Modelo matricial de Leslie: conceitos algébricos no estudo de crescimento populacional por faixa etária

Abstract

In many areas of the knowledge, the Mathematics is present as an important tool that assists in solving problems. Through it possibility the creation of mathematical models that represent a real situation, which facilitates the data collection and analysis of results. In order to demonstrate a practical application of Mathematics in another area, this paper presents a matrix model used by biologists and demographers to estimate population growth, called the Leslie's matrix model. This model make possible to describe the growth of female animals or human populations by age group, taking into account the expectation of survival and birth rates in each band. For better understanding of this model it is necessary to know some concepts of linear algebra such as eigenvalues, eigenvectors and matrix diagonalization. By studying the eigenvalues of the Leslie matrix is possible to determine whether, over time, the population increases, decreases or stabilizes, and also in what proportion it happens. This information helps researchers that use this model to determine the best sampling periods to determine whether certain species are going extinct, among others.