Multiscale Analysis of Adaptive Population Dynamics [Elektronische Ressource] / Shidong Wang. Mathematisch-Naturwissenschaftliche Fakultät

Multiscale Analysis of AdaptivePopulation DynamicsDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen Fakult atderRheinischen Friedrich-Wilhelms-Universit at Bonnvorgelegt vonShidong WangausShandong, CHINABonn, September 2011Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakult at derRheinischen Friedrich-Wilhelms-Universit at Bonn.1. Gutachter: Prof. Dr. Anton Bovier2. Gutachter: Prof. Dr. Patrik FerrariTag der Promotion: 20.12.2011Erscheinungsjahr: 2011AbstractIn this thesis we study a spatial population model based on a class of interacting locallyregulated branching processes. The results consist of three parts which are independentof each other. The rst part, which is the main part of this thesis as presented inChapter 2 and 3, is concerned with a three-time-scale analysis of a spatially structuredpopulation speci ed with adaptive tness landscape. More precisely, we obtain a newmodel, the so-called trait substitution tree (TST), in the limiting system by taking a raremutation limit against a slow migration limit. These limits can be either simultaneouswith a large population limit from a microscopic point of view (Chapter 3), or basedon a deterministic approximation (Chapter 2). The TST process is a measure-valuedMarkov jump process with a well-described branching tree structure.