Specifications for MSE Trials for Atlantic Tropical Tunas

1 Introduction

The tropical tunas (TT) fishery, under the management of the International Commission for the Conservation of Atlantic Tuna (ICCAT), is undergoing a management strategy evaluation (MSE) process. This fishery mainly target bigeye (BET), skipjack (SKJ), and yellowfin (YFT) tunas.

Management strategy evaluation

Process used in fisheries management to simulate and assess the performance of different management strategies under varying conditions and uncertainties (Figure 1).

There are three main components in an MSE process:

  • Operating models (OMs): a collection of mathematical/statistical models that describe alternative hypotheses of the historical fishery dynamics and specifications for simulating the collection of data and implementation of management measures in the future;
  • Candidate management procedures (CMPs): a set of proposed algorithms that generate management recommendations from fishery data and will be evaluated in the MSE;
  • Performance metrics (PMs): statistics used to quantitatively evaluate the CMPs against specified management objectives.

The OMs, CMPs, and PMs are developed as a collaborative effort between scientists, decision-makers, and other stakeholders in the fishery.

flowchart LR
    subgraph B1["Operating model"]
        direction TB
        i1["Biological and <br> fishery model"]
        f1["Data generation"]
    end

    subgraph B2["Management procedure"]
        direction BT
        i2["Estimation method"] 
        f2["Harvest control rule"]
    end
    f1 --> i2
    f2 --Implementation--> i1
    i1 --> f1
    i2 --> f2
    B1 --> i3["Performance metrics"]
    style B1 fill:#d4f5ba
    style B2 fill:#b9c8fc
    style i3 fill:#fcf7b9
    style i1 fill:#ffffff
    style f1 fill:#ffffff
    style i2 fill:#ffffff
    style f2 fill:#ffffff
    
    %% Set all nodes to black text
    linkStyle default color:#000000
    classDef blackText color:#000000;
    class i1,f1,i2,f2,i3,B1,B2 blackText;
Figure 1: Management strategy evaluation (MSE) framework.

1.1 About this document

This document describes the specifications for the OMs, CMPs, and PMs that have been proposed and developed for the TT fishery. It is a living document and will be continued to be updated so that it reflects the current state of the multi-stock TT MSE process. Members of the Tropical Tuna Species Group (TTSG) are encouraged to provide feedback, comments, or edits to any part of this document.

The document is written using the Quarto format and can edited in any text editor. The source document is available on the MSE GitHub repository. TTSG members can make edits to the document either directly in the online repository or by cloning the repository and submitting pull requests with their edits. Alternatively, they can email questions or comments to the authors. The former approach has the advantage that all comments, questions, and edits are immediately visible to all members of the TTSG. The Discussions feature on the Github repository can also be used to post questions, comments, or points for discussion related to any aspect of this document or the MSE process in general.

This document is available at the TT MSE homepage.

2 MSE framework

The R software has been used to developed the MSE code for the TT fishery. All code is open-source and can be found on the MSE GitHub repository.

The code developed for the TT MSE uses the FLBEIA framework. FLBEIA (Garcia et al., 2017) is an R package that has been developed for conducting bio-economic evaluation of fisheries management strategies. The software allows the bio-economic evaluation of a wide range of management strategies in a great variety of case studies such as multi-stock, multi-fleet, stochastic and seasonal configurations. FLBEIA is built using FLR libraries. FLR is a collaborative project oriented to develop quantitative fisheries management tools.

3 Stock assessment

In this section, we describe the main aspects of the last stock assessment models for BET, SKJ, and YFT, which were then used to condition the OMs. These assessments use the areas-as-fleets approach, which aims to account for the regional differences in fishing behavior and selectivity using a single-area model configuration (Waterhouse et al., 2014). These regions are shown in Figure 2.

Figure 2: Definition of regions used in the stock assessment models for the three TT stocks.

3.1 Bigeye

The last stock assessment was conducted in 2021 (ICCAT, 2021) using the Stock Synthesis (SS3) platform (Methot and Wetzel, 2013). The data used in the BET assessment and the structure and assumptions of the assessment model are summarized in the sections below.

Table 1: Fishing fleets included the BET stock assessment. See Figure 2 for the definition of regions. The last column indicates if the fleet had an associated index of abundance (catch-per-unit-effort, CPUE).
Fleet code Description Region CPUE included?
1_PS_6485 Purse seine (all fleets except Ghana, USA, and Venezuela) R2/R1 No
2_PS_8690 Purse seine (all fleets except Ghana, USA, and Venezuela) R2/R1 No
3_PS_FSC_9119 Purse seine free school (all fleets except Ghana, USA, and Venezuela) R2/R1 No
4_PS_FAD_9119 Purse seine FADs (all fleets except Ghana, USA, and Venezuela) R2/R3 Yes
5_BBPS_Ghana Ghana baitboat and purse seine R2 No
6_BB_South_Dakar Baitboat South Dakar (all fleets except Ghana) R2s No
7_BB_North_Dakar_6280 Baitboat North Dakar (all fleets except Ghana) R2n No
8_BB_North_Dakar_8119 Baitboat North Dakar (all fleets except Ghana) R2n No
9_BB_North_Azores Baitboat North Azores (all fleets except Ghana) R1 No
10_Japan_LL_N Longline North Japan R1 No
11_Japan_LL_TRO Longline Tropical Japan R2 Yes
12_Japan_LL_S Longline South Japan R3 No
13_Other_LL_N Longline North Other (all fleets except Japan and Chinese Taipei) R1 No
14_Other_LL_TRO Longline Tropical Other (all fleets except Japan and Chinese Taipei) R2 No
15_Other_LL_S Longline South Other (all fleets except Japan and Chinese Taipei) R3 No
16_CTP_LL_N Longline North Chinese Taipei R1 No
17_CTP_LL_TRO Longline Tropical Chinese Taipei R2 No
18_CTP_LL_S Longline South Chinese Taipei R3 No
19_RR_West RR West Atlantic USA, Canada, UK-Sta Helena R1 No
20_HL_BRA Handline Brazil R2 No
21_PS_West Purse seine West Atlantic (USA, Venezuela) R1 No
22_OTH Other R1/R2/R3 No

3.1.1 Data

The period covered was from 1950 to 2019. The assessment mainly used landings data from longline (LL), purse seine (PS), and baitboat (BB) fleets, with a total of 22 fleets included in the model (Table 1 and Figure 3). There were two indices of abundance: one derived from echosounder information from buoys and one derived from the LL Japan in region 2 (Figure 4). The catchability coefficients for the CPUE indices were assumed to be time-invariant.

Figure 3: Summary of the data used in the BET stock assessment.

Length composition data for most fleets (excluding handline Brazil) were included in the model (Figure 3). The effective sample size (ESS) for the length composition data was established by adjusting ESS until unity was reached between modeled ESS and the Francis suggested sample size (Francis, 2011).

Figure 4: Indices of abundance (CPUE) included in the BET assessment model.

3.1.2 Model structure

The model was configured yearly with four seasons per year, one sex, one area, and a total of 11 age groups (0 to 10+). The spawning timing was January 1st.

3.1.3 Biological Parameters

Natural mortality was age-specific and parametrized following Then et al. (2015), assuming a maximum age of 17, 20, or 25 years. Maturity-at-age was knife-edge, with 50% at age-3 and 100% thereafter. Fecundity was proportional to body weight. Growth was parametrized following the Richards curve (Richards, 1959). Variability of lengths-at-age was assumed to be a function of mean length-at-age. Figure 5 shows a summary of the biological parametrization.

Figure 5: Growth, maturity, and natural mortality parametrized in the BET assessment model. Natural mortality assumed a maximum age of 20.

3.1.4 Stock-Recruitment

Expected recruitment to age-0 was calculated from the total spawning stock biomass using the Beverton-Holt stock-recruit function. Recruitment settlement was assumed to occur at month 1, 4, 7, and 10 (i.e., start of every season). The standard error for the log-normally distributed recruitment deviations (sigmaR) was fixed to 0.2, 0.4, or 0.6. Steepness was fixed to values of 0.7, 0.8, or 0.9.

3.1.5 Selectivity

Selectivity was modelled as a function of length and was assumed to be time-invariant. Dome-shaped selectivity was allowed for several LL and BB fleets, while cubic splices were used for PS and some BB fleets.

3.2 Skipjack

The last stock assessment was conducted in 2022 (ICCAT, 2022) using the SS3 platform. The data used in the SKJ assessment and the structure and assumptions of the assessment model are summarized in the sections below.

Table 2: Fishing fleets included the SKJ stock assessment. See Figure 2 for the definition of regions. The last column indicates if the fleet had an associated index of abundance (CPUE).
Fleet code Description Region CPUE included?
1_PS_6385 Purse seine EU (Spain, France) East R1/R2/R3 No
2_PS_8690 Purse seine EU (Spain, France) East R1/R2/R3 No
3_PS_FSC_91 Purse seine free school East R1/R2/R3 No
4_PS_FAD_91 Purse seine FADs East R1/R2/R3 Yes
5_PSBB_Ghana Ghana baitboat and purse seine East R1/R2/R3 No
6_PSBB_SouthDakar Baitboat South Dakar East R2s/R3 No
7_PSBB_Dakar62-80 Baitboat Dakar East R2n No
8_PSBB_Dakar81 Baitboat Dakar East R2n No
9_BB_North25Lat Baitboat North25 East R1 Yes
10_LL All longline fleets East R1/R2/R3 No
11_Acoustic_Buoy Acoustic buoy index East R1/R2/R3 Yes

3.2.1 Data

The period covered was from 1950 to 2020. The assessment mainly used landings data from LL, PS, and BB fleets, with a total of 11 fleets included in the model (Table 2 and Figure 6). There were a total of three indices of abundance available for the assessment: one derived from echosounder information from buoys (\(11\_Acoustic\_Buoy\)), one derived from PS operating on fishing aggregating devices catch and effort information (\(4\_PS\_FAD\_91\)), and one derived from the BB in region 1 (Figure 7). The \(4\_PS\_FAD\_91\) and \(11\_Acoustic\_Buoy\) indices were not included together in a model run. The catchability coefficients for the CPUE indices were assumed to be time-invariant.

Figure 6: Summary of the data used in the SKJ stock assessment.

Length composition data for all fleets were included in the model (Figure 6). The ESS for the length composition data was established by adjusting ESS until unity was reached between modeled ESS and the Francis suggested sample size (Francis, 2011).

Figure 7: Indices of abundance (CPUE) included in the SKJ assessment model.

3.2.2 Model structure

The model was configured yearly with four seasons per year, one sex, one area, and a total of 7 age groups (0 to 6+). The spawning timing was January 1st.

3.2.3 Biological Parameters

Natural mortality (M) was age-specific and parametrized following Lorenzen (1996), with a reference M equal to 0.55 for age 6. Maturity-at-length followed a logistic function. Fecundity was proportional to body weight. Growth was parametrized following the von Bertalanffy curve (Schnute, 1981) with three different set of parameters, which also impacted the derived M-at-age values. Variability of lengths-at-age was assumed to be a function of mean length-at-age. Figure 8 shows a summary of the biological parametrization.

Figure 8: Growth, maturity, and natural mortality parametrized in the SKJ assessment model. Growth used the 0.5 quantile (see ICCAT (2022)).

3.2.4 Stock-Recruitment

Expected recruitment to age-0 was calculated from the total spawning stock biomass using the Beverton-Holt stock-recruit function. Recruitment settlement was assumed to occur at month 1, 4, 7, and 10 (i.e., start of every season). sigmaR was fixed to 0.4 and steepness was fixed to values of 0.7, 0.8, or 0.9.

3.2.5 Selectivity

Selectivity was modelled as a function of length and was assumed to be time-invariant. Dome-shaped selectivity was allowed for most fleets, while a logistic shape was modelled for the LL fleet.

3.3 Yellowfin

The last stock assessment was conducted in 2024 (ICCAT, 2024) using the SS3 platform. The data used in the YFT assessment and the structure and assumptions of the assessment model are summarized in the sections below.

Table 3: Fishing fleets included the YFT stock assessment. See Figure 2 for the definition of regions. The last column indicates if the fleet had an associated index of abundance (catch-per-unit-effort, CPUE).
Fleet code Description Region CPUE included?
1_PS_ESFR_6585 Purse seine EU (Spain, France) R2/R1 No
2_PS_ESFR_8690 Purse seine EU (Spain, France) R2/R1 No
3_PS_ESFR_FS_9122 Purse seine free school EU (Spain, France) R2/R1 Yes
4_PS_ESFR_FOB_9122 Purse seine FADs EU (Spain, France) R2/R3 Yes
5_BB_PS_Ghana_6522 Ghana baitboat and purse seine R2 No
6_BB_area2_Sdak Baitboat South Dakar R2s No
7_BB_DAKAR_6280 Baitboat North Dakar R2n No
8_BB_DAKAR_8122 Baitboat North Dakar R2n No
9_North_BB_Azores Baitboat North Azores R1 No
10_Japan_LL_N Longline North Japan R1 Yes
11_Japan_LL_TRO Longline Tropical Japan R2 Yes
12_Japan_LL_S Longline South Japan R3 Yes
13_Other_LL_N Longline North Other R1 No
14_Other_LL_TRO Longline Tropical Other R2 No
15_Other_LL_S Longline South Other R3 No
16_HL_Braz_N Handline Brazil R2 No
17_US_RR RR West Atlantic R1 No
18_PS_WEST Purse seine West Atlantic R1 No
19_OTH_OTH Other R1/R2/R3 No

3.3.1 Data

The period covered was from 1950 to 2022. The assessment mainly used landings data from LL, PS, and baitboat BB fleets, with a total of 19 fleets included in the model (Table 3 and Figure 9). There were a total of five indices of abundance available for the assessment: one derived from PS operating on floating objects catch and effort data (\(4\_PS\_ESFR\_FOB\_9122\)), one derived from PS operating on free schools catch and effort data (\(4\_PS\_ESFR\_FS\_9122\)), and three indices derived from LL for region 1, 2, and 3 (Figure 10). The catchability coefficients for the CPUE indices were assumed to be time-invariant.

Figure 9: Summary of the data used in the YFT stock assessment.

Length composition data for most fleets were included in the model (Figure 9). The ESS for the length composition data was established by adjusting ESS until unity was reached between modeled ESS and the Francis suggested sample size (Francis, 2011). Conditional age-at-length (CAAL) data was also included for four fleets (Figure 9).

Figure 10: Indices of abundance (CPUE) included in the YFT assessment model.

3.3.2 Model structure

The model was configured yearly with four seasons per year, one sex, one area, and a total of 11 age groups (0 to 10+). The spawning timing was January 1st.

3.3.3 Biological Parameters

Natural mortality (M) was age-specific and parametrized following Lorenzen (1996), with a reference M (\(M_{ref}\)) equal to 0.3 for age 7 assuming a maximum age of 18 years (Hamel and Cope, 2022). Alternative \(M_{ref}\) values of 0.25 and 0.35 were also tested. Maturity-at-length followed a logistic function. Fecundity was proportional to body weight. Growth was parametrized following the Richards curve (Richards, 1959). Variability of lengths-at-age was assumed to be a function of mean length-at-age. Figure 11 shows a summary of the biological parametrization.

Figure 11: Growth, maturity, and natural mortality parametrized in the YFT assessment model. \(M_{ref}\) was 0.3.

3.3.4 Stock-Recruitment

Expected recruitment to age-0 was calculated from the total spawning stock biomass using the Beverton-Holt stock-recruit function with flat-top beyong unfished biomass. Recruitment settlement was assumed to occur at month 1, 4, 7, and 10 (i.e., start of every season). sigmaR was freely estimated and steepness was fixed to 0.7, 0.8, or 0.9.

3.3.5 Selectivity

Selectivity was modelled as a function of length and was assumed to be time-invariant. Dome-shaped selectivity was modelled for most LL and BB fleet, while cubic splines was modelled for the PS fleets.

4 Operating Models

4.1 Reference OMs

In 2025, the TTSG developed a set of OMs considering the axes of uncertainty evaluated in the stock assessment for each stock (Table 4). A factorial combination of these axes produced a total of 4374 models, which were the Reference OMs in the MSE.

Table 4: Description of the axes of uncertainty for each stock.
Description Code
Bigeye
Axis 1 Maximum age for natural mortality: 17, 20, 25 M17, M20, M25
Axis 2 Steepness: 0.7, 0.8, 0.9 h0.7, h0.8, h0.9
Axis 3 sigmaR: 0.2, 0.4, 0.6 sigmaR0.2, sigmaR0.4, sigmaR 0.6
Skipjack
Axis 1 Inclusion of index: acoustic buoy, PSFAD catch and effort noPS, noBuoy
Axis 2 Growth quantile: 0.25, 0.5, 0.75 25thGrowth, 50thGrowth, 75thGrowth
Axis 3 Steepness: 0.7, 0.8, 0.9 h0.7, h0.8, h0.9
Yellowfin
Axis 1 M reference value: 0.35, 0.3, 0.25 highM, midM, lowM
Axis 2 Steepness: 0.7, 0.8, 0.9 h07, h08, h09

4.2 Robustness OMs

The TT MSE evaluated the impacts of potential decrease in the mean recruitment level in future years. To do so, the \(R_0\) parameter of the Beverton-Holt relationship decrased by 20% in the simulation period (Figure 12) from the estimated values in the Reference OMs for the three stocks. This set of runs with smaller \(R_0\) is our Robustness OMs.

4.3 Validation

4.3.1 Summary Report

Summary reports summarize the estimated parameters, the calculated biological reference points, and the estimated stock status relative to those reference points per stock (Table 5).

Table 5: OM summary reports.
Stock Report
Bigeye See Summary report
Skipjack See Summary report
Yellowfin See Summary report

4.3.2 Diagnostic Reports

Individual diagnostic reports with objective function values and plots of model fits and patterns in residuals are available for each of the Reference OMs. Table 6 presents the diagnostics reports for all models in the uncertainty grid for each stock.

Table 6: OM diagnostics reports per stock. See Table 4 for more information on the axes of uncertainty.
Bigeye Skipjack Yellowfin
M17_h0.7_sigmaR0.2 noBuoy_25thGrowth_h0.7 highM_h07
M17_h0.7_sigmaR0.4 noBuoy_25thGrowth_h0.8 highM_h08
M17_h0.7_sigmaR0.6 noBuoy_25thGrowth_h0.9 highM_h09
M17_h0.8_sigmaR0.2 noBuoy_50thGrowth_h0.7 lowM_h07
M17_h0.8_sigmaR0.4 noBuoy_50thGrowth_h0.8 lowM_h08
M17_h0.8_sigmaR0.6 noBuoy_50thGrowth_h0.9 lowM_h09
M17_h0.9_sigmaR0.2 noBuoy_75thGrowth_h0.7 midM_h07
M17_h0.9_sigmaR0.4 noBuoy_75thGrowth_h0.8 midM_h08
M17_h0.9_sigmaR0.6 noBuoy_75thGrowth_h0.9 midM_h09
M20_h0.7_sigmaR0.2 noPS_25thGrowth_h0.7
M20_h0.7_sigmaR0.4 noPS_25thGrowth_h0.8
M20_h0.7_sigmaR0.6 noPS_25thGrowth_h0.9
M20_h0.8_sigmaR0.2 noPS_50thGrowth_h0.7
M20_h0.8_sigmaR0.4 noPS_50thGrowth_h0.8
M20_h0.8_sigmaR0.6 noPS_50thGrowth_h0.9
M20_h0.9_sigmaR0.2 noPS_75thGrowth_h0.7
M20_h0.9_sigmaR0.4 noPS_75thGrowth_h0.8
M20_h0.9_sigmaR0.6 noPS_75thGrowth_h0.9
M25_h0.7_sigmaR0.2

M25_h0.7_sigmaR0.4

M25_h0.7_sigmaR0.6

M25_h0.8_sigmaR0.2

M25_h0.8_sigmaR0.4

M25_h0.8_sigmaR0.6

M25_h0.9_sigmaR0.2

M25_h0.9_sigmaR0.4

M25_h0.9_sigmaR0.6

4.4 Conditioning

The Reference OMs were conditioned in FLBEIA with the same biological configuration. The conditioned fleet structure in the OMs is shown in Table 7.

Table 7: Fleet conditioning in the OMs.
Fleet Description Bigeye Skipjack Yellowfin
PS Purse seine, divided in two metiers: FSC (free school) and LS (log school) Check Check Check
PSBB_GH Purse seine and baitboat Ghana Check Check Check
Dakar_BB Dakar baitboat Check Check Check
North_BB North baitboat Check Check Check
JP_LL Japan longline Check Xmark Check
Other_LL Other longline Check Check Check
CTP_LL Chinese Taipei longline Check Xmark Xmark
RR_US RR U.S. Check Xmark Check
HL_Bra Handline Brazil Check Xmark Check
West_PS West purse seine Check Xmark Check
Others Other gears Check Xmark Check

The historical period in the MSE corresponds to the years covered in the assessment model (Figure 12). On the other side, the simulation period corresponds to the years when the harvest control rules (HCR) are evaluated. The simulation period started in 2023 and ended in 2050. Since the YFT and SKJ assessments ended prior to 2023, some initial runs were needed for those stocks assuming average catches from the last three years (Figure 12).

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gantt
    dateFormat  YYYY-MM-DD
    section Bigeye
    End of historical period :done, a1, 2017-01-01, 3y
    Initial runs     :active, a2, after a1  , 3y
    Start of simulation period:after a2, 6y
    section Skipjack
    End of historical period :done, b1, 2017-01-01, 4y
    Initial runs     :active, b2, after b1  , 2y
    Start of simulation period:after b2, 6y
    section Yellowfin
    End of historical period :done, c1, 2017-01-01, 6y
    Start of simulation period:after c1, 6y
    todayMarker off
Figure 12: Periods in the MSE.

4.4.1 Observation error model

Autocorrelation in CPUE residuals were introduced in the historical and simulation periods for all the Reference OMs based on the calculated autocorrelation coefficient at lag 1 (Figure 13).

Figure 13: Autocorrelation coefficient (\(\rho\)) at lag 1 for abundance indices per stock. Dots represent different model configurations in the uncertainty grid.

5 Management Procedure

Simulated data was included in a stochastic surplus production model in continuous time (SPiCT). SPiCT is a full state-space model, where biomass and fishing dynamics are modelled as states, which are observed indirectly through biomass indices and commercial catches sampled with error (Pedersen and Berg, 2017). SPiCT calculates maximum sustainable yield (MSY) reference points and is able to make short-term projections. SPiCT is the estimation method in the MSE.

Figure 14: Example of a harvest control rule.

Per stock, a total allowable catch (TAC) is derived from a HCR (Figure 14). We evaluated a total of 9 HCRs produced by the combinations of \(F_{tgt}\) and \(B_{thr}\) shown in Figure 15. \(B_{lim}=0.4\times B_{msy}\) and \(F_{mim}=0.1\times F_{msy}\) for all cases.

Figure 15: HCR evaluated in the MSE. These HCR come from combinations of \(F_{tgt}\) (rows) and \(B_{thr}\) (columns).

In a multi-stock framework, stock-specific advice can be conflicting when different stocks are caught within the same fishery. Therefore, the annual management advice was produced based on the minimum effort, following the FcubEcon approach (Hoff et al., 2010), among the three stocks. A summary of these steps is shown in Figure 16.

flowchart TB
    subgraph BET["<b>Bigeye MP</b>"]
        direction TB
        bet1["SSB<sub>BET</sub>"]
        bet2["TAC<sub>BET</sub>"]
        bet3["QS<sub>f,BET</sub>"]
        bet4["Quota<sub>f,BET</sub>"]
    end
    subgraph SKJ["<b>Skipjack MP</b>"]
    direction TB
        skj1["SSB<sub>SKJ</sub>"]
        skj2["TAC<sub>SKJ</sub>"]
        skj3["QS<sub>f,SKJ</sub>"]
        skj4["Quota<sub>f,SKJ</sub>"]
    end
    subgraph YFT["<b>Yellowfin MP</b>"]
    direction TB
        yft1["SSB<sub>YFT</sub>"]
        yft2["TAC<sub>YFT</sub>"]
        yft3["QS<sub>f,YFT</sub>"]
        yft4["Quota<sub>f,YFT</sub>"]
    end
    bet5["E<sub>f,BET</sub>"]
    skj5["E<sub>f,SKJ</sub>"]
    yft5["E<sub>f,YFT</sub>"]
    HCR["E<sub>f</sub>=min(E<sub>f,BET</sub>,E<sub>f,SKJ</sub>,E<sub>f,YFT</sub>)"]
    bet7["Catch<sub>f,BET</sub>"]
    skj7["Catch<sub>f,SKJ</sub>"]
    yft7["Catch<sub>f,YFT</sub>"]

    bet1 --HCR<sub>BET</sub>--> bet2 --> bet4
    bet3 --> bet4 --> bet5
    bet5 --> HCR
    skj1 --HCR<sub>SKJ</sub>--> skj2 --> skj4
    skj3 --> skj4 --> skj5
    skj5 --> HCR
    yft1 --HCR<sub>YFT</sub>--> yft2 --> yft4
    yft3 --> yft4 --> yft5 
    yft5 --> HCR
    HCR --> bet7
    HCR --> skj7
    HCR --> yft7
    style BET fill:#ffffff
    style bet1 opacity:0.5,fill:#dca06d
    style bet2 opacity:0.5,fill:#dca06d
    style bet3 opacity:0.5,fill:#dca06d
    style bet4 opacity:0.5,fill:#dca06d
    style bet5 opacity:0.5,fill:#dca06d
    style bet7 opacity:0.5,fill:#dca06d
    style SKJ fill:#ffffff
    style skj1 opacity:0.5,fill:#a55b4b
    style skj2 opacity:0.5,fill:#a55b4b
    style skj3 opacity:0.5,fill:#a55b4b
    style skj4 opacity:0.5,fill:#a55b4b
    style skj5 opacity:0.5,fill:#a55b4b
    style skj7 opacity:0.5,fill:#a55b4b
    style YFT fill:#ffffff
    style yft1 opacity:0.5,fill:#b184b3
    style yft2 opacity:0.5,fill:#b184b3
    style yft3 opacity:0.5,fill:#b184b3
    style yft4 opacity:0.5,fill:#b184b3
    style yft5 opacity:0.5,fill:#b184b3
    style yft7 opacity:0.5,fill:#b184b3
    style HCR fill:#ffffff
    
    %% Set all nodes to black text
    linkStyle default color:#000000
    classDef blackText color:#000000;
    class bet1,bet2,bet3,bet4,bet5,bet7,skj1,skj2,skj3,skj4,skj5,skj7,yft1,yft2,yft3,yft4,yft5,yft7,HCR,BET,SKJ,YFT blackText;
Figure 16: Example of how the annual management advice is derived. \(QS_f\) represents the quota share per fleet. \(E\) represents effort.

6 Performance Metrics

15 PMs have been developed for the TT MSE (Table 8) and are grouped into four types:

  • Status: metrics related to stock status

  • Safety: metrics related to the probability of the stock not falling below the biological reference points

  • Yield: metrics related to the catch in the projection years

  • Stability: metrics related to the variation in the catches or TAC between management cycles

Each PM was calculated for every Reference OM. Examples of each PM is given below.

Table 8: Performance metrics and description.
Type Metric Symbol Description
Status Minimum spawner biomass relative to \(B_{msy}\) \(minB\) Minimum \(B/B_{msy}\) value
Status Mean spawner biomass relative to \(B_{msy}\) \(meanB\) Geometric mean of \(B/B_{msy}\)
Status Mean fishing mortality relative to \(F_{msy}\) \(meanF\) Geometric mean of \(F/F_{msy}\)
Status Probability (%) of being in the Kobe green quadrant \(pGreen\) Proportion of years in green quadrant (see Figure 14)
Status Probability (%) of being in the Kobe red quadrant \(pRed\) Proportion of years in red quadrant (see Figure 14)
Safety Probability (%) of \(B>B_{lim}\) \(pBlim\) Proportion of years that \(B>B_{lim}\)
Safety Probability (%) of \(B_{lim}<B<B_{msy}\) \(pBmsy\) Proportion of years that \(B_{lim}<B<B_{msy}\)
Yield Mean catch (short term) \(Csht\) Mean catch from 1 to 3 years
Yield Mean catch (medium term) \(Cmed\) Mean catch from 5 to 10 years
Yield Mean catch (long term) \(Clon\) Mean catch from 15 to 28 years
Stability Mean absolute proportional change (%) in catch \(Cc\) Mean of \(\mid\frac{C_y - C_{y-1}}{C_{y-1}}\mid\)
Stability Standard deviation in catch \(Csd\) Catch standard deviation
Stability Probability (%) of shutdown \(pShw\) Proportion of years that TAC=0
Stability Probability (%) of TAC change over a certain level \(pTX\) Proportion of management cycles when the ratio of change \(\frac{TAC_y - TAC_{y-1}}{TAC_{y-1}} > 10\%\)
Stability Maximum amount of TAC change (%) between management periods \(maxTc\) Maximum ratio of TAC change

6.1 Examples

6.1.1 Status

Figure 17: Status performance metrics. The blue dots or lines indicate the meaning of the metric. Find more details in Table 8.

6.1.2 Safety

Figure 18: Safety performance metrics. The blue dots indicate the meaning of the metric. Find more details in Table 8.

6.1.3 Yield

Figure 19: Yield performance metrics. The blue lines indicate the meaning of the metric. Find more details in Table 8.

6.1.4 Stability

Figure 20: Stability performance metrics. The blue lines, arrows, or dots indicate the meaning of the metric. Find more details in Table 8.

7 Results

7.1 Bigeye

Table 9: Performance metrics results for bigeye. Numbers indicate the median over all the PMs calculated per HCR and OM. The color scale is independent for every column.
Ftgt Bthr
Status
Safety
Yield
Stability
minB meanB meanF pGreen pRed pBlim pBmsy Csht Cmed Clon Cc Csd pShw pTX maxTc
0.8 0.8 1.00 1.23 0.82 81% 0% 100% 4% 69,976 83,791 77,859 1% 10,399 0% 38% 25%
0.8 1.0 1.00 1.23 0.82 81% 0% 100% 4% 69,976 83,791 77,832 1% 10,628 0% 38% 25%
0.8 1.2 1.00 1.24 0.81 81% 0% 100% 0% 69,647 83,557 77,107 1% 11,193 0% 50% 25%
1.0 0.8 0.76 1.06 0.98 37% 26% 100% 41% 73,552 91,616 79,961 1% 13,054 0% 62% 25%
1.0 1.0 0.77 1.07 0.96 39% 26% 100% 37% 73,453 91,539 79,596 0% 13,677 0% 62% 25%
1.0 1.2 0.80 1.10 0.91 44% 19% 100% 33% 71,927 90,746 78,654 0% 14,336 0% 62% 25%
1.2 0.8 0.63 0.94 1.09 26% 48% 100% 48% 74,915 94,844 81,856 0% 14,956 0% 62% 25%
1.2 1.0 0.64 0.96 1.06 30% 41% 100% 46% 74,569 94,430 80,985 0% 15,222 0% 75% 25%
1.2 1.2 0.70 1.01 1.00 35% 33% 100% 41% 73,338 93,496 80,624 0% 15,425 0% 75% 25%

7.2 Skipjack

Table 10: Performance metrics results for skipjack. Numbers indicate the median over all the PMs calculated per HCR and OM. The color scale is independent for every column.
Ftgt Bthr
Status
Safety
Yield
Stability
minB meanB meanF pGreen pRed pBlim pBmsy Csht Cmed Clon Cc Csd pShw pTX maxTc
0.8 0.8 1.39 2.04 0.29 100% 0% 100% 0% 179,980 222,733 210,975 1% 26,812 0% 44% 25%
0.8 1.0 1.39 2.05 0.29 100% 0% 100% 0% 179,980 222,733 210,917 1% 27,015 0% 44% 25%
0.8 1.2 1.39 2.06 0.28 100% 0% 100% 0% 179,490 222,527 207,582 1% 28,566 0% 50% 25%
1.0 0.8 1.20 1.82 0.33 100% 0% 100% 0% 193,168 237,141 223,221 1% 27,102 0% 25% 20%
1.0 1.0 1.20 1.84 0.33 100% 0% 100% 0% 192,859 237,045 220,077 1% 28,669 0% 25% 20%
1.0 1.2 1.20 1.87 0.32 100% 0% 100% 0% 188,526 236,305 214,299 1% 31,198 0% 25% 22%
1.2 0.8 1.03 1.71 0.36 100% 0% 100% 0% 199,648 241,094 231,316 0% 26,419 0% 0% 9%
1.2 1.0 1.04 1.73 0.36 100% 0% 100% 0% 198,891 240,678 228,071 0% 28,749 0% 12% 12%
1.2 1.2 1.12 1.79 0.33 100% 0% 100% 0% 193,667 239,632 221,759 0% 30,527 0% 25% 20%

7.3 Yellowfin

Table 11: Performance metrics results for yellowfin. Numbers indicate the median over all the PMs calculated per HCR and OM. The color scale is independent for every column.
Ftgt Bthr
Status
Safety
Yield
Stability
minB meanB meanF pGreen pRed pBlim pBmsy Csht Cmed Clon Cc Csd pShw pTX maxTc
0.8 0.8 1.37 1.59 0.66 100% 0% 100% 0% 97,226 115,445 105,987 1% 16,739 0% 50% 25%
0.8 1.0 1.37 1.59 0.65 100% 0% 100% 0% 97,226 115,445 105,962 1% 17,017 0% 50% 25%
0.8 1.2 1.36 1.60 0.65 100% 0% 100% 0% 96,729 114,973 105,039 1% 17,820 0% 50% 25%
1.0 0.8 1.17 1.45 0.76 89% 0% 100% 0% 103,321 127,575 111,423 1% 19,429 0% 50% 25%
1.0 1.0 1.17 1.45 0.75 89% 0% 100% 0% 102,945 127,575 111,397 1% 20,351 0% 62% 25%
1.0 1.2 1.18 1.47 0.72 89% 0% 100% 0% 101,177 126,238 107,743 1% 21,778 0% 62% 25%
1.2 0.8 1.03 1.35 0.85 67% 0% 100% 0% 106,245 132,116 116,425 1% 21,223 0% 50% 22%
1.2 1.0 1.04 1.37 0.82 74% 0% 100% 0% 105,225 131,420 114,449 1% 22,010 0% 50% 23%
1.2 1.2 1.09 1.41 0.78 85% 0% 100% 0% 102,938 129,501 111,121 1% 22,646 0% 62% 25%

8 Glossary

Term Definition
TT Tropical tunas
BET Bigeye
SKJ Skipjack
YFT Yellowfin
OM Operating model
CMP Candidate management procedure
PM Performance metric
TTSG Tropical Tunas Species Group
SS3 Stock Synthesis 3 platform
ESS Effective sample size
M Natural mortality
sigmaR Variability in recruitment
h Steepness in the stock-recruit function
OEM Observation error model
HCR Harvest control rule
TAC Total Allowable Catch

References

Francis, R.I.C.C., 2011. Data weighting in statistical fisheries stock assessment models. Canadian Journal of Fisheries and Aquatic Sciences 68, 1124–1138. https://doi.org/10.1139/f2011-025
Garcia, D., Sánchez, S., Prellezo, R., Urtizberea, A., Andrés, M., 2017. FLBEIA: A simulation model to conduct Bio-Economic evaluation of fisheries management strategies. SoftwareX 6, 141–147. https://doi.org/10.1016/j.softx.2017.06.001
Hamel, O.S., Cope, J.M., 2022. Development and considerations for application of a longevity-based prior for the natural mortality rate. Fisheries Research 256, 106477. https://doi.org/10.1016/j.fishres.2022.106477
Hoff, A., Frost, H., Ulrich, C., Damalas, D., Maravelias, C.D., Goti, L., Santurtún, M., 2010. Economic effort management in multispecies fisheries: The FcubEcon model. ICES Journal of Marine Science 67, 1802–1810. https://doi.org/10.1093/icesjms/fsq076
ICCAT, 2024. Report of the 2024 ICCAT yellowfin tuna stock assessment meeting (No. SCRS/2024/009). ICCAT (International Commission for the Conservation of Atlantic Tunas).
ICCAT, 2022. Report of the 2022 skipjack stock assessment meeting (No. SCRS/2022/008). ICCAT (International Commission for the Conservation of Atlantic Tunas).
ICCAT, 2021. Report of the 2021 bigeye stock assessment meeting (No. SCRS/2021/011). ICCAT (International Commission for the Conservation of Atlantic Tunas).
Lorenzen, K., 1996. The relationship between body weight and natural mortality in juvenile and adult fish: A comparison of natural ecosystems and aquaculture. Journal of Fish Biology 49, 627–642. https://doi.org/10.1111/j.1095-8649.1996.tb00060.x
Methot, R.D., Wetzel, C.R., 2013. Stock synthesis: A biological and statistical framework for fish stock assessment and fishery management. Fisheries Research 142, 86–99. https://doi.org/10.1016/j.fishres.2012.10.012
Pedersen, M.W., Berg, C.W., 2017. A stochastic surplus production model in continuous time. Fish and Fisheries 18, 226–243. https://doi.org/10.1111/faf.12174
Richards, F.J., 1959. A Flexible Growth Function for Empirical Use. Journal of Experimental Botany 10, 290–301. https://doi.org/10.1093/jxb/10.2.290
Schnute, J., 1981. A versatile growth model with statistically stable parameters. Canadian Journal of Fisheries and Aquatic Sciences 38, 1128–1140. https://doi.org/10.1139/f81-153
Then, A.Y., Hoenig, J.M., Hall, N.G., Hewitt, D.A., Handling editor: Ernesto Jardim, 2015. Evaluating the predictive performance of empirical estimators of natural mortality rate using information on over 200 fish species. ICES Journal of Marine Science 72, 82–92. https://doi.org/10.1093/icesjms/fsu136
Waterhouse, L., Sampson, D.B., Maunder, M., Semmens, B.X., 2014. Using areas-as-fleets selectivity to model spatial fishing: Asymptotic curves are unlikely under equilibrium conditions. Fisheries Research 158, 15–25. https://doi.org/10.1016/j.fishres.2014.01.009