Mestrado em Matemática (IME)
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Navegando Mestrado em Matemática (IME) por Autor "Aguiar Júnior, Dióscoros Brito"
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Item Tempo de sobrevivência em um modelo estocástico para evolução de espécies(Universidade Federal de Goiás, 2014-02-27) Aguiar Júnior, Dióscoros Brito; Vargas Júnior, Valdivino; http://lattes.cnpq.br/1795859800919467; Vargas Júnior, Valdivino; Gava, Renato Jacob; Silva, Tatiane Ferreira do Nascimento Melo daIn this work ,we will consider two stochastic models for evolution os species. First, births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event then the type is killed is the one with smallest fitness. We show that there is a sharp phasetransitionwhentheprobabilityislargerthanthedeathprobability.Thesetofspecies with fitness higher than a certain critical value approach an uniform distribution. On the other hand all the species with fitness less than the crital disappear after a finite (random) time. The second model, we consider a stochastic model for species evolution. A new species is born at rateλ and a species dies at rate µ. A random number, sampled from a given distribution F, is associated with each new species and assumed as its fitness, at the time of birth. Likewise the first model, every time there is a death event, the species that is killed is the one with the smallest fitness. We consider the (random) survival time if a species with a given fitness f. We show that the survival time distribution depends crucially on whetherffc where fc is a critical fitness that is computed explicit.