Abstract：

Interactions among the underlying units of a complex system are not limited to dyads, but can also occur in larger groups. However, no generic model for capturing both lower- and high-order interactions has been developed, making it impossible to chart a comprehensive picture of internal workings within complex communities.

Here, we propose a new norm of statistical mechanics derived from the integration of evolutionary game theory and behavioral ecology theory to encode all units (nodes) and their bidirectional, signed, and weighted interactions (including links and hyperlinks) at various orders into hypernetworks.

We apply our method to multi-species microbial communities, showing that the method can distinguish between how pairwise interactions modulate the abundance of the third species and how the altered abundance of each species in turn governs interactions between other species and further predict the eco-evolutionary trajectories of community structure and behavior.

We validate the new method by designing a series of in vitro mono-, co-, and tri-cultural experiments of three bacterial species. Our hypernetwork model paves the way for inferring a detailed network fundamental to complex systems (joint work with Li Feng, Shen Zhang, Chengwen Xue, Shuo Li Liu, Ang Dong, Christopher H. Griffin, and Shing-Tung Yau).