Um estudo do processo evolutivo de Moran em grafos

• Ano de defesa: 2019
• Autor(a) principal: Evandro Pereira de Souza
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; Brasil; ICX - DEPARTAMENTO DE MATEMÁTICA; Programa de Pós-Graduação em Matemática; UFMG
• Palavras-chave em Português: Cadeias de Markov; Processos de Nascimento e Morte; Teoria de Jogos Evolutivos; Teoria Evolutiva em Grafos; Análise Assintótica; Matemática – Teses; Cadeias de Markov – Teses; Teoria evolutiva em Grafos – Teses; Análise assintótica.– Teses.
• Link de acesso: http://hdl.handle.net/1843/43920

We discuss the Moran process [10]: a stochastic model developed in 1958 for the genetic evolution of a haploid population with asexual reproduction, assuming no mutations, and fixed finite size. In this work, we deal with two extensions of this process: in Evolutionary Game Theory and in Evolutionary Graph Theory. In the context of game theory, Taylor et al. [14] present a classification of the evolutionary scenarios for the Moran process with two strategies. We briefly study this classification and the characteristic shapes for the graph of the fixation probability for each evolutionary scenario. We also analyze the behavior of fixation probability when the population size tends to infinity. In the context of Evolutionary Graph Theory, we discuss some of the results published in [9] and [2]. In particular, we generalize for the case of frequency dependent fitnesses and unifying the BD (birthdeath) and DB (death-birth) cases the solution found by Broom and Rychtár for the Moran process in the star graph. Finally, we also make some considerations on the asymptotic behavior of the solution that we present.