Strategy abundance in 2x2 games for arbitrary mutation rates

Area of Science:

• Evolutionary Game Theory
• Population Genetics
• Mathematical Biology

Background:

• Evolutionary game dynamics model interactions between strategies in populations.
• Previous findings on strategy abundance were limited to specific conditions like low mutation or weak selection.

Purpose of the Study:

• To generalize the condition for Strategy A outcompeting Strategy B.
• To demonstrate the robustness of the abundance criterion across various evolutionary parameters.

Main Methods:

• Analysis of evolutionary game dynamics in finite, well-mixed populations.
• Utilizing a wide class of stochastic birth-death processes.
• Investigating average abundances of two competing strategies (A and B).

Main Results:

• The condition for Strategy A being more abundant than Strategy B, a(N-2)+bN > cN+d(N-2), is shown to be valid.
• This criterion holds irrespective of mutation rate and selection intensity.
• The result is applicable to a broad spectrum of stochastic birth-death processes.

Conclusions:

• The derived condition for strategy dominance is broadly applicable in evolutionary game dynamics.
• The study extends previous results by removing limitations on mutation rates and selection strengths.
• This provides a more universal understanding of strategy competition in finite populations.