单  位：美国 Louisville 大学 

题  目：Spreading Speeds, Traveling Waves, and Minimal Domain
        Size in Stage-Structured Models 

时  间： 2013年10月15日上午 9:00 

地 点：  理科楼-202 

摘  要: How growth, removal, and dispersal in a species affect the species’ spread and persistence constitutes an important problem in spatial ecology. We discuss stage-structured models for species with the reproductive stage and dispersal stage in bounded and unbounded spatial domains. The population dynamics in the reproductive stage is described by a discrete nonlinear map that measures the density of the population at the end of the reproductive stage as a function of the density of the population at the beginning of the reproductive stage. The dynamics in the dispersal stage is governed by a nonlinear reaction-diffusion equation. We demonstrate that a period doubling bifurcation and a period undoubling bifurcation occurs in the corresponding non-spatial model. We provide a spatially explicit theoretical framework that links species vital rates (survival or fecundity rates) and dispersal characteristics with species' spreading speeds, traveling wave speeds, as well as and minimal domain size. We give a formula for the spreading speed in terms of model parameters, and show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We also show how the minimal domain size is determined by the model parameters. Numerical simulations are presented to demonstrate the theoretical results. (Joint work with Mark A. Lewis)