Mutation in evolutionary games can increase average fitness at equilibrium

Area of Science:

• Evolutionary Game Theory
• Population Genetics
• Mathematical Biology

Background:

• Evolutionary game theory models interactions between strategies within a population.
• Mutation is a key driver of evolutionary change, introducing new variations.
• Understanding mutation's impact on population fitness is crucial for evolutionary dynamics.

Purpose of the Study:

• To investigate if introducing mutation from strategy A to strategy B can increase average population fitness at equilibrium.
• To classify two-by-two games and identify conditions favoring enhanced fitness through mutation.
• To analyze the effects of bidirectional mutations on population productivity and equilibrium payoff.

Main Methods:

• Analysis of two-by-two games using payoff matrices [(a,b),(c,d)].
• Classification of game types based on payoff values.
• Mathematical modeling of mutation dynamics and its effect on average fitness.

Main Results:

• Mutation from A to B enhances average population fitness when a and d are less than (b + c)/2, or when c is less than b.
• Specific conditions for maximizing the productivity of strategy A were identified.
• Mutation can increase equilibrium payoff in cultural and genetic contexts, especially with frequency-dependent selection.

Conclusions:

• Introducing specific types of mutation can be beneficial for increasing average population fitness in evolutionary games.
• The study provides a framework for understanding mutation's role in enhancing population-level outcomes.
• Results have implications for genetic, cultural, and biological systems where strategy modification occurs.