Tempo de sobrevivência em um modelo estocástico para evolução de espécies
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2014-02-27
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Universidade Federal de Goiás
Resumo
In 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 whetherf<fc ,f=fc orf>fc where fc is a critical fitness that is computed
explicit.
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AGUIAR JUNIOR, Dióscoros Brito. Tempo de sobrevivência em um modelo estocástico para evolução de espécies. 2014. 58 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2014.