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Evolutionary game theory on graphs reveals that population structure can alter selection dynamics. Contrary to intuition, strong selection doesn't always eliminate noise, especially in structured populations with specific update rules.

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Population Dynamics

Background:

  • Evolutionary games on graphs model strategic interactions and population structure's impact on evolutionary success.
  • Graph structures can amplify or suppress selection, affecting mutant fixation probability compared to well-mixed populations.
  • Mean fixation times exhibit complex behavior under strong selection, challenging common intuitions.

Purpose of the Study:

  • To investigate mean fixation times in structured populations under strong frequency-dependent selection.
  • To analyze the influence of different microscopic evolutionary update rules (death-birth and birth-death) on fixation times.
  • To challenge and refine existing intuitions about selection strength and demographic noise in evolutionary graph theory.

Main Methods:

  • Analysis of mean fixation times on a cycle graph.
  • Application of strong frequency-dependent selection.
  • Derivation of exact analytical results for two update rules: death-birth and birth-death.

Main Results:

  • Established exact analytical results for fixation times under strong selection on cycle graphs.
  • Demonstrated that some coexistence games exhibit fixation times polynomial in population size, contrary to expectations.
  • Showed that demographic noise can persist under strong selection in death-birth updates but is largely eliminated in birth-death updates.

Conclusions:

  • Intuitions regarding fixation speed and noise elimination under strong selection can be misleading in structured populations.
  • The specific microscopic update rule (death-birth vs. birth-death) critically determines the persistence of demographic noise.
  • Strong selection's effect on evolutionary dynamics is highly dependent on both game structure and the update mechanism.