Modelagem matemática em genética de populações
Carregando...
Data
2019-01-03
Autores
Oliveira, Vinícius Freitas de [UNESP]
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Estadual Paulista (Unesp)
Resumo
A genética de populações é a ciência que estuda o comportamento das frequências alélicas e genotípicas nas populações e quais os possíveis fenômenos que podem alterá-las ao longo do tempo. A fim de exercer uma interdisciplinaridade entre Biologia e Matemática, este trabalho exibiu a construção de modelos matemáticos que contemplam o comportamento dessas frequências no tempo. Para tanto, foram utilizados conceitos de probabilidade, estatística e equações de diferenças. Foram construídos seis modelos a partir de princípios pré-estabelecidos, do mais simples ao mais complexo. A possibilidade da contemplação do equilíbrio de Hardy-Weinberg foi verificada em cada modelo proposto. O primeiro modelo a ser exibido foi o modelo básico, que contou com as seguintes premissas: acasalamento aleatório, gerações não-sobrepostas, população infinita, população monoica, e ausência de seleção, mutação e migração. Outros quatro modelos sem a presença de seleção foram elaborados a partir do modelo básico, alternando as premissas iniciais. Por fim, o último modelo, construído a partir da premissa de populações com seleção, contou com o método teia de aranha para a análise qualitativa dos resultados.
Population genetics is the science that studies the behavior of allelic and genotype frequencies in populations and what possible phenomena may change them over time. In order to establish an interdisciplinarity between Biology and Mathematics, this work has exhibited the construction of mathematical models that contemplate the behavior of these frequencies in time. For this, concepts of probability, statistics and equations of differences were used. Six models were constructed from pre-established principles, from the simplest to the most complex. The possibility of the contemplation of the Hardy-Weinb erg equilibrium was verified in each proposed model. The first model to be exhibited was the basic model, which had the following assumptions: random mating, non-overlapping generations, infinite population, monoic population, and absence of selection, mutation, and migration. Four other models without the presence of selection were elaborated from the basic model, alternating the initial assumptions. Finally, the last model, built from the premise of populations with selection, counted on the cobweb method for the qualitative analysis of the results.
Population genetics is the science that studies the behavior of allelic and genotype frequencies in populations and what possible phenomena may change them over time. In order to establish an interdisciplinarity between Biology and Mathematics, this work has exhibited the construction of mathematical models that contemplate the behavior of these frequencies in time. For this, concepts of probability, statistics and equations of differences were used. Six models were constructed from pre-established principles, from the simplest to the most complex. The possibility of the contemplation of the Hardy-Weinb erg equilibrium was verified in each proposed model. The first model to be exhibited was the basic model, which had the following assumptions: random mating, non-overlapping generations, infinite population, monoic population, and absence of selection, mutation, and migration. Four other models without the presence of selection were elaborated from the basic model, alternating the initial assumptions. Finally, the last model, built from the premise of populations with selection, counted on the cobweb method for the qualitative analysis of the results.
Descrição
Palavras-chave
Genética de populações, Equações de diferença, Modelagem matemática, Biomatemática, Population genetics, Difference equations, Mathematical modeling, Biomathematics