AUTHOR=Tekin Elif , Yeh Pamela J. , Savage Van M. TITLE=General Form for Interaction Measures and Framework for Deriving Higher-Order Emergent Effects JOURNAL=Frontiers in Ecology and Evolution VOLUME=6 YEAR=2018 URL=https://www.frontiersin.org/journals/ecology-and-evolution/articles/10.3389/fevo.2018.00166 DOI=10.3389/fevo.2018.00166 ISSN=2296-701X ABSTRACT=

Interactions are ubiquitous and have been extensively studied in many ecological, evolutionary, and physiological systems. A variety of measures—ANOVA, covariance, epistatic additivity, mutual information, joint cumulants, Bliss independence—exist that compute interactions across fields. However, these are not discussed and derived within a single, general framework. This missing framework likely contributes to the confusion about proper formulations and interpretations of higher-order interactions. Intriguingly, despite higher-order interactions having received little attention, they have been recently discovered to be highly prevalent and to likely impact the dynamics of complex biological systems. Here, we introduce a single, explicit mathematical framework that simultaneously encompasses all of these measures of pairwise interactions. The generality and simplicity of this framework allows us to establish a rigorous method for deriving higher-order interaction measures based on any of the pairwise interactions listed above. These generalized higher-order interaction measures enable the exploration of emergent phenomena across systems such as multiple predator effects, gene epistasis, and environmental stressors. These results provide a mechanistic basis to better account for how interactions affect biological systems. Our theoretical advance provides a foundation for understanding multi-component interactions in complex systems such as evolving populations within ecosystems or communities.