Hypernetwork modeling and topology of high-order interactions for complex systems

Area of Science:

• Complex Systems Science
• Statistical Mechanics
• Evolutionary Game Theory
• Behavioral Ecology

Background:

• Interactions in complex systems extend beyond pairwise relationships to include higher-order interactions (HOI).
• Existing models lack a generic framework to comprehensively represent these multi-agent HOI alongside pairwise interactions.
• Understanding HOI is crucial for a detailed depiction of complex system dynamics.

Purpose of the Study:

• To develop a unified statistical mechanics framework for modeling high-order interactions (HOI) in complex systems.
• To differentiate between active and passive HOI and their impact on system evolution.
• To apply and validate the hypernetwork model in microbial communities.

Main Methods:

• Integration of evolutionary game theory and behavioral ecology into a statistical mechanics framework.
• Development of hypernetworks to represent agents and their multi-order, signed, and weighted interactions.
• Application of GLMY homology theory for topological analysis of reconstructed hypernetworks.
• Validation through in vitro mono-, co-, and tricultural experiments with bacterial species.

Main Results:

• The hypernetwork model successfully captures both active and passive high-order interactions (HOI).
• Analysis revealed distinct roles for pairwise interactions and HOI in shaping microbial community behavior and dynamics.
• Experimental validation confirmed the statistical relevance of the developed hypernetwork model.

Conclusions:

• The proposed hypernetwork framework offers a generic approach to model complex systems with HOI.
• Distinguishing active and passive HOI provides deeper insights into system evolution across multiple scales.
• The model's application to microbial communities highlights the interplay between different interaction orders in ecological dynamics.