Modelos não lineares aplicados ao crescimento da macrófita Lemna minor

Abstract

The study of aquatic plants (macrophytes) has been considered relevant because these plants present the potential of being used in ecotoxicology studies, as bioindicators and even in wastewater treatment. The growth modeling of such plants, specifically Lemna minor, proved to be relevant for optimizing the above-mentioned applications. It is therefore, necessary to stablish the best growth model of such specie. Since growth curves are the basis on which nonlinear models are applied and they are obtained by collecting growth data of a determined sample over time, the hypothesis of independent residuals, which is very often assumed in the basic models of regression, may not be appropriate in this case. Once there can be a correlation between the residual of an observation over a period of time and the residual of previous observations, the most advisable course of action is to check the correlation between residuals. The objective of this paper was to determine the nonlinear model that best describes the growth of the macrophyte Lemna minor grown in a Steinberg medium. Five nonlinear models were fitted to the growth data using the Gauss-Newton algorithm for the ordinary minimum square method. The Durbin-Watson test, which identifies the residual autocorrelation, has been used an the results pointed to the existence of autocorrelated residuals in the von Bertalanffy model. After the adjustment of the parameters of autocorrelation for each of the tested models, it was concluded that the model that best describes the growth of the Lemna minor is the Logistic model.