Spatial multitype population models with type interaction

具有类型交互作用的空间多类型种群模型。该项目侧重于人口模型，特别强调人口的空间和类型结构。所考虑的时间演化的关键要素是繁殖(分枝或重采样)、迁移、突变、选择和重组。这些结果将为理解进化论中的问题提供数学工具。我们特别关注的方面是空间互动、类型互动以及谱系和历史结构。为了理解这种长期行为，我们使用了三个关键工具：历史过程、多尺度分析与分层平均场极限相结合以及最终的非线性分析来控制与随机系统相关联的映射的轨道。

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.