Evolutionary game dynamics with non-uniform interaction rates in finite population

Area of Science:

• Evolutionary game theory
• Mathematical biology
• Population dynamics

Background:

• Evolutionary game dynamics typically assume uniform interactions.
• Finite populations introduce stochasticity not always captured by standard models.
• Understanding fixation probability is key to predicting evolutionary outcomes.

Purpose of the Study:

• To investigate the impact of non-uniform interaction rates on evolutionary game dynamics in finite populations.
• To analyze how fixation probability is influenced by interaction heterogeneity under weak selection.
• To explore the potential for evolutionary complexity arising from non-uniform interactions.

Main Methods:

• Diffusion approximation of the Moran process.
• Analysis of stochastic dynamic properties.
• Case-specific analysis of two-phenotype games with non-uniform interaction rates.

Main Results:

• Non-uniform interaction rates can significantly influence fixation probability.
• Weak selection combined with interaction heterogeneity can lead to complex dynamics.
• The study provides a framework for analyzing evolutionary games in finite, non-uniform populations.

Conclusions:

• Non-uniform interaction rates are a crucial factor in evolutionary game dynamics within finite populations.
• These rates can introduce emergent complexity not observed in uniformly interacting populations.
• The findings have implications for understanding evolution in diverse biological and social systems.