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Traveling waves with dispersive variability and time delay.

S Harris1

  • 1College of Engineering and Applied Sciences, State University of New York, Stony Brook, New York 11794, USA. Stewart.Harris@sunysb.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
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Few dispersers can drive population expansion waves similarly to the Fisher equation. A generalized Cook model with time delays accurately models historical population spread, like the Neolithic transition.

Area of Science:

  • Mathematical Biology
  • Population Dynamics
  • Ecological Modeling

Background:

  • The Fisher equation and Cook model are used to study population expansion waves.
  • Previous linearized wavefront analysis suggested few dispersers can significantly impact wave speed.
  • The Cook model, like the Fisher equation, has limitations in describing historical population spread.

Purpose of the Study:

  • To determine an approximate traveling wave profile for the Cook model with a small number of dispersers.
  • To generalize the Cook model by incorporating time-delay effects.
  • To assess the generalized Cook model's accuracy in describing historical population spread, specifically the Neolithic transition.

Main Methods:

  • Approximate traveling wave profile determination for the Cook model with few dispersers.

Related Experiment Videos

  • Linearized wavefront analysis for comparison.
  • Generalization of the Cook model to include time-delay effects.
  • Comparison of model predictions with historical data.

    • Main Results:

    • The approximate traveling wave profile for the Cook model with few dispersers is determined.
    • Results align with linearized analysis, showing few dispersers can drive expansion waves with speeds comparable to single-disperser populations.
    • The dimensionless wavespeed is found to be close to unity.
    • The generalized Cook model with time delays shows close agreement with the historical record of the Neolithic transition.

    Conclusions:

    • Relatively few dispersers can significantly influence population expansion wave speed, contrary to initial intuition.
    • The generalized Cook model, incorporating time delays, offers a more accurate representation of historical population spread compared to the basic Cook model or Fisher equation.
    • This work provides a refined mathematical tool for understanding past and potentially future population dynamics.