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This work explores the long-standing question of which forces drive the maintenance of MHC diversity in vertebrates. More precisely, it investigates whether a special form of heterozygote advantage can explain the characteristic features of MHC genes, as the large number of alleles, the characteristic distribution of allele frequencies, and the trans-species polymorphism. This special overdominance variant is based on the divergent allele advantage hypothesis (Wakeland et al., 1990), and therefore the corresponding model is called the divergent allele advantage model. The novel tool of diversity profiles (qDZ) will be used to characterise and compare allelic diversity of different overdominance models, and to contrast simulation results with observed data. Chapters 2 and 3 perform a stability analysis of a n-allele system at equilibrium. Different overdominance models are compared in a common framework, and a novel model, based on the divergent allele advantage hypothesis, is introduced while its properties are analysed. Chapter 4 explores a more realistic scenario that includes mutation and drift and compares a modified divergent allele advantage model to traditional models of heterozygote advantage. Implications of the results of the previous chapters are discussed in chapter 5. Finally, chapter 6 extends the analysis of the divergent allele advantage model to a structured population, thus additionally including migration, and explores whether the findings of the previous chapters also hold in a more realistic scenario of a metapopulation of interacting subpopulations. The results of this work demonstrate that the novel model based on the divergent allele advantage hypothesis can explain the main features of the diversity of the Major Histocompatibility Complex genetic region, but it predicts the existence of many genotypes that increase susceptibility to disease.