Evolutionary dynamics in finite populations with zealots

Area of Science:

• Evolutionary Game Theory
• Population Dynamics
• Mathematical Biology

Background:

• Evolutionary dynamics in finite populations are crucial for understanding strategy adoption.
• Zealots, individuals with fixed strategies, can significantly alter evolutionary trajectories.
• Previous models often lack the influence of non-adaptive or fixed strategic behavior.

Purpose of the Study:

• To investigate the evolutionary dynamics of two-strategy matrix games incorporating zealots.
• To analyze the fixation time of strategies in finite populations with zealots.
• To identify conditions influencing fixation speed, particularly the role of selection intensity.

Main Methods:

• Mathematical modeling of two-strategy matrix games.
• Analysis of fixation time dynamics in finite populations.
• Simulation and theoretical analysis of zealot influence on evolutionary outcomes.

Main Results:

• Fixation time exhibits three distinct regimes: one short and two exponentially long concerning population size.
• A critical threshold in selection intensity exists, below which fixation is rapid, irrespective of the payoff matrix.
• Zealot strategy alignment simplifies fixation, but non-aligned zealots introduce complex dynamics.

Conclusions:

• Zealots introduce novel dynamics to evolutionary games, altering fixation times significantly.
• The identified selection intensity threshold offers a key parameter for predicting evolutionary stability.
• Results provide insights into social dilemma games and the impact of fixed beliefs on population behavior.