Comparison of the Quality Adjusting of Nonlinear Models for Organs, Carcass and Body Components in Meat-Type (Coturnix Coturnix Coturnix) and Laying- Type (Coturnix Coturnix Japonica) Quail

The objective of this study was to evaluate the adjustment quality of nonlinear models to data organs growth, carcass and body components of meat-type (Coturnix coturnix coturnix) and japanese laying-type (Coturnix coturnix japonica) quail. A total of 1350 quails from one to 42 d old were distributed in a completely randomized design, with five replicates each. To determine the organs growth (gut, heart, liver and gizzard), carcass and body components (wing, thigh and drumstick, back and breast), two quails per repetition were slaughtered weekly. The data were evaluated in function of different nonlinear models (Logistical, Brody, Richards, Von Bertalanffy and Gompertz). All models studied adjusted the data, differing in adjustment quality. Brody model showed the best description of gut length to all treatments. For the data gizzard weight, heart, liver and gut, the models that best adjusted, presenting smaller residual mean square and numbers iterations were Gompertz and Logistical. The Gompertz, Logistic and Von Bertalanffy models were the most adequate to describe the thigh and drumstick growth, back and breast, and Gompertz models and Logistic to describe the wing growth and carcass, showing lesser number of iterations to achieve the convergence of date, as well as low residual mean square and squares sums of the regression residuals. The Gompertz model was the most appropriate to describe the organs growth and body components in meatand laying-type quail when evaluated in growth phase.


IntRoduCtIon
The development of the bird as a whole can be interpreted as the sum of the organs weights and parts, where each part has its own characteristics of growth, which should be evaluated in ideal conditions or not limiting, for the occurrence the of expression of their maximum genetic potential.
There are several factors that interfere in the growth curves, as well as: genetics, gender, nutrition, management and ambience.The bird's growth study is very important in animal production, for providing data which can be used to optimize the quail's growth, in order to increase the size of the prime cuts, keeping the proper size of the organs, thereby avoiding future metabolic disorders (Marcato, 2010).
One of the main advantages that the simulation of growth through mathematical models provides is an estimate of the parts; weight and

Animals and diets
The following experimental procedure was approved by the ethics committee on the use of animals (CEUA) of the State University of Maringá (UEM) (Protocol N o .061/2012).
A total of 1350 non-sexed quails of one day of age were used, consisting of 400 of the meat-type quail strain (Coturnix coturnix coturnix), 450 of the yellow laying strain (Coturnix coturnix japonica) and 500 of the red laying strain (Coturnix coturnix japonica).The meat-type strain is used commercially and the yellow and red are laying strains that were genetically improved in the genetic improvement program of the UEM.
The quails were housed in a conventional shed, divided into 15 cages of 5.0 m 2 , where each cage was considered an experimental unit.It They were distributed in a completely randomized design with three treatments (each treatment corresponded to one quail strain) and five replicates with 80 birds per experimental unit of the meat-type quail strain, 90 birds of the yellow strain and 100 birds of the red strain.The experimental period was from 1 to 42 days of age.
Throughout the experimental period, the quail were raised in a conventional system, receiving feed and water ad libitum.The formulated diets were based on maize and soya bean meal and the values for feed chemical composition were determined according to Rostagno et al. (2011) depending on the nutritional requirements of quails at different stages of growth (Table 1).

Organs weight and carcass components
To determine the growth of organs and carcass components of the quails, the methodology described by Sakomura & Rostagno (2016) was used.The slaughters were performed weekly for a total of five quails per treatment at one day of age and two quails per replicate (one male and one female) at 7, 14, 21, 28, 35 and 42 days of age.The birds were selected based on the average body weight (± 5%) in each experimental unit.Subsequently, the birds were fasted for six hours, weighed again and then slaughtered via electronarcosis and posterior displacement of the occipital bone and atlas.The gut length and the weight of the following carcass components and organs were measured post mortem: wings (weight of two wings together), thighs and drumsticks (weight of two thighs and drumsticks together), back, breast, heart, liver, gizzard and gut.

Statistical analysis
Using values for carcass components and organs weights, growth curves were prepared (SAS Inst.Inc., Cary, NC) using the following non-linear models: Gompertz (Fialho, 1999), A.e -e-B (t-C) ; Brody (1945), A (1 -Be -kt ); Von Bertalanffy (1957), A (1 -Be -kt ) 3 ; Logistics (Nelder, 1961), A (1 + Be -kt ) -1 and Richards (1959) , A (1 -Be -kt ) M , where for all the models the parameter A is the weight at maturity (g), K is the maturity rate (d -1 ), B is a constant of integration without biological interpretation, except in Gompertz that has biological interpretation, representing the relative growth at the inflection point (g/d per g); M e C represent the age (d) of the inflection point of the growth curve; e is the neperian logarithm.For Brody model m = 1 (g/d), Von Bertalanffy m = 3 (g/d), Logistics m = -1 (g/d) and to Richards m is the variable.
Parameter K (for Brody, Von Bertalanffy, Logistic and Richards) and B (for Gompertz), is the growth rate of the animal, in which the higher rate indicates that the animal growth is faster, requiring less time to reach the adult weight (Carneiro et al., 2014).Already, the Residual mean square (RMS); squares sum of the regression residuals (SSRR); number (N).For Brody, Von Bertalanffy, Logistic and Richards, the parameter A (g) is the weight at maturity, K (d -1 ) is the maturity rate, B is a constant of integration without biological interpretation and C for Richards is also the integration constant.For Gompertz, A (g) is the maturity weight; B (d -1 ) is the maturity rate and C (d) is the time to maximal growth.parameter C for Gompertz means the age at which the animal's growth rate is maximal, that is, the inflection point of the curve goes from increasing to decreasing, where daily weight gains begin to decrease gradually (Freitas, 2005).
To choose the most appropriate model, the adjustment quality to the data was taken into consideration as well as the following criteria: convergence of the models, residual mean square (RMS) and square sum of the regression residuals (SSRR) beyond the factor of computational difficulty of the adjustment model, which relates to the number of iterations for convergence of functions.Therefore, the higher values of the RMS and SSRR and the higher numbers of iterations, the quality of adjustment of the non-linear models to the date is worse, and It is not indicated to describe the growth of the animals.

Organs growth
All analyzed models adjusted to the data, however they differ in the adjustment quality (Table 2, 3 and 4).
The Brody model was the best to describe gut growth (weight and length), in meat-type quail (Table 2), given its RMS (1.48 and 44.10) and greater Residual mean square (RMS); squares sum of the regression residuals (SSRR); number (N).For Brody, Von Bertalanffy, Logistic and Richards, the parameter A (g) is the weight at maturity, K (d -1 ) is the maturity rate, B is a constant of integration without biological interpretation and C for Richards is also the integration constant.For Gompertz, A (g) is the maturity weight; B (d -1 ) is the maturity rate and C (d) is the time to maximal growth.computational speed, with iteration numbers of 12 and 8.For the heart, these same models best adjusted, with RMS (0.10 and 0.09, respectively) and SSRR (5.9 and 5.6, respectively), beyond a smaller number of iterations for convergence of data (9 for both models, respectively).With relation to the liver weight, the Gompertz models and Von Bertalanffy, respectively, were considered the most appropriate, because it had lower SSRR (53.9 and 53.4).The gizzard showed better adjustment to the Gompertz models and Logistic, because they have shown smaller RMS (0.76 and 0.74, respectively) and SSRR (46.9 and 46.1, respectively).
According to Table 3, the Gompertz models and Logistic best describe the gut (weight) growth, heart, liver and gizzard in red laying quail.For the gut (weight) growth, the Gompertz model and Logistic showed the same values of RMS (0.70) number of iterations (7) and SSRR (43.6).For heart variable, the same models were chosen because they have the same RMS (0.02) SSRR (1.5) and number of iterations ( 7).O Gompertz model to the liver present a low RMS (0.22), and to the gizzard has low RMS (0.13), SSRR (8.2) and number of iterations ( 6).The Logistical model and Von Bertalanffy also showed good adjustment, but with values very close to the Gompertz.The model that best adjust the Residual mean square (RMS); squares sum of the regression residuals (SSRR); number (N).For Brody, Von Bertalanffy, Logistic and Richards, the parameter A (g) is the weight at maturity, K (d -1 ) is the maturity rate, B is a constant of integration without biological interpretation and C for Richards is also the integration constant.For Gompertz, A (g) is the maturity weight; B (d -1 ) is the maturity rate and C (d) is the time to maximal growth.For yellow laying quail, Gompertz was also featured in adjustment quality among the models analyzed (Table 4).However, Brody better adjusted to the data of gut length, presenting low number of iterations (6), RMS (16.84) and SSRR (1044.4),already to the weight of gut, Gompertz presented low RMS (0.45).For weight of heart, Gompertz and Logistic were the best adjustment, showing smaller RMS (0.03 for both, respectively).Gompertz was the most appropriate to describe the gizzard growth and liver according to their number of iterations (7 and 9, respectively) and their smallest SSRR (0.21 and 0.30, respectively).

Component carcass growth
All analyzed models adjusted to the data, however they differ in the adjustment quality (Table 5, 6 and 7).
For body components of meat-type quail data, (Table 5) the Gompertz model was the best adjustment to date to describe the wing growth, it is due the fact of this have shown a lower RMS (0.90), SSRR (55,6) Residual mean square (RMS); squares sum of the regression residuals (SSRR); number (N).For Brody, Von Bertalanffy, Logistic and Richards, the parameter A (g) is the weight at maturity, K (d -1 ) is the maturity rate, B is a constant of integration without biological interpretation and C for Richards is also the integration constant.For Gompertz, A (g) is the maturity weight; B (d -1 ) is the maturity rate and C (d) is the time to maximal growth.and number of iterations ( 7).The Von Bertalanffy model obtained better quality adjustment to date of weight of thigh and drumstick, back and breast, because it showed low values of RMS (2.58;8.59;7.67,respectively),but the Gompertz model stands out quality adjustment and for these variables showed a low number of iterations for convergence of data (7, respectively).
In red laying quail, it was observed that the Gompertz models and Logistic were the most adequate to describe the wing growth, thigh, drumstick and breast (Table 6).The adjustment quality of Gompertz was better, because in all variables it had low RMS (0.31;0.88;4.19),low SSRR (19.5;55.6;259.9)and a smaller number of iterations for convergence of data (6; 7; 7), respectively.For back, Gompertz was also the best model, with low values of RMS (1.89), SSRR (117.1) and iteration numbers (6).
The Gompertz and Logistic models were the most adequate to describe the wing growth and thigh and drumstick, being the first slightly higher, showing less numbers of iterations to achieve the convergence of Residual mean square (RMS); squares sum of the regression residuals (SSRR); number (N).For Brody, Von Bertalanffy, Logistic and Richards, the parameter A (g) is the weight at maturity, K (d -1 ) is the maturity rate, B is a constant of integration without biological interpretation and C for Richards is also the integration constant.For Gompertz, A (g) is the maturity weight; B (d -1 ) is the maturity rate and C (d) is the time to maximal growth.Residual mean square (RMS); squares sum of the regression residuals (SSRR); number (N).For Brody, Von Bertalanffy, Logistic and Richards, the parameter A (g) is the weight at maturity, K (d -1 ) is the maturity rate, B is a constant of integration without biological interpretation and C for Richards is also the integration constant.For Gompertz, A (g) is the maturity weight; B (d -1 ) is the maturity rate and C (d) is the time to maximal growth. dISCuSSIon Choosing the best model to describe the quail growth is extremely important to help the researchers make better decisions.According to Fitzhugh Jr. & Taylor (1976) in the minimum three items should be analyzed to choose the best model: the possibility of biological interpretation of the parameters, adjustment quality and computational difficulties.On this assumption, the results found in this work are correct, since all these items were considered in the evaluation method used.However, Mota et al. (2015), showed other criteria for choosing the best model to describe the growth curve of genetic groups of quail, such as, adjusted determination coefficient (R²), the asymptotic standard deviation, the average deviation absolute of the residues, the asymptotic index, the Bayesian information criterion, Akaike criterion and the mean square of the error.
Grieser DO, Furlan AC, Ribeiro PM, Zancanela V, Del Vesco AP, Gasparino E Zardin AMSO, Marcato SM Comparison of the Quality Adjusting of Nonlinear Models for Organs, Carcass and Body Components in Meat-Type (Coturnix Coturnix Coturnix) and Laying-Type (Coturnix Coturnix Japonica) Quail intestine length was Brody with RMS (15.37),SSRR (952.6) and low number of iterations (5).

Table 2 -
Estimated values of the nonlinear models parameters for weight of organs (gut, liver, gizzard and heart) in meattype quail

Table 3 -
Estimated values of the nonlinear models parameters for weight of organs (gut, liver, gizzard and heart) in red laying quail

Table 4 -
Estimated values of the nonlinear models parameters for weight of organs (gut, heart, liver and gizzard) in yellow laying quail

Table 5 -
Estimated values of the nonlinear models parameters for weight of carcass components (wings, thighs and drumsticks, back and breast) and carcass in meat-type quail

Table 6 -
Estimated values of the nonlinear models parameters for weight of carcass components (wings, thighs and drumsticks, back and breast) and carcass in red laying quail

Grieser DO, Furlan AC, Ribeiro PM, Zancanela V, Del Vesco AP, Gasparino E Zardin AMSO, Marcato SM Comparison of the Quality Adjusting of Nonlinear Models for Organs, Carcass and Body Components in Meat-Type (Coturnix Coturnix Coturnix) and Laying- Type (Coturnix Coturnix Japonica) Quail data
, as well as low SSRR and RMS (Table7).For back and breast, Von Bertalanffy and Gompertz models showed better adjustment, being that Gompertz stood out presented lower values of RMS (1.66; 1.97, respectively) and number of iterations (7 for both, respectively).

Table 7 -
Estimated values of the nonlinear models parameters for weight of carcass components (wings, thighs and drumsticks, back and breast) and carcass in yellow laying quail