0671.0671.0671.067
Digestible methionine 0.5250.5410.5570.5730.589
Digestible met+cys 0.7900.7900.7900.7900.790
Sodium 0.2010.2010.2010.2010.201
Digestible threonine 0.7040.7040.7040.7040.704
Fat 6.7606.9227.0857.2477.410

1Premix vitamin/kg: Folic Acid 106.00 mg; Pantothenic 2,490 mg; Antifungal 5,000 mg; Antioxidant 200 mg; Biotin 21mg; Coccidiostatic 15,000 mg; Choline 118,750 mg; Vitamin K3 525.20 mg; niacin 7,840 mg; Pyridoxine 210 mg; Riboflavine 1,660 mg; Thiamine 360 mg; Vitamin A 2,090,000 UI; Vitamin B12 123,750 mcg; Vitamin D3 525,000 UI; Vitamin E 4,175 mg. Cu 2,000 mg; I 190 mg; Mn 18,750 mg; Se 75 mg; Zn 12,500 mg.

 

Para evaluar el comportamiento del peso de los pollos de ceba según la edad e inclusión de harina de yuca, se propusieron ajustes del modelo de regresión: exponencial, Weibull, logístico, Gompertz, potencia, tangente hiperbólica y gamma (tabla 5).

 
Table 5.  Regression models evaluated
Regression ModelsEquation
Exponential Yi=w exp(β0+β1Ti+β2Mandi )εi
Weibull Yi=exp(β0+β1Ti+β2Mandi)exp(εi)
Logistic Yi= w1+exp(β0+β1Ti+β2Mandi )+εi
Gompertz Yi=w exp(exp(β0+β1Ti+β2Mandi))+εi
Power Yi=β0Tiβ1Mandiβ2εi
Hyperbolic Tangent Yi=w tanh(β0Tiβ1Mandiβ2εi)
Gamma Yi=(β0+β1Ti+β2Mandi )2+εi

where, Yiis the observed weight of the i-th broiler chickens after birth; Tiis the i-th evaluation day; Mandiis the percentage of cassava added to the diet of the i-th broiler chickens after birth and εiis the i-th error associated with weight, where presents exponential parameter distribution α to exponential model, Weibull distribution of parameters α and γ, normal distribution of mean 0 and constant variance σ² to logistic, Gompertz, power and hyperbolic tangente and Gamma distribution of parameters α and β. The metrics ω, β0, β1 and β2are the parameters associated with the model.

 

Los siguientes criterios evaluaron los modelos: Coeficiente de determinación del modelo (R²), Criterio de información de Akaike (AIC) y Suma del cuadrado de los residuos (SSR).

Let Y^i los valores del i-ésimo peso de los pollos de ceba después del ajuste del modelo y Y ̅ el peso medio de los pollos de ceba, defina la SSR para este estudio mediante la siguiente expresión:

 
SSR =i=17(Yi-Y^i)²  
 

El coeficiente de determinación del modelo se expresa por:

 
R2=1-i=17(Yi-Y^i)²i=17(Yi-Y-)²  
 

El criterio de información de Akaike (AIC), como lo define Akaike (1974)Akaike, H. 1974. "A new look at the statistical model identification". IEEE Transactions on Automatic Control, 19(6): 716-723, ISSN: 1558-2523, DOI: https://doi.org/10.1109/TAC.1974.1100705., está dado por:

 
AIC= -2lnLx\θ^+2p  
 

donde, L(x\ θ^) es la función de máxima verosimilitud, definida como la producción de la función de densidad y p es el número de parámetros del modelo.

Se utilizó el análisis de conglomerados mediante el método de Ward para verificar que modelos son más similares a sus criterios de adecuación.Posteriormente, se realizó un análisis de residuos para validar la calidad del modelo que mejor se ajustaba al crecimiento ponderal de los pollos de ceba según la edad y los diferentes niveles de inclusión de harina de yuca en su dieta. La validación del modelo se realizó mediante residuos estudentizados, análisis de apalancamiento y puntos de influencia y gráfico cuantil-cuantil de distribución normal.

Let hat matrix (H),

 
H=X(X'X)-1X  
 

y,

 
rankH= i=1nhii =p  
 

donde,  hii son los elementos diagonales de la matriz H. Suponga que cualquier observación que exceda el doble del promedio (hii> 2p/n") está lo suficientemente alejada del resto de los datos para ser considerada un punto de apalancamiento .

Residuos estudentizados definidos por:

 
ri= eiSSRn-p(1-hii)  
 

donde, ei es el residuo de la i-ésima observación del modelo (diferencia entre el peso observado y ajustado).

Para detectar un punto de influencia usamos la distancia de Cook, definida por:

 
Di= ri2phii(1-hii)  
 

if Di>2pn , punto influyente denotado.

Para realizar los análisis se utilizó el software R-project versión 2.13.1 para Windows.

Resultados y Discussión

El peso medio de las aves en relación con el tiempo de vida y las diferentes dietas con harina de yuca se muestra en la tabla 6. Para todos los períodos de evaluación, se verificó que no hubo diferencia (p-valor> 0.05) en el peso de los pollos de ceba en relación con diferentes niveles de harina de yuca en la dieta (tabla 6)

 
Table 6.  Broiler chickens weight according to lifetime and inclusion of cassava meal in diet
lifetime (days)Broiler chickens weight (g) in inclusion of cassava meal p-value
0%25%50%75%100%
7158.8±11.1161.4±10.1170.9±6.4166.8±6.3159.2±15.20.309
14457.2±22.5475.8±10.9470.9±21.2458.6±24.4456.8±25.50.514
21978.8±35.5993.2±42.7978.1±67.4965.1±58.4962.0±46.20.878
281,787.4±36.61,778.9±80.21,771.5±96.41,725.2±153.51,729.5±57.70.751
352,443.2±76.02,448.4±117.22,450.5±146.92,408.4±184.92,408.4±75.00.964
423,193.7±64.43,286.3±171.43,314.7±159.43,342.1±214.13,320.0±59.40.552
 

Los resultados de este estudio corroboran con los encontrados por de Sousa et al. (2012)Souza, J.P.L., Rodrigues, K.F., Albino, L.F.T., Santos-Neta, E.R., Vaz, R.G.M.V., Parente, I.P., Silva, G.F. & Amorim, A.F. 2012. "Bagaço de mandioca em dietas de frangos de corte". Revista Brasileira de Saúde e Produção Animal, 13(4): 1044-1053, ISSN: 1519-9940, DOI: https://doi.org/10.1590/S1519-99402012000400012. verificaron una diferencia en la ganancia de peso de pollos de ceba alimentados con 20 % de harina de yuca en la fase inicial (1-21 días), mientras que en la fase final (22-40 días) no hubo diferencia en la ganancia de peso. Carrijo et.al (2010)Carrijo, A.S., Fascina, V.B., Souza, K.M.R., Ribeiro, S.S., Allaman, I.B., Garcia, A.M. A. & Higa, J.A. 2010. "Níveis de farelo da raiz integral de mandioca em dietas para fêmeas de frangos caipiras". Revista Brasileira de Saúde e Produção Animal, 11(1): 131-139, ISSN: 1519-9940., Souza et al. (2011)Souza, K.M.R., Carrijo, A.S., Kiefer, C., Fascina, V.B., Falco, A.L., Manvailer, G.V. & García, A.M.L. 2011. "Farelo da raiz integral de mandioca em dietas de frangos de corte tipo caipira". Archivos de Zootecnia, 60(231): 489-499, ISSN: 1885-4494. y Holanda et al. (2015)Holanda, M.A.C., Holanda, M.C.R., Vigoderes, R.B., Dutra Jr., W.M. & Albino, L.F.T. 2015. "Desempenho de frangos caipiras alimentados com farelo integral de mandioca". Revista Brasileira de Saúde e Produção Animal, 16(1): 106-117, ISSN: 1519-9940, DOI: http://dx.doi.org/10.1590/S1519-99402015000100012., encontraron que no hubo diferencias en el aumento de peso de los pollos de ceba de granja alimentados con diferentes niveles de harina de yuca.

La tabla 7 muestra que los modelos exponencial, Weibull, logístico y Gompertz presentaron potencia explicativa menor que 0,90, además de presentar las mayores sumas de cuadrados de los residuos, indicando pobre adecuación de estos modelos para explicar el peso de los pollos de ceba en función de la edad y porcentaje de harina de yuca introducida en su dieta.

 
Table 7.  Adjusted regression models and model adequacy criteria to growth broiler chickens weight fed with levels of cassava meal in the diet
Regression ModelsRegression EquationSSRAIC
Exponential Y^i=exp(-2.003+0.0835T-0.00013Mand) 0.7857.84 56.2
Weibull Y^i=exp(-1.862+0.0815T-0.00027Mand) 0.70810.618.4
Logistic Y^i=3.3421+exp(4.61-0.18T-0.0016Mand) 0.8921.7766.32
Gompertz Y^i= 3.342 exp(-exp(2.63-0.129T-0.0015Mand)) 0.8884.0775.19
Power Y^i= 0.0056T1.705Mand0.001 0.9970.09-82.34
Hyperbolic T. Y^i= 3.342 tanh(0.0008T2.03Mand0.0046) 0.9750.90 8.46
Gamma Y^i= (0.113+0.042T-0.00002Mand)2 0.9940.24-93.82

R²- model determination coefficient; SSR-sum of squares of residues; AIC- Akaike information criterion; Y^i is the adjusted weight of model of the i-th broiler chickens after birth; T is the lifetime; Mand is the percentage of cassava

 

La tabla 8 muestra las estimaciones de los parámetros de los modelos con sus respectivos errores estándar, estadísticos de prueba y valor p, mostrando la significancia de cada parámetro.

 
Table 8.  Estimative, standard error, t value and p-value of parameters models
EstimateStd. errort valuep-value
Exponential
β0 -2.003 0.523 13.83<0.0001
β1 0.0835 0.017 4.91<0.0001
β2 -0.00013 0.00005 -5.93<0.0001
Weibull
β0 -1.862 0.14 -13.26<0.0001
β1 0.0815 0.005 15.96<0.0001
β2 -0.00027 0.0001 10.26<0.0001
Logistic
β0 4.61 0.353.16<0.0001
β1 -0.18 0.0116.31<0.0001
β2 -0.0016 0.00031.58<0.0001
Gompertz
β0 2.63 0.416.45<0.0001
β1 -0.129 0.013-9.96<0.0001
β2 -0.0015 0.0004-6.36<0.0001
Power
β0 0.0056 0.0014-95.788<0.0001
β1 1.705 0.01799.84<0.0001
β2 0.001 0.000497.35<0.0001
Hyperbolic Tangent
β0 0.00080.00002-28.63<0.0001
β1 2.03 0.07925.51<0.0001
β2 0.0046 0.0018 24.10<0.0001
Gamma
β0 0.113 0.0073 15.57<0.0001
β1 0.042 0.0004 116.89<0.0001
β2 -0.000020.000009 18.53<0.0001
 

Lucena et al. (2017)Lucena, L.R.R., Holanda, M.A.C., Holanda, M.C.R. & Sousa, A.A. 2017. "Ajuste de modelos de regressão lineares, não lineares e sigmoidal no ganho de peso simulado de frangos de corte". Agrarian Academy, 4(8): 34-45, ISSN: 2357-9951, DOI: https://doi.org/10.18677/Agrarian_Academy_2017b4. verificaron que los modelos exponencial, Weibull y Gompertz presentaron poder explicativo de 0,993, 0,916 y 0,948, respectivamente. Rizzi et al. (2013)Rizzi, C., Contiero, B. & Cassandro, M. 2013. "Growth patterns of Italian local chicken populations". Poultry Science, 92(8): 2226-2235, ISSN: 1525-3171, DOI: https://doi.org/10.3382/ps.2012-02825. observaron que el modelo de Gompertz fue el más adecuado para explicar el crecimiento de pollos de ceba con poder explicativo superior al 99 %, estos resultados divergentes de este estudio, que se puede explicar por la introducción de niveles crecientes de yuca en la dieta de los pollos de ceba causaron una pérdida de rendimiento de estos modelos, ya que estos autores solo evaluaron el crecimiento del peso en función del tiempo de vida de las aves.

El modelo de tangente hiperbólico presentó poder explicativo de 0,975 y sumas de cuadrados residuales de 0,90. Estos criterios clasifican estos modelos con buena precisión en la estimación del peso de los pollos de ceba, sin embargo, estos resultados son inferiores a los presentados por los modelos de potencia y gamma, (tabla 7). Michalczuk et al. (2016)Michalczuk, M., Damaziak, K. & Goryl, A. 2016. "Sigmoid models for the growth curves in medium-growing meat type chickens, raised under semi-confined conditions". Annals of Animal Science, 16(1): 65-77, ISSN: 2300-8733, DOI: https://doi.org/10.1515/aoas-2015-0061., Liu et al. (2015)Liu, X.H., Li, X.L., Li, J. & Lu, C.X. 2015. "Growth curve fitting of Bashang long-tail chicken during growth and development". Acta Agriculture Zhejiangensis, 27(5): 746-750, ISSN: 1004-1524, DOI: https://doi.org/10.3969/j.issn.1004-1524.2015.05.07., Zhao et al. (2015)Zhao, Z., Li, S., Huang, H., Li, C., Wang, Q. & Xue, L. 2015. "Comparative study on growth and developmental model of indigenous chicken breeds in China". Open Journal of Animal Sciences, 5(2): 219-223, ISSN: 2161-7597, DOI: https://doi.org/10.4236/ojas.2015.52024., Selvaggi et al. (2015)Selvaggi, M., Laudadio, V., Dario, C. & Tufarelli, V. 2015. "Modeling Growth Curves in a Nondescript Italian Chicken Breed: an Opportunity to Improve Genetic and Feeding Strategies". Japanese Poultry Science, 52(4): 288-294, ISSN: 0029-0254, DOI: https://doi.org/10.2141/jpsa.0150048. y Mohammed (2015)Mohammed, F.A. 2015. "Comparison of three nonlinear functions for describing chicken growth curves". Scientia Agriculturae, 9(3): 120-123, ISSN: 2310-953X, DOI: https://doi.org/10.15192/PSCP.SA.2015.9.3.120123 presentaron resultados similares para el modelo logístico, mientras que los resultados para el modelo de tangente hiperbólico corroboran con lo descrito por Lucena et al. (2017)Lucena, L.R.R., Holanda, M.A.C., Holanda, M.C.R. & Sousa, A.A. 2017. "Ajuste de modelos de regressão lineares, não lineares e sigmoidal no ganho de peso simulado de frangos de corte". Agrarian Academy, 4(8): 34-45, ISSN: 2357-9951, DOI: https://doi.org/10.18677/Agrarian_Academy_2017b4., es decir, para todas las investigaciones reportadas, el comportamiento del peso de los animales es similar al utilizar estos modelos

Los modelos de potencia y gamma presentaron los coeficientes de determinación del modelo más alto, las sumas más bajas de cuadrados de los residuos y los criterios de información de Akaike más bajos (tabla 7). Estos criterios indican que estos modelos son los más eficientes para estimar el peso de los pollos de ceba en función del tiempo de vida y la introducción de harina de yuca. Resultados similares fueron reportados por Lucena et al. (2017)Lucena, L.R.R., Holanda, M.A.C., Holanda, M.C.R. & Sousa, A.A. 2017. "Ajuste de modelos de regressão lineares, não lineares e sigmoidal no ganho de peso simulado de frangos de corte". Agrarian Academy, 4(8): 34-45, ISSN: 2357-9951, DOI: https://doi.org/10.18677/Agrarian_Academy_2017b4. donde verificaron que el modelo de potencia fue el más adecuado para explicar el peso de los pollos de ceba con una precisión de 0,997 seguido del modelo gamma con un poder explicativo de 0,989.

Debido a los diferentes objetivos de selección aplicados por los genetistas en las últimas décadas, los parámetros de crecimiento de los genotipos de pollos de ceba pueden diferir en varias características, incluidas las que afectan sus curvas de crecimiento potencial, con el peso y las tasas de maduración (Sakomura et al. 2011Sakomura, N.K., Gous, R.M., Marcato, S.M. & Fernandes, J.B.K. 2011. "A description of the growth of the major body componentes of 2 broiler chicken strains". Poultry Science, 90(12): 2888-2896, ISSN: 1525-3171, DOI: https://doi.org/10.3382/ps.2011-01602.).

Las diferencias entre las funciones en la tasa de crecimiento reflejan directamente el comportamiento en el ajuste de datos. Las funciones no lineales se han utilizado ampliamente para representar cambios en el peso de los pollos de ceba en función de la edad, de modo que se pueda valorar el potencial genético de los animales (Kuhi et al. 2019Kuhi, H.D., López, S., France, J., Mohit, A., Shabanpour, A., Zadeh, N.G.H. & Falahi, S. 2019. "A sinusoidal equation as an alternative to classical growth functions to describe growth profiles in turkeys". Acta Scientiarum Animal Sciences, 41: 1-7, ISSN: 1806-2636, DOI: https://doi.org/10.4025/actascianimsci.v41i1.45990.).

La estimación temprana del peso en la madurez y la tasa de crecimiento en relación con el tamaño corporal puede ser importante para fines de selección, dada su asociación con otras características y la economía de producción (Kuhi et al. 2019Kuhi, H.D., López, S., France, J., Mohit, A., Shabanpour, A., Zadeh, N.G.H. & Falahi, S. 2019. "A sinusoidal equation as an alternative to classical growth functions to describe growth profiles in turkeys". Acta Scientiarum Animal Sciences, 41: 1-7, ISSN: 1806-2636, DOI: https://doi.org/10.4025/actascianimsci.v41i1.45990.). La exploración de estos parámetros en modelos de crecimiento mediante el ajuste de curvas utilizando la edad con el peso vivo puede mejorar positivamente los rendimientos económicos (Salako 2014Salako, A.E. 2014. "Asymptotic nonlinear regression models for the growth of White Fulani and N'dama cattle in Nigeria". Livestock Research for Rural Development, 26(5), ISSN: 0121-3784, Available: <http://www.lrrd.org/lrrd26/5/sala26091.htm>.).

El éxito en el estudio de las características de crecimiento de los pollos de ceba ayudará a definir dietas más adecuadas para cubrir los altos requerimientos nutricionales durante la fase de crecimiento, desde la eclosión hasta la edad en el punto de sacrificio. Además, seleccionar la mejor función basada en la capacidad para describir la relación entre el peso vivo y la edad es el primer paso para desarrollar un programa de mejora genética (Selvaggi et al. 2015Selvaggi, M., Laudadio, V., Dario, C. & Tufarelli, V. 2015. "Modeling Growth Curves in a Nondescript Italian Chicken Breed: an Opportunity to Improve Genetic and Feeding Strategies". Japanese Poultry Science, 52(4): 288-294, ISSN: 0029-0254, DOI: https://doi.org/10.2141/jpsa.0150048.). Los parámetros de la curva de crecimiento brindan la oportunidad de planificar estrategias de selección, modificando las prácticas dietéticas o la composición genética de la forma de la curva de crecimiento (Selvaggi et al. 2015Selvaggi, M., Laudadio, V., Dario, C. & Tufarelli, V. 2015. "Modeling Growth Curves in a Nondescript Italian Chicken Breed: an Opportunity to Improve Genetic and Feeding Strategies". Japanese Poultry Science, 52(4): 288-294, ISSN: 0029-0254, DOI: https://doi.org/10.2141/jpsa.0150048.).

La figura 1 muestra que el modelo de potencia presentó mejores estimaciones de los pesos de los pollos de ceba que el modelo Gamma, porque el modelo de potencia mostró solo un valor discrepante del peso observado de los pollos que ocurrió en el día 28, mientras que el modelo Gamma presentó dos pesos discrepantes ocurridos (día 28 y 42).

 
Figure 1.  Estimates of the broiler chickens weight in the power (a) and gamma (b) models.
 

Mediante el método de conglomerado de Ward utilizando la métrica de criterios de adecuación del modelo, se verificó la formación de dos grupos de modelos al utilizar una altura de corte mayor de 60, un grupo formado por los modelos de potencia y gamma (modelos que presentaron mayor R² y menor SSR y AIC), y el segundo formado por los otros modelos (modelos que no presentaron criterios similares a los modelos gamma y de potencia) (figura 2).

 
Figure 2.  Cluster of adjusted regression models to growth broiler chickens weight fed with levels of cassava meal in the diet
 

Evaluando los tres criterios de adecuación del modelo, el análisis de conglomerados y las estimaciones de los pesos de los pollos de ceba, se propuso el modelo de potencia como el más adecuado para explicar el crecimiento de los pollos de ceba en función del tiempo de vida y los diferentes porcentajes de yuca en su dieta

Luego de definir el modelo de potencia como el más apropiado, se realizó el análisis de los residuos (figura 3). No se diagnosticaron residuos discrepantes (figura 3a), debido a que ninguno se encuentra fuera de los límites de [-2; 2], además, no se detectó apalancamiento o influencia residual (figura 3b y 3c) debido a que ningún punto excedió los criterios definidos por las líneas punteadas, el supuesto de normalidad de los residuos se diagnosticó en el gráfico cuantil-cuantil de la distribución normal, donde los residuos están dentro de las bandas de confianza (figura 3d).

 
Figure 3.  Analysis of residues of the power modelin broilers that consume cassava meal
 

La harina de yuca en la suplementación dietética de los pollos de ceba, además de promover un mejor desempeño zootécnico, disminuye los costos de producción, ya que para las dietas sin inclusión de la harina de yuca el costo de producción fue mayor porque se utilizó más maíz ($ 0.27 por kg de alimento para 0%; $ 0.26 por kg de alimento para el 25%; $ 0.24 por kg de alimento para el 50%; $ 0.23 por kg de alimento para el 75%; $ 0.21 por kg de alimento para el 100%), mientras que el costo con inclusión del 100% de harina de yuca fue menor porque se utilizó la mitad de la cantidad de maíz para la dieta de control.

En muchos problemas prácticos, como la estimación de parámetros, los valores de las funciones son inciertos o están sujetos a variación. Por lo tanto, no es necesaria una solución de alta precisión. En estas situaciones lo único que se busca es una mejora en el ajuste de la función, lo que se puede observar en el uso del modelo de potencia.

El crecimiento de peso de las aves alimentadas con harina de yuca puede estimarse utilizando el modelo de regresión de potencia. El uso del modelo de potencia proporciona información sobre el mejor nivel de inclusión de harina de yuca (100 %) y el mejor momento para el sacrificio de aves (42 días) maximizando el peso en 3295 g.