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Area of Science:

  • Population dynamics
  • Evolutionary game theory
  • Theoretical ecology

Background:

  • Environmental variations coherently affect population fitness.
  • Understanding mutant fixation is crucial for community dynamics.

Purpose of the Study:

  • To analyze the fixation probability of a mutant in a two-species community under environmental variations.
  • To differentiate fixation dynamics between pairwise and global competition models.
  • To investigate the role of selection strength and population size.

Main Methods:

  • Mathematical modeling of population dynamics.
  • Calculation of mutant fixation probability as a function of fitness, variation amplitude, and duration.
  • Application of Wentzel-Kramers-Brillouin (WKB) technique for strong selection regimes.

Main Results:

  • Global competition enhances mutant fixation probability due to noise-induced stabilization.
  • In weak selection, global competition yields an N-independent fixation constant for deleterious mutants, while pairwise competition shows a (ln N)⁻¹ decay.
  • A general formula for fixation probability in strong selection was derived using WKB.

Conclusions:

  • Environmental noise and competition structure significantly alter evolutionary trajectories.
  • Global competition can stabilize populations and increase fixation rates for mutants.
  • The study provides insights into long-term persistence of suboptimal populations and stochastic tunneling.