Continuous stability and evolutionary convergence

Area of Science:

• Evolutionary biology
• Game theory
• Mathematical modeling

Background:

• Understanding long-term evolutionary dynamics requires integrating mutation and selection processes.
• Population games model strategic interactions within populations, influencing evolutionary trajectories.
• Asexual reproduction simplifies evolutionary models by removing genetic recombination.

Purpose of the Study:

• To define and analyze a stochastic process for long-term evolution in asexual populations.
• To investigate the relationship between evolutionary stability and game-theoretic stability under mutation and selection.
• To determine the influence of mutation characteristics on evolutionary stability.

Main Methods:

• Defined a stochastic evolutionary process incorporating mutation and selection.
• Analyzed population dynamics using a one-dimensional continuous strategy space in a population game.
• Focused on the impact of small-effect mutations on evolutionary stability.

Main Results:

• Established an equivalence between long-term dynamic stability in the evolutionary process and continuous stability in the population game.
• Demonstrated that for one-dimensional strategy sets, this equivalence is largely independent of mutation distribution.
• Showcased the critical role of mutation size in linking evolutionary and game-theoretic stability.

Conclusions:

• Continuous stability in population games is a key predictor of long-term evolutionary stability for asexual populations with small mutations.
• The dimensionality of the strategy set is crucial for the robustness of this stability relationship.
• Mutation distribution has minimal impact on evolutionary stability when strategies are one-dimensional, simplifying evolutionary predictions.