Is Pearson's correlation coefficient enough for functional connectivity in fMRI?

Functional connectivity (FC) is commonly defined as the temporal coincidence of neurophysiological events, often quantified by the statistical dependency among signals from different brain regions and measured by Pearson's correlation coefficient in fMRI. However, Pearson's r captures only linear dependencies, potentially overlooking nonlinear interactions. Recently, Multiscale Graph Correlation (MGC) was introduced to measure statistical dependencies of both linear and nonlinear relationships across multiple scales, offering an "optimal scale" at which such dependencies can be inferred. In this study, we systematically compared FC measurements by Pearson's r and MGC across datasets, evaluating their reliability, sensitivity to data quantity, and ability to capture distinct experimental conditions (deeper anesthesia in macaques) and brain-behavior association. Results showed highly similar spatial connectivity patterns and strong alignment between Pearson's r and MGC for within-network FC, where optimal scales were frequently global. However, local optimal scales emerged between networks, suggesting the presence of nonlinear dependencies of FC. Reliability was higher for Pearson's r overall, but both measurements improved as the quantity of data increased. Notably, MGC revealed variability in the optimal scales under altered brain states in deeper anesthesia, highlighting its potential for detecting local-scale dependencies across states. Despite these advantages, MGC required greater computational resources and did not outperform Pearson's r in detecting brain-behavior associations. Consequently, Pearson's r remains a sufficient and reliable measure for many standard applications, whereas MGC can offer more nuanced insights in scenarios where nonlinear dynamics are of particular interest. Researchers should, therefore, balance the potential gains from MGC against its added complexity and computational cost when selecting methods to quantify FC.