Seminário de Biomatemática 2 de Dezembro 2008, 16h00 Abstract: We show that simple evolutionary models, like the Moran or the Wright-Fisher processes can be naturally divided in two time scales, the first related to natural selection, the second to genetic drift. We obtain the large population limit of these processes in different scalings. In one precise scaling it is possible to keep both effects. In this case, we have as limit model a partial differential drift-diffusion equation of degenerated type. We analyze this equation from the mathematical point of view, show some numerics related to fixation probabilities to finite populations and discuss the role of mutations in mathematical terms. | back |