"Adaptive dynamics" is the study of evolution driven by rare mutations with small effects. The essential tool is the "invasion fitness", the expected number of offspring for a rare mutant in a resident community at equilibrium. The first part of this thesis starts by generalising the "canonical equation of adaptive dynamics", a first-order approximation of the speed of change of multidimensional traits under directional selection, so that it holds for general physiologically structured (i.e., arbitrarily complex) population models. Secondly, it proves that near evolutionary singularities and up to second-order terms, such models have the same invasion fitness as the much simpler Lotka-Volterra models (but third-order terms can differ). Thirdly, it combines those results in a recipe for studying analytically the complete dynamics of evolutionary models with limited mutational effects. A prerequisite for models of sympatric speciation to work is the evolution of assortative mating, which has never been validated against alternatives. Therefore the second part compares in a general setting the relative probabilities of the evolution of assortative mate choice to that of dominance interactions, and the conditions favouring each one. This part also shows that allowing for the possibility of sexual dimorphism makes sympatric speciation much less likely.NWO-ALW PhD grant 809.34.002. NWO Dutch-Hungarian exchange grant 048.011.039. ERTN ModLife funding through HPRN-CT-2000-00051 EU grant. NWO-Veni grant for co-author Tom Van Dooren (2 chapters). OTKA T049689 and TS049885 research and travel grants for co-author Geza Meszena (1 chapter).UBL - phd migration 201
