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Dynamical phase transition in a model for evolution with migration.

Bartłomiej Waclaw1, Rosalind J Allen, Martin R Evans

  • 1SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom.

Physical Review Letters
|January 15, 2011
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Summary
This summary is machine-generated.

Evolutionary dynamics shift at a critical migration rate, altering genetic makeup. Even minimal migration can significantly impact evolutionary outcomes, demonstrating high sensitivity.

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Area of Science:

  • Evolutionary biology
  • Theoretical ecology
  • Population genetics

Background:

  • Quasispecies models explore evolution in changing environments.
  • Understanding migration's role in shaping population genetics is crucial.
  • Fitness landscapes differ across habitats, influencing evolutionary trajectories.

Purpose of the Study:

  • To investigate the impact of one-way migration between two habitats with distinct fitness landscapes on evolutionary dynamics.
  • To identify critical migration rates that induce significant changes in evolutionary outcomes.
  • To analyze the sensitivity of evolutionary trajectories to migration.

Main Methods:

  • Utilized a simple quasispecies model.
  • Simulated one-way migration between two habitats with differing fitness landscapes.
  • Applied concepts from localization theory to analyze critical phenomena.

Main Results:

  • Identified a dynamical phase transition at a critical migration rate.
  • Observed divergence in the time to reach steady state at the transition.
  • Demonstrated qualitatively different genetic compositions above and below the critical migration rate.
  • Showed that the critical migration rate can be very small.

Conclusions:

  • Evolutionary outcomes are highly sensitive to migration, even at low rates.
  • A small amount of migration can fundamentally alter population genetic structure.
  • Dynamical phase transitions are key to understanding evolutionary responses to habitat coupling.