Jack Mackerel Assessment SCW16
SPRFMO
South Pacific Regional Fisheries Management Organisation
Jack Mackerel Working Group
Jack Mackerel Assessment SCW16
This focused report summarizes the completed SCW16 model outputs for the SC13 baseline (0.00), the current final model (0.12), the 2018 Peruvian CPUE catchability-break sensitivity (0.13), the data sensitivities completed so far (1.01-1.04), and the additional SC13 downweighting sensitivity (SC13_1.15). Two additional diagnostic trials (1.05 and 1.06) are shown separately from the data sensitivities under “Other trials.” ADNUTS MCMC diagnostics for the final 0.12 configuration are included for the single-stock and two-stock hypotheses.
1 Model Set
| Model | Role | Description |
|---|---|---|
| 0.00 | SC13 baseline | Baseline SC13 framing for the single-stock and two-stock hypotheses. |
| 0.12 | Final model | Current final bridging configuration; as 0.11 but with the DEPM abundance-index series removed. |
| 0.13 | Catchability sensitivity | As 0.12 but adds a 2018 catchability break for the Peruvian CPUE index. |
| 1.01 | Data sensitivity | As 0.12 but replaces `Chile_CPUE` with the 0.00 Chilean CPUE series. |
| 1.02 | Data sensitivity | As 0.12 but replaces `Peru_CPUE` with the 0.00 Peruvian CPUE series. |
| 1.03 | Data sensitivity | As 0.12 but drops `Peru_Acoust_S1` and `Peru_Acoust_S2`. |
| 1.04 | Data sensitivity | As 1.03 but adds the old 0.00 `Peru_Acoustic` index, with selectivity tied to the FarNorth fishery. |
| 1.05 | Other trial | As 0.12 but replaces `Peru_CPUE` with a noisy (CV = 60%) nominal CPUE series for 1990-2025. |
| 1.06 | Other trial | As 1.05 but removes `Peru_Acoust_S1` and `Peru_Acoust_S2`. |
| SC13_1.15 | SC13 sensitivity | Additional SC13 run that fully downweights the Acoustic N and Peruvian CPUE index series across all years. |
You’ll need to be in the jjm/assessment directory in order for the code here to run.
2 Updated Data
2.1 Datasets
3 Fit Summaries
The fit summaries are useful for checking convergence and for comparing runs that share the same data and likelihood structure. Several rows in this table intentionally change the data configuration, so negative log-likelihood values should not be interpreted as a strict ranking across all models.
| Hypothesis | Model | Run | N parameters | NLL | Max gradient |
|---|---|---|---|---|---|
| h1 | 0.00 | h1_0.00 | 1865 | 1323.818 | 0.0002112 |
| h1 | 0.12 | h1_0.12 | 1871 | 3820.555 | 0.0003189 |
| h1 | 0.13 | h1_0.13 | 1872 | 3768.890 | 0.0002346 |
| h1 | 1.01 | h1_1.01 | 1871 | 3811.122 | 0.0002282 |
| h1 | 1.02 | h1_1.02 | 1871 | 3831.319 | 0.0002985 |
| h1 | 1.03 | h1_1.03 | 1843 | 1306.689 | 0.0002805 |
| h1 | 1.04 | h1_1.04 | 1844 | 1354.092 | 0.0003000 |
| h1 | SC13_1.15 | h1_1.15 | 1865 | 1166.248 | 0.0002013 |
| h2 | 0.00 | h2_0.00 | 1648 | 1249.606 | 0.0002636 |
| h2 | 0.12 | h2_0.12 | 1932 | 2712.406 | 0.0001995 |
| h2 | 0.13 | h2_0.13 | 1933 | 2680.857 | 0.0002882 |
| h2 | 1.01 | h2_1.01 | 1932 | 2699.890 | 0.0003842 |
| h2 | 1.02 | h2_1.02 | 1932 | 2692.811 | 0.0002865 |
| h2 | 1.03 | h2_1.03 | 1904 | 1275.404 | 0.0004646 |
| h2 | 1.04 | h2_1.04 | 1905 | 1311.022 | 0.0002846 |
| h2 | SC13_1.15 | h2_1.15 | 1648 | 1049.019 | 0.0002749 |
4 Terminal-Year Metrics
| Hypothesis | Model | Stock | Year | SSB | Total biomass | Recruitment | Max total F at age |
|---|---|---|---|---|---|---|---|
| h1 | 0.00 | Stock_1 | 2025 | 15183 | 21807 | 17018 | 0.589 |
| h1 | 0.12 | Stock_1 | 2025 | 3211 | 6342 | 10667 | 2.462 |
| h1 | 0.13 | Stock_1 | 2025 | 4118 | 7541 | 11115 | 2.601 |
| h1 | 1.01 | Stock_1 | 2025 | 3342 | 6471 | 10365 | 1.064 |
| h1 | 1.02 | Stock_1 | 2025 | 5998 | 9922 | 11610 | 3.061 |
| h1 | 1.03 | Stock_1 | 2025 | 5187 | 8917 | 12005 | 2.074 |
| h1 | 1.04 | Stock_1 | 2025 | 5223 | 8955 | 11927 | 2.109 |
| h1 | SC13_1.15 | Stock_1 | 2025 | 4675 | 8081 | 9536 | 0.837 |
| h2 | 0.00 | Stock_1 | 2025 | 11075 | 16426 | 15257 | 0.596 |
| h2 | 0.00 | Stock_2 | 2025 | 936 | 1507 | 1118 | 0.483 |
| h2 | 0.12 | Stock_1 | 2025 | 6719 | 11510 | 21317 | 2.212 |
| h2 | 0.12 | Stock_2 | 2025 | 37 | 277 | 444 | 37.232 |
| h2 | 0.13 | Stock_1 | 2025 | 6719 | 11510 | 21317 | 2.212 |
| h2 | 0.13 | Stock_2 | 2025 | 37 | 282 | 445 | 6.176 |
| h2 | 1.01 | Stock_1 | 2025 | 7973 | 13164 | 22503 | 0.694 |
| h2 | 1.01 | Stock_2 | 2025 | 37 | 277 | 444 | 37.232 |
| h2 | 1.02 | Stock_1 | 2025 | 6719 | 11510 | 21317 | 2.212 |
| h2 | 1.02 | Stock_2 | 2025 | 34 | 277 | 445 | 7.674 |
| h2 | 1.03 | Stock_1 | 2025 | 6719 | 11510 | 21317 | 2.212 |
| h2 | 1.03 | Stock_2 | 2025 | 253 | 634 | 979 | 8.301 |
| h2 | 1.04 | Stock_1 | 2025 | 6719 | 11510 | 21317 | 2.212 |
| h2 | 1.04 | Stock_2 | 2025 | 1083 | 1747 | 1420 | 0.292 |
| h2 | SC13_1.15 | Stock_1 | 2025 | 4596 | 7841 | 9432 | 0.748 |
| h2 | SC13_1.15 | Stock_2 | 2025 | 766 | 1269 | 948 | 1.062 |
| Hypothesis | Model | Stock | Year | SSB (%) | Total biomass (%) | Recruitment (%) | Max total F at age (%) |
|---|---|---|---|---|---|---|---|
| h1 | 0.00 | Stock_1 | 2025 | 372.8 | 243.8 | 59.5 | -76.1 |
| h1 | 0.12 | Stock_1 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h1 | 0.13 | Stock_1 | 2025 | 28.2 | 18.9 | 4.2 | 5.6 |
| h1 | 1.01 | Stock_1 | 2025 | 4.1 | 2.0 | -2.8 | -56.8 |
| h1 | 1.02 | Stock_1 | 2025 | 86.8 | 56.4 | 8.8 | 24.3 |
| h1 | 1.03 | Stock_1 | 2025 | 61.5 | 40.6 | 12.5 | -15.7 |
| h1 | 1.04 | Stock_1 | 2025 | 62.6 | 41.2 | 11.8 | -14.3 |
| h1 | SC13_1.15 | Stock_1 | 2025 | 45.6 | 27.4 | -10.6 | -66.0 |
| h2 | 0.00 | Stock_1 | 2025 | 64.8 | 42.7 | -28.4 | -73.1 |
| h2 | 0.00 | Stock_2 | 2025 | 2418.0 | 444.4 | 151.8 | -98.7 |
| h2 | 0.12 | Stock_1 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 0.12 | Stock_2 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 0.13 | Stock_1 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 0.13 | Stock_2 | 2025 | 0.2 | 2.0 | 0.1 | -83.4 |
| h2 | 1.01 | Stock_1 | 2025 | 18.7 | 14.4 | 5.6 | -68.6 |
| h2 | 1.01 | Stock_2 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 1.02 | Stock_1 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 1.02 | Stock_2 | 2025 | -8.9 | 0.2 | 0.2 | -79.4 |
| h2 | 1.03 | Stock_1 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 1.03 | Stock_2 | 2025 | 580.9 | 129.0 | 120.3 | -77.7 |
| h2 | 1.04 | Stock_1 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 1.04 | Stock_2 | 2025 | 2811.2 | 531.3 | 219.6 | -99.2 |
| h2 | SC13_1.15 | Stock_1 | 2025 | -31.6 | -31.9 | -55.8 | -66.2 |
| h2 | SC13_1.15 | Stock_2 | 2025 | 1960.5 | 358.5 | 113.3 | -97.1 |
5 0.00 to 0.12 Bridge
Model 0.12 is the current final bridge configuration used for model diagnostics. The plots below compare 0.12 to the 0.00 SC13 baseline for each stock-structure hypothesis.
5.1 Single-Stock Hypothesis
5.2 Two-Stock Hypothesis
6 Final Model Diagnostics
The diagnostics below use model 0.12 as the current final model. Retrospective diagnostics use the standard five peels that have already been run.
6.1 Single-Stock Hypothesis
For the single-stock final model, the diagnostics are interpreted as evidence about the internally aggregated stock trajectory. The main diagnostic tension is expected in recent composition and index data because the final bridge configuration removes DEPM and relies on the remaining fishery, acoustic, and CPUE information to resolve the recent scale and age/length structure.
The index fits provide the primary check on whether the final model follows the retained abundance-index signals after dropping DEPM. The single-stock model fits a common population trajectory to all retained indices, so departures among individual series should be read as conflicts in relative scale and timing rather than as stock-specific deviations.
The catchability time series show the fitted q path used to scale vulnerable biomass to each retained abundance index. Step changes identify indices with block-specific or time-varying catchability estimates, while flat segments indicate periods sharing the same catchability estimate.
The selectivity plots show the time-varying age pattern that links each fishery and survey/index series to the modeled population. For the single-stock model, the fishery panel shows the strongest temporal changes in the FarNorth and Chilean fisheries, while the survey/index panel shows the selectivity assumptions used for acoustic and CPUE index observations. These plots are included as selectivity diagnostics; CPUE series remain relevant here even though CPUE age weights are not treated as age-composition fits below.
The fishery age-composition plots show the final model tracking the main modal shifts in the Chilean and offshore-trawl age data. The corrected ggplot panels keep each fishery separate; this avoids mixing the northern Chile, south-central Chile purse-seine, and offshore-trawl observations and makes the recent modal ages easier to compare among fleets.
The OSA and aggregate age-composition diagnostics summarize the non-CPUE age-composition fits at a coarser level. They include the fishery age compositions and the acoustic-survey age compositions available in the final model output, such as the central-south and northern Chile acoustic series. CPUE-index age weights are excluded here because they are not interpreted as age-composition observations for this diagnostic.
The FarNorth fishery length-composition panels now use the same observed-point and predicted-line style as the age fits. This makes the model fit to the long FarNorth length series easier to scan by year, particularly in years with narrow observed modes or sparse tails.
The Peru acoustic length-composition panels show the fit to the new seasonal Peru acoustic length data. These are survey length compositions rather than fishery compositions, so they are shown separately from the FarNorth fishery length series; this distinction is important because the Peru acoustic series also enter the abundance-index sensitivity tests.
The length-composition OSA and aggregate diagnostics combine the FarNorth fishery, which represents the Peruvian/FarNorth fishery length data in the model output, with the two seasonal Peru acoustic length-composition series. These diagnostics show whether the broad residual pattern is concentrated in the fishery length data or in one of the acoustic-season series after the year-by-year panels are collapsed.
The retrospective SSB plot checks whether recent biomass estimates are stable when terminal years are peeled from the assessment. Any systematic peel pattern would indicate that the final years are exerting leverage on the single-stock biomass scale.
The retrospective recruitment plot provides the corresponding check for year-class estimates. Recruitment peels are expected to be more variable than biomass peels, but persistent directional changes would be evidence that recent data are revising the estimated strength of terminal cohorts.
6.2 Two-Stock Hypothesis
For the two-stock final model, diagnostics are interpreted by stock. The southern stock carries the age-composition information, while the FarNorth stock carries the FarNorth fishery and Peru acoustic length-composition information. This split is important when comparing the diagnostic behavior with the data sensitivities because several sensitivity runs affect the FarNorth stock without changing the southern-stock trajectory.
The two-stock index fits show how the final model partitions retained abundance indices between the southern and FarNorth stocks. The FarNorth index behavior is especially important because the terminal 0.12 run estimates very low FarNorth spawning biomass and high fishing mortality.
The two-stock catchability time series show which abundance-index catchability estimates apply to each stock. This panel is useful for checking whether the final configuration is using fixed or stepped catchability paths for the southern-stock and FarNorth-stock indices.
The two-stock selectivity plots separate the southern-stock fleets from the FarNorth fishery and survey/index selectivities. The fishery panel emphasizes the different selectivity structure assigned to the southern Chilean/offshore fisheries and the FarNorth fishery, while the survey/index panel shows the corresponding acoustic and CPUE selectivity patterns used by the retained abundance indices. The Peru acoustic selectivity appears in the survey/index panel, and its length-composition fits are shown separately for the FarNorth stock below.
The age-composition diagnostics for the two-stock model apply to the southern stock. The same fleet-specific ggplot display is used here as in the single-stock model, which makes differences in modal age and tail behavior among the southern-stock fisheries easier to identify.
The OSA and aggregate age-composition diagnostics for the two-stock model summarize the southern-stock non-CPUE age-composition residuals. They retain the fishery age compositions and the Chilean acoustic-survey age compositions available for the southern stock, while excluding CPUE-index age weights. These diagnostics are complementary to the year-by-year age panels because they show whether residual departures are broadly distributed or concentrated in specific fleets, surveys, or ages.
The FarNorth fishery length-composition diagnostics are shown on stock 2 for the two-stock model. These fits are central to evaluating the FarNorth component because the FarNorth terminal biomass and fishing mortality are highly sensitive to the treatment of Peruvian data.
The Peru acoustic length-composition panels are also shown on stock 2 for the two-stock model. They provide a direct check on the seasonal Peru acoustic length data that are removed in 1.03 and replaced with the older Peru acoustic configuration in 1.04.
The FarNorth-stock length-composition OSA and aggregate diagnostics combine the FarNorth fishery with Peru_Acoust_S1 and Peru_Acoust_S2. These are the length-composition sources that directly inform the FarNorth stock in the two-stock model, so the panel provides a compact check on whether residual structure is driven mainly by the fishery data or by either seasonal Peru acoustic survey series.
The two-stock retrospective SSB plot should be read by stock because peel behavior can differ between the southern and FarNorth components. The FarNorth trajectory is the key diagnostic target given the low terminal biomass in 0.12 and the sensitivity of that result to Peru acoustic data treatment.
The two-stock recruitment retrospectives evaluate whether recent year-class estimates are stable under the same five peels. As with biomass, the FarNorth recruitment estimates should be interpreted alongside the data sensitivities because the composition and abundance-index information for that stock is more limited and more influential.
7 0.13 Catchability-Break Diagnostics
Model 0.13 is the deterministic sensitivity that starts from the final 0.12 bridge configuration and adds a 2018 catchability break for the Peruvian CPUE index. The diagnostics in this section are included to evaluate how that catchability change affects the fitted index scaling, selectivity, and composition residual patterns. No ADNUTS MCMC diagnostics are included for 0.13, and retrospective diagnostics are not shown because the 0.13 retrospective peels have not been run.
7.1 Single-Stock Hypothesis
For the single-stock hypothesis, 0.13 changes the way the Peruvian CPUE index is scaled after 2018 while retaining the same underlying data structure as 0.12. The diagnostic emphasis is therefore on whether the catchability break relaxes the recent Peruvian CPUE conflict without creating new residual structure in the retained age- and length-composition data.
The single-stock index-fit panel checks whether the 2018 catchability break improves the recent Peruvian CPUE fit while preserving the broader fit to the acoustic and other CPUE indices. Because the single-stock model has one aggregate biomass trajectory, any improvement in the Peruvian CPUE fit should be interpreted together with the other retained index series.
The catchability panel is the primary diagnostic for 0.13. It shows the fitted catchability paths for each abundance index and makes the 2018 Peruvian CPUE break visible as a step change rather than as a change in the observed data.
The selectivity diagnostics provide a check that the 0.13 change is confined to index catchability scaling and does not imply a different interpretation of fishery or survey/index vulnerable biomass through selectivity. The fishery and survey/index panels should therefore be read alongside the catchability panel.
The fishery age-composition diagnostics check whether the 0.13 index-scaling change materially affects the age-fit patterns for the Chilean and offshore-trawl fisheries. These panels should remain broadly comparable with 0.12 because the composition data and selectivity structure are unchanged.
The age OSA and aggregate diagnostics summarize the non-CPUE age-composition residuals for the 0.13 single-stock run. CPUE index age weights are excluded from this diagnostic for the same reason as in the final-model diagnostics: they are not interpreted as age-composition observations here.
The FarNorth fishery length-composition panels provide the closest composition check on whether the Peruvian CPUE catchability break changes the recent FarNorth signal in a way that conflicts with the fishery length data.
The Peru acoustic length-composition diagnostics are retained for 0.13 because the catchability-break run keeps the two seasonal Peru acoustic series in the model. These panels help separate residual behavior in the Peru acoustic length data from the Peruvian CPUE catchability treatment.
The length-composition OSA and aggregate diagnostics combine the FarNorth fishery and the two seasonal Peru acoustic length series. This provides a compact check on whether the 0.13 catchability treatment leaves the same broad length-residual pattern as the final 0.12 run.
7.2 Two-Stock Hypothesis
For the two-stock hypothesis, the 0.13 change is most directly relevant to the FarNorth stock because the Peruvian CPUE index informs that component. The diagnostics below therefore emphasize whether the catchability break reduces the extreme recent Peruvian CPUE leverage while keeping the southern-stock diagnostics comparable with the final 0.12 configuration.
The two-stock index-fit panel shows how the retained abundance indices are partitioned between the southern and FarNorth stocks. The key comparison for 0.13 is whether the Peruvian CPUE index can be fit with a post-2018 catchability shift without requiring the FarNorth biomass trajectory to absorb the full recent index change.
The catchability panel is the central two-stock diagnostic for 0.13. It shows the Peruvian CPUE catchability break in the context of the other retained survey and CPUE catchability paths, including the indices assigned to the FarNorth stock.
The two-stock selectivity diagnostics check whether the southern and FarNorth selectivity patterns remain consistent with the intended 0.13 change. The fishery panel separates the FarNorth fishery from the southern fisheries, while the survey/index panel shows the index selectivity assumptions retained under the catchability-break run.
The two-stock age-composition diagnostics are shown for the southern stock. Because the 0.13 change targets the Peruvian CPUE index, these age-composition panels are expected to remain close to the final 0.12 southern-stock diagnostics.
The southern-stock age OSA and aggregate diagnostics summarize the non-CPUE age-composition residuals for 0.13. They provide a check that the FarNorth-oriented catchability change does not introduce a new broad residual pattern in the southern-stock age data.
The FarNorth fishery length-composition diagnostics are central for the two-stock 0.13 run because the Peruvian CPUE catchability break changes the scaling of an index that informs the same FarNorth component as the fishery length data.
The Peru acoustic length-composition panels remain part of the 0.13 diagnostics because both seasonal Peru acoustic series are retained. These panels help distinguish the Peruvian CPUE catchability signal from any residual structure in the acoustic length observations.
The FarNorth length OSA and aggregate diagnostics combine the FarNorth fishery and the two seasonal Peru acoustic length series. This diagnostic checks whether the catchability break changes the broad length-residual pattern in the FarNorth stock while keeping the same composition sources as 0.12.
8 ADNUTS MCMC Diagnostics
ADNUTS was run for the final 0.12 configuration under both stock-structure hypotheses using four chains and 1,000 iterations per chain, with 500 warmup and 500 post-warmup iterations. These diagnostics are intended to check posterior sampling behavior for the final deterministic configuration, not to compare alternative data sensitivities.
h1_0.12 single-stock produced 2,000 post-warmup draws, with 0 divergences, 0 maximum-tree-depth hits, maximum Rhat of 1.040, minimum bulk ESS of 106, and median bulk ESS of 1554. h2_0.12 two-stock produced 2,000 post-warmup draws, with 0 divergences, 0 maximum-tree-depth hits, maximum Rhat of 1.080, minimum bulk ESS of 54, and median bulk ESS of 1566. Both runs had zero post-warmup divergences and zero post-warmup maximum-tree-depth hits, so the short runs did not show the clearest NUTS geometry failures. The Rhat and ESS diagnostics are still not fully satisfactory: the single-stock run shows mild residual mixing concerns concentrated in fishing-mortality and recruitment-deviation parameters, while the two-stock run shows stronger mixing concerns in fishery-selectivity parameters. These MCMC results should therefore be read as diagnostics of the final model configuration rather than as final posterior summaries for inference.
The pair and trace plots focus on the parameters with the highest Rhat values from each run, so they deliberately emphasize the parameters most likely to reveal mixing problems.
| Model | Chains | Iterations | Warmup | Post-warmup per chain | Divergences | Max treedepth hits | Max Rhat | Min bulk ESS | Median bulk ESS |
|---|---|---|---|---|---|---|---|---|---|
| h1_0.12 single-stock | 4 | 1000 | 500 | 500 | 0 | 0 | 1.04 | 106 | 1554 |
| h2_0.12 two-stock | 4 | 1000 | 500 | 500 | 0 | 0 | 1.08 | 54 | 1566 |
| Model | Parameter | Bulk ESS | Rhat |
|---|---|---|---|
| h1_0.12 single-stock | fmort[180] | 106 | 1.018 |
| h1_0.12 single-stock | fmort[181] | 106 | 1.019 |
| h1_0.12 single-stock | fmort[12] | 120 | 1.027 |
| h1_0.12 single-stock | fmort[179] | 123 | 1.014 |
| h1_0.12 single-stock | fmort[31] | 124 | 1.020 |
| h1_0.12 single-stock | fmort[14] | 125 | 1.026 |
| h1_0.12 single-stock | fmort[67] | 125 | 1.022 |
| h1_0.12 single-stock | fmort[68] | 126 | 1.023 |
| h1_0.12 single-stock | fmort[13] | 127 | 1.025 |
| h1_0.12 single-stock | rec_dev[11] | 129 | 1.031 |
| h2_0.12 two-stock | log_selcoffs_fsh[4][173] | 54 | 1.080 |
| h2_0.12 two-stock | log_selcoffs_fsh[4][155] | 56 | 1.075 |
| h2_0.12 two-stock | log_selcoffs_fsh[4][145] | 57 | 1.078 |
| h2_0.12 two-stock | log_selcoffs_fsh[4][146] | 58 | 1.076 |
| h2_0.12 two-stock | log_selcoffs_fsh[4][154] | 65 | 1.066 |
| h2_0.12 two-stock | log_selcoffs_fsh[4][163] | 65 | 1.069 |
| h2_0.12 two-stock | log_selcoffs_fsh[4][172] | 65 | 1.072 |
| h2_0.12 two-stock | log_selcoffs_fsh[4][181] | 70 | 1.064 |
| h2_0.12 two-stock | log_selcoffs_fsh[4][136] | 71 | 1.070 |
| h2_0.12 two-stock | log_selcoffs_fsh[4][127] | 72 | 1.066 |
The single-stock MCMC diagnostics should be read as a check on the aggregate-stock final model. The trace and pair plots emphasize the highest-Rhat monitored parameters; stable trace overlap across chains indicates adequate mixing for the most diagnostic subset of monitored parameters, while tree-depth hits indicate where NUTS required long trajectories even when chains otherwise mixed.
The two-stock MCMC diagnostics are especially important for the FarNorth component because the deterministic 0.12 result estimates very low terminal FarNorth biomass and high fishing mortality. The selected pair and trace diagnostics therefore provide a practical check on whether the posterior sampling is showing clear non-mixing in the parameters most flagged by Rhat and ESS.
9 Data Sensitivities
These sensitivities all start from the 0.12 final bridge configuration, except 1.04, which starts from 1.03 and adds back the old Peru_Acoustic series from 0.00. Model 0.13 keeps the 0.12 data and adds only a 2018 catchability break for the Peruvian CPUE index. The terminal-year metric and percent-difference tables are provided near the beginning of the report and are not repeated here.
SC13_1.15 is included as an additional SC13-style sensitivity. It fully downweights the Acoustic N and Peruvian CPUE index series across all years, effectively removing their likelihood contribution rather than only reducing the influence of terminal-year observations. The run should therefore be interpreted as a diagnostic of how strongly those two complete index series affect the final-year stock status and fishing mortality pattern rather than as a competing final-model configuration.
9.1 Single-Stock Hypothesis
Under the single-stock hypothesis, the sensitivities retain the broad increase in biomass after the mid-2010s but differ in the magnitude of the rebuilding signal. Adding the 2018 Peruvian CPUE catchability break (0.13) raises terminal biomass relative to 0.12, but less than replacing the Peruvian CPUE (1.02) or dropping the two Peru acoustic series (1.03). Replacing the Chilean CPUE series (1.01) leaves terminal biomass close to 0.12, while adding the old Peru acoustic series back in 1.04 leaves the single-stock trajectory close to 1.03, indicating that the larger single-stock biomass response is driven mainly by removal of the two seasonal Peru acoustic series rather than by the replacement index itself. The SC13 downweighting sensitivity (SC13_1.15) is intermediate: terminal biomass is above 0.12 but below 1.02-1.04.
The biomass panel shows the strongest separation among single-stock sensitivities after about 2015. 1.02, 1.03, and 1.04 all imply a higher recent biomass trajectory than the final model, whereas 1.01 remains close to 0.12. The 0.13 catchability-break sensitivity and SC13_1.15 both give moderate upward shifts.
Recent recruitment remains elevated relative to the preceding low period across all single-stock sensitivities. The Peruvian CPUE and Peru acoustic sensitivities (1.02-1.04) produce somewhat higher terminal recruitment than 0.12; 0.13 is only slightly higher than the final model, while SC13_1.15 gives lower terminal recruitment despite its higher terminal biomass.
The fishing-mortality response is not monotonic with biomass. 1.01 reduces terminal fishing mortality relative to 0.12, 0.13 and 1.02 increase it, and 1.03-1.04 remain slightly below the final model but above the Chilean CPUE replacement. This indicates that the data substitutions and catchability treatment affect both scale and recent selectivity/catch-at-age reconciliation, not only biomass level.
9.2 Two-Stock Hypothesis
Under the two-stock hypothesis, the southern stock is insensitive to the FarNorth-only data changes in 0.13 and 1.02-1.04, so its biomass, recruitment, and fishing mortality trajectories remain essentially the same as 0.12 in those runs. The FarNorth stock is much more sensitive: the 2018 Peruvian CPUE catchability break (0.13) leaves terminal biomass near the final-model level but reduces terminal fishing mortality, removing the most extreme terminal-F behavior without changing the biomass scale. Removing the two Peru acoustic series (1.03) raises FarNorth biomass from the very low final-model level, and adding back the old Peru acoustic series (1.04) produces the largest FarNorth terminal biomass and the lowest terminal fishing mortality among the data sensitivities. The SC13 downweighting sensitivity (SC13_1.15) reduces southern-stock biomass relative to 0.12 while raising FarNorth biomass well above the final model but below 1.04.
The biomass panel highlights the stock-specific nature of the sensitivity results. Southern-stock biomass changes mainly under 1.01 and SC13_1.15, whereas the FarNorth biomass trajectory is controlled by the Peru acoustic/CPUE treatment and is much higher in 1.03, 1.04, and SC13_1.15 than in 0.12. The 0.13 catchability-break run stays close to the final-model FarNorth biomass trajectory.
Recruitment follows the same split. Southern-stock recruitment is unchanged for 0.13 and 1.02-1.04 but is lower under SC13_1.15; FarNorth recruitment increases when the seasonal Peru acoustic series are removed or replaced, with 1.04 giving the highest FarNorth terminal recruitment among the current data sensitivities. The 0.13 catchability-break run leaves terminal FarNorth recruitment close to 0.12.
FarNorth fishing mortality is the clearest diagnostic contrast among the two-stock sensitivities. The final model estimates very high terminal FarNorth fishing mortality, while 0.13, 1.02, 1.03, and especially 1.04 reduce that estimate. The 0.13 result indicates that allowing a 2018 catchability break in the Peruvian CPUE index can reduce the extreme terminal-F estimate even when terminal FarNorth biomass remains close to 0.12. SC13_1.15 also moves FarNorth fishing mortality downward relative to 0.12, consistent with fully downweighting the Acoustic N and Peruvian CPUE index series that otherwise pull the FarNorth stock to a very low terminal biomass.
10 Other trials
These trials are shown separately from the formal data sensitivities because they are diagnostic checks on the Peruvian/FarNorth signal rather than candidate bridge configurations. The motivation is that the Peruvian/FarNorth fishery continues to catch jack mackerel, so the trials ask whether the very low FarNorth biomass and very high terminal fishing mortality in the final 0.12 two-stock model are driven primarily by the standardized Peruvian CPUE and seasonal Peru acoustic survey signals.
Model 1.05 starts from 0.12 and replaces Peru_CPUE with a noisy (CV = 60%) nominal CPUE series for 1990-2025. Model 1.06 starts from 1.05 and removes the two seasonal Peru acoustic abundance-index series, Peru_Acoust_S1 and Peru_Acoust_S2. Both trials are compared directly with 0.12 below.
| Hypothesis | Model | Run | N parameters | NLL | Max gradient |
|---|---|---|---|---|---|
| h1 | 0.12 | h1_0.12 | 1871 | 3820.555 | 0.0003189 |
| h1 | 1.05 | h1_1.05 | 1871 | 3781.912 | 0.0002602 |
| h1 | 1.06 | h1_1.06 | 1843 | 1315.561 | 0.0002240 |
| h2 | 0.12 | h2_0.12 | 1932 | 2712.406 | 0.0001995 |
| h2 | 1.05 | h2_1.05 | 1932 | 2701.650 | 0.0003403 |
| h2 | 1.06 | h2_1.06 | 1904 | 1270.705 | 0.0002805 |
| Hypothesis | Model | Stock | Year | SSB | Total biomass | Recruitment | Max total F at age |
|---|---|---|---|---|---|---|---|
| h1 | 0.12 | Stock_1 | 2025 | 3211 | 6342 | 10667 | 2.462 |
| h1 | 1.05 | Stock_1 | 2025 | 4097 | 7509 | 11050 | 2.541 |
| h1 | 1.06 | Stock_1 | 2025 | 5768 | 9672 | 12359 | 2.121 |
| h2 | 0.12 | Stock_1 | 2025 | 6719 | 11510 | 21317 | 2.212 |
| h2 | 0.12 | Stock_2 | 2025 | 37 | 277 | 444 | 37.232 |
| h2 | 1.05 | Stock_1 | 2025 | 6719 | 11510 | 21317 | 2.212 |
| h2 | 1.05 | Stock_2 | 2025 | 34 | 274 | 439 | 9.677 |
| h2 | 1.06 | Stock_1 | 2025 | 6719 | 11510 | 21317 | 2.212 |
| h2 | 1.06 | Stock_2 | 2025 | 296 | 693 | 1015 | 3.626 |
| Hypothesis | Model | Stock | Year | SSB (%) | Total biomass (%) | Recruitment (%) | Max total F at age (%) |
|---|---|---|---|---|---|---|---|
| h1 | 0.12 | Stock_1 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h1 | 1.05 | Stock_1 | 2025 | 27.6 | 18.4 | 3.6 | 3.2 |
| h1 | 1.06 | Stock_1 | 2025 | 79.6 | 52.5 | 15.9 | -13.9 |
| h2 | 0.12 | Stock_1 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 0.12 | Stock_2 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 1.05 | Stock_1 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 1.05 | Stock_2 | 2025 | -9.5 | -1.0 | -1.3 | -74.0 |
| h2 | 1.06 | Stock_1 | 2025 | 0.0 | 0.0 | 0.0 | 0.0 |
| h2 | 1.06 | Stock_2 | 2025 | 695.3 | 150.3 | 128.5 | -90.3 |
10.1 Single-Stock Hypothesis
Under the single-stock hypothesis, replacing the standardized Peruvian CPUE with the noisy nominal CPUE (1.05) increases terminal biomass moderately relative to 0.12 while leaving terminal fishing mortality close to the final model. Removing the two seasonal Peru acoustic series as well (1.06) produces a larger biomass increase and lowers terminal fishing mortality below 0.12. The single-stock pattern therefore indicates that the nominal CPUE trial alone changes scale modestly, while the additional removal of the seasonal Peru acoustic series has the larger effect on the recent biomass trajectory.
10.2 Two-Stock Hypothesis
Under the two-stock hypothesis, these trials mainly affect the FarNorth stock. The southern stock remains effectively unchanged from 0.12 because the altered data are assigned to the Peruvian/FarNorth component. For the FarNorth stock, 1.05 leaves terminal biomass near the final-model level but sharply reduces terminal fishing mortality, indicating that the noisy nominal CPUE relaxes the most extreme terminal-F behavior even without removing the seasonal Peru acoustic surveys. Model 1.06 then raises FarNorth terminal biomass and recruitment and further reduces terminal fishing mortality after Peru_Acoust_S1 and Peru_Acoust_S2 are removed.
