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From Fixation Probabilities to d-player Games: An Inverse Problem in Evolutionary Dynamics.

Fabio A C C Chalub1, Max O Souza2

  • 1Departamento de Matemática and Centro de Matemática e Apliçoes, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal.

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Researchers can now infer population interaction patterns by analyzing trait fixation probabilities. This inverse problem approach uses game theory to reveal underlying social structures from evolutionary data.

Keywords:
Fixation probabilityGame theoryInverse problemsWright–Fisher process

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Area of Science:

  • Evolutionary biology
  • Population genetics
  • Mathematical biology
  • Game theory

Background:

  • Fixation probability, the likelihood of a trait becoming universal, is key in evolutionary studies.
  • While calculable, fixation probability offers limited insight into individual interactions within populations.
  • Existing models often treat populations as homogeneous, overlooking complex interaction structures.

Purpose of the Study:

  • To solve the inverse problem: inferring population interaction games from observed fixation patterns.
  • To develop a method for understanding the 'game' played by individuals based on evolutionary outcomes.
  • To link macroscopic evolutionary properties (fixation patterns) to microscopic interaction structures.

Main Methods:

  • Utilizing a framework to derive fitness functions that produce specific fixation patterns in the Wright-Fisher model.
  • Approximating derived fitness functions using d-player game theory for arbitrary precision.
  • Analyzing the emergent payoff matrices from game theory to reveal interaction structures.

Main Results:

  • A method is established to find fitness functions realizing given fixation patterns.
  • Any such fitness function can be approximated by d-player game theory with sufficient d.
  • The resulting game payoff matrices provide insights into individual interaction patterns not evident from fixation data alone.

Conclusions:

  • The study successfully bridges the gap between macroscopic fixation patterns and microscopic interaction dynamics.
  • Game theory, particularly with a sufficiently large number of players (d), offers a powerful tool for inferring evolutionary games.
  • This approach enhances our understanding of the relationship between population-level evolution and individual behavior.