omparison of some non-linear models for describing the growth curve in Makooei sheep

 The Makooei sheep is a medium-sized, fat-tailed breed, carpet wool and white color breed. This breed dispreads mainly in the north west of the Iran in West Azerbaijan province. This sheep breed is called White Karaman in Turkey. Growth curve is the graph of weight as a function of age on time. The changes taking place in animal's body weight with the passage of time that is often sigmoid in shape. Further, information on the growth pattern helps determine feeding and management plans and planning breeding strategies to improve the efficacy of whole growth process. Using growth models is one of the ways that can be used to predict and measuring animal’s performance, such as weight gain. In fact, growth models are linear or nonlinear regression functions that can predict growth at different ages of animal life. Non-linear mathematical functions, empirically developed by depicting body weight against age, have been appropriate to characterize the growth curve in different animal classes. Therefore, the objective of this study was to describe the growth curve of Makooei sheep using non-linear models. The Negative exponential, Brody, Gompertz, Logistic and von Bertalanffy models were used to evaluate their efficiency in describing the growth curve of Makooei sheep.

The used data included 5913 body weight records from 1966 male lambs and 7092 body weight records from 2354 female lambs (from birth to 225 days), collected during 1993 to 2011, at the Makooei Sheep Breeding station, in West Azerbaijan, Iran. In the station, each ram was randomly mated to 10-15 ewes. Lambing was in January and March and lambs were weaned until ~3 months of age. The lambs were weighed and ear tagged after birth.  Data were checked several times, so defective and out of range records were deleted. The Negative exponential, Brody, Gompertz, Logistic, and Von Bertalanffy functions were fit to the data to model the relationship between weight and age. Each model was fitted separately to body weight records for all lambs, male and female lambs using the NLIN procedure in SAS 8.2. The non-linear mixed models were examined for goodness of fit using Adjusted Coefficient of Determination (R2adj), Root Mean Square Error (RMSE), Akaike’s information criterion (AIC) and Bayesian information criterion (BIC). Finally, the best model was selected with the highest R2adj and the lowest RMSE, AIC and BIC.

 All non-linear models showed good capacities of fitting for describing the growth curve in Makooei sheep. The R2adj for the Brody model was found the highest (0.8799) and the lowest for Logistic model (0.8505) for all lambs. The A parameter is an estimate of asymptotic weight which can be interpreted as the weight at maturity. For the studied dataset the highest and lowest values for the parameter A were obtained by Brody model (for all lambs = 39.04) and logistic model (for all lambs = 32.08), respectively. The parameter B represents an integration constant, related to the initial animal weight but lacking a clear biological interpretation. The highest and lowest values for the B parameter were obtained in Logistic model (for all lambs = 6.28) and Von Bertalanffy model (for all lambs = 0.52), respectively. The parameter k that defined the maturation rate is another important feature to be considered, since it indicates the growth speed to reach the asymptotic weight. Therefore, animals that have higher k values will reach puberty sooner. The estimate of k was highest in the Von Bertalanffy model (for all lambs = 0.10), while Brody (for all lambs = 0.01) and Negative exponential (for all lambs = 0.01) models showed lowest values. The results of this study showed that the Brody model with the highest R2adj and the lowest RMSE, AIC and BIC was able to describe the growth curve better than other growth models in Makooei sheep. In growth curve the most important biological relationship has been found between A and k. The lowest and highest correlation between the two parameters of A and k for all lambs was found for the logistic (-0.59) and Brody (-0.97) models, respectively.

 The results of this study suggest that the Brody model can be useful for set some management strategies such as determining nutritional programs and the appropriate age for slaughter of Makooei sheep