Date: Wednesday, March 27, 2013
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: On Interaction between Stochasticity and Nonlinearity: In the Context of Stochastic Competitive Population Dynamics
Abstract: Biological dispersal is a classic problem in mathematical biology. One of the core question is, whether there exists an evolutionarily stable (ES) strategy for dispersion. In the deterministic models with passive diffusion, it has been proven that no dispersal is evolutionary stable. However, recent numerical studies showed that demographic fluctuation would enhance dispersal, and the underlying mechanism of the enhancement had not been identified.
This talk will start with heuristic examples, along with one published numerical study by Kessler and Sander in `09, to describe of the problems of interests. After the context is set up, I will present two models we developed to investigate the problem. The objective is to explore whether the evolutionarily stable dispersal rate exists, and if so, how it functionally depends on various parameters of the systems.
This topic is a continuation of our previous proposed "live-fast-die-young" (LFDY) model, which was presented by Prof. Doering in the AIM seminar in January. I will show that, combining the novel asymptotic analysis we proposed in the LFDY-model with a conventional asymptotic analysis, we are able to obtain closed forms of asymptotic solutions of both the dispersal models. Numerical evidence will be presented to support our analysis. I will present the insight of the dynamical mechanisms, which is hinted in the mathematical expressions: the outcome of the competition are due to the nonlinearity and the stochasticity of the system at a high order of asymptotic expansion.
Speaker: Yen Ting Lin
Institution: University of Michigan
Event Organizer: Bowei Wu boweiwu@umich.edu
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