General Form for Interaction Measures and Framework for Deriving Higher-Order Emergent Effects

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.

Nutrient dominance governs the assembly of microbial communities in mixed nutrient environments

“…Any deviation between the null model prediction and the observed (measured) composition reveals that nutrients are not acting independently, but rather "interact" to shape community composition. This definition of an interaction as a deviation from a null model that assumes independent effects is commonplace in systems-level biology [12,13].…”

High-order interactions distort the functional landscape of microbial consortia

“…The operational detection of interactions as deviations from the prediction of an interaction-free null model has a long history and has been previously used in ecology (e.g., Billick and Case [68]) as well as in many other fields of biology (e.g., [50,51,69–71]). In the context of communities, recent work has used the same analogy with fitness landscapes to detect high-order and complex interactions in ecological systems [6,72].…”

Hidden layers of density dependence in consumer feeding rates

“…This occurs despite the tremendous utility that exists in identifying scenarios in which access to multiple resources synergistically promotes or retards growth (Sperfeld et al ., 2012; Jeyasingh et al ., 2020). Indeed, from trophic interactions and growth models to epistasis (Poelwijk et al ., 2016; Sailer & Harms, 2017a,b) and drug–drug interactions (Tekin et al ., 2018; Katzir et al ., 2019), there are countless areas of biology in which researchers are interested in ways to quantify similar forms of non‐independence and non‐additivity. Our mathematical framework provides a general basis with which to explore each of these and others, following a tradition of embracing biological complexity rather than shying away from it (Evans et al ., 2013).…”