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 correlation coefficients to causal inference -- rely on distinct quantitative theories that remain largely disconnected. Here we introduce a library of 249 statistics for pairwise interactions and assess their behavior on 1053 multivariate time series from a wide range of real-world and model-generated systems. Our analysis highlights new commonalities between different mathematical formulations, providing a unified picture of a rich, interdisciplinary literature. We then show that leveraging many methods from across science can uncover those most suitable for addressing a given problem, yielding high accuracy and interpretable understanding. Our framework is provided in extendable open software, enabling comprehensive data-driven analysis by integrating decades of methodological advances.