Fixation probabilities of evolutionary coordination games on two coupled populations

Area of Science:

• Evolutionary game theory
• Population dynamics
• Mathematical modeling

Background:

• Previous studies on single populations focused on fixation probabilities and times.
• Evolutionary forces from inter-population competition are known to alter single-population dynamics.

Purpose of the Study:

• To investigate the effect of interaction strength on fixation probabilities in a two-interdependent-population model.
• To analyze the impact of coupling strength on evolutionary dynamics and equilibria.

Main Methods:

• Linear stability analysis in the well-mixing limit.
• Classification of different equilibria and bifurcation patterns.
• Numerical simulations for validation.

Main Results:

• Interactions between populations critically alter dynamic behavior.
• A threshold coupling strength delays the critical initial density for fixation of strategy s1.
• Populations can evolve to an all-s2 state, supporting the Red Queen hypothesis.
• Explicit delineation of strategy s1 extinction time as an exponential form.

Conclusions:

• Inter-population competition introduces complex dynamics not seen in isolated populations.
• The Red Queen hypothesis is supported under strong inter-population coupling.
• The model provides a framework for understanding evolutionary outcomes in interdependent populations.