The ergodicity solution of the cooperation puzzle

Area of Science:

• Complex Systems
• Evolutionary Biology
• Mathematical Modeling

Background:

• Cooperation and apparent altruism are common in nature.
• Classical explanations for cooperation often rely on immediate benefits like complementarity.
• The drivers of cooperation in rudimentary environments remain an active area of research.

Purpose of the Study:

• To investigate whether cooperation is predictable without assuming immediate benefits.
• To explore cooperation in a model with self-multiplying resources and fluctuations.
• To provide a baseline explanation for observed cooperation.

Main Methods:

• Developed a mathematical model with self-multiplying resources and inherent fluctuations.
• Analyzed two growth rates: ensemble-average and time-average.
• Investigated the impact of resource pooling and sharing on growth rates.

Main Results:

• Identified non-ergodicity where time-average growth is lower than ensemble-average growth.
• Demonstrated that resource pooling reduces fluctuation size.
• Showed that cooperation increases the time-average growth rate, approaching the ensemble-average rate.

Conclusions:

• Cooperation is advantageous in the model due to increased growth rates, even without immediate benefits.
• This provides a candidate explanation for cooperation in simple systems.
• The findings offer a behavioral baseline for understanding cooperation more broadly.