The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction

Functional connectivity (FC) is frequently operationalized as a correlation. Many studies have examined changes in correlation networks across time, claiming to link time-varying fluctuations to ongoing mental operations and physiological processes. Other studies, however, have called these results into question, noting that statistically indistinguishable patterns of time-varying fluctuations can be obtained by windowing synthetic time series generated from ground-truth stationary correlation structure. Recently, we developed a technique for tracking rapid (framewise) fluctuations in network connectivity over time. Here, we show that these "edge time series" are mathematically equivalent to interaction terms in a specific family of general linear models. We exploit this fact to further demonstrate that time-varying connectivity carries explanatory power above and beyond brain activations. This observation suggests that time-varying connectivity is likely more than a statistical artifact. SUMMARYBrain activity and connectivity have been linked to ongoing behavior and mentation but usually in isolation and almost never in the same model. Here, we show that "edge time series" - a recently proposed method for tracking moment-to-moment connectivity changes - are equivalent to an interaction term in a linear model. By including terms for activations in the same model, it provides an elegant framework for assessing the relative explanatory power of edges and activations. In our work, we use this modeling framework to study time-varying behavior in zebrafish, worms, and humans. We find that connectivity contains unique explanatory power above and beyond activity.