Historical Barents Sea capelin quota advices compared using original and updated (2023) forecast model configurations

The Barents Sea capelin stock assessment and quota advice are made in two steps. In the first step abundance, biomass and demography of capelin is estimated based on the annual Russian-Norwegian Barents Sea Ecosystem Survey (Eriksen et al. 2018). In the second step, the estimated biomass of maturing capelin from this survey is used in a 6-month forecast to estimate the spawning biomass which is the key input for the harvest control rule. The forecast is done using the model Bifrost (GitHub - IMRpelagic/bifrost: Capelin stock assessment package).

The settings of the forecast model were evaluated during the 2022 capelin benchmark (WKCAPELIN; ICES, 2023a), and some assumptions and parameter settings were changed; The estimated cod consumption of capelin from 1 January to 1 April was changed to more realistically reflect the assumed natural cod consumption (Annex 3, WD_BS7 in ICES, 2023a). The estimated mortality of capelin in the autumn was also updated to include a wider range of possible mortality values (Annex 3, WD_BS6 in ICES, 2023a). There were also made changes to which cod are spatially excluded from feeding on maturing capelin based on updated survey estimates. Cod growth and mortality was also assumed to cancel out in the updated model configuration reflecting updated knowledge of the cod stock. Finally, a simplification was made to how the maturing proportion of the capelin stock is defined.

These changes were implemented during the 2023 capelin assessment and applied to provide the catch advice for 2024. As part of the evaluation of harvest control rules for capelin, there was a request from the managers to revise how the quota advice would have been for the advice years 1990-2023 with the updated model configuration. In this document, we compare the quota advice derived from using the updated and the original model configuration and evaluate the impact of each configuration change on the final quota advice.

1.2 - Approach

1.2.1 - Basis for comparison

The capelin assessment and advice are based on a two-step procedure which includes first an estimation of the maturing capelin stock on 1 October and second a forecast of the maturing stock until the assumed end of spawning on 1 April. Here, we focus on the second step which is the forecast.

The stochastic forecast of maturing capelin includes natural mortality from 1 October to 1 January, and next capelin mortality from 1 January to 1 April which is explicitly modeled as consumption by immature cod, plus catch (see section below and the stock annex ICES, 2023b for further details).

1.2.2 - Years included in the comparison

It was requested to focus the comparison on the years 1990 and onwards. However, we could not fully meet this request for reasons presented in the following.

A Barents Sea capelin quota advice on the form 5% probability of SSB < 200 000 t was first given for the advice year 2000 (Gjøsæter et al. 2002). Prior to that, the advice was associated with a different harvest control rule and stochasticity was not added. We therefore believe a comparison of advice years prior to 2000 has limited value in this context, and these early years are not included. We also exclude the years 2000-2004 since the ecosystem survey time series providing the data for the current forecast began in 2004, and a full validation of the forecast from Bifrost in R (see section below) has been done only for this time series. Lastly, we exclude the advice for the years 2015 and 2023 since ad hoc adjustments to the advice were made for these years due to incomplete survey coverage.

Despite the exclusion of years, we have a range of years for comparison including several years with zero-catch advice and several years with relatively high catch advices.

1.2.3 - Basis for historical forecasts

From 2002 to 2022, the capelin forecasts in the operational assessments were conducted using CapTool, an @Risk add-on to MS Excel customized for capelin stock assessment. Some forecast parameters were set in CapTool while others were estimated using the model framework Bifrost developed in Mathematica. More detail about the historical assessment can be found in Gjøsæter et al. (2002, 2015).

In 2021, the Bifrost framework together with the CapTool forecast tool were converted into the R programming language (GitHub - IMRpelagic/bifrost: Capelin stock assessment package), and comparisons with historical CapTool forecasts showed very high consistency. In the 2023 capelin assessment, the Bifrost R package was used for the forecast with parameter settings updated according to what was agreed during the capelin benchmark WKCAPELIN (ICES, 2023a) and subsequent discussions between PINRO and IMR.

For the present comparison, we have reorganized the Bifrost R package to streamline data flow, enable faster computation, and improve reproducibility and transparency.

1.2.4 - Assumptions and parameter settings

Table 1 provides an overview of the configurations that changed from the original to the updated model. Below, we describe these configurations in some more detail.

Maturation. Prior to the forecast, the capelin stock as estimated from the survey data must be divided into an immature and a maturing component of which only the maturing component is used in the forecast. The division is done according to capelin length and follows:

𝑚_𝑙 = 1/(1 + exp (4𝑝₁(𝑝₂ − 𝑙)))

where 𝑚_𝑙 is the proportion of maturing fish at length l in cm. 𝑝₂ is the length at 50% maturation and 𝑝₁ (maturation intensity) is the slope.

In the original configuration, a p₁ of 3.5 was assumed and a p₂ of 13.89±SD 0.075 (See table 1 below and WD_BS9 in Appendix 3 of the WKCAPELIN report; ICES, 2023a). The updated configuration uses the parameterization p₁=50 and p₂=14. Since the length resolution in the data is 0.5 cm, the effect of this parameterization is in practice a cut-off between immatures and maturing capelin at 14.0 cm.

Mortality in the autumn. The parameterization of mortality of capelin from 1 October to 1 January is based on survey data (See Tjelmeland and Bogstad, 1993 and WD_BS6 in Appendix 3 of the WKCAPELIN report; ICES, 2023a). In the updated configuration, the procedure is to compare the abundance of immature capelin at age 2 in a survey year (Y) with the total abundance of capelin at age 3 in the following survey year (Y+1). Assuming that the annual natural mortality is the source of the difference between these two estimates, the autumn mortality (i.e. the monthly mortality) can be derived from this. For each simulation run in the forecast, a value for the mortality in autumn is drawn from a distribution of monthly mortalities derived from the years 1987 and until present, except years associated with incomplete survey coverage.

Also in the original configuration, autumn mortality was based on survey data, but mortality from age 3 to age 4 was included in addition to mortality from age 2 to age 3, and parameter values per year were the output of a likelihood function including the maturity parameters p₁ and p₂ resulting in 1000 replicate values per year which were drawn from in each simulation run of the CapTool forecasts. Using mortalities from age 3 to age 4 was relevant in the 1970s and early 1980s, but thereafter the age 4 abundance has in most years been extremely low and thus using age 3 to age 4 mortality was no longer relevant. Importantly, the mortality values for some years (seems to be the ones with highest and lowest values) were excluded from the forecast based on an expert evaluation in the period 2011-2022. In the updated configuration all years are included except those years associated with poor survey quality, and this was the case also prior to 2011.

Functional response parameters (C_max and C_half) for cod consumption rate of capelin. In the original configuration, the cod consumption rate of capelin followed a functional response of type II. However, the parameters used for C_max and C_half resulted in a type I response within the range of abundances of cod and capelin observed in nature. This was probably not intentional since it is not reflected in the old stock annex (ICES, 2009). Following from WKCAPELIN, parameters C_max and C_half for a Type III functional response curve were re-estimated which is described in WD_BS7 in Appendix 3 of the WKCAPELIN report, ICES, 2023a.

Proportion of immature cod in Svalbard area. Immature cod in the Svalbard area are assumed not to feed on maturing capelin due to lack of overlap in distribution. In the original configuration, the proportion of immature cod in the Svalbard area was estimated based on data from several surveys covering a period from 1983-2004. Following from WKCAPELIN, the updated configuration uses the estimated proportion of immature cod by age in strata 24-26 (Svalbard area) in the Barents Sea winter survey from 2014 until the assessment year (see Fall et al. 2024 for map of stratas). For both the original and the updated configurations, the values used in each simulation run are drawn randomly from the years available.

Mortality of immature cod. In the original configuration a cod mortality of Z/12 per month was assumed from 1 January to 1 April, where the Z equaled the cod mortality used in the annual cod assessment for generating the cod prognosis. The updated configuration follows from WKCAPELIN and it is now assumed that immature cod biomass is constant from 1 January to 1 April on the rationale that in biomass terms, decreased abundance at age due to mortality cancels out increased weight at age due to growth (See section 2.1.8 in WKCAPELIN report, ICES, 2023a).

Data and parameters that were not changed for the comparison included:

CV by age for capelin abundance. This was fixed at 0.2 with the original configuration and we keep it at 0.2 for the updated configuration. The recommendation from the WKCAPELIN benchmark was that an average CV by age from the last 5 survey years be used, but the 2023 assessment revealed that this was inappropriate in cases where the most recent estimate of abundance at age for some age groups is much higher than the previous 4 survey years.

CV by age for cod abundance. This is kept at 0.3 and is based on the cod assessment.

Suitability of capelin for cod. This parameter used in the cod consumption module provides the assumed proportion of each cod age group that consumes capelin.

Cod abundance, individual weight and maturation. The cod abundance, individual weight and maturation used in the forecast are from the cod assessment prognosis. We use these prognoses also for the comparison here. It is possible to parameterize with cod abundance from the updated cod assessment similar to what was done in Gjøsæter et al. (2015), but that is outside the scope of the present comparison.

Capelin abundance and individual weight. We use the capelin abundance estimates that were used for the original advice. These estimates have been updated for the years 2004-2015 (WKCAPELIN Appendix 3 WD_BS1; ICES, 2023a), but we consider it most relevant for this comparison to use original estimates.

1.3 - Results

Figure 1 shows the original quota advice compared to the quota advice using the 2022 configuration and 2023 configuration, respectively. The advices are also summarized in table 2. The 2022 model configuration corresponds to what was used historically except that parameterization of autumn mortality was different for the advice years 2008 to 2011 (see table 1). If the same natural mortality were assumed, the catch advice would have been close to 50% lower.

For the 2023 model configuration the catch advice would have been higher, ranging from a 16.3 to a 128.4 % increase. The forecast trajectories for all years investigated are shown in Figure A2. It should be noted that the years with advised catch >0 is the same for all configurations.

Figure 2 shows the advised catch using the 2023 model configuration but with one parameter at the time set according to the 2022 configuration. The results show that the updated parameterization of the functional response curve for the cod consumption (C_max and C_half) has a great impact on the advice and generally leads to increased advice. The updated autumn mortality also has big impact and generally leads to increased advice. The other parameters matter less; updated maturity leads to a slight decrease in the advice since no capelin <14.0 cm are now included in the forecast whereas a small proportion of 13.5 cm capelin was included with the original setting. Updated cod mortality also leads to slightly lower advice likely resulting from a marginally higher modelled predation pressure. Similarly, the updated Svalbard component leads to a slightly reduced advice since a generally lower proportion of the immature cod is assumed to be in the Svalbard area (hence assuming no overlap with maturing capelin) than what was assumed before implying a slight increase in predation pressure (See figure A1 in Appendix).

1.4 - Conclusions and future work

-This comparison of original and updated model configuration for the capelin forecast shows that the advice is strongly influenced by the model settings, but that advises of zero-catch remain the same independent of model configuration.

-Overall, catch advice for non-zero advice years increased with the updated model configuration.

-The changes in settings with the most important impact on the advice were parameters for the cod consumption rate, and parameters for capelin mortality from 1 October to 1 January.

-It must be noted that the comparison was limited to settings explored at the WKCAPELIN benchmark, and that other settings might be relevant to explore further, for instance alternative maturation functions (See Jokar et al. 2021).

-Uncertainty in the forecast is being introduced by extracting cod stock size from the cod assessment prognosis (Gjøsæter et al. 2015). The prognosis might diverge significantly from later cod assessments when more knowledge about the stock has been acquired and the effect of this must be explored in future work.

1.5 - References

Fall, J., Wenneck, T. de Lange, Bogstad, B., Eidset, E., Fuglebakk, E., Godiksen, J. A., Høines, Å., Johannesen, E., Midtun, H. Aa., Moksness, I., Skage, M. L., Skaret, G., Staby, A., Tranang, C. Aa., Windsland, K., Russkikh, A. A., and Kharlin, S. 2024. Fish investigations in the Barents Sea winter 2024. IMR-PINRO Joint Report Series 8-2024, 156 pp.

Eriksen E, Gjøsæter H, Prozorkevich D, Shamray E, Dolgov A, Skern-Mauritzen M, Stiansen JE, Kovalev Y, Sunnanå K. From single species surveys towards monitoring of the Barents Sea ecosystem. Progress in Oceanography 2018, 166:4-14, doi:https://doi.org/10.1016/j.pocean.2017.09.007.

Gjøsæter, H., Bogstad, B., and Tjelmeland, S. 2002. Assessment methodology for Barents Sea capelin, Mallotus villosus (Müller). ICES Journal of Marine Science, 59: 1086-1095.

Gjøsæter, H., Bogstad, B., Tjelmeland, S., and Subbey, S. 2015. A retrospective evaluation of the Barents Sea capelin management advice. Marine Biology Research, 11: 135-143.

ICES. 2009. Report of the Benchmark Workshop on Short‐lived Species (WKSHORT). 34. 166 pp.

ICES 2023a. Benchmark workshop on capelin (WKCAPELIN). ICES Scientific Reports. 5:62. 282 pp. https://doi.org/10.17895/ices.pub.23260388 .

ICES 2023b. Stock annex: Capelin ( Mallotus villosus ) in subareas 1 and 2 (Northeast Arctic), excluding Division 2.a west of 5°W (Barents Sea capelin). ICES Stock Annexes. Report.

Jokar, M., Subbey, S., and Gjøsæter, H. 2021. A logistic function to track time-dependent fish population dynamics. Fisheries Research, 236: 105840.

Tjelmeland, S., and Bogstad, B. 1993. The Barents Sea capelin stock collapse: A lesson to learn. National Research Council Canada. Canadian Special Publication of Fisheries and Aquatic Sciences, 120: 127-139.

1.6 - Appendix

Figure A2. Comparison of original and updated (using 2023 configuration) forecast of maturing capelin from 1st October (end of survey) to 1st April (end of spawning). In the legend ‘historical’ gives original catch advice, and ‘updated’ catch advice with updated configuration. Note that advices given in 2014 and 2022 (for advice years 2015 and 2023) have not been compared since these original advices were adjusted.