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Evolutionary regime transitions in structured populations.

Fernando Alcalde Cuesta1,2, Pablo González Sequeiros3,2, Álvaro Lozano Rojo4,5,2

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Graph structure significantly impacts evolutionary dynamics. Most small graphs amplify selection, but some can suppress it, especially with increasing mutant fitness, offering insights for biology and network science.

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Area of Science:

  • Evolutionary dynamics
  • Graph theory
  • Population genetics

Background:

  • Evolutionary dynamics in finite populations are influenced by spatial structure, often modeled as undirected graphs.
  • Graph structures can either amplify or suppress selection, affecting the spread of advantageous mutants.
  • Understanding these evolutionary regimes is crucial for various scientific fields.

Purpose of the Study:

  • To analyze the distribution of evolutionary regimes (amplifiers and suppressors of selection) for all undirected graphs with N ≤ 10 vertices.
  • To identify graphs that transition between amplification and suppression regimes based on mutant fitness.
  • To explore methods for suppressing selection using symmetrical graph structures.

Main Methods:

  • Systematic analysis of all undirected graphs up to N=10 vertices.
  • Application of computer-aided techniques for symbolic computation of fixation probabilities and evolutionary regimes.
  • Investigation of specific graph families, including highly symmetrical ones.

Main Results:

  • Most undirected graphs with N ≤ 10 vertices act as amplifiers of selection.
  • Some graphs exhibit regime transitions, shifting from amplification to suppression as mutant fitness increases.
  • Analysis of graphs with N=8 to N=10 reveals complex evolutionary dynamics with multiple regime transitions.

Conclusions:

  • The spatial structure of populations, represented by graphs, plays a critical role in evolutionary outcomes.
  • The discovery of suppression mechanisms that can reverse amplification is significant for biology and network science.
  • Further research into complex evolutionary dynamics in larger graphs is warranted.