Parametrizações de modelos não lineares no estudo da curva de crescimento de Lhamas (Lama glama) no primeiro ano de idade

Abstract

Growth curves are a way to describe growth over a specific period of time. Several non-linear functions (Gompertz, Richards, von Bertalanffy, and Logistic) have been widely used indifferent livestock species to describe body weight development. Most of the non-linear models used in the modeling of growth curves in domestic animals feature different parameterizations and may be theoretically reasonable, but they can include parameters that are difficult to interpret. In practice, this can complicate their understanding, affect non-linearity measures, and influence inferences about the parameters. In this context, the objectives of this study were to investigate different parameterizations of the non-linear models of Brody, von Bertalanffy, and Gompertz in describing the growth curve of llamas from birth to 12 months of age, as wellas to evaluate the environmental effects of sex and animal type on the growth curve parameters.The data analyzed were obtained from the Quimsachata Experimental Center, part of the National Institute of Agricultural Innovation in Puno, Peru. Individual body weights of male and female llamas belonging to two animal types: K'ara and Ch'accu, were used. Parameter estimates were obtained using the iterative Gauss-Newton method implemented in the nls() function of the R software. Non-linearity measures described by Bates and Watts (1980) were obtained using the rms.curv() function of the MASS package in R. The quality of the fit was evaluated based on the values of the adjusted coefficient of determination (Ra2), residual standard deviation (RSD), Willmott's concordance index (d), and non-linearity measures, both intrinsic (cI) and parametric (cθ). A completely randomized design with a 2 × 2 factorialarrangement (two sexes and two animal types) was used to evaluate the environmental effects of sex and animal type on the growth curve parameters using the agricolae package in R. All models showed good fits, but parameterizations 1 and 2 of the Brody model had the highest Ra2 values (99.5%), the lowest RSD values (0.67), the highest d values (0.999), and the lowest non-linearity measures (cI= 0.04, cθ= 0.74). It is concluded that the first two parameterizations of the Brody model were the most appropriate for describing the growth of llamas at one year of age, providing more reliable parameter estimates. Female llamas attained higher asymptotic weights (41.68 kg) than males (40.98 kg), and K’ara-type llamas exhibited greater asymptotic weights (41.97 kg) than Ch'accu-type llamas (40.69 kg).