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My thesis focuses on the asymptotic analysis of integro-differential models quantifying the influence of certain features of sexual reproduction on the eco-evolutionary dynamics of spatially distributed species characterized by quantitative traits with complex genetic architecture. It extends the analytical toolkit to study the dynamics of singular distributions arising in a regime where diversity introduced by reproduction is small. In the first chapter, I use separation of times scales techniques and completely characterize the equilibria of a population living in a discrete heterogeneous environment connected by migration, whose local adaptation is quantified by the action of selection on a quantitative trait resulting from a large number of small diallelic effects. In the second chapter, I explicit the biological framework underlying the previous chapter thanks to individual-based simulations with an explicit genetic description. In a third chapter, I propose a new hybrid model allowing to include the effect of a major gene onto the trait characterizing local adaptation in the previous context, whose analysis sheds some lights on an undocumented evolutionary phenomenon. In the fourth chapter, I present an explicit long-time approximation of the solution of a reaction-diffusion equation modelling the phenomenon of evolution of dispersion along range expansions, where the diffusion coefficient is the trait under evolution. In the fifth chapter, I analyse a new integro-differential model which describes the dynamics of quantitative alleles under general allelic interaction and selection function. In an annex, I present my contribution to a modelling project of the COVID-19 epidemic in Mayotte. ; Ma thèse porte sur l’étude asymptotique de modèles intégro-différentiels quantifiant l’influence de certains aspects de la reproduction sexuée sur la dynamique éco-évolutive d’espèces spatialement distribuées caractérisées par des traits quantitatifs à architecture génétique complexe. Elle étend la gamme d’outils ...
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