Fig 1.
Conceptual basis of the statistical model.
On the right, the abundance and length distributions of fish in the sea, the distribution of the fishery catch, and the partitioning of lengths between landings and discards, are essentially unobserved. All we know is the biomass of fish which are landed—and for the reference species the biomass discarded. On the left, we have information on the abundance and lengths of fish in the trawl surveys. From this we can estimate the biomass and length composition of catch and the partitioning between landings and discards, given information on the catch ratio, capture and retention selectivities. Equation numbers refer to equations in the text.
Table 1.
Estimated parameters in the full model fitted simultaneously to the five reference species for which both landings and discards data are available, and the choice of priors.
Table 2.
Estimated parameters in the reduced model for a single species where only landings data are available, and the choice of priors.
Table 3.
Legal minimum landing sizes of North Sea fish species under UK Statutory Instruments (SI) and European Council Regulations (CR) post-introduction of the Common Fisheries Policy in 1983.
Table 4.
De-facto landing sizes of species for which there is no legal minimum.
Fig 2.
Relationships between legal or de-facto minimum landing size (MLS), and estimated or fitted values of RL50 (the length at 50% retention).
Red circles: MLS vs observer data estimates of RL50 for species subject to a legal landing size limit (cod, haddock, whiting, plaice, sole, saithe, hake—see S5 Table). Black triangles: de-facto MLS vs observer data based RL50 for species with no legal landing size limit (gurnard, dab, turbot, brill. Green symbols: legal MLS vs RL50 for reference species estimated by the full model. Blue line: 1:1 relationship; black line fitted regression through the origin for full model reference species data. Regression coefficient = 0.874 (r2 = 0.817).
Fig 3.
Full model fitted estimates of the total proportions of catch discarded (p) for the reference species.
Blue line and shading: fitted proportions and 95% credible intervals. Red symbols: observed proportions from ICES stock assessment reports.
Fig 4.
Full model estimates of the quantity-related proportions of catch discarded (q).
Blue line and shading: median of estimated proportions and 95% credible intervals. Red symbols: quantity-related discard proportions derived from data on catch and discard numbers and mean weights-at-age. In this case, the model was not fitted to the observed data so coincidence between the model and data is an independent validation of the model.
Table 5.
Mean ages of cod, haddock, whiting and plaice in discards and landings (weighted by the mass in each age class), averaged over decades.
Fig 5.
Cross-validation test of the reduced model: discarded weights of the reference species.
Blue line and shading: median of estimated weight discarded and 95% credible intervals from the reduced model. Red symbols: observed weights discarded from ICES stock assessment reports. In this case, the model was not fitted to the observed data so coincidence between the model and data is a validation of the reduced model.
Table 6.
Recovery of the appropriate catch ratio (Q) in the cross-validation runs of the reduced model.
Fig 6.
Modelled and observed time series of the survey biomass index (ut) for the reference and other species.
Blue line and shading: median of estimated index and 95% credible intervals. Red symbols: observed index. Results for the five reference species from the full model; results for all other species from the reduced model.
Fig 7.
Modelled and observed time series of the weight landed for the reference and other species.
Blue line and shading: median of estimated landings and 95% credible intervals. Red symbols: observed weight landed. Results for the five reference species from the full model; results for all other species from the reduced model.
Fig 8.
Modelled time series of the weight discarded for the reference and other species.
Blue line and shading: median of estimated total discarded weight and 95% credible intervals; red line estimated size-related weight discarded. Black symbols for reference species only: observed weight discarded. Results for the five reference species from the full model; results for all other species from the reduced model.
Fig 9.
Modelled time series of the proportion of catch discarded for the reference and other species.
Blue line and shading: median of estimated total proportion discarded and 95% credible intervals; red line estimated quantity-related proportion discarded. Black symbols for reference species only: observed total proportion discarded. Results for the five reference species from the full model; results for all other species from the reduced model.
Fig 10.
Comparison of modelled and observed proportions discarded.
Mean observed proportions of catch discarded from the ICES data in the case of the reference species (averaged over 2001–2010), and from fragments of data harvested from the literature in the case of all other species (S3 Table). Estimated proportion discarded averaged over 2001–2010 from the reduced model in all cases. Horizontal dashed lines indicate ± 1 s.d. of logit transformed observed data. Red circles: reference species; blue circles: all other species. Black line indicates the 1:1 relationship.
Fig 11.
Summary of model results for the entire demersal fish assemblage.
(a) Annual proportion of total demersal fish catch discarded (mean and 95% credible interval). (b) Total catch and landings of demersal fish. The blue line and shaded area indicates the mean and 95% credible interval of model estimated total catch, whilst the vertical bars indicate the measured landings. (c) Quantities (thousands of tonnes) of all demersal fish discarded. Blue line and shaded area indicates the mean and 95% credible interval of total discard quantity. The red line indicates the size-related weight of fish discarded, hence the area between the red and blue lines represents quantity-related discards. (d) Annual proportions of the eight most abundant species in the discarded weight of demersal fish (in rank order of long-term average proportions: plaice, haddock, dab, whiting, cod, saithe, gurnard, ling).
Fig 12.
Model results for non-TAC species.
(a) Annual catch and discard quantities (tonnes) for the group of species which, in 2010, were not subject to any landing quota (TAC) restrictions (bass, gurnards, halibut, ling, mullets, pollack, tusk, wolfish, and the ‘other marketable’ and ‘discard-only’ groups). (b) catch and discards of non-TAC species as proportions of total demersal catch and discards (solid lines), and the discard rate (proportion of catch discarded) for non-TAC species as a group (dashed line). 95% credible intervals around each of the time series indicated by shaded regions and/or thin lines.