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Fixation in finite populations evolving in fluctuating environments.

Peter Ashcroft1, Philipp M Altrock2, Tobias Galla3

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A changing environment can surprisingly boost mutant survival in evolutionary games. Dynamic environments, by exploiting environmental noise, can increase fixation probability beyond static conditions.

Keywords:
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Area of Science:

  • Evolutionary biology
  • Population dynamics
  • Theoretical ecology

Background:

  • Environmental changes significantly influence evolutionary selection.
  • Population dynamics are governed by birth and death rates, which can fluctuate over time.
  • Environmental states can be modeled using Markov processes.

Purpose of the Study:

  • To develop a general theory for mutant fixation probability and fixation times in changing environments.
  • To apply this theory to evolutionary games with time-varying payoff structures.
  • To investigate the impact of environmental noise on evolutionary dynamics.

Main Methods:

  • Developing a general mathematical theory for fixation probability and fixation times.
  • Applying the theory to evolutionary games with time-dependent payoff matrices.
  • Analyzing population dynamics driven by birth and death events in a Markovian environment.

Main Results:

  • A dynamic environment can increase mutant fixation probability beyond that of static environments.
  • Environmental noise can be exploited by mutants, leading to higher fixation probabilities.
  • Two approximations for stationary distributions were found, applicable to rapid and slow environmental switching.

Conclusions:

  • Environmental fluctuations can create novel evolutionary dynamics and outcomes.
  • The study provides a theoretical framework to understand evolution in non-stationary environments.
  • The findings have implications for evolutionary game theory and understanding adaptation in fluctuating conditions.