Modelos matemáticos para evolução de resistência de insetos-praga a transgênicos

Abstract

Genetically Modified Organisms (GMOs) are organisms that have undergone artificial changes in their genetic material. We can cite as an example of GMOs, genetically modified crops or, simply, transgenic crops. The main objectives of these crops are to meet certain needs, which conventional crops do not offer, such as: resistance to diseases, insects and chemical insecticides, increased production, drought tolerance, among others. However, the intense use of transgenic crops can lead to some problems that make this technology inefficient, among them, the main one is related to the development of resistance to the insecticidal toxins of these cultures, by the pest insects. One of the ways found to delay or even prevent insects from becoming resistant to toxins is to make use of the refuge area, which consists of planting a variety without transgenic technology. In this work, we formulated discrete models to describe the evolution of resistance to transgenic crops observed in insect pest populations. The models are formulated in terms of Difference Equations - in which space is treated implicitly - and Coupled Map Lattices - which explicitly consider the spatial variable. The proposed models, allows us to analyze the effects of the size and structure of the refuge on the evolution of resistance to transgenic cultures. Our results indicate that the larger the size of the refuge, the lower the frequency of the allele that confers resistance. In general, the configurations around the refuge and block resulted in a lower rate of increase in the frequency of the resistant allele when considering a local movement. On the other hand, when the movement is non-local, the best results, in the sense of delaying the evolution of resistance, were obtained with the refuge distributed at random and in bands. In addition, the fitness that individuals show, both in the refuge area and in the transgenic area, has a great influence on the evolution of resistance to proteins with an insecticidal effect introduced in transgenic cultures.