Abordagem Bayesiana na Modelagem da Curva de Crescimento do Fungo Botrytis cinerea

Abstract

The study of the growth curve of phytopathogenic fungi allows us to understand the stages of their growth and the factors that influence it. Generally, in such specific research, the data are analyzed over time, which can generate autocorrelated residues and compromise the inference process. As a way to consider residual autocorrelation in modeling, it was incorporated AR(p) structure for the model errors. The bayesian approach has been efficient in the study of growth curves and allows some advantages such as the ease at modeling of more complexity structures and the ability to analyze relatively small samples. Furthermore, the fact to consider the parameters as random variables allows direct interpretations to be made on them and obtain greater clarity in extracting information. Therefore, the present study aimed to evaluate the performance of the bayesian approach regarding: modeling the growth curve of the fungus Botrytis cinerea under effect of essential oils, through adjustment of the logistic model, considering autocorrelation of errors; and the impacts of reduced sample sizes on the analysis accuracy and inference process as well. Data on radial mycelial growth under the influence of essential oils were found in Vismara et al. (2019)† , in which measurements from the nine replications were collected over ten days. To study radial mycelial growth, the nonlinear logistic regression model was adjusted. Given the results obtained, it can be concluded that the bayesian approach proved to be efficient in modeling the growth curve of the fungus Botrytis cinerea, considering AR(p) structure for errors, in addition to producing more accurate estimates with both informative and uninformative priors. The approach also enabled analysis with reduced sample sizes without changing interval estimates significantly, considering overlapping HPD intervals of 95% credibility increase despite the decrease in the precision of the estimates. Adopting the bayesian approach was essential to identify the effect of Patchouli treatment in relation to maximum growth, represented by β1 parameter of the adjusted model, in addition to the effect of the Guaçatonga in reducing the growth rate, represented by the β3 parameter, which was not possible to identify on the study that originated the sample. Ultimately, the study concluded that all essential oils evaluated were effective on the control of the fungus Botrytis cinerea, with Patchouli and Melaleuca being the greatest ones.