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Related Experiment Video

Updated: Jun 16, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Published on: February 22, 2018

Spreading speeds in slowly oscillating environments.

François Hamel1, Julien Fayard, Lionel Roques

  • 1LATP, Aix-Marseille Université, France.

Bulletin of Mathematical Biology
|January 22, 2010
PubMed
Summary

This study provides exact estimates for reaction-diffusion model spreading speeds in large periodic environments. Findings reveal higher-than-expected speeds in slowly oscillating settings and zero speeds with Allee effects.

Area of Science:

  • Mathematical Biology
  • Theoretical Ecology
  • Partial Differential Equations

Background:

  • Reaction-diffusion models are crucial for understanding species spread.
  • Environmental fragmentation significantly impacts population dynamics.
  • Previous models lacked explicit formulas for slowly oscillating environments.

Purpose of the Study:

  • Derive exact asymptotic estimates for spreading speeds in large periodic environments.
  • Quantify the effect of environmental fragmentation on these speeds.
  • Analyze models with Fisher-KPP and Allee effects.

Main Methods:

  • Exact asymptotic analysis for large periods.
  • Numerical simulations.
  • Investigation of Shigesada-Kawasaki-Teramoto models.

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Last Updated: Jun 16, 2026

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Published on: February 22, 2018

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Main Results:

  • Analytical estimates and simulations show higher spreading speeds than expected in slowly oscillating environments.
  • Spreading speeds approach zero in very slowly oscillating environments with strong Allee effects.
  • Allee effects demonstrate an unfavorable aggregation impact in reaction-diffusion models.

Conclusions:

  • Environmental fragmentation has a complex effect on spreading speeds.
  • The derived formulas fill a gap in understanding environmental influences.
  • Allee effects can halt population spread in fragmented habitats.