Model validation by means of fitting and hindcasting the historical stock dynamics of (a,b) Baltic cod, (c,d) sprat and (e,f) herring. The left column shows the fit of the BALMAR food-web model (Lindegren et al. 2009), where SSB levels (black) accurately represent the observed dynamics (circles) of cod, sprat and herring from 1977 to 2004. (The degree of explained variance is: (a) 0.95; (c) 0.89 and (e) 0.98). The right column demonstrates hindcast SSB levels (black), where the historical stock dynamics were simulated based only on the starting biomasses (i.e. in 1977) as initial conditions. Grey lines are upper and lower 95% prediction intervals.

Probability of cod stock falling below ecologically safe levels (B_lim) given future changes in climate and fishing mortalities. (a) Probabilities are calculated from simulations of mean decrease in salinity from 0 to 5 psu and F levels from 0 to 1. In (b) the additional effect of increasing environmental autocorrelation in future climate time series (i.e. alpha from 0 to 1) is investigated by studying the change in the slope of the ‘probability landscape’ at a projected salinity decline of 0.8 psu specifically (see red rectangle in (a)). Simulations were conducted over a range of fishing mortalities (F from 0 to 0.6) while the projected increase in SST remained fixed at 3.5°C. The green solid line marks the actual alpha in the salinity time series, while the dashed line aims to represent a correction for possible underestimations of forecasted global climate model autocorrelations, i.e. here set to a maximum of 20 per cent. White areas indicate low probabilities of cod biomass being below ecologically safe limits (B_lim), while black areas demonstrate high probabilities.

A coupled food web–climate model approach to forecasting Baltic cod stock dynamics in the twenty-first century. The BACC assessment uses a three dimensional (3D) ocean circulation model to explore the range of projected climate changes in the Baltic Sea region based on climate scenarios from the PRUDENCE ensemble model. The BACC assessment conducted ‘time-slice’ simulations for 2071–2100 but no transient time series are available. In order to facilitate coupling with the food-web model, an AR(1) climate model was used to simulate transient time series based on the future projections for each variable. Additionally, multiple simulations were run in order to represent the variability and uncertainty in climate forcing in the twenty-first century. Finally, the response of the cod stock to climate and fisheries management was studied by forcing the food-web model with fishing mortalities for cod (C) as well as for sprat (S) and herring (H). Cod stock dynamics are forecasted as a 95% probability distribution of future spawning stock biomass (SSB) by running multiple stochastic simulations including random noise. SST, sea surface temperature; RCM, regional climate model; GCM, global climate model; AR(1), first order autoregressive.

Future climate and management scenarios and a 95% probability distribution of Baltic cod SSB. (a) A ‘control scenario’ where climate (SST and salinity) and fishing mortalities (F) fluctuate at mean 1974–2004 levels. Hindcasted simulations from 1977 to 2007 (i.e. based on the observed climate and F levels for these years) are compared with observed SSB (yellow circles) to validate the predictive accuracy of the model. (b) A predicted increase in mean SST by 3.5°C and decrease in mean salinity by 4.8 psu combined with mean F levels. (c) As in (b) but with F reduced to the previously recommended precautionary reference levels (F_pa). (d) Exploitation at F_pa but with a predicted decrease in salinity by only 0.8 psu. Solid horizontal lines mark the recommended ecological levels of Baltic cod, the precautionary stock level, B_pa (green) and limiting stock level, B_lim (red). (Note that the use of these biomass reference points is currently being re-evaluated). Black contour lines show the 90 and 95% prediction intervals within which the cod stock dynamics of each replicated run fluctuates.

A sustainable management strategy for Baltic cod under different scenarios of climate change. In (a, b) the theoretical carrying capacity (K) and corresponding maximum sustainable fishing mortality (F_MSY) for Baltic cod is shown for each combination of projected changes in salinity and SST. In order to address the indirect effects of species interactions on cod stock response to climate change, the lower panels (c,d) include fishing pressures for sprat and herring, given a projected increase in SST by 3.5°C. Fishing mortalities range from mean historical levels (F_mean) to the recommended precautionary levels (F_pa) for sprat and herring, respectively (see the electronic supplementary material, figure S5). The middle planes represents mean K and F_MSY while upper and lower planes, respectively, illustrate the upper and lower confidence levels of each scenario.