Table 1.
Sources and types of uncertainty included in this stock assessment process.
Fig 1.
Schematic diagram of the approach.
The approach has three steps: Generating the candidate assumptions, estimating the parameters of the stock assessment models and averaging across the model variants. Process and model uncertainty are introduced when generating the candidate assumptions. Estimation uncertainty is introduced during parameter estimation. The result is a single stock assessment that integrates across the multiple sources of uncertainty. M is natural mortality, SR is the stock-recruitment relationship, F-pattern is the fishing mortality pattern, survey Q is the survey catchability pattern.
Table 2.
Values of the marginal triangle distribution parameters for the von Bertalanffy growth parameters.
Table 3.
The stock assessment model options for the 18 different stock assessment models.
Fig 2.
Including process uncertainty through the von Bertalanffy growth parameters.
Top row: Pair wise scatter plots of 1000 samples of the von Bertalanffy growth parameters L∞, k and t0 that are used in the length-slicing and in the ‘Gislason’ natural mortality model. Bottom row: histograms showing the triangle marginals of the growth parameters. The spread of values in the plots reflects the process uncertainty in the parameter values.
Fig 3.
Variance in the von Bertalanffy growth curve resulting from the process uncertainty in the growth parameters L∞, k and t0.
Median (solid black line) and 5% and 95% quantiles (dashed black lines). The deterministic growth curve using values for the growth parameters from the last ICES assessment (L∞ = 130, k = 0.164 and t0 = 0) is the blue, dashed line that runs through the median of the box plot.
Fig 4.
Example age-based stock data after the length-based data has been sliced using the uncertain von Bertalanffy growth parameters.
Natural mortality, catch numbers and mean weights by age after slicing the length-based data. Median (solid line) and 5% and 95% quantiles (dashed line) are shown. The values are for the year 2012. Only ages up to 12 are shown for brevity. The two different natural mortality models are shown in the top panel. The ‘Gislason’ model is black and the ‘0.4’ model is blue. The variance in the ‘Gislason’ model represents the process uncertainty. The ‘0.4’ model has no process uncertainty and therefore no variance.
Fig 5.
The impact of model uncertainty on the summary stock assessment results.
Summary stock assessment results (recruitment, spawning stock biomass (SSB), mean fishing mortality (Fbar) and catch) from fitting a single iteration of the biological parameters with the 26 combinations of stock assessment and natural mortality models. This is equivalent to performing stock assessments without process or estimation uncertainty and only including model uncertainty. There are clear differences between the patterns and trends of the fits from each model, particularly in the most recent years. Note that the recruitment and SSB are shown on a log scale to allow the differences between the model results to be more visible. The recruitment, SSB and Fbar results can be broadly separated into two groups, driven by the natural mortality model. The ‘Gislason’ natural mortality model (blue lines) estimates higher recruitment and Fbar and lower SSB than the ‘0.4’ model (black lines). The results from the most recent ICES stock assessment are shown as the thick, dashed, red line.
Fig 6.
Regression trees showing which stock assessment and natural mortality model components had the biggest impact on the estimated stock assessment summary results.
The summary stock assessment results are spawning stock biomass (SSB), mean fishing mortality (Fbar) and recruitment. The notation for F, Q and R refers to the submodel number in Table 3. For example, Q = qmd1 means the second qmodel (the logistic model). M refers to the natural mortality model, either ‘0.4’ or ‘Gislason’. The numbers are the mean residuals from each model component on the logarithm of each summary measure.
Fig 7.
Comparing the model averaged results to the model variant with the lowest median GCV (the ‘best’ assessment).
Summary metrics (recruitment, spawning stock biomass (SSB), mean fishing mortality (Fbar) and catch) from the model averaged results (red, sold line), the model with the lowest median GCV which can be used as an indicator of which model is ‘best’ (blue, thin dashed line) and the ICES assessment (thick dashed line). For the model averaged results and the GCV model, the lines show the medians and the ribbons show the 10 and 90% quantiles.
Fig 8.
Distribution of the mean fishing mortality in the final year of the assessment for all model variants and model averaged results.
The model labelling on the y-axis refers to the combination of the stock assessment submodels and the natural mortality model (see Table 3). GCV is the model averaged result using median GCV weighting. The points show the median value, the lines extend to the 5% and 95% quantile.