Diferenciação numérica de dados experimentais aplicado em estudos de crescimento de peixes

Abstract

In experimental research usually it is need to extract derivatives from the obtained data for the study and characterization of the phenomenon in question. Such data contains random noise and / or statistical errors and usual techniques of numerical di erentiation, such as nite di erences, can amplify the noise. Keep the noise inherent to the data under control is essential to avoid misinterpretation of the phenomenon. In the present study we applied an alternative methodology to analyze sh growth curves. In this methodology the growth curve is approximated by a smooth function that is not associated with a growth model and therefore is independent of parameter estimation. The method is based on Tikhonov regularization process and consists in a simple and reliable procedure for calculating derivative from experimental data. The process is independent of the nature of the data and can handle points which are not evenly distributed. The method can be extended to derivatives of higher order and can also be used to smooth experimental data. We apply the method to the adjustment for growth curves of the three species of sh: curema Mugil, Thunnus obesus and Pseudupeneus maculatus, whose data were previously analyzed through growth models. We conclude that the methodology here employed approximates accurately the curves of the rst and second derivative and provides information on the instantaneous rate animal growth.