Fig. 1: Integration of interannual SST variation corresponds to low-frequency fluctuations in biomass.

In this example from the North Sea, autoregressive modelling of high-frequency sea-surface temperature (SST; red lines) generates patterns that match variations in population biomass (black lines) across three trophic levels. Results on the right show correlations at each trophic level between: spring SST data and biomass (r_sst); auto-regressed SST and biomass (r_red); and between a cubic smoothing spline (smoothing parameter: 0.5) through the biomass data and auto-regressed SST (r_{red_sp}). The latter was included for a more direct comparison of low-frequency variability that may be masked in relatively uncertain biomass assessments. The p-values are determined using data simulations (see “Methods”). *Poor association for sandeels could be caused by substantial sampling errors in assessment data⁴⁸. Data used can be found in Supplementary Data files 1 and 2.