a, Detecting trend of ENSO amplitude in ‘pseudo-corals’. Histogram of Holocene (7–0 kyr ago) linear trends of ENSO amplitude derived from 30-year ‘pseudo-coral’ records of the Niño3.4 SST in TRACE. A linear trend (regression coefficient) is derived from the ENSO amplitudes of a random set of 50 (red) ‘corals’, with each ENSO amplitude as the standard deviation of the interannual (1.5–7 years) SST variability of a 30-year section of ‘coral record’. The PDF on the right (marked with TRACE) is derived from the linear trends of 100,000 randomly formed sets of coral records, whereas the PDF on the left (marked with Null) is the null hypothesis of no trend in ENSO amplitude, and is derived from the linear trend of a time series after random scrambling of the Niño3.4 SST. Two additional PDFs are derived with the number of corals increased to 200 (blue) and 1,000 (black) in each set. The right-side one-tailed 95% significance levels are 0.106 (red), 0.052 (blue) and 0.024 (black) for the null hypothesis, and the left-side one-tailed 95% significance levels are 0.036 (red), 0.088 (blue) and 0.116 (black) for TRACE. With 50 corals, the trend in TRACE cannot be identified at the 95% level because the significance level in TRACE is below that of NULL (0.036 < 0.106); with 200 corals, the trend can be identified at the 95% level because the significance level of TRACE is beyond that of NULL (0.088 > 0.052); with 1,000 corals, the 95% significance levels are well beyond the NULL (0.116 0.024), implying a highly significant trend of ENSO strengthening in the Holocene. b, ENSO amplitude in TRACE in a 100-year window (red thick line, same as in Fig. 1e) and a 30-year window (blue thin line) (both on the left axis) as well as the ENSO variance reconstructed from corals in the central Pacific6 (dark green dots) and from the variance of annual SST range from mollusc shells along the Peru coast21 (black horizontal bars). The two data sets are plotted in changes relative to the present ENSO amplitude (on the right axis), which is then rescaled with the model ENSO amplitude such that the relative change in model ENSO amplitude can also be scaled on the right axis. All the model and proxy data are aligned and referenced to their last millennium average (1–0 kyr ago).