Modeling growth curve parameters in Peruvian llamas using a Bayesian approach

The objective of this study was to fit four nonlinear models (Brody, von Bertalanffy, Gompertz and Logistic) to realizations of llama weight, using frequentist and Bayesian approaches. Animals from both sexes and types (K'ara and Ch'accu) were observed. Data consisted of 43,332 monthly body weight records, taken from birth to 12 months of age from 3611 llamas, collected from 1998 to 2017 in the Quimsachata Experimental Station of the Instituto Nacional de Innovación Agraria (INIA) in Peru. Parameters for Non-linear models for growth curves were estimated by frequentist and Bayesian procedures. The MCMC method using the Metropolis-Hastings algorithm with noninformative prior distributions was applied in the Bayesian approach. All non-linear functions closely fitted actual body weight measurements, while the Brody function provided the best fit in both frequentist and Bayesian approaches in describing the growth data of llamas. The analysis revealed that female llamas reached higher asymptotic weights than males, and K'ara-type llamas exhibited higher asymptotic weights compared to Ch'accu-type animals. The asymptotic body weight, estimated for all data using the Brody model, was 42 kg at 12 months of age in llamas from Peru. The results of this research highlight the potential of applying nonlinear functions to model the weight-age relationship in llamas using a Bayesian approach. However, limitations include the use of historical data, which may not fully represent current growth patterns, and the reliance on non-informative priors, which could be improved with prior knowledge. Future studies should refine these aspects.