Mathematical Modeling of Egg Production Curve in Khazak Indigenous Hens

Document Type : Original Paper


1 Research Center of Special Domestic Animals, University of Zabol, Zabol, Iran

2 Department of Animal Science, Faculty of Agriculture, University of Zabol, Zabol, Iran


The number of eggs produced in a given period (egg production rate) is an important trait in layers that change over time and can be presented as a curve. This study aimed to fit the weekly egg production data of Khazak indigenous hens using non-linear regression models and to select an appropriate model for describing the egg production curve for this bird. Biweekly egg production of 144 laying hens over 52 weeks of egg production was used to evaluate the egg production curve. Seven non-linear models (Gamma, McNally, Compartmental II, Nelder, Yang, Lokhorst, and Narushin-Takma) were fitted to egg production data. The four goodness fit criteria (Akaike’ s information criterion, Mean square error, Log Likelihood, and Bayesian information criterion) were used to compare the models. The results of the goodness of fit criteria showed that the Narushin-Takma and Yang models were the best and worst models, respectively, for describing the egg production curve of Khazak hens. The time and egg production at the peak with the Narushin-Takma model was similar to the actual values, and this model was significantly better than other studied models. The correlation between actual and predicted egg production indicated that the Narushin-Takma model could accurately predict the egg production of this breed. As a result, the Narushin-Takma model can be used to predict the egg production curve of Khazak hens in breeding programs and nutritional management.


Aboul-Seoud DIM. 2008. Divergent selection for growth and egg production traits in Japanese quail. Unpublished PhD Thesis, Department of Animal Production, Faculty of Agriculture Al-Azhar University, Egypt.
Adli DN & Sjofjan O. 2022. Modelling egg production of New-Kampong crossbreed chicken (KUB) as promotion of indigenous chicken breeds using three mathematical methods.  6th International Seminar of Animal Nutrition and Feed Science, Atlantis Press.
Agaviezor BO, Ajayi FO, Adebambo OA & Gunn HH. 2011. Nigerian indigenous vs. exotic hens: the correlation factor in body weight and laying performance. An International Multi-Disciplinary Journal, 5(1): 405-413. DOI: 10.4314/afrrev.v5i1.64537
Ahmadu A, Kabir M, Iyiola-Tunji AO, Akinsola OM & Igbadun H. 2017. Mathematical modelling of egg production curves of Shikabrown parents. Nigerian Journal of Animal Production, 44 (1): 61-75. DOI:
Akaike H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 9 (6): 716–723. DOI: 10.1109/TAC.1974.1100705
Akilli A & Gorgulu O. 2020. Comparative assessments of multivariate nonlinear fuzzy regression techniques for egg production curve. Tropical Animal Health and Production, 52(4): 2119-2127. DOI: 10.1007/s11250-020-02226-5
Anang A & Indrijani H. 2000. Mathematical models to describe egg production in laying hens (review). Journal Ilmu Ternak, 6(2): 91-95.
Bindya LA, Murthy HNN, Jayashankar MR & Govindaiah MG. 2010. Mathematical models for egg production in an Indian colored broiler dam line. International Journal of Poultry Science, 9: 916–919. DOI: 10.3923/ijps.2010.916.919
Deljoisaraian J, Alipanah M & Mohamadnia Koushki R. 2011. Factors affecting hatching and fertile eggs in indigenous chicken of Khazak. Proceeding 1st Congress Science New Technology Agriculture, Zanjan, Iran.
Dogan N, Emre K, Mehmet ZF & Tulin A. 2010. Comparison of non-linear growth models to describe the growth in Japanese quail. Journal of Animal and Veterinary Advances, 9(14): 1961-1966. DOI: 10.3923/javaa.2010.1961.1966
Fairfull RW & Gowe RS. 1990. Genetics of egg production in chickens. In: Crawford RD (Eds.), Poultry breeding and genetics. Elsevier Science Publishers, Amsterdam. pp. 705–759.
Faraji-Arough H, Rokouei M, Maghsoudi A & Mehri, M. 2019. Evaluation of Non- linear Growth Curves Models for Native Slow-growing Khazak Chickens. Poultry Science Journal, 7(1): 25-32. DOI: 10.22069/psj.2019.15535.1355
Faridi A, Mottaghitalab M, Rezaee F & France J. 2011. Narushin-Takma models as flexible alternatives for describing economic traits in broiler breeder flocks. Poultry Science, 90 (2): 507–515. DOI: 10.3382/ps.2010-00825
Gerber N. 2006. Factors affecting egg quality in the commercial laying hen: A review. Egg Producers Federation of New Zealand Inc Web. Accessed on March 1. 2022.
Gheisari AA, Maghsoudinejad G & Azarbayejani A. 2016. Evaluation of laying performance and egg qualitative characteristics of indigenous hens reared in rural areas of Isfahan province. Iranian Journal of Applied Animal Science, 6(4): 957-962.
Gonzalez Ariza A, Arbulu AA, Jurado JML, González FJN, Baena SN & Vallejo MEC. 2022. Mathematical modeling of egg production curve in a multivariety endangered hen breed. Research in Veterinary Science, 144: 196-203. DOI: 10.1016/j.rvsc.2021.11.001
Grossman M & Koops WJ. 2001. A model for individual egg production in chickens. Poultry Science, 80: 859-867. DOI: 10.1093/ps/80.7.859
Grossman M, Grossman TN & Koops WJ. 2000. A model for persistency of egg production. Poultry Science, 79: 1715–1724. DOI: 10.1093/ps/79.12.1715
Iranian Council of Animal Care. 1995. Guide to the Care and Use of Experimental Animals. Vol. 1. Isfahan University of Technology, Isfahan, Iran.
Khalafalla AI, Awad S & Hass W. 2001. Village poultry production in Sudan. University of Khartoum Publications, Khartoum, North Sudan.
Kim KG, Cho EJ, Choi ES, Kwon JH, Jung HC & Sohn SH. 2019. Comparison of production performances between early-and late-feathering chickens in parent stocks of Korean native chicken. Korean Journal of Poultry Science, 46(4): 279-286. DOI: 10.5536/KJPS.2019.46.4.279
Kingori AM, Wachira AM & Tuitoek JK. 2010. Indigenous chicken production in Kenya: a review. International Journal of Poultry Science, 9: 309-316. DOI: 10.3923/ijps.2010.309.316
Leonard T & Hsh JSJ. 2001. Bayesian methods: an analysis for statisticians and interdisciplinary. Cambridge University Press, Cambridge, PP 333.
Lokhorst C. 1996. Mathematical curves for the description of input and output variables of the daily production process in aviary housing systems for laying hens. Journal of Poultry Science, 75: 838–848. DOI: 10.3382/ps.0750838
Mahmoud BYF, Emam AM & El-Full EA. 2021. Evaluation of four nonlinear models describing egg production curve of Fayoumi layers. Egyptian Poultry Science Journal, 41(1): 147-159. DOI: 10.21608/epsj.2021.160062
McMillan I. 1981. Compartmental model analysis of poultry egg production curve. Poultry Science, 60: 1549–1551. DOI: 10.3382/ps.0601549
McNally DH. 1971. Mathematical model for poultry egg production. Biometrics, 27(3): 735-738. DOI: 10.2307/2528612
Mehri M. 2013. A comparison of neural network models, fuzzy logic, and multiple linear regression for prediction of hatchability. Poultry Science, 92(4): 1138-1142. DOI: 10.3382/ps.2012-02827
Miguel JA, Asenjo B, Ciria J & Calvo JL. 2007. Growth and lay modelling in a population of Castellana Negra native Spanish hens. British Poultry Science, 48(6): 651-654. DOI: 10.1080/00071660701598414
Narinc D, Uckardes F & Aslan E. 2014. Egg production curve analyses in poultry science. World's Poultry Science Journal, 70(4): 817-828. DOI: 10.1017/S0043933914000877
Narushin VG & Takma C. 2003. Sigmoid model for the evaluation of growth and production curves in laying hens. Biosystems Engineering, 84: 343–348. DOI: 10.1016/S1537-5110(02)00286-6
Nelder JA. 1961. The fitting of a generalization of the logistic curve. Biometrics, 17 (1): 89–110. DOI: 10.2307/2527498
Osman AI. 2020. Genetic evaluation of productive and reproductive traits for some Egyptian local strains of chickens. M.Sc. Thesis, Faculty of Agriculture, Sohag University, Egypt. 
Otwinowska-Mindur A, Gumułka M & Kania-Gierdziewicz J. 2016. Mathematical models for egg production in broiler breeder hens. Annals of Animal Science, 16(4): 1185-1198. DOI: 10.1515/aoas-2016-0037
Pinheiro J, Bates D, DebRoy S, Sarkar D, Heisterkamp S & Van Willigen B. 2014. R Core Team. nlme: linear and nonlinear mixed effects models. R package version 3.1-128. Available at nlme.
Rahimzadeh R, Rokouei M, Faraji-Arough H, Maghsoudi A & Keshtegar B. 2017. Short-term egg production curve fitting using nonlinear models in Japanese quail. Animal Production, 19(2): 299-310. DOI: 20.1001.1.20096776.1396.
Ramlah AH. 1996. Performance of village chicken in Malasia. World’s Poultry Science, 52: 75-79. DOI: 10.1079/WPS19960009
Safari-Aliqiarloo A, Zare M, Faghih-Mohammadi F, Seidavi A, Laudadio V, Selvaggi M & Tufarelli V. 2018. Phenotypic study of egg production curve in commercial broiler breeders using Compartmental function. Revista Brasileira de Zootecnia. 47: e20170225. DOI: 10.1590/rbz4720170225
Savegnago RP, Cruz VAR, Ramos SB, Caetano SL, Schmidt GS, Ledur MC, El Faro L & Munari AD. 2012. Egg production curve fitting using nonlinear models for selected and nonselected lines of White Leghorn hens. Poultry Science, 91(11): 2977-2987. DOI: 10.3382/ps.2012-02277
Savegnago RP, Nunes BN, Caetano SL, Ferraudo AS, Schmidt GS, Ledur MC & Munari DP. 2011. Comparison of logistic and neural network models to fit to the egg production curve of White Leghorn hens. Poultry Science, 90(3): 705-711. DOI: 10.3382/ps.2010-00723
Sowunmi IO, Ikeobi CON & Adebambo OA. 1998. Effect of body weight at caging on pre-peak production performance of white feather Yaafa layers: Egg number and Egg size. NSAP silver anniversary conference/WASAP inaugural conference. Topo, Badagry, March 21-26, pp 21–26.
Spiess AN & Neumeyer N. 2010. An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach. BMC Pharmacology, 10 (1): 6. DOI: 10.1186/1471-2210-10-6
Vali N. 2008. Indigenous chicken production in Iran: a review. Pakistan Journal of Biological Sciences, 15: 2525-2531.  DOI: 10.3923/pjbs.2008.2525.2531
Van der Klein SAS, Kwakkel RP, Ducro BJ & Zuidhof MJ. 2020. Multiphasic nonlinear mixed growth models for laying hens. Poultry Science, 99(11): 5615-5624. DOI: 10.1016/j.psj.2020.08.054
Wit E, Heuvel EVD & Romeijn JW. 2012. All models are wrong...’: an introduction to model uncertainty. Statistica Neerlandica, 66(3): 217-236. DOI: 10.1111/j.1467-9574.2012.00530.x
Wood PDP. 1967. Algebratic model of the lactation curve in cattle. Nature, 216: 164-165. DOI: 10.1038/216164a0.
Yang N, Wu C & McMillan I. 1989. New mathematical model of poultry egg production. Poultry Science, 68: 476-481.  DOI: 10.3382/ps.0680476