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

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).