Amplitude death in coupled replicator map lattice: Averting migration dilemma

Area of Science:

• Evolutionary Game Theory
• Complex Systems
• Mathematical Biology

Background:

• Cooperation dynamics in populations with subpopulations (demes) and migration are crucial in evolutionary game theory.
• The 'migration dilemma' highlights the conflict between cooperators avoiding exploitation and the need for migration to spread cooperation.

Purpose of the Study:

• To investigate the emergence and sustenance of cooperation in a network of demes with random migration.
• To analyze the impact of migration, heterogeneous demes, network structure, and migration costs on cooperation levels.

Main Methods:

• A theoretical model using a coupled map lattice of replicator maps for two-player-two-strategy games.
• Exploration of various coupling types, heterogeneous demes, network degrees, and migration costs.

Main Results:

• Random migration was found to be highly effective in maintaining a uniform cooperator fraction across the population.
• This uniformity persisted regardless of the specific replicator dynamics or inter-deme interactions.

Conclusions:

• Random migration is a key mechanism for sustaining cooperation in structured populations.
• The study demonstrates the robustness of cooperation under random migration, irrespective of complex network dynamics.