Comparison of mathematical functions in estimation of the growth function of Arabic sheep breed

Document Type : Research Paper

Authors

Khuzestan Ramin Agricultural & Natural Resources University

Abstract

In order to describe the growth curve of Arabic sheep breed, some statistical models (such as Von Bertalanffy, Gompertz, Brody, Logistic and Richards) were compared. In this order from 7008 records related to body weight (from birth to 300 days of age) that have been recorded as daily from 1752 head during the years 1995 to 2009 were used. Goodness of fit for individual growth model was determined using adjusted multiple coefficient of determination, Akaike’s information criterion, mean square error and Bias. The results of the present research indicate that Brody growth model with the highest accuracy (R2Adj = 0.9778) and the lowest error (MSE = 11.22 and Bias = 0.000) could give a better fit than the other growth models and being followed by Von Bertalanffy, Gompertz, Richards and Logistic growth models, respectively. Brody function showed that the difference between the growth curve of various classes of each of the environmental factors of sex and type of birth has been increased with age. After choosing the best nonlinear fixed model, as the second aim of the present research, growth parameter estimations of this model were also obtained with nonlinear mixed model (NLMIXED). All the models evaluation criteria indicated that the Brody mixed effect model fitted the data better than the corresponding fixed effect model and the males have greater diversity within group than females (44.19 kg vs. 27.22 kg).

Keywords

References

بحرینی بهزادی، م. ر. (1394). مقایسه مدل­های مختلف رشد و شبکه­های عصبی مصنوعی در برازش منحنی رشد در گوسفند لری بختیاری. نشریه پژوهش در نشخوارکنندگان. شماره 2، ص ص. 148-125.
رحیمی­کاکلکی، م.، فرهنگ­فر، ه.، منتظرتربتی، م. ب. و اقبال، ع. (1393). توصیف منحنی رشد در نژادهای مختلف گوسفندان ایران با استفاده از تابع غیرخطی گمپرتز. مجله تحقیقات دام و طیور. شماره 4، ص ص. 38-22.
سرایی، ح.، فرهنگ­فر، ه. و نعیمی­پور، ح. (1392). تغییرات فنوتیپی صفت حداکثر سرعت رشد روزانه در بره­های بلوچی. نشریه پژوهشهای علوم دامی ایران. شماره 1، ص ص. 76-69.
عالم زاده، ب.، کردونی، ع. و نوروزی، س. (1386). تعیین سن و فصل مناسب پرواربندی گوسفند در خوزستان. پژوهش و سازندگی. شماره 77. ص ص. 112-105.
نیکخواه، م.، متقی­طلب، م. و زواره، م. (1388). مقایسه "مدل­های رشد هایپربولستیک" با مدل­های رشد کلاسیک در توصیف منحنی رشد جوجه­های نر گوشتی سویه راس. مجله علوم دامی ایران. شماره 40، ص ص. 78-71.
Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Automatic Control. 19:716-723.
Arango, J. and Van Vleck, L.D. (2002). Size of beef cows: early ideas, new developments. Genetics and Molecular Research. 1:51-63.
Bahreini Behzadi, M., Aslaminejad, A., Sharifi, A. and Simianer, H. (2014). Comparison of Mathematical Models for Describing the Growth of Baluchi Sheep. Journal of Agricultural Science and Technology. 16:57-68.
Bathaei, S. and Leroy, P. (1996). Growth and mature weight of Mehraban Iranian fat-tailed sheep. Small Ruminant Research. 22:155-162.
Brody, S. (1945). Bioenergetics and growth. Reinhold Publishing, New York.
Brown, J., Fitzhugh, H. and Cartwright, T. (1976). A comparison of nonlinear models for describing weight-age relationships in cattle. Journal of Animal Science. 42:810-818.
Canaza-Cayoa, A.W., Huancab, T., Gutiérrezc, G.P. and Beltrán, P.A. (2015). Modelling of growth curves and estimation of genetic parameters for growth curve parameters in Peruvian young llamas (Lama glama). Small Ruminant Research. 130:81-89.
Gbangboche, A., Glele-Kakai, R., Salifou, S., Albuquerque, L. and Leroy, P. (2008). Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep. Animal. 2:1003-1012.
Ghavi Hossein-Zadeh, N. (2015). Modeling the growth curve of Iranian Shall sheep using non-linear growth models. Small Ruminant Research. 130:60-66.
Kachman, S.D. and Gianola, G. (1984). A Bayesian estimator of variance and covariance components in nonlinear growth models. Journal of Animal Science. 59:176.
Keskin, I., Dag, B., Sariyel, V. and Gokmen, M. (2010). Estimation of growth curve parameters in Konya Merino sheep. South African Journal of Animal Science. 39:163-168.
Laird A. K. 1966. Postnatal growth of birds and mammals. Growth. 30:349-363.
Loibel, S., Andrade, M.G., do Val, J.B. and de Freitas, A.R. (2010). Richards growth model and viability indicators for populations subject to interventions. Anais da Academia Brasileira de Ciências. 82:1107-1126.
Naesholm, A. and Danell, O. (1996). Genetic relationships of lamb weight, maternal ability, and mature ewe weight in Swedish finewool sheep. Journal of Animal Science-Menasha then Albany then Champaign Illinois. 74:329-339.
Nelder, J. (1961). The fitting of a generalization of the logistic curve. Biometrics. 17:89-110.
Oberstone, J. (1990). Management science: instructors manual with solutions of text exercises to accompany: concepts, insights, and applications. West Publishing Company.
Papajcsik, I.A. and Bodero, J. (1988). Modelling lactation curves of Friesian cows in a subtropical climate. Animal Production. 47:201-207
Richards, F. (1959). A flexible growth function for empirical use. Journal of experimental Botany. 10:290-300.
SAS Institute Inc. (2003). SAS 9.1.3 Help and documentation, Cary, NC: SAS Institute Inc.
Topal, M., Ozdemir, M., Aksakal, V., Yildiz, N. and Dogru, U. (2004). Determination of the best nonlinear function in order to estimate growth in Morkaraman and Awassi lambs. Small Ruminant Research. 55:229-232.
Von Bertalanffy, L. (1957). Quantitative laws in metabolism and growth. Quarterly Review of Biology. 32:217-231.
Animal Sciences Journal
Volume 30, Issue 115
September 2017
Pages 117-126

Files

Share

How to cite

Statistics