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.
Highlights
We have a thorough understanding of pairwise interactions and the various interaction categorization measures defined across distinct subject areas such as statistical physics, gene networks, and prey-predator systems
We start by defining X and Y as random variables and will show that the generalized formula reduces to the covariance formulation and mutual information by the choice of different algebraic operations of and △
The higher-order interaction formulations of these concepts differ from the higher-order covariance when there are more than three components, as derived in Appendix A in Supplementary Material
Summary
Because of their key role in understanding the dynamics of complex biological, physical, and social systems, there is a long and rich history of studying interactions and their consequences (Wootton, 1993; Billick and Case, 1994; Darling and Côté, 2008; Mihaila et al, 2010; Hamilton, 2011; Toprak et al, 2013; Barrios-O’neill et al, 2014; Foucquier and Guedj, 2015; Palmer et al, 2015; Podgornaia and Laub, 2015; Nishikawa and Motter, 2016; Shi, 2016) These approaches have often been complemented and enhanced by network theory that has led to important advances in prediction of patterns (Segrè et al, 2005; Yeh et al, 2006; Braun and Shah, 2015). We have a thorough understanding of pairwise interactions and the various interaction categorization measures defined across distinct subject areas such as statistical physics, gene networks, and prey-predator systems Despite this focus on interactions at the pairwise level, a general and comprehensive framework for two-way interaction categorizations has not been established. Recent studies have provided evidence that there is a large amount of higher-order interactions, suggesting a critical need to include higher-order effects to better understand complex systems and alterations of ecosystem processes (Weinreich et al, 2013; Taylor and Ehrenreich, 2015a,b; Beppler et al, 2016; Tekin et al, 2016; Levine et al, 2017; Mayfield and Stouffer, 2017)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
