Fixation probabilities in evolutionary games with the Moran and Fermi processes.

Area of Science:

• Evolutionary game theory
• Mathematical modeling
• Population dynamics

Background:

• Understanding the evolution of cooperation is crucial in various biological and social systems.
• Existing models often use simplified update mechanisms, limiting their applicability.
• The interplay between different evolutionary dynamics is not fully understood.

Purpose of the Study:

• To develop and analyze an evolutionary dynamic model incorporating both Moran and Fermi update mechanisms.
• To investigate the impact of these mixed dynamics on the fixation probability of cooperative strategies.
• To compare the model's outcomes with neutral evolution scenarios.

Main Methods:

• Construction of a finite population model (N+M individuals).
• Implementation of distinct update rules: N individuals use the Moran process, M individuals use the Fermi process.
• Derivation and analysis of balance equations for fixation probability.
• Examination of specific case scenarios.

Main Results:

• The fixation probability of a single co-operator employing the Fermi process is higher than under neutral evolution.
• Increased numbers of individuals using the Fermi process correlate with higher fixation probabilities for co-operators.
• The mixed-mechanism model yields distinct outcomes compared to models with homogeneous update rules.

Conclusions:

• The Fermi update mechanism can significantly promote the evolution of cooperation within a finite population.
• Hybrid evolutionary dynamics, combining different update rules, offer a more nuanced understanding of cooperation.
• Future research should explore variations in population size and the proportion of individuals using each mechanism.