Shiftograms of (A) the BSI and (B) the WBSS recruitment time series.

<p>The broken vertical lines indicate years of potential structural breaks (shifts), the open rectangles with broken lines encircle the three major shift detection criteria (AICC, p-joint, power panel).</p

Cushing model [Equation (1) – see text] fitted to Rügen herring recruitment data.

<p>(A) Plot of log_e recruitment <i>R</i> (numbers in log_e-thousands) against log_e spawning-stock biomass SSB (log_e-t); the continuous line represents the predicted values of log_e<i>R</i> based on the Cushing model, the open dots connected by a dotted line and annotated by year represent observed log_e values of <i>R</i> at observed log_e SSB, and the light blue area the 95% prediction interval related to the Cushing model. (B) Plot of log_e<i>R</i> over time (years); the continuous line represents the predicted values of log_e<i>R</i> based on the Cushing model, the open dots the observed log_e values of <i>R</i>, and the light blue area the 95% prediction interval related to the Cushing model.</p

Map of the Baltic Sea area surrounded by neighbouring countries.

<p>The inset shows the location of the study area (south-eastern coast of Rügen Island plus the Greifswalder Bodden). The straight broken line connects Oslo (Norway) with Szczecin (Poland) representing the direct geographical distance between the two locations the BSI atmospheric pressure index has been calculated for.</p

Conceptual illustration of the variable and model selection algorithm.

<p>Conceptual illustration of the variable and model selection algorithm.</p

Plots of the dataseries of log_e(<i>R</i>), log_e(SSB), and winter BSI from 1991 to 2011, where <i>R</i> is WBSS herring recruitment, SSB is spawning-stock biomass for WBSS herring, and BSI the Baltic Sea index.

<p>Left panels: Non-stationary (original) dataseries (open dots connected by solid lines) with significant linear trend lines (broken lines). Right panels: stationary dataseries, with lines as in the three left panels, and values distributed around zero (detrended by taking 1^st order differences).</p

General pattern of the autocorrelation function (ACF) and the partial autocorrelation function (PACF) relative to the type of process, where AR is the autoregressive component of order <i>p</i> of the process, MA the moving average component of order <i>q</i> of the process, and ARMA a combination of both.

<p>General pattern of the autocorrelation function (ACF) and the partial autocorrelation function (PACF) relative to the type of process, where AR is the autoregressive component of order <i>p</i> of the process, MA the moving average component of order <i>q</i> of the process, and ARMA a combination of both.</p