An evaluation of ABC and TAC projections for the Bering Sea and Aleutian Island groundfish
Introduction
Annual ABC and TAC decisions in the Bering Sea and Aleutian Islands (BSAI) groundfish fisheries set the management ceilings that balance conservation, stability, and economic planning. Multi-year advice provides predictable expectations, but it is built on forecasts that can change as new data arrive, which can create abrupt revisions in advice.
This work evaluates whether two-year model projections provide a meaningful improvement over a simple rollover of the previous year’s values. Quantifying when projections track final outcomes, and when they do not, helps interpret the reliability of advice, supports communication with stakeholders, and identifies where interim updates may add value.
This document compares final (lag 1) ABC and TAC values to their two-year projections (lag 2) using OY = 1 records. The seven main species listed above account for about 88% of total ABC, so most of the signal comes from them.
Methods
Data were compiled for the 1986–2025 period for the Bering Sea and Aleutian Islands (BSAI) region, consistent with the management framework described in the BSAI fishery management plan and the BSAI groundfish amendments action summary. The dataset includes ABCs, TACs, and OFLs set by management for the next year and the year after (lag 1 and lag 2). We first evaluated overall variability across the main stocks for both ABC and TAC, then examined patterns in the Pollock stock in more detail.
As an exploratory extension, we attempted to replace the ATTACH catch function with a DSEM-based approach that maps ABC inputs to expected TACs for key species while modeling cross-species dependence and temporal dynamics. This provides a direct comparison to the static SUR-style framework in ATTACH and helps assess whether a dynamic model can better replicate management outcomes.
Performance measures
For each species \(s\) and projection year \(t\), let \(X_{t,1}\) be the final (lag 1) value and \(X_{t,2}\) the two-year projection (lag 2), where \(X\) is either ABC or TAC. We computed percent differences as:
\[ \Delta X_{t} = \frac{X_{t,1} - X_{t,2}}{X_{t,2}}. \]
To keep ABC and TAC deltas on a common scale, TAC percent changes were scaled by the two-year ABC:
\[ \Delta TAC_{t} = \frac{TAC_{t,1} - TAC_{t,2}}{ABC_{t,2}}. \]
Absolute changes in thousand tons are:
\[ \Delta X_{t}^{(kt)} = \frac{X_{t,1} - X_{t,2}}{1000}. \]
Interannual variability was summarized using the coefficient of variation:
\[ CV(X) = \frac{sd(X)}{mean(X)}. \]
For the projection-versus-rollover comparison, we used absolute percent error against the final value:
\[ APE_{model}(X) = \frac{\lvert X_{t,1} - X_{t,2} \rvert}{X_{t,1}}, \quad APE_{roll}(X) = \frac{\lvert X_{t,1} - X_{t-1,1} \rvert}{X_{t,1}}. \]
Dynamic structural equation model setup
This section sets up a dynamic structural equation model (DSEM) using the dsem package. DSEMs blend structural equation modeling with state-space time-series dynamics to estimate both contemporaneous effects and temporal persistence, allowing mechanistic interpretation of multivariate ecological systems (Thorson et al. 2024). The dependent variables are TACs for Pollock and Pacific cod, and the independent variables are ABCs for all other species. The code below fits a parsimonious AR(1) structure for each TAC with contemporaneous ABC effects and shows how to generate expected TACs given new ABC inputs.
Seemingly unrelated regression (SUR) provides a useful static reference point for understanding dynamic structural equation models (DSEM). In SUR, multiple regression equations are estimated jointly, allowing for contemporaneous correlation among equation-specific error terms while excluding any dynamic feedback or causal coupling across outcomes (Zellner 1962). DSEM can be viewed as a strict generalization of this framework: correlated disturbances are retained, but are embedded within a dynamic state-space formulation that allows for autoregressive behavior, latent processes, and explicit structural pathways across variables and time (Asparouhov, Hamaker, and Muthén 2018). From this perspective, SUR corresponds to a single-time-slice, purely contemporaneous special case of DSEM in which temporal dependence and structural effects are suppressed. This connection clarifies how joint modeling gains efficiency through shared stochastic components, while DSEM extends that logic by separating persistent process variation from transient noise and propagating information forward through time.
In the BSAI context, the ATTACH model implemented in the catchfunction package uses a two-step regression workflow (ABC → TAC, then TAC → catch) with SUR linking TAC-stage errors across species, and an ensemble of alternative error structures in the catch stage to reflect correlated shocks and the ecosystem cap (Faig and Haynie 2020). This provides a static, cross-equation baseline that motivates the move to DSEM when temporal dynamics and lagged effects are of interest.
For clarity and understanding, we constructed similar log-log TAC~ABC regressions for the main stocks and pooled “Others”. Here, TACs for each stock were estimated statistically using a log-linear model. For \(j = 1, 2, \ldots, n\) stocks, the general model for stock \(i\) took the form:
\[ \ln(\mathrm{TAC}_{i,t}) = \alpha_i + \beta_i \ln(\mathrm{ABC}_{i,t}) + \sum_{j \ne i}^{n} \beta_{ij} \ln(\mathrm{ABC}_{j,t}) + \sum_{k=1}^{m} \beta_k I_{k,t} + \varepsilon_{i,t}. \]
where \(\alpha_i\) is the stock-specific intercept for species \(i\), \(\beta_i\) is the elasticity of the TAC of species \(i\) with respect to its own ABC, and \(\beta_{ij}\) is the elasticity for the ABC of species \(j \neq i\) in the TAC equation for species \(i\). The effect (\(\beta_k\)) of \(k = 1, 2, \ldots, m\) events or policy changes (e.g., changes in management, area closures, or implementation of catch share programs) on TAC was also estimated, where \(I_{k,t}\) is an indicator variable for event \(k\) in year \(t\), and \(\varepsilon_{i,t}\) denotes the residual error for the prediction in year \(t\).
Results
Variability across species
Figure 1 shows the interannual CVs for ABC and TAC. Pacific ocean perch has the highest ABC variability (CV about 0.95), while Pollock has the lowest TAC variability (CV about 0.12), indicating tighter management consistency for the largest stock.
BSAI Pollock
Pollock provides a clear example of how ABC, OFL, and TAC move together over time (see Figure 2). OFL generally sits above ABC, and TAC sits below ABC, with tighter TAC variability consistent with the low CV reported above.
Two-year vs final differences (percent)
Figure 3 summarizes the percent difference between final and two-year values, scaled by the two-year ABC to keep ABC and TAC deltas on the same scale. Across species, the average ABC adjustment is about 4.8%, while TAC adjustments are smaller at 2.4%. Atka mackerel has the largest positive mean ABC revision (13.0%), while Northern rock sole shows the only negative mean ABC adjustment (-1.7%); Pollock has the most negative mean TAC change (-3.7%).
Two-year vs final differences (kt)
The heatmaps in Figure 4 highlight the absolute magnitude of adjustments in thousands of tons. Large swings cluster in the biggest stocks (notably Pollock), while smaller species show less absolute movement even when percent changes are sizable.
The results shown in Figure 5 is provided to show contrast among other stocks with pollock removed.
Rollover scenario
To gauge a simple alternative, Figure 6 compares final values to a naive rollover that uses the previous year’s final value as the “projection.” The average rollover changes are small but positive (2.7% for ABC and 2.0% for TAC), suggesting a mild upward drift when viewed against a strict carry-forward baseline.
Projection vs rollover accuracy
Using the overlap period (2001 onward), we compared how close the two-year model projections (lag 2) and a naive rollover (previous year’s lag 1 value) came to the final values used (lag 1). On average, the model-based projections show slightly lower absolute percent error for ABC (13.1% vs 13.8%), and a similarly small improvement for TAC (11.5% vs 12.0%). However, the model is closer than the rollover in only 52% of ABC cases and 35% of TAC cases, and the mean advantage appears in 3 of 7 stocks for ABC and 4 of 7 stocks for TAC. This suggests there is enough information to compare the two approaches, but the performance edge of two-year projections over a rollover baseline is modest and uneven—more evident for ABC than for TAC. Table 1 summarizes the mean absolute percent errors by species for each approach.
| Species | ABC model | ABC rollover | ABC model - rollover | TAC model | TAC rollover | TAC model - rollover |
|---|---|---|---|---|---|---|
| Atka mackerel | 16.1% | 19.8% | -3.7% | 15.5% | 15.0% | 0.6% |
| Flathead sole | 5.5% | 5.5% | 0.0% | 17.3% | 17.7% | -0.4% |
| Northern rock sole | 17.7% | 18.4% | -0.7% | 10.7% | 10.7% | 0.0% |
| Pacific cod | 10.4% | 9.6% | 0.9% | 9.1% | 8.6% | 0.5% |
| Pacific ocean perch | 9.7% | 13.5% | -3.8% | 7.6% | 12.5% | -4.9% |
| Pollock | 18.0% | 17.0% | 1.0% | 8.4% | 7.1% | 1.3% |
| Yellowfin sole | 14.1% | 12.7% | 1.4% | 11.8% | 12.4% | -0.6% |
Projected vs used time series
Figure 7 contrasts the two-year projections with the final values used in the next year. The projected series are generally smoother, with the largest departures in higher-variability stocks (Pacific ocean perch and Flathead sole), which aligns with the elevated CVs in Figure 1.
TAC cross-species relationships
Figure 8 shows pairwise relationships among TAC values for the main species, with all remaining species pooled as “Others,” using points with a smooth fit in the lower triangle.
TAC-ABC regressions
As noted, we fit multiple regressions for the five main species (Pollock, Pacific cod, Yellowfin sole, Atka mackerel, Northern rock sole) and a pooled “Other” category comprising all remaining species. Each model uses log(ABC) for the focal stock, separate log(ABC) terms for each other stock group, and a centered year term to proxy policy indicators.
| n | Intercept | log(ABC) | Year (centered) | R2 | log(ABC Pollock) | log(ABC Yellowfin sole) | log(ABC Pacific cod) | log(ABC Atka mackerel) | log(ABC Northern rock sole) | log(ABC Other) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Pollock | 38 | 10.218 | 0.364 | −0.005 | 0.782 | NA | −0.016 | 0.034 | 0.025 | −0.067 | −0.079 |
| Yellowfin sole | 38 | 11.507 | 0.758 | 0.002 | 0.866 | −0.615 | NA | 0.166 | 0.014 | −0.132 | −0.050 |
| Pacific cod | 38 | 2.805 | 0.700 | 0.000 | 0.862 | 0.036 | −0.164 | NA | 0.071 | 0.151 | −0.027 |
| Atka mackerel | 38 | −7.435 | 0.543 | 0.008 | 0.709 | 0.375 | −0.008 | −0.363 | NA | 0.562 | 0.356 |
| Northern rock sole | 38 | 34.044 | 0.366 | 0.013 | 0.607 | −0.772 | −0.343 | 0.028 | −0.207 | NA | −0.787 |
| Other | 38 | 33.128 | −0.175 | 0.021 | 0.728 | −0.782 | −0.202 | −0.527 | −0.203 | 0.286 | NA |
DAGs for the DSEM
DSEM estimates
This DSEM estimates TAC dynamics for Pollock and Pacific cod with two components: (1) AR(1) persistence in each TAC time series and (2) contemporaneous influence of ABCs from the other species. The model is fit on scaled inputs for stability, then predictions are transformed back to the original TAC units for interpretation.
| Estimate | Std. Error | z | p | |
|---|---|---|---|---|
| ABC -> TAC | ||||
| ABC_Atka_mackerel -> TAC_Pacific_cod | 0.019 | 0.115 | 0.17 | 0.866 |
| ABC_Atka_mackerel -> TAC_Pollock | 0.183 | 0.126 | 1.45 | 0.146 |
| ABC_Atka_mackerel <-> ABC_Atka_mackerel | 0.932 | 0.104 | 8.95 | 0.000 |
| ABC_Flathead_sole -> TAC_Pacific_cod | −0.102 | 0.129 | −0.79 | 0.430 |
| ABC_Flathead_sole -> TAC_Pollock | −0.013 | 0.144 | −0.09 | 0.928 |
| ABC_Flathead_sole <-> ABC_Flathead_sole | 0.965 | 0.108 | 8.95 | 0.000 |
| ABC_Northern_rock_sole -> TAC_Pacific_cod | 0.309 | 0.147 | 2.10 | 0.036 |
| ABC_Northern_rock_sole -> TAC_Pollock | −0.442 | 0.168 | −2.63 | 0.008 |
| ABC_Northern_rock_sole <-> ABC_Northern_rock_sole | 0.934 | 0.104 | 8.96 | 0.000 |
| ABC_Pacific_ocean_perch -> TAC_Pacific_cod | 0.099 | 0.136 | 0.73 | 0.464 |
| ABC_Pacific_ocean_perch -> TAC_Pollock | −0.121 | 0.150 | −0.81 | 0.420 |
| ABC_Pacific_ocean_perch <-> ABC_Pacific_ocean_perch | 0.985 | 0.110 | 8.95 | 0.000 |
| ABC_Yellowfin_sole -> TAC_Pacific_cod | −0.370 | 0.125 | −2.96 | 0.003 |
| ABC_Yellowfin_sole -> TAC_Pollock | 0.024 | 0.140 | 0.17 | 0.866 |
| ABC_Yellowfin_sole <-> ABC_Yellowfin_sole | 0.892 | 0.100 | 8.96 | 0.000 |
| Autoregressive (lagged TAC) | ||||
| TAC_Pacific_cod -> TAC_Pacific_cod (lag 1) | 0.767 | 0.103 | 7.48 | 0.000 |
| TAC_Pollock -> TAC_Pollock (lag 1) | 0.590 | 0.110 | 5.38 | 0.000 |
| Other | ||||
| TAC_Pacific_cod <-> TAC_Pacific_cod | 0.570 | 0.064 | 8.92 | 0.000 |
| TAC_Pollock <-> TAC_Pollock | 0.635 | 0.071 | 8.93 | 0.000 |
Discussion
Projection updates under new data and assessment
Multi-year catch advice inevitably embeds a forecasting problem: projections are conditioned on assumptions about future recruitment, selectivity, mortality, and implementation error, all frozen at the time advice is issued (Mid-Atlantic Fishery Management Council 2012; International Council for the Exploration of the Sea (ICES) 2023). The literature above converges on a shared observation: when a new assessment assimilates additional data, the posterior state of the stock can shift abruptly relative to those earlier projections (Sánchez-Maroño, Dolder, and Needle 2021). The impact of updating data and assessment creates a discontinuity and reflects the consequence of evolving data streams and analyses.
Interim management procedure (MP) work reframes the problem by explicitly separating assessment cadence from advice cadence (Huynh et al. 2020; Klibansky et al. 2022). Rather than treating interim updates as ad-hoc corrections, these approaches formalize how limited new information (recent catches, survey indices, environmental indicators) should update catch advice between full assessments. The goal is not to eliminate snap—information shocks are unavoidable—but to bound it, so that revisions are predictable, explainable, and risk-consistent.
This framing is directly relevant to BSAI groundfish, where large stocks (pollock, cod, flatfish) dominate total ABC and where management stability is highly valued. Multi-year ABCs smooth year-to-year variability, but smoothing pushes uncertainty forward in time. When a subsequent assessment revises recruitment trajectories or selectivity patterns, the resulting adjustment can appear disproportionate relative to the modest interim changes that preceded it. The Canadian and U.S. guidance documents emphasize that this tension is intrinsic: stability and responsiveness trade off, and neither can be maximized simultaneously (Krohn et al. 2019; Mid-Atlantic Fishery Management Council 2012; South Atlantic Scientific and Statistical Committee 2022).
The ICES and MSE-oriented literature adds an important synthesis (International Council for the Exploration of the Sea (ICES) 2023). Geromont and Butterworth (Geromont and Butterworth 2015) and Walter et al. (Walter et al. 2023) show that systems relying on simple, pre-tested update rules often experience smaller and more interpretable snaps than systems that defer all learning to infrequent, high-dimensional assessments. In that sense, forecast-to-assimilation snap is best understood as a design property of the advice system, not merely an outcome of assessment error. For BSAI groundfish, this perspective motivates explicit evaluation of how multi-year projections, rollover rules, and interim updates distribute learning over time—shaping not only biological risk, but also the credibility and usability of scientific advice.
References
Asparouhov, Tihomir, Ellen L. Hamaker, and Bengt O. Muthén. 2018. “Dynamic Structural Equation Models.” Structural Equation Modeling 25 (3): 359–88. https://doi.org/10.1080/10705511.2017.1406803.
Faig, Amanda, and Alan Haynie. 2020. The ATTACH Model (Catchfunction Package) Vignette. https://github.com/amandafaig/catchfunction/blob/master/doc/ATTACH_vignette.pdf.
Geromont, H. F., and D. S. Butterworth. 2015. “Complex Assessments or Simple Management Procedures for Efficient Fisheries Management.” ICES Journal of Marine Science 72: 262–74. https://doi.org/10.1093/icesjms/fsu017.
Huynh, Q. C., A. E. Punt, T. R. Carruthers, and C. M. Dichmont. 2020. “The Interim Management Procedure Approach for Assessed Stocks: Responsive Management Advice and Lower Assessment Frequency.” Fish and Fisheries 21 (3): 663–79. https://doi.org/10.1111/faf.12453.
International Council for the Exploration of the Sea (ICES). 2023. “ICES Advice Framework and Advice Sheets.” International Council for the Exploration of the Sea. https://doi.org/10.17895/ices.advice.22116890.
Klibansky, Nikolai, Cassidy Peterson, Kyle Shertzer, Matthew Vincent, and Erik Williams. 2022. “Evaluating Procedures for Updating Catch Advice Between Stock Assessments of Reef Fishes with Management Strategy Evaluation.” NOAA Technical Memorandum NMFS-SEFSC-779. Washington, DC: National Oceanic; Atmospheric Administration, National Marine Fisheries Service, Southeast Fisheries Science Center. https://doi.org/10.25923/7q4k-0b32.
Krohn, M. M., G. Chaput, D. E. Duplisea, N. M. T. Duprey, A. M. Edwards, B. P. Healey, K. L. Howland, B. Lester, M. J. Morgan, and R. F. Tallman. 2019. “Guidelines for Providing Interim-Year Updates and Science Advice for Multi-Year Assessments.” DFO Canadian Science Advisory Secretariat Research Document 2018/035. Ottawa, ON: Fisheries; Oceans Canada. https://publications.gc.ca/collections/collection_2019/mpo-dfo/fs70-5/Fs70-5-2018-035-eng.pdf.
Mid-Atlantic Fishery Management Council. 2012. “Considerations for Setting Multi-Year Acceptable Biological Catch Limits.” Mid-Atlantic Fishery Management Council. https://www.mafmc.org/s/multi-year-ABC-considerations-3-11-12.pdf.
Sánchez-Maroño, S., P. J. Dolder, and C. L. Needle. 2021. “Effects of Advice Lag and Update Frequency on Fisheries Management Performance.” ICES Journal of Marine Science 78: 2495–2507.
South Atlantic Scientific and Statistical Committee. 2022. “Catch Level Projections Workgroup Report.” SEDAR.
Thorson, J. T., A. Andrews, T. Essington, and S. Large. 2024. “Dynamic Structural Equation Models Synthesize Ecosystem Dynamics Constrained by Ecological Mechanisms.” Methods in Ecology and Evolution. https://doi.org/10.1111/2041-210X.14289.
Walter, J. F., A. E. Punt, R. I. C. C. Francis, et al. 2023. “When to Conduct, and When Not to Conduct, Management Strategy Evaluation.” Fish and Fisheries 24: 1–18.
Zellner, Arnold. 1962. “An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias.” Journal of the American Statistical Association 57 (298): 348–68. https://doi.org/10.1080/01621459.1962.10480664.