应6163银河线路检测中心刘胜强教授的邀请，美国加州大学戴维斯分校著名生物数学与理论生态学学者Sebastian Schreiber教授将于2019年6月27日下午在科学园2H栋(航天馆)417室举办学术讲座，欢迎相关专业的老师和同学参加。

报告题目：Explosions, extinctions, and metastability

报告时间：2019年6月27日 16:00-17:00；

报告地点：科学园2H栋(航天馆)417室

报告摘要：Populations in nature consist of finite numbers of individuals and are at constant risk of extinction. The dynamics of these populations are well-represented by Markov processes on countable state spaces. For small, asexual populations, extinction risk is particularly acute and interactions among individuals are rare. Branching processes provide a useful approximation for these dynamics and (generically) exhibit a fundamental dichotomy: extinction in finite time or unbounded growth which is often interpreted as population persistence or establishment. This unbounded growth only occurs with positive probability if individuals on average replace themselves. In contrast, for small, sexual populations, individuals must mate to reproduce and, consequently, exhibit frequency-dependent interactions. Using mean limit ODEs, I will present results that determine whether unbounded growth occurs with positive probability or not in frequency-dependent branching processes. For large populations, interactions among individuals are common but extinction tends to be far into the future. Consequently, Markov processes representing these dynamics often exhibit long-term persistent behavior (meta-stability) before extinction occurs. Using large deviation theory and tools from dynamical systems, I will show how this transient behavior is characterized by attractors of associated mean-limit equations, and how the length of these transients scales with the size of the system.

专家简介：

Sebastian Schreiber is a professor at University of California, Davis. He serves on the editorial boards of Discrete and Continuous Dynamical Systems B, Ecology/Ecological Monographs, Journal of Mathematical Biology, Theoretical Ecology, and Theoretical Population Biology. His speciaties include community ecology, Evolutionary ecology and life history strategies, and population dynamics. Web page: https://schreiber.faculty.ucdavis.edu