NONLINEAR GROWTH MODELS FOR INDIGENOUS VIETNAMESE RI CHICKEN

H. X. Bo^1,*, D. V. Hoa3, D. T. Nhung², D. T. Hue¹, and D. D. Luc¹

¹Department of Animal Breeding and Genetics, Faculty of Animal Science, Vietnam National University of Agriculture, Hanoi, Vietnam

²Departmen of Animal Nutrition and Feed Technology, Faculty of Animal Science, Vietnam National University of Agriculture, Hanoi, Vietnam

³Department of Livestock System and Environment Research, National Institute of Animal Sciences, Hanoi, Vietnam

*Corresponding Author’s email: hxbo@vnua.edu.vn

ABSTRACT

Chicken growth performance is an important economic trait, so finding the growth curve is essential for the chicken industry including indigenous chicken. Vietnam has many different native chicken breeds and Ri is one of the most famous native chickens. The objective of this study was to find out the best model to estimate the growth of Ri chicken. The body weight of 358 Ri chicken was measured every week until week 20 of age and growth data was analyzed in R using six mathematical functions (Bertalanffy, Bridges, Janoschek, Gompertz, Logistic, and Richards). The results showed that the best models to describe the growth of Ri males and females were Gompertz and Bridges, respectively. The upper asymptotic body weight (α) was estimated for males from 2,130 g (Logistic) to 2,600 g (Bertalanffy), whereas this α value for females was from 1,500 g (Logistic) and 1,816 g (Bertalanffy). Age at the start of the growth acceleration phase was estimated from 2.80 to 3.90 weeks for males and from 2.00 to 3.30 weeks for females. The inflection point for males (7.54 to 9.72 weeks of age) was higher than for females (7.10 to 9.43 weeks of age). Age at the end of the growth deceleration phase was estimated from 16.65 to 24.80 weeks for males and from 12.70 to 25.15 weeks for females. In conclusion, the best model for reporting the Ri chickens’ growth curve was the Gompertz for males and Bridges for females.

https://doi.org/10.36899/JAPS.2022.6.0562
Published first online June 11, 2022

INTRODUCTION

Vietnam is located in Southeast Asia and has good conditions for agricultural development including poultry production. The poultry is raised more than 3000 years ago and is well developed in different regions in Vietnam (Duc and Long 2008). There are at least 37 local chicken breeds that were recognized in Vietnam (Lan Phuong et al. 2015), and they play an important role in the development of the chicken industry. The native chicken population was approximately 70% of the total chicken in Vietnam (Hanh et al. 2007) and produced about 75% of the egg production (Tieu et al. 2008).

Ri is one of the most famous indigenous chickens and is very popular in different areas of Vietnam (Moula et al. 2011). Ri chicken has similar characteristics and morphology as other Vietnamese native chickens, such as yellow skin and a red single comb, however, the Ri male has a black-tailed red color and the feather of the Ri female is yellow (Su et al. 2004). Ri chicken has the highest annual egg performance, and it can adapt well to difficult conditions compared to other indigenous chickens (Lan Phuong et al. 2015; Mui and Dang 2016). Although the body weight of Ri chicken is small, Ri chicken is still very famous because of its meat quality. Thus, Ri chicken plays an important position in livestock production and the specialty chicken market in Vietnam (Thinh et al. 2020).

Understanding animal growth plays an important role in providing solutions for feeding practices to maximize the growth rate, and the growth curve in chickens has been investigated in Vietnam (Nguyen Hoang et al. 2021), Italy (Selvaggi et al. 2015), Ghana (Osei-Amponsah et al. 2014), and China (Yang et al. 2006). The poultry growth curve is nonlinear and has been described by various mathematical functions that include Bertalanfy (Von Bertalanffy 1957), Bridges (Bridges et al. 1992), Janochek, Gompertz (Gompertz 1825),Logistic (Pearl 1977), and Richards (Richards and Kavanagh 1945). Estimating the growth of Ri chicken in Vietnam using the Gompertz model had investigated by Moula et al. 2011, however, whether or not Gompertz was the best model for describing the growth of Ri chicken. The comparison of some models that describe the growth of chicken have been investigated, for example, Richards, Logistics and Gompertz (Aggrey 2002), Bertalanffy, Logistics and Gompertz (Zhao et al. 2015, and Yang et al. 2006). In this study, six mathematical functions (Bertalanffy, Bridges, Janoschek, Gompertz, Logistic, and Richards,) were used for reporting the growth of Ri chicken raised on an industrial farm in the north-central region of Vietnam and the objective of this study was to find out the best model to describe the growth of Ri chicken in Vietnam among nonlinear growth models.

MATERIALS AND METHODS

This study was carried out from October 2020 to March 2021 on Ri chicken raised under industrial conditions in Dien Chau district, Nghe An province, Vietnam. Nghe An is located in the middle of Vietnam which has a seasonal change based on wind direction, with two distinct seasons of summer and winter (GSO 2018). The average temperature is about 25.2^o C and the total sunshine time is about 1,420 h (GSO 2018).

A total of 318Ri chickens (159 males and 159 females) on the first day of age were used in this study.Chickens that were healthy and had good conditions at hatching were chosen and the sex of each young chick was identified based on feather and vent sexing.Males and females were raised separately on floor pens with rice husks litter in the same ventilated building. All chickens weregiven the same feed (Table 1) and the same vaccine program (Table 2) based on their age. From birth to week 4 of age, the chickens were kept under a heating lamp with a density of 20chickens per square meter. The densities were 15 and 5 chickens per square meter for the period from 5 to 8 weeks and 9 to 20 weeks, respectively. The chickens were offered ad libitum feed and water from the first day. The chicken body weight (BW) was measured individuallyon day 1 and every week until 20 weeks of age. The growth of chicken is calculated based on initial and mature BW and Ri chicken is mature around 20 weeks of age. Additionally, according to local knowledge, the Ri chicken was selected for breeding at 20 weeks of age.

Table 1. The diets from the first day to 20 weeks of age for Ri chicken

Table 2. Vaccination program for Ri chicken

Statistical data and growth curves were analyzed in R software (R version 4.0.5, R Core Team 2021). Sixfunctional models including Bertalanfy (Von Bertalanffy 1957), Bridges (Bridges et al. 1992), Janochek, Gompertz (Gompertz 1825),Logistic (Pearl 1977), and Richards (Richards and Kavanagh 1945)(Table 3)were used for describingthe growth for males and females separately. The BW was estimated every week from the first day until 20 weeks of age using different models.

The growth performance of Ri chicken was analyzed using a randomized complete block design with sex as the experimental unit and week of age as the blocks. Analysis of variance was generated using the lm() command in the stats package in R software. The anova() command was used for testing the significance of effects. A linear model including the fixed effects (sex, week of age) and interaction between these two factors is presented in the statistical model as below:

y_ijk = µ + S_i + W_j + S_i*W_j + e_ijk

where, y_ijk = growth performance of chicken k; µ = overall mean; S_i = fixed effect of sex i (male, and female); W_j = fixed effect of week j (j = 1 to 20); S_i*W_j = interaction between sex and week; e_ijk = residual errors. The means of body weight were compared using Tukey’s test.

The six mathematical equations (Bertalanffy, Bridges, Janochek, Gompertz,Logistic, and Richards) were fitted using the nlsLM() function inthe minpack.lm package (Elzhov et al. 2016) in R for each gender, and then some parameters were created such as the upper asymptotic body weight (α), estimated mature growth rate (k), which characterizes the first part of growth before the point of inflection (β) and the shape parameter determining the position of the curve point (m).

In addition, Akaike's information criterion (AIC) and Bayesian information criterion (BIC)were generated using AIC() and BIC() commands in R software. The AIC and BIC parameters were usually used for comparing model performance. The best model was confirmed if AIC and BIC were the lowest.

The predicted BW of the chicken was calculatedusing the predict() function and then plotted using the ggplot2 package in R software. The Pearson’s correlation was calculated between the predicted BW and measured BW using the cor() function in R software.

Table 3. The details of different nonlinear growth models

BWt—body weight (g) at the time t; BW₀- initial body weight (g); α - upper asymptotic body weight (g); t - age (weeks); β, k, and m - parameters specific for the function; β - characterizes the first part of growth before the point of inflection; k describes the second part in which growth rate decreases until the animal reaches the upper asymptotic body weight or mature body weight (α), m is the shape parameter determining the position of the curve point inflection, e – the Euler’s number (~ 2.718282).

RESULTS

The BW of Ri chicken increased steadily during the research period (Table 4), andthe BW of males was higher than females at all time points (Table 4). At the 20^th week of age, the BW of Ri chicken was 2,103.10 g and 1,456.50 g for males and females, respectively.

The estimated parameters for the growth curve model in Ri chicken were different between males and females(Table 5). The upper asymptotic body weight (α) reaches the maximum value when the chicken is mature. In this study, α values for males were higher than females in all models that were suitable for reality. This α value for Ri males was estimated from 2,130.00 g (Logistic) to 2,600.0 g (Bertalanffy) and this value for females was from 1,500.00 g (Logistic) and 1,816.00 g (Bertalanffy).The α was the highest in the Bertalanffy model and was the lowest in the Logistic model for both genders.

The estimated mature growth rate (k) of males in the Richards, Bertalanffy Logistic, and Gompertz, models was higher than that of the females. The k values of the Logistic model were highest, and the k values inthe Bridges and Janochek model were lowest.

The goodness of fit or coefficient of determination (R²), AIC, and BIC of growth curves are important criteria to evaluate a fitted model. The best model for the growth curve was identified if it had the highest R² and the lowest AIC and BIC. The R² of the growth curve for Ri chicken at all models herein was higher than 96% (Table 6). For the males, the Gompertz function was the best model that described growth rate with the highest coefficient of determination (R² = 97.25 %) and the lowest was AIC and BIC values (AIC = 40328 and BIC = 40352.3) among the six models (Table 6). However, the Bridges function was the best model that described the growth rate of Ri females, because this Bridges model had the highest coefficient of determination (R² = 98.74) and the lowest AIC and BIC (AIC = 37905.8 and BIC = 37936.2).

Interestingly, the Logistic function was the worst described growth rate with the lowest coefficient of determination, and AIC and BIC values were the highest in both males and females.

In addition, correlations between the measured BW and predicted BW in all models were always higher than 0.98 (Table 6). The correlation value of the Bridges function was the highest for female data while the correlation values of the Logistic function were the lowest for both males and females data. The growth curves of the measured BW and predicted BW using the best models (Gomperts (GOM) for males and Bridges (BRI) model for females) were overlapped (Figure 1). The similar values of measured BW and predicted BW (Figure 1) indicated that Gomperts and Bridges are the best models to describe the growth of Ri males and females.

Table 4. The body weight of Ri chicken from the first day to 20 weeks

n: sample size; Mean: the average of body weight; SD: Standard deviation

Table5. Different estimated parameters in growth curve models of Ri chickens

BW₀ - initial body weight (g); α— upper asymptotic body weight (g); t—age (weeks); β, k, and m—parameters specific for the function; β characterizes the first part of growth before the point of inflection; k describes the second part in which growth rate decreases until the animal reaches the upper asymptotic body weight or mature body weight (α), m is the shape parameter determining the position of the curve point inflection.

Table6. Coefficient of determination, correlation, Akaike’s information criterion, and Bayesian information criterionin the models to estimate the growth of Ri chicken

AIC: Akaike’s information criterion,

BIC: Bayesian information criterion,

Cor: Pearson’s correlation between predicted and actual body weights.

R²: Coefficient of determination

Table 7. Estimated age and weight at different growth phases of Ri chicken

¹Age at which the chick attains 10% of its final body weight and represents the beginning of the growth acceleration phase (Osei-Amponsah et al., 2014)

²Represents the end of the growth acceleration phase and the beginning of the deceleration phase.

³Age at which the chick attains 90% of its final body weight and represents the end of the growth deceleration phase (Osei-Amponsah et al., 2014).

The growth phases of Ri chicken using six models were different (Table 7). The Ri males had an estimated age and weight higher than that of females, except at the end of the growth deceleration phase (Table 7). Age at the start of the growth acceleration phase was estimated from 2.80 to 3.90 weeks for males and from 2.00 to 3.30 weeks for females, respectively. Similarly, the estimated age at the inflection point for males (7.54 to 9.72 weeks) was higher than for females (7.10 to 9.43 weeks). However, the estimated age at the end of the growth deceleration phase for males (16.65 to 24.80 weeks) was lower than for females (12.70 to 25.15 weeks). In addition, the males also had a higher estimated weight at the start of the growth acceleration phase, inflection point, and the end of the growth deceleration phase than the females in all models (Table 7).

DISCUSSION

This study found that the best functions to describe the growth of Ri chicken were the Gompertz for males and Bridges for females. This finding was consistent with previous studies (Aggrey 2002; Rizzi et al. 2013; Zhao et al. 2015; Nguyen Hoang et al. 2021. Especially, some previous studies had a similar result that demonstrated the Gompertz model was the most appropriate for modeling chicken growth (Nguyen Hoang et al. (2021), Zhao et al. (2015), Moula et al. (2011).

The upper asymptotic body weight (α) of Gompertz function in Ri chicken was lower than the values reported in Ri chicken (Moula et al. 2011), Italian local chicken (Rizzi et al. 2013), Creole chicken (Mata-Estrada et al. 2020), Castellana Negra chicken (Miguel et al. 2008), and Mia chicken (Nguyen Hoang et al. 2021). In a similar study using Ri chicken raised in household conditions, asymmetric weight (α) of the Gompertz model reached 2,794.6 g for males and 1,714.2 g for females (Moula et al. 2011). This figure for Mia chicken was 2,623.86 g for males and 1,915.75 g for females (Nguyen Hoang et al. 2021). However, these α values in this current study were higher than 1,777 g for males and 1,322 g for females raised in Ghana (Osei-Amponsah et al. 2014). The differences among the studies are possibly from feeding, housing, breeding, management, and using the method for evaluation.

In terms of predicted performance, both coefficient of determination (R²) and correlations (r) between the predicted and measured body weight was high in all models (R² > 96%, and r > 0.98). This finding suggests that we can use any model in these six models to describe the growth of Ri chicken. Correlations in this study were lower than correlations reported by Nguyen Hoang et al. (2021) (r = 0.99). However, the coefficient of determination (R²) of all six models herein was higher than that in a study by Osei-Amponsah et al. (2014) (86.6 to 96.7 %) and lower than that by Yang et al. 2006 (99.52 to 99.91 %).

The growth rate factor (maturation rate k) observed by the Gompertz function for Ri chickens in this study was similar to males and females (k = 0.18 and 0.17 g/week for males and females, respectively). These results in our study were higher than the values studied in the Chinese Yellow chicken (k = 0.13 g/week for males and 0.14 g/week for females, Yang et al. 2006), Mia chicken (k = 0.13 g/week for both males and females, Nguyen Hoang et al. 2021), Ri chicken (k = 0.148 and 0.129 g/week for males and females, Moula et al. 2011), and Korean native chicken (k = 0.102 g/week, Manjula et al. (2018)).

In terms of the inflection point, the age and body weight of Ri chicken was estimated lower than the values obtained for other local chicken breeds (Yang et al. 2006; Miguel et al. 2008; Rizzi et al. 2013; Osei-Amponsah et al. 2014; Mata-Estrada et al. 2020; Nguyen Hoang et al. 2021). The age at the inflection point of Mia chicken was 9.32 weeks (males) and 8.53 weeks (females), Nguyen Hoang et al. (2021). However, this value for Creole chicken was from 64.3 to 80.9 days (males) and 54.4 to 72.4 days (females), Mata-Estrada et al. (2020). However, the age and body weight at the inflection point of Ri chicken was like the values studied in Shaobo, Huaixiang, and Youxi chicken raised in China (Zhao et al. 2015). The study by Osei-Amponsah et al. (2014) showed that the age at the start of the growth acceleration phase of Forest chicken in Ghana was from 3.6 to 4.7 weeks for females and from 4.1 to 5.0 weeks for males; the age at the end of the growth deceleration phase of wild chicken in Ghana was from 21.5 to 24.7 weeks for females and from 22.6 to 26.6 weeks for males.

Conclusion: The best function for modeling the growth of Ri chicken was the Gompertz for males and Bridges for females. Thus, applying these models to predict the growth of Ri chicken is more accurate and it helps to improve the management of feeding programs, forecast the growth data, and make productive plans for chicken farming.

Ethical Approval: Not applicable for this type of study in Vietnam.

Conflict of interest: The authors declare that they have no conflict of interest.

REFERENCES

1. Aggrey S.E. (2002) Comparison of three nonlinear and spline regression models for describing chicken growth curves. Poultry Science 81: 1782-1788.
2. Bridges T.C., Turner L.W., Stahly T.S., Usry J.L. and Loewer O.J. (1992) Modeling the physiological growth of swine part I: Model logic and growth concepts. Transactions of the ASAE 35: 1019-1028.
3. Elzhov T.V., Mullen K.M., Spiess A., Bolker B., Mullen M.M. and Suggests M. (2016) Package ‘minpack. lm’. Title R Interface to the Levenberg-Marquardt Nonlinear Least-Squares Algorithm Found in MINPACK, Plus Support for Bounds’. Available at: https://cran. rproject. org/web/packages/minpack. lm/minpack. lm. pdf.
4. Duc, N. V., and T. Long. 2008. Poultry production systems in Vietnam. Rome: Food and agriculture organization.
5. Gompertz B. (1825) XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. FRS andc. Philosophical transactions of the Royal Society of London, 513-583.
6. GSO (2018) Statistical Handbook of Vietnam. Statistical Publishing House, General Statistics office: Ha Noi, Vietnam.
7. Hanh P.T.H., Burgos S. and Roland-Holst D. (2007) The poultry sector in Viet Nam: prospects for smallholder producers in the aftermath of the HPAI crisis. In: Pro-Poor Livestock Policy Initiative Research Report, Food and Agriculture Organisation of the United Nations.
8. Lan Phuong T.N., Dong Xuan K.D.T., and Szalay I. (2015) Traditions and local use of native Vietnamese chicken breeds in sustainable rural farming. World's Poultry Science Journal 71: 385-396.
9. Manjula P., Park H.B., Seo D., Choi N., Jin S., Ahn S.J., Heo K.N., Kang B.S. and Lee J.H. (2018) Estimation of heritability and genetic correlation of body weight gain and growth curve parameters in Korean native chicken. Asian-Australas J Anim Sci 31: 26-31.
10. Mata-Estrada A., González-Cerón F., Pro-Martínez A., Torres-Hernández G., Bautista-Ortega J., Becerril-Pérez C.M., Vargas-Galicia A.J. and Sosa-Montes E. (2020) Comparison of four nonlinear growth models in Creole chickens of Mexico. Poultry Science 99: 1995-2000.
11. Miguel J.A., Ciria J., Asenjo B. and Calvo J.L. (2008) Effect of canonization on growth and carcass and meat characteristics in Castellana Negra native Spanish chickens. Animal 2: 305-311.
12. Moula N., Dang P.K., Farnir F., Ton V.D., Binh D.V., Leroy P. and Antoine-Moussiaux N. (2011) The Ri chicken breed and livelihoods in North Vietnam: characterization and prospects. Journal of Agriculture and Rural Development in the Tropics and Subtropics (JARTS) 112: 57-69.
13. Mui N.B. and Dang P.K. (2016) Reproductive capacity of Ri chicken and crossbred chicken raised in An Duong District, Hai Phong city. Vietnam Journal Agriculture Science 14: 392-399.
14. Nguyen Hoang T., Do H.T.T., Bui D.H., Pham D.K., Hoang T.A. and Do D.N. (2021) Evaluation of non‐linear growth curve models in the Vietnamese indigenous Mia chicken. Animal Science Journal 92: e13483.
15. Osei-Amponsah R., Kayang B.B., Naazie A., Barchia I.M. and Arthur P.F. (2014) Evaluation of models to describe temporal growth in local chickens of Ghana. Iranian Journal of Applied Animal Science 4: 855-861.
16. Pearl R. (1977) The biology of population growth. Ayer Publishing.
17. R Core Team (2021) R: A language and environment for statistical computing. R foundation for statistical computing Vienna, Austria.
18. Richards O.W. and Kavanagh A.J. (1945) The analysis of growing form. pp. 188-229. Oxford: Oxford Univ.
19. Rizzi C., Contiero B. and Cassandro M. (2013) Growth patterns of Italian local chicken populations. Poultry Science 92: 2226-2235.
20. Selvaggi M., Laudadio V., Dario C. and Tufarelli V. (2015) Modelling Growth Curves in a Nondescript Italian Chicken Breed: an Opportunity to Improve Genetic and Feeding Strategies. The Journal of Poultry Science 52: 288-294.
21. Su V.V., Thien N.V., Nhiem D.T., Ly L.V., Hai N.V. and Tieu H.V. (2004) Atlas of Farm Animal Breeds in Vietnam. Agricultural Publisher, Hanoi, Vietnam.
22. Thinh N.H., Doan B.H., and Giang N.T.P. (2020) Growth and meat quality of Ri Lac Son Chicken. Journal of Animal Husbandry Sciences and Technics 256: 14-18.
23. Tieu H.V., Ly L.V., Sat L.M., Cuong V.C. and Su V.V. (2008) Vietnamese livestock genetic resources conservation and exploitation from 1990 to 2007. Vietnamese Journal of Animal Science and Technology special volume: 1-10.
24. Von Bertalanffy L. (1957) Quantitative laws for metabolism and growth. The quarterly review of biology 32: 217-231.
25. Wickham H. (2016) ggplot2: elegant graphics for data analysis. Springer.
26. Yang Y., Mekki D.M., Lv S.J., Wang L.Y., Yu J.H. and Wang J.Y. (2006) Analysis of fitting growth models in Jinghai mixed-sex yellow chicken. International Journal of Poultry Science 5: 517-521.
27. Zhao Z., Li S., Huang H.L., Li C., Wang Q. and Xue L. (2015) Comparative study on growth and developmental model of indigenous chicken breeds in China. Open Journal of Animal Sciences 5: 219.