Fig. 3: Convergent cross-mapping of the precipitation [log(Ca/Fe)] and vegetation (tree-pollen) datasets from Tenaghi Philippon.

a Correlation of cross-mapped against observed values (‘CCM skill’) as a function of the timeseries (library) length ‘L’. The blue line represents the effect of log(Ca/Fe) on tree-pollen, whereas the red line represents the effect of tree-pollen on log(Ca/Fe). Both lines are above the blue and red shaded areas, which represent the 5th to 95th percentiles of the ‘CCM skill’ for 100 surrogate timeseries from null models, suggesting that convergence is significant for both pairs. As higher ‘CCM skill’ indicates stronger causality (Methods), the CCM analysis demonstrates a strong bidirectional coupling between precipitation [log(Ca/Fe)] and forest cover [tree-pollen] at Tenaghi Philippon. The black dashed line represents the cross-correlation of the two timeseries. b Time displacements maximizing CCM skill corresponding to the causal relationship between log(Ca/Fe) and tree-pollen (marked with stars). As the maximum ‘CCM skill’ of the effect of log(Ca/Fe) on tree-pollen is negative and closer to 0 (blue line) than the effect of tree-pollen on log(Ca/Fe) (red line), the analysis suggests a real causal and rapid effect of precipitation change on forest cover. Shaded areas represent the 95% confidence interval for predictions from the smoothing model.