时 间：2023年11月16日 14:00-15:00
地 点: 普陀校区理科大楼A1514
报告人：Grégoire Véchambre 中国科学院 助理教授
主持人：俞锦炯 华东师范大学助理教授
摘 要：
Wright-Fisher diffusions offer popular models in population genetics. They can be used to model the frequency of a gene in a large constant size population. In a recent joint work with F. Cordero (Bielefeld University) and S. Hummel (UC Berkeley) we consider a class of Lambda-Wright-Fisher diffusions with a general form of selection and environmental effects. We reveal a rich variety of long-term behaviors for processes in this class and provide explicit criteria to discriminate between them. That includes the situation of long-term coexistence maintained by selection alone, which is a new phenomenon in this context and has interesting biological implications. When fixation or extinction occur almost surely, we derive decay rates for the probability that fixation or extinction has not essentially taken place after a long time. This decay is sometimes polynomial and sometimes exponential, depending on parameter choices. When both fixation and extinction occur with positive probability we provide a representation of the fixation probability. Aspects of our methodology include a Siegmund duality for our processes, approximation by Lévy processes that allow to use fluctuation theory of Lévy processes, building renewal times for the dual process, and studying coalescing properties of its flow. Our methods allow us to treat models that so far could not be analyzed by means of classical dualities and to close an existing gap in the literature.
报告人简介：
Grégoire Véchambre obtained his PhD from Orléans University in France and then worked as a postdoc in NYU Shanghai. He is currently assistant professor in AMSS (Chinese Academy of Sciences). His research interests are Lévy processes and random population models.