Specifications for MSE Trials for North Atlantic Albacore

1 Introduction

The North Atlantic Albacore (N-ALB) fishery, under the management of the International Commission for the Conservation of Atlantic Tuna (ICCAT), is undergoing a management strategy evaluation (MSE) process.

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 indicators (PIs): statistics used to quantitatively evaluate the CMPs against specified management objectives.

The OMs, CMPs, and PIs 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 indicators"]
    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 PIs that have been proposed and developed for the N-ALB fishery. It is a living document and will be continued to be updated so that it reflects the current state of the N-ALB MSE process. Members of the Albacore Species Group (ALBSG) 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. ALBSG 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 MSE developers. The former approach has the advantage that all comments, questions, and edits are immediately visible to all members of the ALBSG. 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 N-ALB MSE homepage.

2 MSE framework

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

The code developed for the N-ALB 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

Previously, the N-ALB OMs were based on the 2013 stock assessment (Merino et al., 2020, 2014) using the MULTIFAN-CL platform (Fournier et al., 1998).

A new stock assessment was conducted in 2023 (ICCAT, 2023) using the Stock Synthesis (SS3) platform (Methot and Wetzel, 2013). The N-ALB OMs have been updated based on this new assessment.

The data used in the 2023 N-ALB assessment as well as the structure and assumptions of the assessment model are summarized in the sections below.

Table 1: Fishing fleets included the 2023 N-ALB stock assessment. The last column indicates if the fleet had an associated index of abundance (catch-per-unit-effort, CPUE).

Fleet code	Description	CPUE included?
1_BB	Baitboat (Spain, France)	Yes
2_BB_isl	Baitboat islands (Portugal Madeira/Azores, Spain Canary) for quarters 1, 3, and 4	No
3_TR_GN	Troll (Spain, France) and Gillnets (France, Ireland)	No
4_MWT	Mid-water trawl (France, Ireland)	No
5_JPLL_N	Japan longline north 30	Yes
6_JPLL_S	Japan longline south 30	Yes
7_TAILL_N	Taiwan longline north 30	Yes
8_TAILL_S	Taiwan longline south 30	Yes
9_USLL_N	US and Canada longline north 30	Yes
10_USLL_S	US longline south 30	Yes
11_VENLL	Venezuela longline	Yes
12_MIX_KR_PA	Mixed flags longline (KR, PA, CHN)	No
13_OthLL	Other longline	No
14_OthSurf	Other surface gears	No
15_BBisl_s2	Baitboat islands (Portugal Madeira/Azores, Spain Canary) for quarter 2	No

3.1 Data

The period covered was from 1930 to 2021. The assessment mainly used landings data from longline (LL) and baitboat (BB) fleets, with a total of 15 fleets included in the model (Table 1 and Figure 2). There were seven LL and one BB (Spain and France) catch-per-unit-effort (CPUE) indices (Figure 3). The catchability coefficients for the CPUE indices were assumed to be time-invariant.

Figure 2: Summary of the data used in the 2023 N-ALB stock assessment. The bubble size represents the quantity or precision of the data.

Length composition data from 12 fleets were included in the model, mostly from LL and BB fleets and for the period after 1970 (Figure 2). 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). Conditional age-at-length (CAAL) data was also included for the BB (France and Spain) fleet.

Figure 3: Indices of abundance (CPUE) by fleet included in the N-ALB assessment model.

3.2 Model structure

The model was configured yearly (one season per year), one sex, one area, and a total of 16 age groups (0 to 15+). The spawning timing was January 1st.

3.3 Biological Parameters

Natural mortality (M) was age-specific and parametrized following Lorenzen (1996), with a reference M equal to 0.36 for age 6 based on the assumption of a maximum age of 15 years (Hamel and Cope, 2022). Maturity-at-age was knife-edge, with 50% at age-5 and 100% thereafter. Fecundity was proportional to body weight. Growth was parametrized following the von Bertalanffy curve (Schnute, 1981) and parameters were estimated within the model. Variability of lengths-at-age was assumed to be a function of age. Figure 4 shows a summary of the biological parametrization.

Figure 4: Growth, maturity, and natural mortality parametrized in the N-ALB assessment model.

3.4 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 6. The standard error for the log-normally distributed recruitment deviations (sigmaR) was fixed to 0.4. Steepness (h) was estimated within the model with a prior of 0.75 taken from the 2013 assessment.

3.5 Selectivity

Selectivity was modelled as a function of length. Dome-shaped selectivity was allowed for several LL and BB fleets, while an asymptotic selectivity was speficied for the US and Venezuela LL fleets. Splines were also used for the BB (Spain and France) and mid-water trawl. Time blocks were specified for some fleets due to changes in length composition data.

4 Operating Models

4.1 Reference OMs

During 2023 and 2024, the ALBSG developed a set of OMs considering variations in natural mortality (M), variability in recruitment (sigmaR), and the weighting of the following data sources:

Base case (no change)
Upweight (\(\lambda=2\)) CPUE data
Upweight (\(\lambda=2\)) size (i.e., length composition) data
Upweight (\(\lambda=2\)) age (i.e., CAAL) data

Per weighting scenario, 400 models were run in SS3 by randomly varying the M and sigmaR values sampled from a normal distribution with mean 0.36 and 0.4, respectively, and a coefficient of variation of 0.2 (Figure 5).

Figure 5: Values of natural mortality (M) and recruitment variability (sigmaR) simulated in the OMs.

Then, 100 models per weighting scenario were selected based on maximum gradient, likelihood, and the ratio of virgin and spawning biomass values in order to remove unrealistic or nonconvergent runs. We consider this final set of 400 models (100 models per weighting scenario) as our Reference OMs.

4.2 Robustness OMs

The robustness scenarios explored the impacts of changes in \(R_0\), recruitment variability, and maximum annual catch:

Changes in \(R_0\): decrease in the \(R_0\) parameter of the Beverton-Holt relationship by 20% in the simulation period from the estimated values in the Reference OMs.
Changes in sigmaR: increase in the recruitment variability by 20% in the simulation period from the estimated values in the Reference OMs.
Maximum catch (\(TAC_{max}\)): maximum annual catch of 100,000 tonnes.

Robustness scenario are currently under development.

4.3 Validation

4.3.1 Summary Report

A Summary Report summarizes the estimated parameters, the calculated biological reference points, and the estimated stock status relative to those reference points, across the 400 Reference OMs.

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 400 Reference OMs. Table 2 presents the diagnostics for a subset of four OMs per weighting scenario with the most extreme M and sigmaR values.

Table 2: OM diagnostics reports. A set of four OMs were chosen per weighting scenario with the most extreme M and sigmaR values.

	M	sigmaR
BaseCase
Smallest M value	0.20	0.40	See diagnostics
Medium M value	0.36	0.26	See diagnostics
Largest M value	0.52	0.33	See diagnostics
Smallest sigmaR value	0.36	0.22	See diagnostics
Medium sigmaR value	0.36	0.40	See diagnostics
Largest sigmaR value	0.27	0.56	See diagnostics
CPUE
Smallest M value	0.15	0.24	See diagnostics
Medium M value	0.36	0.35	See diagnostics
Largest M value	0.53	0.49	See diagnostics
Smallest sigmaR value	0.34	0.18	See diagnostics
Medium sigmaR value	0.37	0.41	See diagnostics
Largest sigmaR value	0.43	0.63	See diagnostics
Size
Smallest M value	0.20	0.32	See diagnostics
Medium M value	0.36	0.27	See diagnostics
Largest M value	0.52	0.33	See diagnostics
Smallest sigmaR value	0.36	0.22	See diagnostics
Medium sigmaR value	0.40	0.40	See diagnostics
Largest sigmaR value	0.27	0.56	See diagnostics
Age
Smallest M value	0.22	0.35	See diagnostics
Medium M value	0.35	0.41	See diagnostics
Largest M value	0.50	0.47	See diagnostics
Smallest sigmaR value	0.36	0.20	See diagnostics
Medium sigmaR value	0.32	0.43	See diagnostics
Largest sigmaR value	0.43	0.63	See diagnostics

4.4 Conditioning

The Reference OMs were conditioned in FLBEIA with the same biological configuration and fleet structure of the SS3 models (Table 1). Two main periods are modelled in the MSE framework: historical and simulation periods (Figure 6), with important differences in the data generation and observation error model (OEM).

timeline
    section 1930 - 2021
        Historical period : - Catches from observations <br> - CPUE from OEM
    section 2022 - 2050
        Simulation period : - Catches from HCR (Model-based CMPs) <br> - CPUE from OEM <br> - Evaluate CMPs

Figure 6: Periods in the MSE and main differences between them.

4.4.1 Observation error model

Autocorrelation in CPUE residuals were introduced in the simulations based on a previous analysis of CPUE residuals in the stock assessment model (Table 3). This observation error was introduced both in the historical and projection period for all the Reference OMs.

Table 3: Evaluation of temporal autocorrelation in CPUE residuals for lag 1. \(\rho\) and \(\sigma\) represent the correlation parameter and the standard deviation of residuals, respectively. ACF is the autocorrelation function. The only fleet that assumed a \(\rho=0\) in the MSE was \(1_BB\).

Index	ρ	σ	Sign. ACF?	Autocorrelation in MSE?	Included in MSE projection period?
1_BB	0.10	0.38	No	No	No
5_JPLL_N	0.25	0.30	No	Yes	Yes
6_JPLL_S	0.39	0.36	Yes	Yes	Yes
7_TAILL_N	0.13	0.29	No	Yes	Yes
8_TAILL_S	0.54	0.33	Yes	Yes	Yes
9_USLL_N	0.65	0.39	Yes	Yes	Yes
10_USLL_S	0.54	0.35	Yes	Yes	Yes
11_VENLL	0.57	0.42	Yes	Yes	No

5 Candidate Management Procedures

5.1 Pseudo-constant catch (PCCatch)

The total allowable catch (TAC) for the next management period (\(t\)) is assumed constant, unless a reference value (\(I_{G}\)) derived from a group of indices of abundance in the last two years falls below a reference value \(I_{ref}=0.91\) (value in 2010, when \(SSB>SSB_{msy}\)):

\[TAC_t = \begin{cases} TAC_{max}, & \text{if }I_{G} \geq I_{ref} \\ TAC_{max}(\frac{I_{G}}{I_{ref}}), & \text{if }I_{G} < I_{ref} \end{cases}\]

where \(TAC_{max}=42,000\) tonnes. \(I_{G}\) was calculated as follows:

\[I_G = exp(\frac{1}{n_i}\sum_{i}log(I^*_i))\]

where \(n_i\) is the number of selected indices of abundance and \(I^*_i\) was calculated for every selected index of abundance \(I_i\) using information from the last two years (\(y\)):

\[I^*_i = \frac{I_{i,y}+I_{i,y-1}}{2}\]

For this case, the indices of abundance \(I_i\) that we used were:

Baitboat
Japan Longline South
Taiwan Longline North
Taiwan Longline South
U.S. Longline North
U.S. Longline South.

In addition, \(TAC_{t} = \pm 15\% TAC_{t-1}\) if the difference between \(TAC_{t}\) and \(TAC_{t-1}\) was larger than 15% and \(I_G < I_{ref}\).

5.2 Index-based

TAC for the next management period \(t\) is calculated as a function of the previous TAC (\(TAC_{t-1}\)):

\[TAC_t = \begin{cases} TAC_{t-1}, & \text{if }(1-\alpha) \leq I_{G} \leq (1+\alpha) \\ (1+\beta)TAC_{t-1}, & \text{if }I_{G} > (1+\alpha) \\ (1-\beta)TAC_{t-1}, & \text{if }I_{G} < (1-\alpha) \end{cases}\]

where we assumed \(\alpha=0.15\) and \(\beta=0.15\). In this case, \(I_{G}\) was calculated as:

\[I_G = exp(\frac{1}{n_i}\sum_{i}log(I^*_i))\]

where \(n_i\) is the number of selected indices of abundance and \(I^*_i\) was calculated for every selected index of abundance \(I_i\) using information from the last two years:

\[I^*_i = \frac{(I_{i,y-1}+I_{i,y-2})/2}{I_{ref}}\]

and \(I_{ref}=1\) (value in 2012, when \(SSB>SSB_{msy}\)). In addition, \(TAC_{t} = TAC_{max}\) when \(TAC_{t} > TAC_{max}\), assuming that \(TAC_{max} = 50,000\) tonnes. Also, \(TAC_{t} = \pm 15\% TAC_{t-1}\) if the difference between \(TAC_{t}\) and \(TAC_{t-1}\) was larger than 15%.

5.3 Model-based

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 7: Example of harvest control rule (HCR).

The management advice is given every three years (management period) and the total allowable catch (TAC) is derived from a harvest control rule (HCR, Figure 7).

In the HCR, \(F_{tgt}\) and \(B_{thr}\) need to be defined, and the following options were tested (Figure 8):

\(F_{tgt}=0.8F_{msy}\) and \(B_{thr}=B_{msy}\)
\(F_{tgt}=F_{msy}\) and \(B_{thr}=B_{msy}\)

Figure 8: Example of harvest control rule (HCR).

In addition, \(B_{lim}=0.4\times B_{msy}\) and \(F_{mim}=0.1\times F_{msy}\) for all cases. These MPs were divided into two groups, depending on the maximum allowed variation between \(TAC_{t}\) and \(TAC_{t-1}\):

Maximum increase or decrease of 10%
Maximum increase of 25% and decrease of 20%

6 Performance Indicators

15 PIs have been developed for the N-ALB MSE (Table 4) and are calculated in the simulation period. These PIs are grouped into four types:

Status: indicators related to stock status
Safety: indicators related to the probability of the stock not falling below the biological reference points
Yield: indicators related to the catch in the projection years
Stability: indicators related to the variation in the catches or TAC between management cycles

Each PI was calculated for every Reference OM (i.e., 400 PIs). Examples of each PI is given below.

Table 4: Performance indicators and description. These indicators were calculated from the simulation period.

Type	Metric	Symbol	Description
Status	Minimum spawner biomass relative to \(B_{msy}\)	\(minB\)	\(min(B_y/B_{msy})\)
Status	Mean spawner biomass relative to \(B_{msy}\)	\(meanB\)	\((\prod_y B_y/B_{msy})^{1/n_y}\)
Status	Mean fishing mortality relative to \(F_{msy}\)	\(meanF\)	\((\prod_y F_y/F_{msy})^{1/n_y}\)
Status	Probability of being in the Kobe green quadrant	\(PGK\)	Proportion of years in green quadrant (see Figure 7)
Status	Probability of being in the Kobe red quadrant	\(PRK\)	Proportion of years in red quadrant (see Figure 7)
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)	\(Cstr\)	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 25 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	\(PTcx\)	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	\(Tcmax\)	Maximum ratio of TAC change

6.1 Examples

6.1.1 Status

Figure 9: Status performance indicators. The blue dots or lines indicate the meaning of the metric. Find more details in Table 4.

6.1.2 Safety

Figure 10: Safety performance indicators. The blue dots indicate the meaning of the metric. Find more details in Table 4.

6.1.3 Yield

Figure 11: Yield performance indicators. The blue lines indicate the meaning of the metric. Find more details in Table 4.

6.1.4 Stability

Figure 12: Stability performance indicators. The blue lines, arrows, or dots indicate the meaning of the metric. Find more details in Table 4.

7 Glossary

Term	Definition
N-ALB	North Atlantic Albacore
OM	Operating model
CMP	Candidate management procedure
PI	Performance indicator
ALBSG	Albacore Species Group
SS3	Stock Synthesis 3 platform
ESS	Effective sample size
CAAL	Conditional age-at-length
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

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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

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Merino, G., De Bruyn, P., Scott, G.P., Kell, L., Arrizabalaga, H., 2014. A preliminary stock assessment for northern albacore using the fully integrated stock assessment model, MULTIFAN-CL (No. SCRS/2013/058). ICCAT (International Commission for the Conservation of Atlantic Tunas).

Merino, G., Kell, L., Arrizabalaga, H., Santiago, J., 2020. Updated consolidated report for North Atlantic albacore management strategy evaluation (No. SCRS/2020/153). ICCAT (International Commission for the Conservation of Atlantic Tunas).

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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

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