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Comparison of Growth Curves by Growth Models in SlowGrowing Chicken Genotypes Raised the Organic System.

Byline: Hasan Eleroglu Arda Yildirim Ahmet Sekeroglu Fikret Nafi CoksAlyler and Mustafa Duman

Abstract

Two hundred and forty slowgrowing chickens consisting of equal numbers of Hubbard S757 (S757) and Hubbard Grey Barred JA (GBJA) strains were utilized for the investigation in organics system and were used to estimate growth curve in Gompertz and Logistic model. The asymptotic weights for GBJA and S757 genotype female; male in the Gompertz model were estimated 3725.34 g; 6109.60 g and 4876.10 g; 6496.47 g and same parameter were found in Logistic model 2133.33 g;2906.35 g and 2790.37 g; 3635.00 g respectively. The Gompertz model was higher estimate than Logistic model for the asymptotic weights parameter. The instantaneous growth rate for GBJA and S757 genotype female; male in the Gompertz model were estimated 0.1424; 0.1288 and 0.1525; 0.1495 and same parameter values were found in Logistic model 0.3753;0.3734 and 0.3873; 0.3949 respectively. Significant difference was observed for the instantaneous growth rate parameter between GBJA and S757 genotypes in each of models. According to the results of goodness of fit in Gompertz and Logistic growth curve models the coefficient of determination (R2) and adjusted coefficient of determination (adj.R2) were detected above 0.996 in boot models for two genotype broilers. The highest value of R2 and adj.R2 were obtained from the Logistic model in GBJA. The two models were all fitted the growth curves of slowgrowing chicken genotypes in organic system very well and the fitting degrees R2 were all above 0.998; for the two models; however Logistic model was the best (0.999%).Copyright 2014 Friends Science Publishers

Keywords: Growth models; Organic production; Slowgrowing; Growth parameters

Introduction

The alternative rearing systems applied to broilers include extensive indoor system free feeding free range label rouge and organic production (Fanatico et al. 2005; Narinc et al. 2010). Currently consumer interest is growing in organic and natural poultry products. It is unavoidable that great economic losses occur with the production of fast growing broiler hybrids under conditions wherein environmental factors are not controlled (Narinc et al.2010). Therefore organic programs use slowgrowing meat birds which were designed for alternative production systems and the gourmet market and have a growing period of at least 81 d (Westgren 1999; Fanatico and Born 2001; OFL 2010).Poultry industries face various decisions in the production cycle that include nutrient and mineral supply to birds cost and type of feed range of bird health welfare and environmental issues that affect the profitability of operation (Darmani Kuhi et al. 2010). Growth curve models are of great importance for animal production in that they provide an opportunity for practical interpretations about these decisions (Akbas and Oguz 1998) and estimation of daily nutrient requirements for growth. These estimates can be used for calculation of total feed requirement (Ahmadi and Mottaghitalab 2007). In this regards through analysis and study of poultry growth curve it could be know dynamically its growth course to forecast the poultry growth law; and instruct the feeding and management programs to improve the selection and breeding effect (Yang et al. 2004). The nonlinear investigation of the growth process has some advantages in not only mathematically explaining of growth but also estimating the relationship between feed requirements and body weight which plays a crucial role in animal husbandry (SengA1/4l and Kiraz 2005).Logistic Gompertz and Bertalanffy equations are often used to fit the growth curve of poultry. Many broiler growth data analyses have been conducted using the well known Gompertz growth function which describes a single sigmoidal growth phase (Wang and Zuidhof 2004). In recent years there are many studies that have been performed with respect to growth analysis in slowgrowing broilers. Santos et al. (2005) used the Gompertz model to analyze growth in two slowgrowing broiler lines housed in indoor and semiopen systems. N'Dri et al. (2006) made estimates of genetic parameters for Gompertz model parameters in slowgrowing broilers reared in the label rouge system. Dottavio et al. (2007) and Dourado et al. (2009) used the Gompertz model to examine growth of slowgrowing broilers reared in the free range system.Three nonlinear growth models Logistic (Gang and Zhen 1997) Gompertz (Mignon-Grasteau et al. 1999) and Bertalanffy (Zheng 1995) were used by Yang et al. (2006) to estimate growth curve of Jinghai yellow mixedsex chicken and compare the three mathematical models fitting for this estimation. Gompertz Logistic and Richards were fitted by Norris et al. (2007) to estimate and compare the growth curve parameters for body weight of indigenous Venda and Naked Neck chickens. They carried out some analyses to test the existence of differences in the growth pattern between these breeds. Narinc et al. (2010) used Bertalanffy Gompertz and Logistic models to estimate the growth curves of mediumgrowing female and male broilers reared in extensive indoor system. A number of growth models can be used to determine the agebody weight relationship of animals. These growth curves have different characteristics and different mathematical limitations. It is understood from previous research (Norris et al. 2007) that it becomes important to carefully consider the choice of an appropriate model that best describes a particular growth pattern.The objective of the current study was comparison of average growth curves with the mean of individual growth curves in slowgrowing genotypes raised in the organic system. The Gompertz and Logistic models were compared to evaluate which model best described the growth curves for two slowgrowing lines of broilers.

Materials and Methods

The study was carried out at Cumhuriyet University Sivas located in the central Anatolian region of Turkey. Two hundred and forty slowgrowing chickens consisting of equal numbers of Hubbard S757 (S757) and Hubbard Grey Barred JA (GBJA) strains were utilized for the investigation. In the study day old male and female chicks were weighed identified with a wing number. The experiment was approved by the Ethics Committee of the Cumhuriyet University in Sivas (Ethics No.20.06.2011/50) Turkey.There were 12 chicken portable shelters (1.5 x 1.5 m) each containing 20 birds per replication with 10 birds/m2 stocking density placed in each of the 100 m2 grazing area. The research was carried out according to the principles and implementation of regulation on organic agriculture (OFL

2010) published by the Republic of Turkey Ministry of Food Agriculture and Livestock. Initially 14 dayold chicks were housed in mobile housing feed and water were provided adlibitum and they were not allowed go out for grazing. After this period chicks were allowed to go out and graze freely and all basal feed and water were provided between the hours 07.0019.00 adlibitum for all chicks during the experimental period. Body weights (BW) were recorded for each bird weekly up to the age of 14 weeks.Widely used nonlinear growth model Gompertz and Logistic were applied to estimate the mean agebody weight relationship. The mathematical notations of growth models are presented in Table 1. Growth curves for poultry generally have the following characteristics: an accelerating phase of growth from hatching a point of inflection in the growth curve at which the growth rate is maximum a phase where growth rate is decelerating and a limiting value (asymptote) mature weight (Wilson 1977). The equations used to estimate the age of inflection point (IPA) weight of inflection point (IPW) and maximal growth rate (MGR) in the models are presented in Table 1. Where W is the corresponding weight at time t. In the models AY0 is the asymptotic (mature) weight parameter AY1 is the scaling parameter (constant of integration) and AY2 is the instantaneous growth rate (per week) parameter (Yang et al. 2006).There are several statistics used to determine the goodness of fit. The model with smallest standard error of prediction is assumed to have the best fit to the data and in order that asymptotic weight values offered the best opportunity to make direct comparisons among all models (Brown et al. 1976). Chisquare test for measurement and estimated values (Chi2) R2 adj.R2 Mean Square Error (MSE) Akaike's information criteria (AIC) and ResidualStandard Deviation (RSD) are used to compare the performances of the estimated models (Akaike 1974; Yang et al. 2006; Narinc et al. 2010; Gurcan et al. 2012; Miguel et al. 2012; Beiki et al. 2013).Gompertz and Logistic growth models were compared to find the optimum growth model for different genders of slowgrowing broilers raised by the organic system. The goodness of fit criteria was summarized in Table 2.The Chisquare test was separately applied for the growth curves of 231 individuals. Microsoft Excel 7.0 wasused for Chisquare calculations. Growth data for anindividual was accepted as fitting the model" when theChisquare value was equal or small then table value(2=2). The number of growth curves that fitted the 0.05 model is given in Table 5 as a percentage of total growth curves. The other goodness of fit criteria was calculated from ANOVA tables of nonlinear regression. Calculations were carried out with nonlinear regression option in the SPSS 15.0 (Inc. Chicago IL. USA). Statistical software package program with LevenbergMarquart estimation method (Marquardt 1963) used for two models.

Table 1: Equations and properties for special cases of

Gompertz and Logistic models

###Gompertz###Logistic

Mathematics model###0exp(-1exp(-2t))###0(1+ 1 exp-2t)-1

Inflection Point Age (IPA)###(ln 1)/2###(ln 1)/2

Inflection Point Weight (IPW)###0 /e###0 /2

Maximal Growth Rate (MGR)###2 IPW###2 IPW/2

Table 2: The goodness of fit criteria based on Gompertz and Logistic models

Results

Criteria###Abbrev.###Equation

Chisquare test###2###n

###(O i - E i ) 2

###i =1

###Ei

Coefficient of determination###R2###1-(SSE/SST)

Adjusted determination coefficient Adj.R2###R2-((k-1/n-k)(1-R2))

Mean Square Error###MSE###SSE/ (n-k)

Akaike's Information Criteria###AIC

###n.ln (SSE/n) 2k

Residual Standard Deviation###RSD###(SSE)1/2/(n-k)1/2

Oi=Measured value at the i###SSE=Sum of###n=the number of

moment###Squared Errors observations

Ei=Estimated value at the i###SST=Total Sum k=the number of

moment###of Square###parameters

Estimations of growth curve parameters using a nonlinear Gompertz and Logistic model on two different slow growing broiler genotypes performed under organic system are shown in Table 3.The values of AY0 parameter for GBJA and S757 genotype female; male in the Gompertz model were estimated 3725.34 g; 6109.60 g and 4876.10 g; 6496.47 g and same parameter were found in Logistic model2133.33 g; 2906.35 g and 2790.37 g; 3635.00 respectively. In addition AY0 parameter was estimated high (P less than 0.01) for S757 and GBJA broilers in each of sex and models. The AY0 values of male and female predicted by the logistic model for two genotypes were compatible with observed body weight values than the predicted by the Gompertz model (Figs. 1 2 3 and 4). This implies that the growth pattern of the GBJA and S757 broiler was closer to the Logistic than the Gompertz model.The values AY2 parameter for GBJA and S757 observed for IPA parameter between genotypes and sex in each of models (P less than 0.01). In addition there were interaction between genotype and sex in Gompertz model (P less than 0.05) but no significant interaction was observed in Logistic model.

Table 3: Means estimation of growth curve parameters using a nonlinear model

###Gompertz Model

Genotype1###Sex2###03###14###25###IPA6###IPW7###MGR8

GBJA###F###3725.34###5.36###0.1424###12.01###1370.58###190.22

###M###6109.60###5.81###0.1288###13.99###2247.79###279.48

S757###F###4876.10###5.41###0.1525###11.54###1793.97###256.27

###M###6496.47###5.84###0.1495###12.11###2390.18###342.76

Pooled SEM9###142.11###0.0367###0.0016###0.1847###52.28###4.093

Genotype###NS###

Sex###

G X S10###NS###NS###NS###NS###NS

###Logistic Model

GBJA###F###2133.33###50.26###0.3753###10.37###1066.67###199.57

###M###2906.35###62.52###0.3734###11.04###1453.18###270.90

S757###F###2790.37###49.38###0.3873###10.02###1395.16###270.02

###M###3635.00###61.79###0.3949###10.40###1817.50###358.50

Pooled SEM9###38.24###0.9921###0.0019###0.0597###19.12###4.027

Genotype###NS###

Sex###NS###

G X S10###NS###NS###NS###NS###NS###

1###6

GBJA = Hubbard Grey Barred JA; S757 = Hubbard S757###IPA = Inflection Point Age

2###7

F = female; M = male###IPW = Inflection Point Weight

3###8

0 = Asymptotic (mature) weight###MGR = Maximal Growth Rate

4###9

1 = Scaling parameter###Mean of Standard Error

5###10

2 = Instantaneous growth rate###Genotype X Sex

###P less than 0.05; P less than 0.01; NS P greater than 0.05.

Table 4: Phenotypic correlations between growth parameters for two nonlinear models

###Gompertz Model

###Genotype1###Sex2###03###14###25###IPA6###IPW7

Sex2###-0.14

03###0.12###0.44

14###-0.02###0.40###0.30

25###0.32###-0.21###-0.65###0.02

IPA6###-0.24###0.26###0.84###0.30###-0.88

IPW7###0.12###0.44###greater than 0.99###0.30###-0.65###0.84

MGR 8###0.43###0.64###0.77###0.44

###-0.18###0.37###0.77

###Logistic Model

Sex2###-0.13

03###0.51###0.63

14###-0.08###0.42###0.21

25###0.28###0.01###0.09###0.34

IPA6###-0.31###0.33###0.11###0.50###-0.62

IPW7###0.51###0.63###greater than 0.99###0.21###0.09###0.11

MGR 8###0.56###0.57###0.94###0.30###0.41###-0.11###0.94

1###6

GBJA=Hubbard Grey Barred JA; S757=Hubbard S757###IPA = Inflection Point Age

2###7

F = female; M = male###IPW = Inflection Point Weight

3###8

0 = Asymptotic (mature) weight###MGR = Maximal Growth Rate

4###9

1 = Scaling parameter###Genotype X Sex

5###

2 = Instantaneous growth rate###P less than 0.05; P less than 0.01

The values MGR for GBJA and S757 genotype female; male in the Gompertz model were estimated 190.22;279.48 and 256.27; 342.76 and same parameter were found in Logistic model 199.57; 270.90 and 270.02; 358.50 respectively. Significant difference was observed for MGR parameter between genotypes and sex in each of models (P less than 0.01). In addition there were interaction between genotype and sex in Logistic model (P less than 0.05) but nosignificant interaction was observed in Gompertz model.The estimated growth curve and observed mean body weight by Gompertz and Logistic model are shown in Fig.1 2 3 and 4. The shape of the growth curve predicted is typically sigmoid. Body weight is rapidly increasing until age at the inflection point (range: 10.0213.99 week) at which maximal growth rate (range: 190.22358.50 g/week) was attained. Body weight range at this age is estimated1066.672390.18 g for each model. Beyond this age growth rate declines and approached zero at maturity.Correlations between growth curve parameters in this study are higher and showed a similar pattern in both models (Table 4).The correlations between the growth curve parameters were found to be negative genotype for IPA (P less than 0.01) but positive for AY2 (P less than 0.01) and MGR (P less than 0.01) in Gompertz model. Similar results were found in addition to positive for IPW (P less than 0.01) in Logistic model.

Table 5: Goodness of fit criteria results for applied Gompertz and Logistic models

###Items###Chi2%

Model###Genotype1###2

###Sex###less than 0.05###R2###Adj.R2###MSE###AIC###RSD

Gompertz###GBJA###F###21.43###0.998###0.998###189.12###296.49###13.75

###M###29.03###0.998###0.998###199.53###331.29###14.13

###S757###F###5.88###0.996###0.996###473.51###427.99###21.76

###M###2.22###0.997###0.997###1130.16###319.25###33.62

Logistic###GBJA###F###71.43###greater than 0.999###greater than 0.999###41.87###212.06###6.47

###M###62.90###greater than 0.999###greater than 0.999###48.82###243.99###6.99

###S757###F###13.24###0.999###0.999###192.15###365.75###13.86

###M###13.33###0.999###0.999###468.07###279.58###21.64

1

GBJA = Hubbard Grey Barred JA; S757 = Hubbard S757###Adj.R2 Adjusted determination coefficient

2

F = female; M = male###MSE Mean Square Error

Chi2(0.05)=23.68 (df=14) n=231###AIC Akaike's Information Criteria

R2 Coefficient of determination###RSD Residual Standard Deviation

Likewise higher positive correlations values were estimated between sex AY0 AY1 IPA IPW and MGR (P less than 0.01) but negative value were found for AY2 (P less than 0.01) in Gompertz model except AY2 values similar result estimated in Logistic model. Although high positive relationships between AY0 and AY1 IPA IPW and MGR were found (P less than 0.01) in two models but negative correlations were estimated between AY0 and AY2 in Gompertz (P less than 0.01) on the other hand higher positive correlation value was estimated as + greater than 0.999 between AY0 and IPA in growth curve parameters of each model.The results of goodness of fit in Gompertz and Logistic growth curve models for female and male broilers of GBJA S757 genotype are presented in Table5. According the results the values of R2 and adj.R2 were detected above 0.996 in both models for two genotype broilers. The highest value of R2 and adj.R2 were obtained from the Logistic model in GBJA. Fitting the growth functions led to the lowest MSE=41.87 48.82;AIC=212.06 243.99 and RSD=6.47 6.99 values of femalesand males GBJA genotype respectively for Logistic model. Chisquare test was applied for measurement and estimated individual values of genotype GBJA S757 males and females for the two models to compare their fitness (Table 5).The values Chi2 % parameter for GBJA and S757 genotype female; male in the Gompertz model wereestimated 21.43; 29.03% and 5.88; 2.22% and same parameter were found in Logistic model 71.43; 62.90% and13.24; 13.33% respectively. There were differences Chi2 % (df = 14 P less than 0.05) between estimated and 0.05 measured individual values for female male of GBJA andS757 genotype in the Gompertz and Logistic model. In terms of Chi2 % values the highest goodness of females 0.05 GBJA was estimated for Logistic model but lowest value was found for male of S757 genotype in Gompertz model.

Discussion

The Gompertz model gives a higher estimate than Logistic model for the AY0 parameter. AY0 parameter values are higher in males than in females for the each models. The data obtained from Gompertz model is found to be higher than that obtained with logistic model is consistent with literature reports (Aggrey 2002; Narinc et al. 2010; Miguel et al.2012). Estimated AY0 parameter values of female and male for GBJA and S757 genotype in the Gompertz and Logistic model were found to be consistent with the values of AY0 parameter for slowgrowing broilers reared in alternative systems by Wang and Zuidhof (2004) Santos et al. (2005) Dourado et al. (2009) Narinc et al. (2010) but higher than result of some research using local genotypes or inbred lines (Aggrey 2002; Ali and Brenoe 2002; Norris et al. 2007; Ahmadi and Golian 2008) and breeding and commercial hybrids (Atil et al. 2007; Riaz et al. 2012).Brody (1945) have suggested that the asymptotic or mature weight rate of attainment of mature weight and the standardized age at which an animal attained the inflection point of the curve were quantities that could be manipulated by geneticists. As pointed out by Barbato (1991) growthfact is under control of genetic and environmental conditionin living organism. In order to compare the dynamics of growth of different genotype broilers 1/2idov (1991) based on the growth curve concluded that realized differences in average body masses were consequence of different origin of broiler chickens and were statistically highly significant in all weekly measuring (Skrbic et al. 2007). According to this view Gompertz and Logistic growth curves obtained from animals reared in the same environmental conditions shows that broiler chickens used in this study are genetically different from each other. The observed differences are explained by the different genetic origins of the flocks used.The range of AY2 values for each genotype in Gompertz model are 0.1288 0.1525 higher than the value 0.031 for the slowgrowing broilers determined in same model by N'Dri et al. (2006) Narinc et al. (2010) and lower than findings of some studies using slowgrowing broiler in alternative rearing systems Santos et al. (2005) and Dourado et al. (2009) or fastgrowing genotypes in conventionally reared (Yakupoglu and Atil 2001; Topal and Bolukbasi2008; Marcato et al. 2008). Significant differences were not found between males and females for each genotype in the present study (P greater than 0.05); however Grossman et al. (1985) and Aggrey (2002) also obtained a higher AY2 value for males than for females using the Logistic model. The range of AY2 values for each genotype in Logistic model were 0.3734 0.3949 higher than the value 0.073 (female) and 0.075 (male) for slowgrowing broiler respectively using the same model by Narinc et al. (2010). The AY2 was also higher for the Logistic model than the Gompertz model (Table 3). The results were similar with that reported by Yang et al. (2006) Nahashon et al. (2006) Miguel et al. (2012) Beiki et al. (2013) but they were higher than the AY2 parameter for the slowgrowing broilers using the Gompertz model determined by N'Dri et al. (2006).In the present study determined the range of IPA values 11.5413.99 that was found to be higher for each models and genotype with several studies (Santos et al.2005; Dourado et al. 2009; Narinc et al. 2010). The range of IPA values were estimated as 44.00 and 49.62 days of age in some of studies for the slowgrowing broilers using Gompertz model (Goliomytis et al. 2003; Santos et al.2005; N'Dri et al. 2006; Dourado et al. 2009) and were determined between 32.07 and 40.46 days of age in conventionally reared fastgrowing broilers (Yakupoglu and Atil 2001; Marcato et al. 2008). On the other hand the point of inflection for chickens in the present study was estimated similar with purebred chickens of unselected populations. Knizetova et al. (1985) have estimated the inflection point at 63.7 79.8 and 81.5 d of age for White Cornish White Leghorn and New Hampshires cockerels respectively.Male broilers showed higher value than females also in terms of the value of IPW for each models and genotype were also found to be in agreement with those of similar studies (Santos et al. 2005; Dourado et al. 2009; Narinc et al. 2010). Gompertz curve characteristic were around the inflection point where maximum growth rate is achieved (Fialho 1999). Slowgrowing GBJA and S757 male birds showed the highest growth potential so that the growth was more accelerated after 1011 weeks of age due to welfare. The IPW values for GBJA and S757 genotype female; male in the Gompertz model were estimated 1370.58 g; 2247.79 g and 1793.97 g; 2390.18 g and same parameter were found inLogistic model 1066.67 g; 1453.18 g and 1395.16 g; 1817.50 respectively. In addition IPW parameter was estimated high (P less than 0.01) for S757 broilers then for GBJA broilers in each of sex and models and these results were also found to be in agreement with those of similar studies (Santos et al.2005; Dourado et al. 2009).The higher the AY0 the lower the AY2 and MGR similar observation was reported for geese chickens and quail (Knizetova et al. 1991; Mignon-Grasteau et al. 1999; Aggrey 2002; Nahashon et al. 2006). The correlation coefficients determined in the study were found to be concordant with various studies that examined growth in the poultry with the Gompertz model (Akbas and Oguz 1998; Akbas and Yaylak 2000; Narinc et al. 2010).Both models were calculated to be positive relationship between AY1 and AY2 IPA IPW (P less than 0.01). Higher negative correlation was estimated between AY2 and IPA in Gompertz Logistic models as -0.88 and -0.62 respectively (P less than 0.01). Between IPW and MGR second highest positive correlation in both models were calculated. Common among growth models was pronounced correlation among the growth parameters estimated (Barbato 1991; Mignon- Grasteau et al. 1999; Aggrey 2002; Narinc et al. 2010) suggested that the position of the IPA strongly influences the AY2 value and AY0. Mignon-Grasteau et al. (1999) on the other hand constrained AY0 within two standard deviations of the mean which resulted in a correlation of 0.98 between the measured and predicted AY0.The two models were all fitted the growth curves ofslowgrowing chicken genotypes in organic system very well and the fitting degrees R2 were all above 0.998; for the two models; however Logistic model was the best (0.999%). The results of goodness of fit in Gompertz and Logistic growth curve models in the study were found to be concordant with various studies (Akbas and Oguz 1998; Akbas and Yaylak 2000; Norris et al. 2007; Narinc et al.2010). Under optimum growing conditions this rate of maturing shows up in the Logistic equation which is a sigmoidal growth curve that describes broiler growth with amazing accuracy.In conclusion different model used to monitor the growth of birds in the poultry industry. This study was used Gompertz and Logistic models included in many models for slowgrowing genotypes reared in organic system. The Gompertz and Logistic growth models were eligible both models after the compatibility tests. However the estimated values of the hatching and mature weights were closer to the observed values in Logistic model. It is possible to follow the change of the growth as taking advantage of both the growth curve in organic production. It needs further research on the growth models of broilers for use in the control of organic production standards.

Acknowledgements

This study was supported by the Research Fund of Cumhuriyet University (Project No: ENF003).

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Publication:International Journal of Agriculture and Biology
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