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Integrating Remote Sensing with Species Distribution Models; Mapping Tamarisk Invasions Using the Software for Assisted Habitat Modeling (SAHM)
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Integrodifference equations in patchy landscapes : I. Dispersal Kernels.

Jeffrey Musgrave1, Frithjof Lutscher

  • 1Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada, musgrave.jeff@gmail.com.

Journal of Mathematical Biology
|August 3, 2013
PubMed
Summary
This summary is machine-generated.

Individual movement behavior in patchy landscapes influences redistribution kernels. Our random walk model reveals how patch-dependent rates and interface conditions create discontinuous dispersal kernels, impacting ecological dynamics.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Spatial Ecology

Background:

  • Understanding how individual movement in heterogeneous environments affects population dynamics is crucial.
  • Patchy landscapes present unique challenges for modeling species redistribution.
  • Redistribution kernels are essential for predicting spatial population spread.

Purpose of the Study:

  • To investigate the effect of individual movement behavior in patchy landscapes on redistribution kernels.
  • To develop a random walk model incorporating patch-dependent rates and interface behaviors.
  • To characterize dispersal kernels as Green's functions of a differential operator.

Main Methods:

  • Derivation of redistribution kernels from a random walk model.
  • Integration of individual behavior at patch interfaces.
  • Characterization of dispersal kernels using Green's functions of second-order differential operators.

Main Results:

  • Interface conditions lead to discontinuous probability density functions for random walkers.
  • Dispersal kernels can be discontinuous, depending on landscape structure and movement rules.
  • Demonstration of discontinuous kernels in scenarios with small dispersal distances, single bounded patches, and periodic landscapes.

Conclusions:

  • Individual movement behavior significantly shapes redistribution kernels in patchy landscapes.
  • The derived model provides a framework for analyzing dispersal in complex environments.
  • Results inform studies on critical patch size and spatial population dynamics.