Using cross-correlations to assess the relationship between time-lagged pressure and state indicators: an exemplary analysis of North Sea fish population indicators

Probst, W. N., Stelzenmüller, V., and Fock, H. 2012. Using cross-correlations to assess the relationship between time-lagged pressure and state indicators: an exemplary analysis of North Sea fish population indicators. – ICES Journal of Marine Science, 69: 670–681. A sustainable ecosystem-based management, as postulated by the European Union-Marine Strategy Framework Directive (MSFD), requires a sound understanding of the cause–effect relationships between human pressures and ecosystem states. In this study, cross-correlations are used to introduce a protocol for the analysis of time-lagged relationships between pressure and state indicators. To perform meaningful cross-correlations, the time-series of the pressure and the state indicator should be prewhitened by fitting autoregressive integrated moving average models to the pressure indicator time-series. This study provides some theoretical examples on the implications of non-prewhitened and prewhitened cross-correlations and exemplifies the use of prewhitened cross-correlations to compare the pressure–state relationship of a well-established indicator suite vs. the relationship of a new indicator proposed under the MSFD. The established indicator suite is fishing mortality (F) vs. spawning-stock biomass (SSB), the new indicator suite is F vs. the 95% percentile of the length frequency distribution (L95). The L95 aims to characterize the proportion of large individuals within a population. The prewhitened cross-correlations for F and SSB are significant for all four analysed species (cod, haddock, saithe, and plaice), the L95 is correlated with F for cod, haddock, and saithe. However, the L95 was also influenced by the annual survey catch and recruitment.