Title page for ETD etd-040207-193250

Document Type thesis

Author Name Leo, Angela A

Email Address angela at alum.wpi.edu

URN etd-040207-193250

Title A Numerical Approach to Calculating Population Spreading Speed

Degree MS

Department Mathematical Sciences

Advisors
Roger Lui, Advisor
Darko Volkov, Co-Advisor

Keywords
density-dependent
density-independet
order-preserving
spreading speed

Date of Presentation/Defense 2007-04-26

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-gig(u_{n}(y)ig)Big)fig(u_{n}
(y)ig)dy + gig(u_{n}(x)ig)fig(u_{n}(x)ig).
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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Document Type	thesis
Author Name	Leo, Angela A
Email Address	angela at alum.wpi.edu
URN	etd-040207-193250
Title	A Numerical Approach to Calculating Population Spreading Speed
Degree	MS
Department	Mathematical Sciences
Advisors	Roger Lui, Advisor Darko Volkov, Co-Advisor
Keywords	density-dependent density-independet order-preserving spreading speed
Date of Presentation/Defense	2007-04-26
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-gig(u_{n}(y)ig)Big)fig(u_{n} (y)ig)dy + gig(u_{n}(x)ig)fig(u_{n}(x)ig). 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