Modelling growth curve in Moghani sheep: comparison of non-linear mixed growth models and estimation of genetic relationship between growth curve parameters

In order to describe the growth curves in Iranian Moghani sheep, five non-linear mixed mathematical equations (Brody, Negative exponential, Logistic, Gompertz and von Bertalanffy) were compared. After selecting the best-fitted model based on purely statistical criteria, variance components and genetic parameters for growth curve characteristics were estimated. The data set and pedigree information used in the current study were obtained from the breeding station of Moghani sheep and included 7905 weight records of 1581 lambs from birth to 400 days of age between the years 1994 and 2012 inclusive. Each model was fitted to body weight records for all lambs, males, females, single and twin lambs using the NLMIXED procedure in SAS and the parameters were estimated. Animal was considered as subject in the models. The non-linear mixed models were examined for goodness of fit using Akaike's information criterion (AIC) and residual variance. Marginal posterior distribution of genetic parameters and variance components were estimated using the Threshold Model programme. The Gibbs sampler was run for 1 000 000 rounds and the first 200 000 rounds were discarded as a burn-in period. Logistic model provided the best fit of growth curve in males, females, singles, twins and all lambs due to the lower values of AIC and residual variance compared with other models. Posterior mean estimates of direct heritabilities for asymptotic weight (A), initial animal weight (B) and maturation rate (K) parameters of Logistic model were 0.21, 0.24 and 0.29, respectively. Also, posterior mean estimates of maternal heritabilities for A, B and K were 0.27, 0.24 and 0.19, respectively. Estimate of correlation between direct and maternal genetic effects for A, B and K parameters were -0.33, -0.69 and -0.51, respectively. Estimates of direct genetic correlation between A-B, A-K and B-K were positive and equal to 0.19, 0.07 and 0.28, respectively. Also, maternal genetic correlations between A-B, A-K and B-K were positive and equal to 0.43, 0.34 and 0.55, respectively. In general, evaluation of different growth equations used in the current study indicated the potential of the non-linear functions to fit body weight records of Moghani sheep. Also, the results of the current study showed that improvement of growth curve parameters of Moghani sheep could be possible in selection programmes. Therefore, development of an optimal selection strategy to achieve a desired shape of growth curve through changing genetically the parameters of model would be very important.