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Data S1. Inspection of the Granger causality time series models: ‘Carry-over’ effects.

Fig. S1. North Atlantic CPR data separated into six regions.

Fig. S2. Correlation analysis by the modified Chelton method, measuring the changing significance values of the correlation coefficient for the relationships between the NAOI (solid blue line and closed blue circles), annual SST (solid green line with closed green circles) and annual westerly wind speed (solid red line with closed red circles), for the abundance of (a) C. finmarchicus and (b) C. helgolandicus for the NE Atlantic region. Correlation was first calculated for 1960–1992. Subsequently, 1 year was added, and at each step a new correlation coefficient calculated until 1960–2010. Black dashed line represents the 5% significance level (due to the use of the modified Chelton method, a guide to significance is given by the average significance level over the three time series: NAOI, SST, westerly wind speed. Note that in all analyses, specific significance levels are used). The sign of the Chelton method coefficient represents the direction of correlation: negative correlation for C. finmarchicus and positive correlation for C. helgolandicus.

Fig. S3. Correlation analysis by Pearson's correlation, a 32-year moving window Pearson's correlation, linear regression coefficient (beta value) and a 32-year moving window of linear regression coefficient (beta value).

Fig. S4. A stationary autoregressive process Yt+1 = c + ϕYt + εt (where c is a constant, εt is white noise, and |ϕ| < 1).

Table S1. The significance of modified Chelton correlation for C. finmarchicus and C. helgolandicus against annual Sea Surface Temperature (SST), annual Westerly Wind speed (WW), and the winter NAOI (*P < 0.05). The sign of the affect of SST, WW or NAOI on abundance is indicated (+ or −).

Table S2. Granger-causality in the relationships between C. finmarchicus and C. helgolandicus abundance versus annual SST and annual westerly wind speed (WW) and the winter NAOI. Significant relationships (P < 0.05) indicated by *. Lag time scale represents years.

Table S3. Decadal relationship between C. finmarchicus and C. helgolandicus abundance against SST for both linear and quadratic regression.

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