标题： 多类型逻辑斯蒂分支过程与选择：大承载能力下的频率过程和谱系 显示英文标题

标题： Multi-type logistic branching processes with selection: frequency process and genealogy for large carrying capacities

摘要： 我们提出一个用于多物种种群增长的模型。 我们考虑两种类型作为具有突变的逻辑斯蒂分支过程进化，其中一种类型具有选择优势，并且我们关注系统承载能力趋向于$\infty$的情形。 我们首先通过与独立分支过程的耦合，研究种群直到几乎达到承载能力的谱系。 然后我们关注种群已达到承载能力的阶段。 在恢复无限承载能力极限下的 Gillespie--Wright--Fisher SDE 后，我们构建了祖先选择图，并展示了线性计数过程向极限扩散的矩对偶的收敛性。 显示英文摘要

摘要： We present a model for growth in a multi-species population. We consider two types evolving as a logistic branching process with mutation, where one of the types has a selective advantage, and are interested in the regime in which the carrying capacity of the system goes to $\infty$. We first study the genealogy of the population up until it almost reaches carrying capacity through a coupling with an independent branching process. We then focus on the phase in which the population has reached carrying capacity. After recovering a Gillespie--Wright--Fisher SDE in the infinite carrying capacity limit, we construct the Ancestral Selection Graph and show the convergence of the lineage counting process to the moment dual of the limiting diffusion.