The Granger-causal influence of the ACC over FEF is shown as GACC→FEF and the Granger-causal influence of FEF over ACC is denoted as GFEF→ACC. The overall influence of ACC over FEF was derived by implementing the (GACC→FEF−GFEF→ACC) equation. The results shown in Fig. 3f,h are obtained by implementing the (GACC→FEF−GFEF→ACC) equation. The results shown in Supplementary Fig. 4A depicts GACC→FEF, Supplementary Fig. 4B shows GFEF→ACC, and Supplementary Fig. 4C shows both GACC→FEF (blue) and GFEF→ACC (red). We tested the difference between the baseline (700 ms before fixation onset) and the delay period (400–1,100 ms following stimulus onset), using a t-test. We further confirmed the results of the t-test by implementing a permutation test. The permutation test procedure is described in detail above.
