Root mean squared relative error (RMSE) and mean relative error (MRE) of reconstructed stock biomass by reconstruction method tested for Arctic cod and North Sea herring.

<p>NA = not available; model failed to reproduce biomass before 1965.</p

The surplus production rate, SPR, as a function of the biomass for mackerel (1992–2011, First_period; 1972–1991, Second_period).

<p>Red lines show linear regressions fitted to the observed SPR.</p

The surplus production rate, SPR, as a function of the biomass of Arctic cod (1982–2011, First_period; 1946–1981, Second_period).

<p>Red lines show linear regressions fitted to the observed SPR.</p

Biomass of North Sea herring fitted by the Schaefer model to the ICES analytical estimates of biomass for the First, Second, and All data years.

<p>Biomass of North Sea herring fitted by the Schaefer model to the ICES analytical estimates of biomass for the First, Second, and All data years.</p

Biomass of Arctic cod fitted by the Schaefer model to the ICES analytical estimates of biomass for the First, Second, and All data years.

<p>Biomass of Arctic cod fitted by the Schaefer model to the ICES analytical estimates of biomass for the First, Second, and All data years.</p

The surplus production rate, SPR, as a function of the biomass of North Sea herring (1982–2011, First_period; 1947–1981, Second_period).

<p>Red lines show linear regressions fitted to the observed SPR.</p

The carrying capacity, B_inf, (10³ t.) and maximum productivity, m, (10³ t.) for cod, herring, and mackerel estimated by the Schaefer model for the First, Second, and All data years.

<p>The standard errors (SE) of the model fits are also provided.</p

Reconstructed biomass of North Sea herring for 1947–1981 using the ICES biomass estimates for 1982–2011 and the constant SPR, linear SPR, logarithmic SPR and stock-production model methods (for comparison, ICES biomass estimates are shown).

<p>Reconstructed biomass of North Sea herring for 1947–1981 using the ICES biomass estimates for 1982–2011 and the constant SPR, linear SPR, logarithmic SPR and stock-production model methods (for comparison, ICES biomass estimates are shown).</p

The median and percentiles of Arctic cod biomass distribution, reconstructed using the constant SPR (a) and logarithmic SPR (b) methods.

<p>The median and percentiles of Arctic cod biomass distribution, reconstructed using the constant SPR (a) and logarithmic SPR (b) methods.</p

The CV of the reconstructed biomass of Arctic cod obtained from the constant SPR, linear SPR, logarithmic SPR and stock-production model methods.

<p>The CV of the reconstructed biomass of Arctic cod obtained from the constant SPR, linear SPR, logarithmic SPR and stock-production model methods.</p