Un modelo de regresión Poisson no lineal para extinción de especies en hábitats fragmentados.

Abstract

Biostatistics is the set of statistical methods used mainly in biology, including the design of biological experiments, the collection of experimental data, and the statistical analysis of these data. Numerous biologists collect di erent data, from di erent corners of the world. These data contain di erent dependent and independent variables which can be analyzed using linear, or nonlinear regression models. At present, the human activities (dam building, deforestation, etc.) and climate change represent a threat to numerous animal and plant species, and the extinction of the species represents a large part of biological and biostatistical research. Regarding the statistical modeling of the extinction of species and its causes, it is common to nd out most of the research are using the Nonlinear Normal Regression, this kind of Regression is mistakenly assumed, the response variable corresponds to the number of species in certain areas of interest with time passing, thus Nonlinear Poisson regression would be a more appropriate assumption. In this project, the Nonlinear Poisson regression is proposed, aiming to t data concerning the number of species in fragmented habitats. In particular, it aims to re ne the Island Biogeographic Model in Gibson et al. (2013), which is a Nonlinear model for the variable number of species, as a function of the area of the fragments and habitat fragmentation. This project proves that Nonlinear Poisson Regression is more e ective than other types of regressions. When tting the data in biostatistics, the variable includes the number of species, time, and the area of fragments. The results showed that there have a negative correlation between the number of remaining species and time, with time passing, the number of remaining species is decreasing, there is a positive correlation between the number of remaining species and the island area, larger islands have more number of remaining species, but with the time passing, the extinction rate of larger islands is higher than small islands, however by the end, the remaining species on the island will eventually become extinct to the situation where only have one or two species remaining. For using Nonlinear Normal Regression and Nonlinear Poisson Regression respectively, comparing the regression original from Luke et al. (2013), the R2 value is also higher than the other two regressions. In other hand, the Nonlinear Poisson Regression has a smaller con dence interval and residual deviance and AIC. We can concluded that when using Nonlinear Poisson Regression, the regression analysis of data is more e ective than using the Nonlinear Normal Regression.