Genetic analysis of growth curve parameters obtained by nonlinear functions in Moghani sheep using Bayesian approach

Develop mentalists are often interested in understanding change processes; so, growth models are the most common analytical tools for examining such processes. Nonlinear growth curves are especially valuable to develop mentalists, because the defining characteristics of growth processes such as estimating initial levels, rates of changes during growth spurts, and asymptotic levels. A variety of growth models are described beginning with the linear growth model and moving to nonlinear models of varying complexity. A detailed discussion of nonlinear models is provided, highlighting the added insights into complex developmental processes associated with their use. Non-linear models can be an option to establish the mathematical behaviour of body development throughout the life of the Iranian sheep breed (Bahreini-Behzadi et al. 2010). These models require lower computational and faster convergence than other methods. Moreover, in genetic evaluation programs with large data sets, non-linear models are more advantageous. Non-linear models were analysed to describe both the biological and commercial growth curves of the Moghani sheep, one of the most important Iranian breeds. Growth models are mathematical functions which are applied for describing the growth pattern. Understanding, estimating, and capturing the defining characteristics of growth processes are key components of developmental research. The aim of this study was to estimate (co)variance components for growth curve parameters and investigate environmental effects on these parameters in Moghani sheep. Data on body weight were collected by Jafarabad sheep-breeding station during 1995 to 2011. The number of records used to estimate (co) variance components of growth curve parameters for birth weight, weaning weight, 6-month weight, 9-month weight, and yearling weight were 7278, 5881, 5013, 2819 and 2883, respectively. Environmental factor such as, age of dam at birth, sex of lambs, type of birth, birth year, and birth season were studied on parameters of growth pattern. The procedure of SAS software was used for studying of fix effects. Based on body weight at different ages and using different initial values, each of the growth curve parameters was estimated using SAS software version 9.1 and NLIN procedure. Growth curve parameters (mature weight, growth rate, and mature rate) were estimated using 4 nonlinear regression models (brody, gompertz, logestic, and bertalanfy). After fitting different models and obtaining growth parameters, the best fit function was selected based on the amount of correction coefficient and corrected Akaeic index and the parameters of the growth pattern were calculated based on the selected function for each animal. The function has the lowest value of the Akaeic index and the highest amount of explanation coefficient, selected as the best function. Estimation of (co)variance components of growth curve parameters was conducted using Bayesian approach implemented in MTGSAM software. The number of Gibbs sampling rounds used was 200,000 rounds. Ten percent of these numbers (20,000 rounds) was burn-in. The convergence criterion for stopping repetitions in this analysis was also considered as 10 decimals (10-10). Sampling intervals of 400 and Gouss Seidel 10000 repetitions were considered. In order to find the best model incorporating the constant and random effects affecting each of the parameters of the growth pattern, the following models, with and without regard to maternal effects including maternal additive genetic effects and permanent maternal environmental effects in the model (Meyer’s models) were tested. The Von Bertalonfy model presented the highest R2 and the lowest AIC compared with the other models and selected as the superior model. Environmental factors such as birth year, sex, and age of mother had significant effects on the mature weight (A) and growth rate (B). Fix effects of birth year and sex had significant effect on the mature rate (K), (P<0.01). Among the six linear models, according to minimum residual variance for mature weight model 4, for growth rate model 6, and for rate of maturity model 5 were selected. Using the most appropriate models in Bayesian approach, the direct heritability for curve parameters was 0.29±0.003, 0.35±0.004 and 0.21±0.004, respectively. The genetic correlation between all the growth curve parameters was positive and small and its value between A and B was 0.007, between both parameters A and k 0.001 and between B and k 0.009. The results obtained in this study contradicted the results of some researchers in this regard (Mollaei et al.2013). The difference in the estimates of different researches depends on the type of model used for analysis, the breed of sheep, and the structure of available information to estimate the parameters, the differences in the management of different herds and the application of different breeding programs (Bathaei and Leroy, 1998). According to the results, the effect of environmental factors on the parameters of the growth pattern is important and should be investigated in the analysis of these parameters.