Evolutionary game dynamics of the Wright-Fisher process with different selection intensities

Area of Science:

• Evolutionary Game Theory
• Population Genetics
• Mathematical Biology

Background:

• Evolutionary game dynamics in finite populations are typically modeled by stochastic processes like the Wright-Fisher model.
• Individual fitness is influenced by environmental factors and the frequency and type of competitors, leading to varied selection intensities.
• Understanding how selection intensities affect strategy fixation is crucial for predicting evolutionary outcomes.

Purpose of the Study:

• To develop a dynamic model of the Wright-Fisher process incorporating different selection intensities for distinct strategies in a 2x2 symmetric game.
• To derive analytical expressions for fixation probabilities under weak selection.
• To specify conditions for natural selection favoring a strategy and for it to be an evolutionary stable strategy (ESS).

Main Methods:

• Developed a dynamic Wright-Fisher process model with differential selection intensities for different strategies.
• Derived analytical expressions for fixation probabilities under weak selection.
• Compared results with the Moran dynamic process and used simulation analysis for prisoner's dilemma, coordination, and coexistence games.

Main Results:

• Fixation probability is determined by both the game matrix and differing selection intensities.
• Conditions for strategy fixation are consistent between the Wright-Fisher and Moran processes.
• In prisoner's dilemma, cooperative strategy fixation probability decreases with its own selection intensity but increases with coordination and coexistence games. It decreases with increasing defection strategy selection intensity across all game types.

Conclusions:

• The developed model provides an effective framework for studying evolutionary dynamics in finite populations with varying selection pressures.
• Selection intensity plays a significant role in determining the fixation probability of strategies, with context-dependent effects observed across different game types.
• The findings offer a nuanced understanding of evolutionary stable strategies and the factors influencing their prevalence.