Extended Data Fig. 2: Relationship between fragmentation and kimberlites.

a, Spearman rank correlation and conditional rank correlation (^†refer to equation (2) for definitions) for ΔF (slope over 9-Myr moving window) and kimberlites for 500–0 Ma, calculated using a Bayesian network¹⁸ (Methods). Here the input is a 5-Myr-resolution series, in which kimberlite count is the total number of events in each 5-Myr interval and ΔF is the slope of the regression line for fragmentation estimated every 5 Myr. Using a simple saturated Bayesian network (in which each node is linked by an arc to every other node in the network), we computed the correlation of ΔF and kimberlite count corr(ΔF, K); then the correlation of ΔF and kimberlite with a lag of 5 Myr (in which ΔF precedes kimberlites) conditional on ΔF (unlagged), that is, corr(ΔF_t−5, K|ΔF); then the correlation at lag 10 Myr, conditional on the lags at 0 and 5 Myr corr(ΔF_t−10, K|ΔF, ΔF_t−5) etc., up to a lag of 50 Myr. This removes the effect of shorter lags and thus the effects of autocorrelation. This test confirms that the maximum correlation between ΔF and kimberlites occurs roughly 25 Myr after fragmentation (with uncertainty of ±4 Myr). b, Cross-correlations between kimberlites⁶ (n = 981) and ΔF (9-Myr window) spanning a billion years (Methods), showing dominant lags at −26 ± 4 Myr (that is, fragmentation preceding kimberlites); dashed blue lines show 95% confidence intervals. c, Cross-correlations between kimberlites and ΔF accounting for potential preservation bias by weighting the number of kimberlites inversely according to surface preservation (inset, from ref. ¹⁰⁸). This analysis does not change the dominant lag (−26 Myr) relative to b. d, Cross-correlations between kimberlites⁶ (n = 665) and ΔF (9-Myr window) from 200 to 0 Ma (Methods), showing the strongest correlation (ρ = 0.52) at a lag of −28 Myr; dashed blue lines show the 95% confidence intervals. Note the different scale on the x axis relative to a–c.

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