Extended Data Table 1: Correlations for all nodes in our final Bayesian Network with (⁸⁷Sr/⁸⁶Sr)_sw.

Note that C_Emp = Empirical Rank Correlation; C_BN = BN Rank Correlation; C_Cond = Conditional Rank Correlation; Av = Average value over a 2.5 Myr window, up to the given lag (in Myr); for example, LIP eruptive area Av 7.5 Myr is the correlation between Sr and the average LIP eruptive area over time ≥(t-7.5) Ma to time <(t-5) Myr (note that if this is not specified the interval is 0 Myr; that is no lag). Nodes with C_Cond greater than the 99 percent confidence interval threshold (CI_thresh, see the Methods for further details) were retained in the BN and are shown here. The reader is directed to Supplementary Data File S3 for the full table of correlations that includes nodes that were subsequently eliminated from the BN. Correlations calculated using (a) original inputs, and (b) simulated inputs (incorporating uncertainty distributions) are shown for comparison. To investigate how input uncertainty might affect the estimated correlations, we took the BN structure obtained using our original ‘best estimate’ data and recalculated all the network parameters using our new simulated data set. The resulting C_Emp, C_BN and C_Cond are shown in the last three columns. This shows that the dominant processes, that is, those nodes with the strongest influence (rows in bold), do not change significantly; and all nodes with the highest C_Cond remain highest within the simulated output.