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Administering and Detecting Protein Marks on Arthropods for Dispersal Research
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Administering and Detecting Protein Marks on Arthropods for Dispersal Research

Published on: January 28, 2016

A short note on short dispersal events.

Frithjof Lutscher1

  • 1Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada. flutsche@uottawa.ca

Bulletin of Mathematical Biology
|February 24, 2007
PubMed
Summary

The speed of spread in integrodifference equations is not accurately predicted by Gaussian approximations, even with finite variance dispersal kernels. Kurtosis provides a better approximation for spread speed, revealing faster-than-Gaussian spread in some cases.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Integrodifference equations model population spread.
  • Dispersal patterns influence spread speed.
  • Gaussian approximations are commonly used but may be inaccurate.

Purpose of the Study:

  • Investigate the relationship between dispersal patterns and spread speed in integrodifference equations.
  • Explain why Gaussian approximations fail to predict spread speed.
  • Develop an improved approximation for spread speed.

Main Methods:

  • Analyzing integrodifference equations with varying dispersal kernels.
  • Utilizing the central limit theorem and kurtosis for approximation.
  • Applying the theory to empirical data (Drosophila pseudoobscura) and theoretical kernels.

Main Results:

  • Gaussian approximations are insufficient for predicting spread speed.
  • Kurtosis of the dispersal kernel improves spread speed approximation.
  • Identified dispersal kernels with compact support exhibiting faster spread than Gaussian kernels.

Conclusions:

  • Spread speed in integrodifference equations is sensitive to dispersal kernel properties beyond variance.
  • Kurtosis offers a more robust parameter for predicting spread speed.
  • Novel dispersal strategies can outperform Gaussian spread.