Biological systems are complex assemblages of a large number of elements (e.g., molecules, cells, tissues, or organisms) that form a multitude of nonlinear and nonstationary interactions at small scales that spontaneously self-organize to affect emergent properties of the whole systems at larger scales. Network science has emerged as a discipline to better understand the function and dynamics of complex interacting systems. However, existing networks are intrinsically limited to revealing pairwise interactions, whereas biological systems are often characterized by higher-order interactions involving groups of three or more elements. Here, by integrating allometric scaling theory and evolutionary game theory, we develop a statistical mechanical model for coalescing all elements of the systems into a dynamically varying, multilayer hypernetwork from big static data. Beyond simple networks that only can identify and describe pairwise interactions as edges, the hypernetwork can also disentangle high-order interactions using hyperedges composed of more than two elements. We classify hypernetworks into two categories, active hypernetworks and passive hypernetworks that reveal how interactions between elements influence, and are influenced by, other elements, respectively. We integrate ecological behavior theory to reconstruct mutualism-, altruism-, aggression-, and antagonism-typical hypernetworks that can fully capture the underlying mechanisms and emergent properties of biological systems. Our ecologically-based statistical mechanical model, empirically validated by microbiome data analysis, provides a tool to more precisely unveil the internal workings of a broader domain of biological communities and systems.

Prof. Rongling Wu

Center for Statistical Genetics

Departments of Public Health Sciences and Statistics

The Pennsylvania State University