The σ law of evolutionary dynamics in community-structured population

Area of Science:

• Evolutionary Game Theory
• Population Genetics
• Mathematical Biology

Background:

• Evolutionary game dynamics in finite populations are crucial for understanding trait selection with frequency-dependent fitness.
• The σ law offers a fundamental framework for predicting selection between two competing strategies (A and B) under weak selection: A is favored if σR+S>T+σP.

Purpose of the Study:

• To investigate the σ law within a community-structured population model using the Moran process.
• To determine if the parameter σ in the σ law accurately reflects characteristics of structured populations and interaction rates.

Main Methods:

• Development of a game model based on a community-structured population.
• Application of the Moran process to analyze evolutionary dynamics.
• Calculation of average payoffs for competing strategies using the effective sojourn time method.

Main Results:

• The parameter σ was found to encapsulate both the characteristics of the structured population and the reaction rates between individuals.
• This indicates that interactions are not uniform and σ can represent the reaction rate between individuals of the same strategy.
• Verification through a modified replicator equation with non-uniform interaction rates in a Prisoner's Dilemma Game (PDG).

Conclusions:

• The σ law is a robust predictor of evolutionary strategy selection in structured populations.
• The parameter σ provides a nuanced understanding of population structure and individual interaction dynamics.
• Findings extend the applicability of the σ law to more complex, non-uniform interaction scenarios.