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Extinction dynamics from metastable coexistences in an evolutionary game.

Hye Jin Park1, Arne Traulsen1

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Stochastic evolutionary dynamics can cause species coexistence to collapse. Using classical mechanics and the Wentzel-Kramers-Brillouin (WKB) approximation, we predict which type goes extinct first.

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Area of Science:

  • Evolutionary game theory
  • Theoretical ecology
  • Mathematical biology

Background:

  • Deterministic evolutionary game dynamics can establish stable coexistence of different types.
  • Stochasticity, or randomness, can disrupt these stable states, leading to the extinction of types.
  • Population size fluctuations often accompany this extinction process.

Purpose of the Study:

  • To investigate the most probable extinction trajectory in stochastic evolutionary models.
  • To identify reliable predictors of extinction events in ecological systems.
  • To apply advanced mathematical methods to understand evolutionary dynamics.

Main Methods:

  • Mapping a stochastic evolutionary model to a classical mechanics problem.
  • Utilizing the Wentzel-Kramers-Brillouin (WKB) approximation.
  • Analyzing population size fluctuations and extinction trajectories.

Main Results:

  • The study found that more abundant types may paradoxically be more likely to go extinct first.
  • The distance between coexistence and extinction points is not a reliable predictor of extinction.
  • The WKB approximation accurately predicts the type that will go extinct first.

Conclusions:

  • The WKB approximation provides a powerful tool for predicting extinction events in evolutionary game dynamics.
  • Understanding extinction trajectories is crucial for predicting the long-term stability of biological communities.
  • The dynamics of extinction are complex and may not align with simple abundance-based predictions.