A simple rule for the evolution of contingent cooperation in large groups

Area of Science:

• Evolutionary biology
• Game theory
• Social behavior

Background:

• Human cooperation in large, unrelated groups is a key evolutionary puzzle.
• Contingent reward and punishment are proposed mechanisms, but can stabilize maladaptive behaviors.
• Understanding the evolution of beneficial cooperation requires analyzing the conditions for rare strategies to increase.

Purpose of the Study:

• To derive a general formula for the relatedness required for contingent cooperation to increase when rare in n-person iterated games.
• To investigate the impact of threshold-based cooperation strategies on invasion dynamics.
• To introduce a novel methodology for studying evolution in structured populations.

Main Methods:

• Derivation of a mathematical formula for invasion fitness of cooperative strategies.
• Analysis of strategies based on a threshold fraction of cooperators.
• Development of a novel methodology for evolutionary modeling in structured populations with group-size regulation and fluctuations.

Main Results:

• A simple formula quantifies the necessary relatedness for contingent cooperation to invade.
• Modest relatedness suffices for strategies requiring a small fraction of cooperators.
• High relatedness is necessary for strategies demanding near-universal cooperation.

Conclusions:

• The findings provide insights into the evolution of large-scale human cooperation.
• The derived rule highlights the importance of relatedness levels in sustaining different cooperation strategies.
• The novel methodology offers a robust framework for studying evolution in complex population structures.