Spatial multitype population models with type interaction

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Spatial multitype population models with type interaction. The project focusses on population models with particular emphasis on spatial and type structure of the population. The key elements of the time evolution considered are reproduction (branching or resampling), migration, mutation, selection and recombination. The results will provide mathematical tools for an understanding of questions from the theory of evolution. The aspects we focus on especially are spatial interaction, type interaction and the genealogical and historical structure. In order to understand the longtime behavior, we use three key tools: the historical process, multiscale-analysis in combination with the hierarchical mean-field limit and finally nonlinear analysis to control the orbit of a map associated with the stochastic system.