A Short Note on Short Dispersal Events |
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Authors: | Frithjof Lutscher |
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Institution: | (1) Department of Mathematics and Statistics, University ofOttawa, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada |
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Abstract: | We study how the speed of spread for an integrodifference equation depends on the dispersal pattern of individuals. When the
dispersal kernel has finite variance, the central limit theorem states that convolutions of the kernel with itself will approach
a suitably chosen Gaussian distribution. Despite this fact, the speed of spread cannot be obtained from the Gaussian approximation.
We give several examples and explanations for this fact. We then use the kurtosis of the kernel to derive an improved approximation
that shows a very good fit to all the kernels tested. We apply the theory to one well-studied data set of dispersal of Drosophila pseudoobscura and to two one-parameter families of theoretical dispersal kernels. In particular, we find kernels that, despite having compact
support, have a faster speed of spread than the Gaussian kernel. |
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Keywords: | Integrodifference equation Asymptotic spreading speed Central limit theorem Gaussian approximation Kurtosis |
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