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A Numerical Approach to Calculating Population Spreading Speed

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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.

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  • English
Identifier
  • etd-040207-193250
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  • 2007
Date created
  • 2007-04-02
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Last modified
  • 2020-12-07

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Permanent link to this page: https://digital.wpi.edu/show/3r074v04j