Growth curves of different free-range chicken lineages by the Gompertz model

The knowledge of the dynamics of animal growth over time can be done through non-linear equations. Thus, the objective was to describe and compare the growth of three free-range chicken lineages based on the Gompertz equation. 180 unsexed chickens assigned to three treatments (Pesadão Vermelho, Pescoço Pelado and Carijó Pesado lineages) in a randomized design with six replicates, with 10 birds per experimental unit. Broilers were weighed weekly (until 77 days of age), these data were used to estimate the growth curve and determine the equation parameters (A, B and C) of model used. The comparison tests between the model parameters for each lineage, demonstrated that it is necessary an equation with different A, B and C parameters for each lineages, the lack-of-fit test was not significant (p>0.05), therefore, the equations of the model are suitable to describe the growth of the lineages. The Pesadão Vermelho lineages is heaviest at inflection point and earlier (BWe =1,528 g at 39 days of age), compared to the Pescoço Pelado (BWe=1,185 g at 38 days of age) and the Carijó Pesado (BWe=1,183 g at 51 days of age) lineage. The adjusted Gompertz curves accurately estimated growth curves of the evaluated line-ages. An equation with different A, B and C parameters is required for each lineage. The Pesadão Vermelho lineage is heaviest at maturity. The Carijó Pesado lineage has a slow growth, with low weight at maturity and the oldest age at maturity.


Introduction
In the last years, there has been a marked growth in free-range poultry farming in alternative production systems (Aisyahet al., 2018;Lemos et al., 2018). This is mainly due to the need for meeting a highly demanding market, which seeks products with organoleptic characteristics distinct from those found in conventional chicken and, which is concerned with animal welfare (Silva et al., 2017;Sousa Júnior et al., 2020).
Alternative production has as a principle the concern for animal welfare since birds conditioned in a semi-intensive system can express their natural behaviors, such as scratch and spreading their wings, which reduces the stress of these animals (Aksoy et al., 2021). This trend has been accompanied by an evolution in the field of genetics, with the emergence of several free-range chicken lineages encompassing characteristics like hardiness and elevated production indices (Del Castilho et al., 2013). However, varying information can be found regarding body growth between these different lineages (Cruz et al., 2018;Ribeiro et al., 2020). Therefore, estimating the growth curve of the chicken lineages used in this production system may allow for the adoption of management practices that optimize meat production, in which the nutritional requirements of each growth phase can be prioritized. In this way, specific feeding programs can be established and the optimum slaughter weight defined (Morais et al., 2015).
It is possible to know the growth dynamics of an animal over time through non-linear equations by using weight-age data, which makes it easier to predict the development of lineages (Tholon and Queiroz, 2009). Several non-linear regression models exist for this purpose; e.g. Brody, Gompertz, Logistic (Souza et al., 2017), Meloun I, Meloun II, Michaelis-Mentem, modified Michaelis-Menten, Richards, Schnute, Von Betalanffy and Weibull (Souza et al., 2013;Fradinho et al., 2016).
However, many authors have proved that the Gompertz equation is the most suitable to describe the growth of poultry lineages, because it can predict the maximum weight obtained at maturity and the efficiency of weight gain over time (Neme et al., 2006;Narinc et al., 2010;Sakomura et al., 2011;Grieser et al., 2015).
In this scenario, predicting the body development of different free-range chicken lineages may assist the producer in choosing the lineages to be farmed, indicating genotypes with potential for increased weight at younger ages. This is based on important information such as the period of maximum feed intake, weight at maturity, feed conversion, daily weight gain estimate, among others. Therefore, the present study was carried out to describe and compare the growth curves of three freerange chicken lineages Pesadão Vermelho, Pescoço Pelado and Carijó Pesado based on the Gompertz equation and to check the equality of equation parameters as well as determine whether there is identity in the model used for the three lineages.

Ethical considerations
All experimental procedures were approved by the Ethics Commission on the Use of Animals (approval no 3/2012).

Location, animals, experimental design and diets
The experiment was developed in São Cristóvão city -Sergipe, during the months of june to august 2012. A total of 180 chicks, males and females, with one day old, ± 33g average initial weight were used in the study. The birds were housed until 28 days of age in an experimental shed build of concrete floor and wood shavings, containing drinkers, feeders, and heating source (infrared electric brooder). After this period the birds were transferred to the free-range poultry sector in the semiconfinement system (Moyle et al., 2014), with free access to paddocks (1.5 x 12m) during the day and collected at night. The sector is characterized by a warehouse with an internal area of 39m 2 , covered with fiber cement tiles, with ceiling height of 2.90m. The warehouse was divided into 18 boxes of 2.16m 2 each (1.5 x 1.44m). All boxes were equipped with a pendant water cooler and a tubular feeder of 20 kg capacity.
The birds were separated into homogeneous lots according to their average weight (859g;745g and 436g, respectively to Pesadão Vermelho, Pescoço Pelado and Carijó Pesado lineages) and distributed in a randomized block design was adopted design with three treatments, six replicates with 10 birds per experimental unit (box), totaling 60 birds per evaluated lineage.
A two-phase feeding system was adopted, in which the starter phase was considered from 1 to 28 days of age and the grower phase from 29 to 77 days of age, as practiced by Sagrilo et al. (2003). In the period from 1 to 28 d of age, all the birds received a diet containing 22% crude protein (CP), 2,950 of metabolizable energy (ME) kcal/kg, 1.20% of digestible lysine (dig. Lys), 0.94% calcium, and 0.42% available phosphorus. From 29 to 77 d of age broilers received diets containing 18% CP, 3,050 kcal of ME/kg, 1.21% of dig. Lys, 0.94% calcium, and 0.42% available phosphorus. The diets were formulated to approximate the nutritional requirements of broilers, initial and grower phase, according to Rostagno et al. (2011).

Statistical analyses
The non-linear Gompertz model was used to estimate the birds body growth curve, as shown below: Research, Society and Development, v. 10, n. 5, e48610515014, 2021 (CC BY 4 The likelihood ratio test with approximations given by F statistics (Regazzi and Silva, 2004;Ribeiro et al., 2020)  The H0 hypothesis of the reduced model was considered adequate when H0 was rejected; i.e., F0 ≥ Fα (Table 1).
To check whether the chosen models were adequate, the lack-of-fit test was applied, in accordance with the methodology of Regazzi and Silva (2004). The adopted model fit criteria were the adjusted coefficient of determination (R 2 ) and Durbin Watson (DW) statistics.

Results and Discussion
The equation parameter estimates (Table 2) revealed that the A parameter values for the CPK lineage were higher (A= 4,155) than those of the PSC (A= 3,223) and CJD lineage (A= 3,216), respectively. As broilers grow older, their weight gain rate (represented by the B parameter) declines, which in turn prolongs the growth curve, especially for broilers of the CJD lineage. By deriving the data from each parameter, we obtain the body weight and weight gain at the inflection point, as described in Table 2. It is observed that maximum body weight at the inflection point, for CPK lineage was higher (BWe = 1,528 g) than PSC (BWe = 1,185 g) and CJD (BWe = 1,183 g) lineages, indicating the broilers of that lineages are heavier and precocious, considering these animals reached the body weight at the inflection point near 39 days of age (C= 39.3996). To the contrary, the CJD lineage showed the highest result (52 days old) for the C parameter, which represents maturity age, demonstrating that this lineage grows slower than the others.
Parametric estimates showed that the CPK lineage was superior compared to other genotypes. In the present study, with high weight to maturity (parameter A), results indicate that the lower maturity rates of PSC and CJD lineage resulted in longer times to reach their maximum body weight (BWe), between 39 and 52 days respectively and, consequently, reach higher body weights at maturity. After these ages, besides growth rates are reduced (Santos et al., 2005), since the maximum body weight (BWe) at the inflection point on growth curve represents the exact moment when growth rate changes from increasing to decreasing (Brito et al., 2021). Thus, interpreting the equation parameters allows inferring the lower values of maturity rate, indicating that the animal showed prolonged growth.
Based on the fitting criteria, R 2 and Durbin Watson (DW), the estimated data are consistent with the observed data. The lack-of-fit test (Table 2) was not significant (p>0.05); thus, the model equations may be considered suitable to describe the data.
Overall, the coefficients of determination (R 2 ) obtained in this study were similar to those reported by Eleroğlu et al. (2014), who found R 2 values close to 100 in experiments with free-range chickens. This suggests that the Gompertz equation was efficient in describing the body growth of the studied lineages, since the observed and estimated data exhibited good correlation according to the coefficient of determination and Durbin-Watson (DW) statistics.
After the lack-of-fit test revealed that the chosen models were suitable to describe the growth of the evaluated lineages, the estimates of body weight and weight gain at 1,7,14,21,28,35,42,49,56,63,70 and 77 days of age by the Gompertz model were presented (Figure 1 and 2). Body weight estimated over time (Figure 1) shows that divergence in body weight of the threelineage evaluated arise from 14 days. The earliness of CPK stood out, as those birds attained the recommended slaughter weight (2.5 kg) at 63 days of age, whereas the other two groups were slow.
The slaughter weight of chickens reared in a free-range system is around 2.5 kg at 70 days of age (MAPA, 1999;Santos et al., 2005). On this basis, the Gompertz equation parameters in the present study showed that, of all evaluated genotypes, only the CPK chickens required less time to attain the recommended slaughter weight. The PSC lineage, on the other hand, displayed a slower growth, which was estimated by weight at maturity, an older age for maximum growth, and lower weight gain at the inflection point compared with the other genotypes. This lower growth rate is possibly related to the fact that this is a dual-purpose lineage (meat and eggs) (Albino and Moreira, 2006). Araújo et al. (2018) obtained similar results, where Carijó birds showed a lower growth rate than CPK chickens, based on derivations of Logistic model parameters. In a study led by Santos et al. (2005), with the free-range lineages CJD and PSC, the former displayed greater growth potential, according to the Gompertz model.
The CPK lineage maintained the highest body weight throughout the evaluated period, followed by PSC and CJD. For weight gain estimated as a function of age (Figure 2), the CPK birds attained maximum weight gain at 39 days, whereas the CJD chickens were later, peaking at 51 days. After those periods, daily weight gain declines, representing the inflection point of the analyzed variable. Another important factor affecting free-range chickens growth rate is related to sex. Del-Castilho et al. (2013) found difference in body weight between sexes, in which CPK males had greater growth potential, with greater muscle deposition capacity and a better-developed bone structure in relation to females; fact currently associated with sexual dimorphism. On the other hand, Santos et al. (2005) did not observe any similarity for growth potential between free-range males and females. Research, Society andDevelopment, v. 10, n. 5, e48610515014, 2021 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v10i5.15014 7 Many studies report differences in the growth of free-range chicken genotypes regardless of the model used (Santos et al., 2005;Rizzi et al., 2013;Eleroğlu et al., 2014;Tavares et al., 2015). This shows that knowing the differences in growth speed between hardy lineages makes it possible to adopt management techniques that can influence bird feeding performance, the rearing system, and the choice of the genetic group to be used (Ribeiro et al., 2020). In doing so, producers can reduce slaughter age and, consequently, production costs.
Regarding nutrition, body growth is determined by protein deposition, fat and ashes, and after reaching the maximum protein deposition rates, birds showed marked reduction in deposition rate related to these body components (Nene et al., 2006), with increase in body fat deposition (Silva et al., 2017). This relationship is strictly controlled by genetic characteristics (Hen et al., 2014), but fast-growing broilers with high energy intake tend to retain dietary energy as fat, compared to protein deposition, while birds with slow growth lipid retention is lower, and protein retention is greater (Boekholt et al., 1994). Therefore, the knowledge of growth trajectory allows, in addition to the information mentioned, planning the adequate nutrition for each specific lineage.
The model parameter estimates as a function of the formulated hypotheses are described in Table 3. The results of the test for the formulated hypothesis (Table 4) showed that only H0 (1), H0 (2), H0 (3) and H0 (6) were significant (p<0.05). Therefore, the reduced models cannot be used. This study revealed that comparing parameters with equality test, can be identified differences between growth curves of the studied strains; this means, that the hypothesis testing models similarity was rejected, demonstrating that the different strains have different parameters A, B and C. Similar results were obtained by Morais et al. (2015), applying equality test for parameters in non-linear models, to describe growth curves in four free-range chicken lines, found that for males is possible to consider the same parameters A, B and D for all lines and, to describe the growth curve, only logarithmic quadratic model parameter C is different for these four strains. Hence, considering the observed body weight data in the preset research, there is similarity with the information estimated by the Gompertz model, indicating good equations assertiveness to predict free-range chickens growth trajectory in each respective strains (Nene et al., 2006).
The details comparing observed and estimated body weight for the strains (Table 5) allows to infer that at 28 days of age CPK birds with observed (BWO) and estimated (BWE) body weight are similar. This comparative demonstrates that this lineage showed higher body weight than the other studied during completely productive period. At 77 days of age, the difference between BWO between CPK and CJD lineage, was about 1337 g.