Extreme Selection Unifies Evolutionary Game Dynamics in Finite and Infinite Populations

Area of Science:

• Evolutionary Game Theory
• Population Dynamics
• Mathematical Biology

Background:

• Discrepancies exist between evolutionary game outcomes in finite versus infinite populations.
• Understanding strategy dynamics requires considering population size and selection intensity.
• Microscopic models like the Moran process and pairwise comparison are crucial for simulating evolution.

Purpose of the Study:

• To resolve the unequivalence between finite and infinite population evolutionary game scenarios.
• To investigate the impact of extreme selection on strategy dynamics in well-mixed populations.
• To analyze the convergence of stochastic processes to deterministic limits under strong selection.

Main Methods:

• Analysis of a 2-player, 2-strategy symmetric game.
• Inclusion of frequency-dependent Moran process and pairwise comparison imitation.
• Examination of selection intensities ranging from neutral to extreme.

Main Results:

• Extreme selection unifies evolutionary game outcomes, yielding dominance, coexistence, and mutual exclusion in populations of any size.
• Seven invasion and fixation scenarios in finite populations reduce to three under strong selection.
• In the extreme selection limit, mutual invasion without fixation emerges, mirroring deterministic coexistence.

Conclusions:

• Extreme selection simplifies evolutionary game dynamics, making outcomes consistent across population sizes.
• The study bridges stochastic models of finite populations and deterministic models of infinite populations.
• Findings provide a unified framework for understanding strategy evolution under strong selective pressures.