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Stochastic resonance in biological nonlinear evolution models.

Jörn Dunkel1, Stefan Hilbert, Lutz Schimansky-Geier

  • 1Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, D-12489 Berlin, Germany. dunkel@physik.hu-berlin.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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Stochastic resonance occurs in nonlinear biological evolution models. This study confirms its presence in the Fisher-Eigen model (FEM) with various fitness functions, revealing a phase lag in the system response.

Area of Science:

  • Evolutionary Biology
  • Theoretical Biology
  • Statistical Physics

Background:

  • The Fisher-Eigen model (FEM) is a fundamental model for biological evolution.
  • Understanding population dynamics under periodically changing environments is crucial.
  • Stochastic resonance (SR) is a phenomenon where noise enhances signal detection.

Purpose of the Study:

  • To investigate stochastic resonance in the nonlinear, one-dimensional Fisher-Eigen model.
  • To analyze the impact of different periodically driven fitness functions on biological evolution.
  • To explore the occurrence of SR in globally coupled biological systems.

Main Methods:

  • Derivation of the exact analytic solution for the asymptotic probability density for a harmonic fitness function.

Related Experiment Videos

  • Development of a general perturbation theory (linear response approximation) for complex systems.
  • Investigation of SR using the spectral amplification measure for various fitness functions (quadratic, quartic, bistable).
  • Comparison of analytical results with numerical simulations.

    • Main Results:

    • A distinct phase lag between the driving signal and the linear response of the system was observed.
    • Stochastic resonance was confirmed to occur in nonlinear, globally coupled biological systems.
    • The spectral amplification measure effectively quantified SR in different fitness landscapes.

    Conclusions:

    • Stochastic resonance is a relevant phenomenon in nonlinear evolutionary models like the FEM.
    • The study provides analytical and numerical evidence for SR in these systems.
    • The findings contribute to understanding how environmental fluctuations can influence evolutionary trajectories.