I will review some important works about stochastic individual-based models of adaptive dynamics, which describe the Darwinian evolution of asexual populations as birth and death processes with competition. Then I will present the counterpart of these models for diploid populations, reproducting according to Mendelian rules. I will present a result of genetic coexistence, showing that diploid populations have a selective advantage with respect to haploid ones : they are able to survive environmental changes much longer. This is a joint work with A. Bovier and R. Neukirch (Uni Bonn).
