Statistical modeling as an aid to academic research and control of citrus greening and citrus canker diseases in orange cultivation

Abstract

This thesis presents statistical solutions to several problems related to agriculture. One of them proposes a platform that generates sampling plans based on theoretical statistics, utilizing computation and considering knowledge from agricultural sciences. The platform was developed to generate automatic sampling plans, aiming to expedite the detection of the proportion of the \textit{greening} disease in orange groves. This is because, in Brazil, it is required to conduct a census to detect such proportions. For this first case, the modeling was structured through sampling techniques, using hierarchies involving count and proportion distributions, specifically the Beta-Binomial and the FlexShape-Binomial. The second problem addressed in this thesis consists of the following: for some years, many scientific journals in the field of agricultural sciences have required two identical trials, conducted at different times, to allow submission to these journals. In other words, only with the results of both trials would it be possible to submit an article to such journals. Thus, using two datasets that almost meet this requirement (i.e., experiments conducted in nearly identical ways), a statistical approach was proposed to demonstrate the equivalence between the two experiments, utilizing Bayesian modeling to compare informative priors and posteriors. The differences between the two datasets occurred during data collection. For this second part of the thesis, the data are derived from experiments designed to detect orange varieties resistant to citrus canker disease. To address this, the proposal consists of presenting a non-linear regression model based on the Gamma probability distribution, associated with growth curves such as Logistic, Gompertz, Weibull, and Hill. In the third problem, the thesis seeks to analyze a set of experimental data, aiming to identify the best combinations of rootstocks for orange varieties that confer resistance to citrus canker disease in new plants. At this stage, the modeling was conducted using the Bayesian Longitudinal Zero-Inflated Beta probability distribution. The three main problems of the thesis were solved, and, in addition, directly or indirectly, other problems and agronomic results, such as the discovery of new varieties resistant to citrus canker disease, were achieved.