Worcester Polytechnic Institute Electronic Theses and Dissertations Collection

Title page for ETD etd-040207-193250


Document Typethesis
Author NameLeo, Angela A
Email Address angela at alum.wpi.edu
URNetd-040207-193250
TitleA Numerical Approach to Calculating Population Spreading Speed
DegreeMS
DepartmentMathematical Sciences
Advisors
  • Roger Lui, Advisor
  • Darko Volkov, Co-Advisor
  • Keywords
  • density-dependent
  • density-independet
  • order-preserving
  • spreading speed
  • Date of Presentation/Defense2007-04-26
    Availability unrestricted

    Abstract

    A population density, $u_{n}(x)$, is recursively defined by the formula egin{equation*} u_{n+1}(x)=int K(x-y)Big(1-ig(u_{n}(yig)Big)ig(u_{n} (yig)dy + ig(u_{n}(xig)ig(u_{n}(xig). end{equation*} Here, $K$ is a probability density function, $g(u)$ represents the fraction of the population that does not migrate, and $f$ is a monotonically decreasing function that behaves like the Beverton-Holt function. In this paper, I examine and modify the population genetics model found in cite{LV06} to include the case where a density-dependent fraction of the population does not migrate after the selection process.Using the expanded model, I developed a numerical application to simulate the spreading of a species and estimate the spreading speed of the population. The application is tested under various model conditions which include both density-dependent and density- independent dispersal rates. For the density-dependent case, I analyzed the fixed points of the model and their relationship to whether a given species will spread.

    Files
  • Leo.pdf

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