Crescimento populacional de palometas na fronteira oeste gaúcha: um problema ambiental à luz da modelagem matemática

Abstract

This work presents a research that brings the mathematical modeling implicit in an environmental problem, whose objective is to investigate the population growth and the possible environmental problems caused by Palometa in the rivers of the western border of Rio Grande do Sul. In the study of the proposal, the models of Malthus, Verhulst, GordonSchaefer and the Fishing Model with Allee Effect were tested. We can see that each of these models has a bias that must be analyzed and considered. Malthus’s model, considered unrealistic, proposes that population growth occurs at an intrinsic rate of growth proportional to the population at that instant of time. In the case of Palometas, we can infer that the population can grow quickly in an environment that provides good resources. The Verhulst Model, on the other hand, is a logistic growth equation, where the population grows up to a sustainable limit. For Palometas, we interpret that intraspecific predation may occur during their encounters. This model satisfactorily describes the behavior of populations with a high number of individuals, being adequate to describe the behavior of Palometas in places where it is considered a native species. Gordon-Schaefer’s model assumes the capture of individuals; and in the case of the Palometas, we can interpret this capture as predatory fishing for the purposes of population control of the Palometas. Finally, the Gordon-Schaefer fishing model with the Allee Effect is suitable for situations involving a low number of individuals. The Allee Effect describes a species difficulty in increasing its population when in small number of individuals.