Unifying pairwise interactions in complex dynamics.

Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems, but these computational methods-from contemporaneous correlation coefficients to causal inference methods-define and formulate interactions differently, using distinct quantitative theories that remain largely disconnected. Here we introduce a large assembled library of 237 statistics of pairwise interactions, and assess their behavior on 1,053 multivariate time series from a wide range of real-world and model-generated systems. Our analysis highlights commonalities between disparate mathematical formulations of interactions, providing a unified picture of a rich interdisciplinary literature. Using three real-world case studies, we then show that simultaneously leveraging diverse methods can uncover those most suitable for addressing a given problem, facilitating interpretable understanding of the quantitative formulation of pairwise dependencies that drive successful performance. Our results and accompanying software enable comprehensive analysis of time-series interactions by drawing on decades of diverse methodological contributions.