Figure 2 – The conceptual structure of the functional connectivity (FC) framework.

A) Each method involves a mapping between observations and target theoretical properties, mediated by methodological properties that enable and/or restrict the possible inferences that can be made. Methodological properties merely shift what inferences are possible, but confounding properties can completely block inferences by creating ambiguities outside the space of causal brain network configurations (e.g., subject motion obscuring FC observations nullifies inferences about neural mechanisms causing FC observations). The grid illustrates the space of all hypotheses under consideration, with each grid point being a particular causal network configuration (of which only one can be true). Each method’s color indicates which hypotheses that method’s results are compatible with (more coverage = more ambiguity). The overlap between methods (purple) illustrates the ability to use multiple FC methods to converge on a more narrow set of possibilities. This advances theory through logical conjunctions across FC methods. B) An illustration of a correlation-based FC measure in a simple 3-node network. The directionality of influences are ambiguous (based on Pearson correlation of neural time series; left side of panel) but this nonetheless constrains the hypothesis space (both likely and unlikely; right side of panel) by providing a higher probability of some causal network configurations than others. C) Another illustration of a simple 3-node network, this time with no correlation between the bottom two nodes. Correlation does especially well in this scenario, given that only a “collider” graph is likely with this set of correlations in a 3-node system⁸⁸.