Analysis of growth curves of Guinea fowl ( Numida meleagris ) fed diets containing dry oregano ( Origanum vulgare L . ) in an organic system

H. Eleroğlu, A. Yıldırım, A. Canikli, M. Duman, and H. Bircan. 2018. Analysis of growth curves of Guinea fowl (Numidea meleagris) fed diets containing dry oregano (Origanum vulgare L.) in an organic system. Cien. Inv. Agr. 45(2): 99-108. In this study, 240 day-old guinea fowl (Numida meleagris) keets were utilized. They were divided into four treatment groups each containing 20 chicks and were randomly distributed into 12 mobile coops placed in a 100-m2 grazing area. Guinea fowl chicks were randomly allocated to 4 treatment diets containing 0%, 5%, 10%, and 15% dry oregano leaf (DOL) supplements. Nonlinear Gompertz and logistic growth models were used to estimate the mean age-body weight. The growth curve parameters for these models and the following characteristics for fowl were estimated: β0, the asymptotic weight parameter; β1, the scaling parameter; β2, the instantaneous per week growth rate; weight at age of inflection point (WIP); maximum weight gain at inflection point (MWG); and age at the inflection point (AIP). The goodness of fit (GF) for the models was assessed using the following variables: coefficients of determination (r2), mean square error (MSE), adjusted determination coefficient (ADR2), Akaike’s information criteria (AIC), chi-square test (Chi.Sq2) and residual standard deviation (RSD). The different nonlinear function results of the individual data indicated that supplementation of diets with DOL had no significant effects on growth curve parameters when compared with the control diet. Greater correlation values were estimated among β0, β1, β2, WIP, MWG and AIP in the Gompertz equation, and similar results were estimated in the logistic equation, but there was no significant correlation between β2-β1 and β2-MWG. According to the results obtained from the GF, high r 2 and ADR2 were estimated in Gompertz and logistic equations (above 0.96).


Introduction
Genetic and environmental conditions affect growth, which is known as the process of a bird gaining body weight with age until it reaches maturity (Porter et al., 2010).Growth measurements for birds and control of the environmental conditions that affect their body weight gain are common practices in the poultry industry because of their economic importance (Aggrey, 2009).In recent years, growth functions have become more prevalent for monitoring and characterizing growth and to estimate the different periods of growth such as the WIP, MWG, AIP and age of sexual maturity (Eleroğlu et al., 2014).These characteristic values are used to explain body weight gains and estimate the expected body weight at a particular age.Moreover, mathematical model results for heritability are high and widely used in research focused on selection, environmental changes (Goto et al., 2010) and prediction of daily feed requirements for several ages (Pomar et al., 2009).Additionally, it is feasible to use mathematical models to determine better management practices to increase animal production (Selvaggi et al., 2015).Growth models will allow the determination of optimal management application and productivity of guinea fowl farms (Nahashon et al., 2006a).The growth curves were applied because of their relevance when diets contain various types of additives (Abbas et al., 2014).Additives may not limit the final weight, but they may influence the shape of growth (Fatten, 2015).
There are many growth functions used to describe changes in body weight.Because these growth functions have several characteristics and different mathematical limitations, it is important to be careful when choosing the mathematical model that best describes the growth type (Norris et al., 2007).
The objective of this study was to evaluate the growth response of guinea fowl (Numida meleagris) that were fed diets containing three different levels of dry oregano (Origanum vulgare L.) raised in an organic system.For this aim, the Gompertz and Logistic growth curves were assessed to measure which model best fit the growth curves for Guinea fowl and the different statistics used to determine the GF.

Materials and Methods
This research study feeding Guinea fowl in organic systems was independently conducted in accordance with the principles and regulations of organic farming practices (OFL, 2010) and was approved by the Ethics Committee of the Cumhuriyet University in Sivas (Ethics No., 04.04.2013/39),Turkey.
In this research, a total of 240-day-old (mixedsex) Guinea fowl (Numida meleagris) keets were utilized after they were weighed and identified with a wing number.They were divided into four treatment groups each containing 20 chicks and were randomly distributed into 12 mobile coops (1.5 × 1.5 m) placed in the 100 m 2 grazing area.
As reported by Eleroğlu et al. (2016), Guinea fowl (Numida meleagris) chicks were randomly allocated to 4 treatment diets containing a 0%, 5%, 10%, or 15% dry oregano (Origanum vulgare L.) supplement.During this experiment, all basal feed and water were provided ad libitum for all keets.Nonlinear Gompertz and logistic growth models are widely used to estimate the relationship between mean age and body weight (Eleroğlu et al., 2014).The mathematical equations for these models and the characteristics of growth curves for poultry WIP, MWG and AIP are presented in Table 1 (Narinc et al., 2010;Eleroğlu et al., 2014).
For each model, β 0 was the asymptotic (mature) weight parameter, β 1 was the scaling parameter (scale parameter related to initial weight), and β 2 was the instantaneous per week growth rate (Yang et al., 2006;Raji et al., 2014;Eleroğlu et al., 2014).
The calculation of GF has different methods to compare the performances of the non-linear models.In this study, GF for the models was assessed using r 2 , MSE, ADR 2 , AIC, Chi.Sq 2 and RSD.The equations for GF are given in Table 2. Microsoft Excel 10.0 was utilized for the Chi.Sq 2 computation.The other GF criteria were calculated using ANOVA tables, and calculations were carried out with the nonlinear regression option in SPSS 15.0 (Inc.Chicago IL., USA).The Levenberg-Marquart estimation method was used for two models within the statistical software package program (Marquardt, 1963).

Results
Table 3 shows the estimated standard error of the mean and the P value for Gompertz and logistic model growth parameters for Guinea fowl (Numida meleagris) genotypes examined in an organic system.The different nonlinear function results of the individual data indicate that supplementation of diets with DOL had no significant effects on growth curve parameters (β 0 , β 1 , β 2 , AIP, WIP, MWG, and r 2 ) when compared with the control diet (P>0.05).
The estimated β 0 parameter was greater for the Gompertz model (1073.37 to 1320.31 g) when compared with the logistic equations (801.77to923.23 g).The values for the β 1 parameter in the Gompertz model were lower (3.52, 3.24, 3.30 3.21 for the supplementation of diets with DOL at levels 0%, 5%, 10%, and 15%, respectively) when compared with the respective values for the logistic model (17.16, 13.28, 13.83, 13.07, respectively).The β 2 parameter was lower in the Gompertz model (0.13 to 0.14) when compared that in the logistic model (0.27-0.29).The range in terms for AIP obtained from the Gompertz (8.62-9.94)and logistic (8.92-9.74)models were similar.
The WIP parameter from the Gompertz model was greater (394.91-485.76)when compared that in the logistic models (294.98-339.67)and was affected by the high β 0 values.Although there was no difference between MWG values from the application, the values obtained from the logistic model (84.06-96.05)were greater than the values obtained from the Gompertz model (53.17-60.41).The average observed and estimated growth curves for body weight obtained from the application of mathematical equations for the Gompertz and Logistic models are represented in Figures 1, 2 and 3. Bodyweight increased with age, and the average AIP was between 9.11 and 9.22 wks when the average MWG (57.20 and 90.20 g wk -1 ) in the Gompertz and logistic models was attained.WIP at this age averaged 440.30-315.22 g for each Gompertz and Logistic equation.After AIP, the growth rate fell and was near zero at maturity.The shapes of the estimated growth curves were distinctive "S" sigmoid.
The correlation coefficients for both models were higher and seem similar in structure (Table 4).Higher correlation coefficients were estimated among β 0 , β 1 , β 2 , AIP, WIP and MWG (P<0.01) in the Gompertz model.Although comparable results were calculated in the logistic model, there were no significant correlations between β 2 -β 1 and β 2 -MWG.The correlations were found to be negative among β 2 and β 0 , β 1 , AIP, WIP and MWG parameters (P<0.01) in the Gompertz model.Although comparable negative results were estimated for β 2 (P<0.01) in the logistic model, there was no significant correlation between β 2  The Gompertz and logistic GF results for DOL levels are presented in Table 5.According to the estimated results, the coefficient of determination (r 2 ) and adjusted determination coefficient (AR 2 ) were found to be greater than 0.94 in both growth models for DOL levels.differences between DOL levels, and the Chi 2 0.05 % parameter values for both models were estimated as higher (100%).

Discussion
No significant differences were detected between the Gompertz and logistic growth curve values for guinea fowl fed diets containing various DOL levels in an organic system (P>0.05).For this reason, average or range values were used for discussion.
The shapes of the growth curves obtained from the Gompertz and logistic nonlinear models were typically sigmoid (Figures 1, 2 and 3).According to the literature for poultry and other animals, the age-body weight and volume of the body and most organs are measured from conception to senescence; the curves of the collected data show a flattened sigmoid curve called "S" shape or nonlinear S-shaped function (Swatland, 1994;Arseniy, 2006).However, the growth curves for meat animals raised under intensive production, free range and organic systems may vary as relatively flat or steep slopes.When the data were obtained from very young animals, the growth curve may become apparent, and the growth rate was nearly stable during the intensive growing period (Swatland, 1994).Initially in the sigmoid curve, the rate of growth was low but increased with advanced age.The growth attained a maximum, it complied with to AIP, and then, it slowly declined to zero once the animals achieved their β 0 (Michael, 1999;Arseniy, 2006).In this research and similar conditions in other studies, the Gompertz and logistic growth curves for guinea fowl (Nahashon et al., 2006b) or slow-growing broiler-raised guinea fowl in an organic system at 16 wks (Eleroğlu et al., 2014) were relatively flat compared with growth curves for guinea fowl raised in commercial conditions at 8 wks (Nahashon et al., 2006a(Nahashon et al., , 2010)).
Table 3 shows that the average β 0 parameter of 868.29 g estimated by the logistic model was lower than the β 0 parameter of 1196.74 g obtained by the Gompertz model.Although the estimated β 0 values of both models were lower than the results from Nahashon et al. (2006b), the β 0 parameter obtained from the Gompertz model was greater than that obtained by the logistic model, which is consistent with the literature (Nahashon et al., 2006a(Nahashon et al., , 2006b;;Narinc et al., 2010;Miguel et al., 2012;Eleroğlu et al., 2014).Based on the average value of β 0 , the growth pattern of the guinea fowl broiler was closer to the Gompertz than the logistic model.
The logistic model showed a greater predicted β 1 (17.16g) for the guinea fowl when compared with the Gompertz model (3.52 g).Similar observations were reported previously for guinea fowl (Nahashon et al., 2006a) and slow-growing chicken genotypes raised in an organic system (Eleroğlu et al., 2014).
The AIP values were similar for the Gompertz and logistic models (from 9.11 to 9.22 wk of age; Table 3, Figures 1, 2 and 3) but were found to be higher for each model in several other studies (Santos et al., 2005;Nahashon et al., 2006aNahashon et al., ,b, 2010)).The range of AIP values for each model was estimated to be 5.72 to 5.94 wk. of age for the meat-type variety of French guinea fowl when conventionally reared for 9 wks of fattening period (Nahashon et al., 2006a(Nahashon et al., , 2010) ) and were determined to be between 6.5 to 8.2 wk. of age for the pearl gray guinea fowl during the slow-growing 22 wks of fattening period (Nahashon et al., 2006b).The range of AIP was high (6.28 and 7.08 wk. of age) in the slow-growing broilers (Santos et al., 2005), whereas the corresponding range was low (4.58 and 5.78 wk. of age) in conventionally reared fastgrowing broilers (Marcato et al., 2008).On the other hand, in this study, the point of inflection for guinea fowl was close to pure-bred chickens of unselected populations, which ranged from 9.1 to 11.64 wk. of age (Knizetova et al., 1985), and over predicted observations (11.54 to 13.99) were reported for the slow-growing chicken genotypes raised in an organic system (Eleroğlu et al., 2014).According to the results, the AIP value is influenced by genotype, rearing system and fattening period.
The WIP, β 1 , and β 2 values can vary depending on the ratio of the nutrient content.Nahashon et al. (2010) observed that WIP values were significantly lower in French guinea broilers fed the 21% CP diet (738 g) than those fed the 23% (780 g) and 25% CP diets (789 g) during the conventionally reared 9 wks of the fattening period.In contrast, in this study, according to the findings Nahashon et al. (2010), low average WIP at this age was estimated to be 440.30-319.46 g for the Gompertz and Logistic models in an organic system during 16 wks of fattening period.The observed differences are explained by the different rearing systems, fattening period and genetic origins of the flocks used.
The β 0 slowly increased with age until the AIP averaged 9.11 and 9.22 wks, at which time the MWG average was 57.20 and 90.20 g wk -1 . in the Gompertz and logistic models, respectively.Beyond this age, MWG declined rapidly and approached zero at maturity.The β 0 , β 1 and β 2 values for guinea fowl predicted by the Gompertz and logistic models for the supplementation of diets with DOL at levels of 0%, 5%, 10%, and 15% were compatible with observed body weight values (Figures 1, 2 and 3).
The two models fit the growth curves for guinea fowl in an organic system very well, and the fitting degrees r 2 were all above 0.95; however, the logistic model was the best performing model (0.965%).The GF for the Gompertz and logistic growth curve models in this study was found to be concordant with various studies (Norris et al., 2007;Narinc et al., 2010).Under optimum growing conditions, this maturation rate showed up in the logistic equation, which is a sigmoidal growth curve that describes broiler growth with amazing accuracy (Eleroğlu et al., 2014).This result implies that the growth pattern of guinea fowl was closer to the logistic than the Gompertz model.Although these results are consistent with previous results by Eleroğlu et al. (2014), the results are not compatible with results of Nahashon et al. (2006b) because of the differences in the duration of fattening and breeding systems.
In the current study, the growth function estimates of β 0 , β 1 , β 2 , AIP, IWP, MWG and r 2 for the guinea fowl fed diets containing DOL at levels 0%, 5%, 10%, and 15%, were 1196.74,3.32,0.14,9.11,440.30,57.20 and 0.96,respectively,in the Gompertz model and 868.29,14.34,0.28,9.22,319.46,90.20 and 0.97, respectively, in the logistic models.These means were not significant in the Gompertz nor the logistic models (P>0.05).Based on the Gompertz and logistic growth model estimates, feeding with DOL at a level of 15% can be recommended as safe and as meat flavor or growth for the guinea fowl in an organic system.

Table 1 .
The mathematical equations for the models and characteristics of growth curves for poultry

Table 2 .
The criteria of the GF test in the selection of Gompertz and logistic models 2 −((k−1/n−k)(1−r 2 )) Mean square error MSE SE/ (n−k) Akaike's information criteria AIC n.ln (SE/n)+2k Residual standard deviation RSD (SE) 1/2 /(n-k) 1/2 O i =measured value; E i =estimated value; SE=sum of squared errors; TS=total sum of squares; n=number of observations; k=number of parameters

Table 3 .
Estimated mean of standard error and P value for Gompertz and logistic model growth parameters in guinea fowl † SEM: Standard error of the mean