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Density-dependent dispersal in integrodifference equations.

Frithjof Lutscher1

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

Journal of Mathematical Biology
|September 14, 2007
PubMed
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Density-dependent dispersal influences population spread and persistence. This study shows intermediate dispersal evolves in changing environments, enabling competitor coexistence and complex wave profiles.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Many species exhibit dispersal patterns influenced by local population density.
  • Positive density-dependence in dispersal means individuals are more likely to move when local populations are crowded.

Purpose of the Study:

  • To model density-dependent dispersal using integrodifference equations.
  • To investigate the effects of dispersal probability on population spread and persistence in fragmented habitats.
  • To explore the role of density-dependence in enabling competitor coexistence and evolution in dynamic environments.

Main Methods:

  • Utilized integrodifference equations to model population dispersal.
  • Analyzed the mathematical properties of the next-generation operator for density-dependent dispersal.

Related Experiment Videos

  • Investigated the impact of dispersal on population dynamics and traveling-wave solutions.

    • Main Results:

    • Density-dependent dispersal can facilitate the coexistence of competing species.
    • An intermediate dispersal probability evolves in time-varying habitats.
    • Spreading speed is not linearly determined, and the next-generation operator exhibits non-standard properties (non-compact, not order-preserving, not monotonicity-preserving).
    • Explicit examples of non-monotone, discontinuous traveling-wave profiles were derived.

    Conclusions:

    • Density-dependent dispersal is a crucial factor shaping population dynamics, spread, and coexistence.
    • Mathematical models reveal complex behaviors, including evolving dispersal strategies and non-intuitive wave patterns.
    • The findings have implications for understanding species persistence in changing and fragmented landscapes.