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.
| Identifer | oai:union.ndltd.org:wpi.edu/oai:digitalcommons.wpi.edu:etd-theses-1187 |
| Date | 02 April 2007 |
| Creators | Leo, Angela A |
| Contributors | Roger Y. Lui, Advisor, , , Darko Volkov |
| Publisher | Digital WPI |
| Source Sets | Worcester Polytechnic Institute |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Masters Theses (All Theses, All Years) |
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