AI 中文总结
波恩大学硕士课程讲义，从随机角度回顾25年适应性动力学工作，重点是新兴缩放极限问题，通过时间、种群大小等参数展现生物学现象，讲义分三部分，涵盖背景工具、缩放机制及模型扩展。
AI 中文摘要
这些是波恩大学硕士项目高级主题课程的讲义。旨在从严格的随机角度，对过去25年围绕适应性动力学主题所做的一些工作进行简要回顾，使具备概率知识尤其是马尔可夫过程理论的学生能够接触该领域。重点是新兴缩放极限问题，缩放参数包括时间、种群大小、突变率和突变步长。这能在相当简单的模型类别中展现多种生物学相关现象。讲义分为三部分，第一部分介绍历史背景、数学设定和主要工具；第二部分是核心，讨论各种缩放机制和缩放极限；第三部分探讨基本模型的一些扩展，如二倍体模型、表型可塑性和随时间变化的环境影响。
英文摘要
These are lecture notes for an advanced topics course in the master's programme at Bonn University. It aims to give a concise review of some of the work that has been done around the topic of adaptive dynamics from a rigorous stochastic point of view over the last 25 years and to make this area accessible to students with a good knowledge of probability in general, and the theory of Markov processes in particular. Our emphasis is on the issue of emerging scaling limits, where scaling parameters are time, population size, mutation rates, and mutation step size. These allow to exhibit within a fairly simple class of models a variety of biologically relevant phenomena. These notes are organised in three parts. Part 1 presents some historical background as well as the mathematical setting and main tools. Part 2 is the core of the notes and discusses the various scaling regimes and scaling limits. Part 3 looks at some extensions on the basic model, notably diploid models, phenotypic plasticity, and effects of environmental changes over time.
Comments158 pages
