Eastern Bering Sea Walleye Pollock SPoRC Assessment

Bridge model using the SPoRC R package

Authors

Jim Ianelli

[Co-authors]

Published

April 26, 2026

1 Executive Summary

This document reports a preliminary Eastern Bering Sea walleye pollock bridge assessment implemented with the SPoRC R package (Cheng et al. 2026). The run uses the 2024 ADMB assessment data stream conditioned into SPoRC input objects, with a single-area, single-sex, age-structured configuration spanning 1964-2024 and 15 modeled ages.

The current SPoRC dev fit estimates 18,988 for spawning stock biomass, 68,827 for total biomass, 166,750 recruits, and a fishery fishing mortality of 0.043 in 2024 (Table 2). These quantities should be read as bridge-model results rather than management advice. The optimizer returned convergence code 1 with message “false convergence (8)”; the Hessian was not positive definite and the maximum absolute fixed-effect gradient was 1.92^{-4} (Table 3).

The bridge comparison with the saved 2024 ADMB result shows broad agreement in some time-series shapes, but important scale differences remain, especially for recruitment and fishing mortality (Figure 20, Table 6). This indicates that the current SPoRC setup is useful for repository development and diagnostics, but not yet a replacement for the accepted ADMB assessment.

2 Data

The SPoRC input file is generated by data-raw/build_ebs_pollock_data.R from the 2024 ADMB data file and saved as data/ebs_pollock.rds. The modeled data include catch, fishery CPUE, fishery age compositions, bottom trawl survey (BTS), acoustic trawl survey (ATS), aerial survey (AVO) indices, and survey age compositions where available. The survey time series are retained as separate information sources because earlier EBS pollock assessment work has shown that multiple surveys can carry distinct signals about abundance, composition, and distribution (O’Leary et al. 2020). Data availability by source is summarized in Table 1 and shown by year in Figure 1.

Show code
gt(data_summary) |>
  cols_label(
    data_series = "Data series",
    n_years_used = "Years used",
    years = "Year range"
  )
Table 1: Summary of data series included in the SPoRC input object.
Data series Years used Year range
Catch Fishery 61 1964-2024
Fishery age composition Fishery 60 1964-2023
Fishery index Fishery CPUE 12 1965-1976
Survey age composition ATS 19 1994-2024
Survey age composition BTS 42 1982-2024
Survey index ATS 19 1994-2024
Survey index AVO 18 2006-2024
Survey index BTS 42 1982-2024
Show code
ggplot(data_availability_df, aes(x = year, y = series)) +
  geom_point(aes(fill = type), shape = 21, size = 2.6, color = "grey20", alpha = 0.9) +
  labs(x = "Year", y = NULL, fill = "Data type") +
  ggthemes::theme_few()
Figure 1: Data availability used in the SPoRC dev model.

3 Model Configuration

The dev model is configured in config/base.yml and fitted by analysis/run_scenarios.R. The model uses one region, one sex, one fishery fleet, and three survey fleets, following the single-region EBS pollock SPoRC case-study configuration (Cheng 2026). Recruitment is modeled with a Beverton-Holt stock-recruit relationship, with fixed steepness and fixed recruitment standard deviations. Initial age-composition deviations are estimated for ages 2 and older and are not penalized as equilibrium recruitment deviations in the current configuration. In this setup, equil_init_age_strc = 0 means the starting age structure is estimated more freely through ln_InitDevs, while equil_init_age_strc = 2 retains the vignette-style geometric/equilibrium initialization and associated initial recruitment penalty. SPoRC’s one-sex spawning biomass calculation applies a 0.5 multiplier internally, so the reported Aggregated_SSB is already on a female spawning-biomass basis for comparison with the ADMB assessment. Natural mortality is fixed at age-specific values, catch uncertainty is fixed, and the current dev configuration estimates penalized time-varying fishery and survey selectivity. Fishery selectivity uses a dome-shaped dbnrml fixed selectivity curve with 2dar1 deviations, correlations fixed at zero, and deviations mapped from 1964 onward; the process-error standard deviation is fixed at 0.30 to allow more interannual variability. BTS survey selectivity uses iid deviations with the underlying logistic age-50 fixed near age 3, and ATS/AVO survey selectivity uses 2dar1 deviations with fleet 3 sharing fleet 2 selectivity parameters. Selectivity is an important bridge-model diagnostic because alternative state-space and time-varying selectivity treatments can materially change catch-at-age assessment behavior (Nielsen and Berg 2014; Nielsen et al. 2021).

Biological inputs used in the terminal model year are shown in Figure 2. The natural mortality curve follows the fixed age-specific values in the configuration, while maturity and spawning weight at age are taken from the conditioned pollock input data.

Show code
ggplot(bio_df, aes(x = age, y = value)) +
  geom_line(linewidth = 0.8, color = "#1b6ca8") +
  geom_point(size = 1.8, color = "#1b6ca8") +
  facet_wrap(~ quantity, scales = "free_y", ncol = 1) +
  labs(x = "Age", y = "Value") +
  ggthemes::theme_few()
Figure 2: Terminal-year biological inputs and natural mortality used in the SPoRC dev model.

The estimated terminal-year selectivity patterns are shown in Figure 3. The fitted selectivity trajectories are shown as ridge plots for the fishery, BTS, and ATS in Figure 4, Figure 5, and Figure 6, following the assessment plotting approach in plot-sel.R. Each fleet-year curve is normalized to its maximum value before plotting so the figures emphasize changes in the age pattern of vulnerability through time.

Show code
ggplot(selectivity_df, aes(x = age, y = value, color = fleet_name)) +
  geom_line(linewidth = 0.9) +
  facet_wrap(~ fleet_type, scales = "free_y", ncol = 1) +
  labs(x = "Age", y = "Selectivity", color = "Fleet") +
  ggthemes::theme_few()
Figure 3: Terminal-year fishery and survey selectivity from the SPoRC dev model.
Show code
plot_selectivity_ridges("Fishery", fill = "#7b3294", compare_models = TRUE)
Figure 4: Relative fishery selectivity over time from the SPoRC dev and vign models. Ridgeline heights are normalized within each model and year.
Show code
plot_selectivity_ridges("BTS", fill = "#1b6ca8")
Figure 5: Relative BTS selectivity over time from the SPoRC dev model. Ridgeline heights are normalized within each year.
Show code
plot_selectivity_ridges("ATS", fill = "#4daf4a")
Figure 6: Relative ATS selectivity over time from the SPoRC dev model. Ridgeline heights are normalized within each year.

4 Results

The dev run estimates increasing spawning biomass over the terminal portion of the time series and a strong terminal recruitment estimate (Figure 7). In 2024, estimated SSB is 18,988, total biomass is 68,827, and recruitment is 166,750 (Table 2).

Show code
current_estimates <- latest_ts[, c("quantity", "value")]
gt(current_estimates) |>
  fmt_number(columns = value, decimals = 3) |>
  cols_label(quantity = "Quantity", value = paste("Estimate in", assessment_year))
Table 2: Terminal-year estimates from the SPoRC dev model.
Quantity Estimate in 2024
F 0.043
SSB 18,987.567
Total_Biom 68,826.798
Recruit 166,750.391
Show code
ggplot(sporc_ts, aes(x = year, y = value)) +
  geom_line(linewidth = 0.8, color = "#1b6ca8") +
  facet_wrap(~ quantity, scales = "free_y", ncol = 2) +
  labs(x = "Year", y = "Value") +
  ggthemes::theme_few()
Figure 7: SPoRC dev model time series for fishing mortality, spawning biomass, total biomass, and recruitment.
Show code
ggplot() +
  geom_line(
    data = srr_curve,
    aes(x = ssb, y = recruitment),
    linewidth = 0.9,
    color = "#1b6ca8"
  ) +
  geom_text(
    data = srr_points,
    aes(x = ssb, y = recruitment, label = year),
    size = 2.4,
    vjust = -0.45,
    check_overlap = TRUE
  ) +
  labs(x = "Spawning biomass", y = "Recruitment") +
  ggthemes::theme_few()
Figure 8: Stock-recruit relationship from the SPoRC dev model. The line is the Beverton-Holt curve using fixed steepness, estimated R0, and the median dynamic unfished spawning biomass; labels show annual model estimates by year.

The catch fit reproduces the observed catch series closely in most years by construction of the catch likelihood and associated fixed catch uncertainty (Figure 9). Index fits show larger departures for some survey and CPUE observations, which is expected at this bridge stage because the model configuration has not yet been tuned to reproduce the accepted ADMB assessment (Figure 10).

Show code
ggplot(catch_df, aes(x = year)) +
  geom_line(aes(y = fitted), linewidth = 0.8, color = "#1b6ca8") +
  geom_point(aes(y = observed), size = 1.8, color = "grey15") +
  facet_wrap(~ fleet_name, scales = "free_y") +
  labs(x = "Year", y = "Catch") +
  ggthemes::theme_few()
Figure 9: Observed and fitted catch for the SPoRC dev model. Points are observations and the line is fitted catch.
Show code
ggplot(index_df, aes(x = year)) +
  geom_line(aes(y = value), linewidth = 0.8, color = "#1b6ca8") +
  geom_point(
    data = index_df[is.finite(index_df$observed), ],
    aes(y = observed),
    size = 1.8,
    color = "grey15"
  ) +
  facet_wrap(~ fleet_name, scales = "free_y", ncol = 2) +
  labs(x = "Year", y = "Index") +
  ggthemes::theme_few()
Figure 10: Observed and fitted fishery and survey indices for the SPoRC dev model. Points are observations and lines are fitted values.

Age-composition fits are shown as predicted proportions at age with observed proportions overlaid for years included in the likelihood. The fishery composition fit is shown in Figure 11, and the survey composition fits are shown separately for BTS and ATS in Figure 12 and Figure 13. The AVO survey does not contribute an age-composition series in the current conditioned input object. Following the assessment diagnostic workflow in plot_osa_comps.R, the composition fits are also summarized with residual bubble plots, normal QQ plots, and aggregate observed-versus-expected fits for the Fishery, BTS, and ATS series (Figure 14, Figure 15, Figure 16, Figure 17, and Figure 18). Age 1 is excluded from the BTS and ATS residual diagnostics because it is not used in those survey composition likelihoods. The residual diagnostic method used in this render is Pearson residual fallback.

Show code
ggplot(fish_agecomp_df, aes(x = age, y = predicted)) +
  geom_line(linewidth = 0.5, color = "#4daf4a") +
  geom_point(aes(y = observed), color = "#1f78b4", size = 0.9, alpha = 0.8) +
  facet_wrap(~ year, ncol = 5, dir = "v") +
  scale_y_continuous(limits = c(0, NA)) +
  labs(x = "Age", y = "Proportion") +
  ggthemes::theme_few()
Figure 11: Observed and predicted fishery age-composition patterns for years included in the SPoRC likelihood.
Show code
ggplot(srv_agecomp_df[srv_agecomp_df$fleet_name == "BTS", ], aes(x = age, y = predicted)) +
  geom_line(linewidth = 0.5, color = "#4daf4a") +
  geom_point(aes(y = observed), color = "#1f78b4", size = 0.9, alpha = 0.8) +
  facet_wrap(~ year, ncol = 4, dir = "v") +
  scale_y_continuous(limits = c(0, NA)) +
  labs(x = "Age", y = "Proportion") +
  ggthemes::theme_few()
Figure 12: Observed and predicted BTS age-composition patterns for years included in the SPoRC likelihood.
Show code
ggplot(srv_agecomp_df[srv_agecomp_df$fleet_name == "ATS", ], aes(x = age, y = predicted)) +
  geom_line(linewidth = 0.5, color = "#4daf4a") +
  geom_point(aes(y = observed), color = "#1f78b4", size = 0.9, alpha = 0.8) +
  facet_wrap(~ year, ncol = 3, dir = "v") +
  scale_y_continuous(limits = c(0, NA)) +
  labs(x = "Age", y = "Proportion") +
  ggthemes::theme_few()
Figure 13: Observed and predicted ATS age-composition patterns for years included in the SPoRC likelihood.
Show code
plot_composition_residual_bubbles("Fishery")
Figure 14: Composition residual bubble diagnostics for the Fishery age-composition fit. Circle size is proportional to the absolute residual; triangles identify absolute residuals greater than 3.
Show code
plot_composition_residual_bubbles("BTS")
Figure 15: Composition residual bubble diagnostics for the BTS age-composition fit. Circle size is proportional to the absolute residual; triangles identify absolute residuals greater than 3.
Show code
plot_composition_residual_bubbles("ATS")
Figure 16: Composition residual bubble diagnostics for the ATS age-composition fit. Circle size is proportional to the absolute residual; triangles identify absolute residuals greater than 3.
Show code
ggplot(composition_residual_df, aes(sample = resid)) +
  stat_qq(color = "#1f78b4", size = 1.2, alpha = 0.75) +
  stat_qq_line(color = "grey35", linewidth = 0.6) +
  geom_text(
    data = composition_sdnr_df,
    aes(x = -Inf, y = Inf, label = label),
    inherit.aes = FALSE,
    hjust = -0.1,
    vjust = 1.4,
    size = 3.2
  ) +
  facet_wrap(~ fleet, nrow = 1) +
  labs(x = "Theoretical quantiles", y = "Sample quantiles") +
  ggthemes::theme_few()
Figure 17: Normal QQ diagnostics for the Fishery, BTS, and ATS composition residuals. Labels show the standard deviation of normalized residuals.
Show code
plot_aggregate_composition_fits()
Figure 18: Aggregate observed and expected age-composition fits for Fishery, BTS, and ATS. Bars are aggregate observed proportions and lines are aggregate expected proportions.

5 Diagnostics

The optimization diagnostics are mixed. The maximum absolute gradient is small, but the optimizer reports singular convergence and the Hessian status should be reviewed directly in Table 3. This is a clear flag that the dev fit should be treated as provisional until additional parameter mapping, starting values, bounds, and likelihood settings are reviewed.

Show code
convergence_summary <- data.frame(
  model = sporc_model_name,
  objective = base_fit$optim$objective,
  convergence_code = base_fit$optim$convergence,
  convergence_message = base_fit$optim$message,
  pd_hessian = isTRUE(base_fit$sdrep$pdHess),
  max_abs_gradient = max(abs(base_fit$sdrep$gradient.fixed), na.rm = TRUE)
)

gt(convergence_summary) |>
  fmt_number(columns = c(objective, max_abs_gradient), decimals = 4) |>
  cols_label(
    model = "Model",
    objective = "Objective",
    convergence_code = "Convergence code",
    convergence_message = "Message",
    pd_hessian = "Positive-definite Hessian",
    max_abs_gradient = "Max. absolute gradient"
  )
Table 3: SPoRC dev model convergence diagnostics.
Model Objective Convergence code Message Positive-definite Hessian Max. absolute gradient
dev 1,779.1095 1 false convergence (8) FALSE 0.0002

Catchability parameters are estimated freely in the current configuration and do not have q priors (Table 4). The very large standard errors for fishery CPUE, BTS, and ATS catchability indicate weak scale identification for those index catchabilities in this provisional bridge fit. This is consistent with the false-convergence optimizer message and should be reviewed against the intended SPoRC case-study specification before using the q estimates interpretively.

Show code
gt(catchability_diagnostics) |>
  fmt_number(columns = c(Estimate, `Std. Error`), decimals = 4) |>
  cols_label(
    fleet = "Fleet",
    parameter = "Parameter",
    instance = "Instance",
    Estimate = "Estimate",
    `Std. Error` = "Standard error",
    q_specification = "q specification",
    q_prior = "q prior"
  )
Table 4: Catchability estimates, standard errors, and current q specification in the SPoRC dev model.
Fleet Parameter Instance Estimate Standard error q specification q prior
Fishery CPUE ln_fish_q 1 0.2388 NaN est_all none
BTS ln_srv_q 1 −1.5015 NaN est_all none

Likelihood contributions are dominated by the configured composition and recruitment components. The current development case is labeled dev; the earlier SPoRC vignette-style case is labeled vign when analysis/outputs/vign.rds is available. The component totals are shown with models in columns in Table 5, and the relative contribution of each component is shown in Figure 19. These values are useful for debugging model weighting and for identifying which data sources are controlling the current fit. The vign case has a nonzero initial recruitment penalty because it keeps the vignette initialization setting equil_init_age_strc = 2; the dev case frees the initial age-composition deviations and sets equil_init_age_strc = 0, so Init_Rec_nLL is zero.

Table 5: Negative log-likelihood components by model case.
Component dev vign
Joint objective 1,779 526
Fishery age composition 396 1,153
Survey age composition 876 846
Survey index 436 −77
Recruitment 86 111
Fishery index 93 −4
Fishing mortality penalty 88 74
Initial recruitment 0 38
Catch −66 −61
Selectivity penalty −130 −1,553
Show code
ggplot(nll_df, aes(x = component, y = value, fill = model)) +
  geom_col(position = "dodge", width = 0.7) +
  coord_flip() +
  labs(x = NULL, y = "Negative log-likelihood", fill = "Model") +
  ggthemes::scale_fill_colorblind() +
  ggthemes::theme_few()
Figure 19: Negative log-likelihood components by SPoRC model case.

6 Bridge Comparison With ADMB

The bridge comparison uses /Users/jim/_mymods/pollock/results/derived/admb_2024.rds as the ADMB reference object. The comparison is limited to shared annual quantities: fishing mortality, spawning biomass, and recruitment. The maximum absolute relative differences are shown in Table 6, and the time series are plotted in Figure 20.

Show code
if (nrow(comparison_summary) > 0) {
  gt(comparison_summary) |>
    fmt_number(columns = max_abs_relative_difference, decimals = 4) |>
    cols_label(
      quantity = "Quantity",
      max_abs_relative_difference = "Max. absolute relative difference"
    )
} else {
  gt(data.frame(note = "ADMB comparison object was not available."))
}
Table 6: Maximum absolute relative difference between the SPoRC dev model and the 2024 ADMB reference object.
Quantity Max. absolute relative difference
F 1.9808
Recruit 8.1190
SSB 5.9496
Show code
if (!is.null(bridge_ts)) {
  ggplot(bridge_ts, aes(x = year, y = value, color = model)) +
    geom_line(linewidth = 0.8) +
    facet_wrap(~ quantity, scales = "free_y", ncol = 1) +
    labs(x = "Year", y = "Value", color = "Model") +
    ggthemes::theme_few()
}
Figure 20: Shared SPoRC and ADMB time series for the dev-model bridge comparison.

The current bridge run does not yet reproduce the ADMB model closely enough for operational use. The largest differences occur in recruitment and fishing mortality, and those differences are large enough to affect interpretation of terminal stock status and future harvest advice. The next development step is to inspect the mapping of recruitment deviations, selectivity forms, catch likelihood treatment, index scaling, and composition likelihood settings against the ADMB model.

7 Reproducibility

The assessment artifacts used by this document are:

  • SPoRC data object: data/ebs_pollock.rds
  • SPoRC dev model: analysis/outputs/base.rds
  • SPoRC vignette-style model: analysis/outputs/vign.rds, regenerated by analysis/run_vignette_case.R
  • SPoRC configuration: config/base.yml
  • ADMB bridge object: /Users/jim/_mymods/pollock/results/derived/admb_2024.rds
  • Five-year retrospective object: analysis/outputs/retro_5_peel.rds
  • SparseNUTS diagnostic MCMC object: analysis/outputs/sparsenuts/sporc_sparsenuts_default.rds

This document can be rendered from the repository root with:

quarto render reporting/EBS_wp_sporc.qmd --to html

References

Cheng, Matthew. 2026. Setting up a Single Region Model (Eastern Bering Sea Pollock). SPoRC vignette. https://chengmatt.github.io/SPoRC/articles/f_single_region_ebs_pollock_case_study.html.
Cheng, Matthew, Dan Goethel, Pete Hulson, and Curry Cunningham. 2026. SPoRC: A Generalized Stochastic Population Model over Regional Components. https://chengmatt.github.io/SPoRC/.
Nielsen, Anders, and Casper W. Berg. 2014. “Estimation of Time-Varying Selectivity in Stock Assessments Using State-Space Models.” Fisheries Research 158: 96–101. https://doi.org/10.1016/j.fishres.2014.01.014.
Nielsen, Anders, Niels T Hintzen, Henrik Mosegaard, Vanessa Trijoulet, and Casper W Berg. 2021. “Multi-Fleet State-Space Assessment Model Strengthens Confidence in Single-Fleet SAM and Provides Fleet-Specific Forecast Options.” ICES Journal of Marine Science 78 (6): 2043–52. https://doi.org/10.1093/icesjms/fsab078.
O’Leary, C. A., J. T. Thorson, J. N. Ianelli, and S. Kotwicki. 2020. “Adapting to Climate‐driven Distribution Shifts Using Model‐based Indices and Age Composition from Multiple Surveys in the Walleye Pollock (Gadus Chalcogrammus) Stock Assessment.” Fisheries Oceanography 29 (6): 541–57. https://doi.org/10.1111/fog.12494.

8 Appendix

8.1 SparseNUTS MCMC

The SPoRC dev model is RTMB-based, so the fitted objective can be passed directly to SparseNUTS. Following the Rceattle assessment workflow, I ran SparseNUTS::sample_snuts() outside the Quarto render using the package defaults for chains, samples, warmup selection, metric selection, initial values, and control settings, with cores = 1 for serial RTMB execution. The sampler output and diagnostic figures are saved as assessment artifacts.

This output is a computational diagnostic rather than accepted posterior inference. The default run reported divergent transitions and () and effective sample size diagnostics indicate non-convergence for catchability parameters, so these posterior summaries should not be used for management interpretation without a longer and retuned MCMC run.

Show code
if (file.exists(sparsenuts_path)) {
  sparsenuts <- readRDS(sparsenuts_path)
  snuts <- sparsenuts$snuts_fit
  snuts_diag <- sparsenuts$diagnostics
  settings <- sparsenuts$sampler_settings
  postwarmup_per_chain <- dim(snuts$samples)[1] - snuts$warmup
  total_postwarmup <- postwarmup_per_chain * dim(snuts$samples)[2]
  max_rhat <- max(snuts$monitor$rhat, na.rm = TRUE)
  min_ess <- min(snuts$monitor$ess_bulk, na.rm = TRUE)
  worst_rhat <- snuts$monitor$variable[which.max(snuts$monitor$rhat)]
  worst_ess <- snuts$monitor$variable[which.min(snuts$monitor$ess_bulk)]
  divergent_transitions <- round(snuts_diag$perc_divergent / 100 * total_postwarmup)

  snuts_status <- data.frame(
    metric = c(
      "Algorithm",
      "Metric",
      "Chains",
      "Warmup iterations per chain",
      "Post-warmup samples per chain",
      "Total post-warmup draws",
      "Minimum bulk ESS",
      "Minimum bulk ESS parameter",
      "Maximum Rhat",
      "Maximum Rhat parameter",
      "Divergent transitions",
      "Percent divergent",
      "Interpretation"
    ),
    value = c(
      snuts$algorithm,
      snuts$metric,
      dim(snuts$samples)[2],
      snuts$warmup,
      postwarmup_per_chain,
      total_postwarmup,
      sprintf("%.1f", min_ess),
      worst_ess,
      sprintf("%.3f", max_rhat),
      worst_rhat,
      divergent_transitions,
      sprintf("%.2f%%", snuts_diag$perc_divergent),
      ifelse(
        snuts_diag$perc_divergent == 0 && max_rhat < 1.01,
        "No obvious warning by divergence and Rhat checks.",
        "Diagnostic only; do not use for inference without retuning."
      )
    )
  )

  gt(snuts_status) |>
    cols_label(metric = "Metric", value = "Value") |>
    tab_header(title = "SparseNUTS Diagnostic Run")
} else {
  gt(data.frame(note = "SparseNUTS output not available. Run analysis/run_sporc_sparsenuts.R."))
}
Table 7: SparseNUTS diagnostic-run summary for the SPoRC dev model.
SparseNUTS Diagnostic Run
Metric Value
Algorithm SNUTS
Metric dense
Chains 4
Warmup iterations per chain 150
Post-warmup samples per chain 1000
Total post-warmup draws 4000
Minimum bulk ESS 6.3
Minimum bulk ESS parameter ln_srv_q[1]
Maximum Rhat 1.694
Maximum Rhat parameter ln_srv_q[1]
Divergent transitions 8
Percent divergent 0.20%
Interpretation Diagnostic only; do not use for inference without retuning.
Show code
fig <- file.path(sparsenuts_fig_dir, "sporc_sparsenuts_pairs.png")
if (file.exists(fig)) knitr::include_graphics(fig)
Figure 21: SparseNUTS pairs plot for the six SPoRC parameters with the largest Rhat values.
Show code
fig <- file.path(sparsenuts_fig_dir, "sporc_sparsenuts_marginals.png")
if (file.exists(fig)) knitr::include_graphics(fig)
Figure 22: SparseNUTS marginal posterior intervals for the twelve SPoRC parameters with the largest Rhat values.
Show code
fig <- file.path(sparsenuts_fig_dir, "sporc_sparsenuts_trace.png")
if (file.exists(fig)) knitr::include_graphics(fig)
Figure 23: SparseNUTS trace plots for the six SPoRC parameters with the largest Rhat values.
Show code
fig <- file.path(sparsenuts_fig_dir, "sporc_sparsenuts_sampler_params.png")
if (file.exists(fig)) knitr::include_graphics(fig)
Figure 24: SparseNUTS sampler-parameter diagnostics for the SPoRC diagnostic run.
Show code
fig <- file.path(sparsenuts_fig_dir, "sporc_sparsenuts_native_marginals.png")
if (file.exists(fig)) knitr::include_graphics(fig)
Figure 25: SparseNUTS::plot_marginals output for the SPoRC diagnostic run.
Show code
fig <- file.path(sparsenuts_fig_dir, "sporc_sparsenuts_Q.png")
if (file.exists(fig)) knitr::include_graphics(fig)
Figure 26: SparseNUTS::plot_Q output for the SPoRC diagnostic run.
Show code
fig <- file.path(sparsenuts_fig_dir, "sporc_sparsenuts_uncertainties.png")
if (file.exists(fig)) knitr::include_graphics(fig)
Figure 27: SparseNUTS::plot_uncertainties output for the SPoRC diagnostic run.

8.2 Retrospective Analysis

A five-year retrospective was run by peeling terminal years from the conditioned SPoRC input data and refitting the same dev configuration. The resulting spawning biomass and recruitment trajectories are shown in Figure 28, with relative differences from the full fit in Figure 29. Mohn’s rho values are calculated from terminal-year relative differences across the five peels and reported in Table 8.

Show code
if (!is.null(retro_df)) {
  ggplot(retro_df, aes(x = year, y = value, color = peel_label, group = peel_label)) +
    geom_line(linewidth = 0.8) +
    facet_wrap(~ quantity, scales = "free_y", ncol = 1) +
    labs(x = "Year", y = "Value", color = "Retrospective peel") +
    ggthemes::theme_few()
}
Figure 28: Five-year retrospective trajectories for spawning biomass and recruitment from the SPoRC dev model.
Show code
if (!is.null(retro_rel)) {
  ggplot(retro_rel, aes(x = year, y = relative_difference, color = peel_label, group = peel_label)) +
    geom_hline(yintercept = 0, linetype = "dashed", color = "grey45") +
    geom_line(linewidth = 0.8) +
    geom_point(data = retro_terminal, size = 2) +
    facet_wrap(~ quantity, scales = "free_y", ncol = 1) +
    labs(x = "Year", y = "Relative difference from full fit", color = "Retrospective peel") +
    ggthemes::theme_few()
}
Figure 29: Relative differences between each retrospective peel and the full SPoRC dev fit. Points identify the terminal year of each peel.
Show code
if (nrow(retro_rho) > 0) {
  gt(retro_rho) |>
    fmt_number(columns = mohns_rho, decimals = 3) |>
    cols_label(
      quantity = "Quantity",
      region = "Region",
      mohns_rho = "Mohn's rho"
    )
} else {
  gt(data.frame(note = "The five-year retrospective output was not available."))
}
Table 8: Mohn’s rho for the five-year SPoRC retrospective analysis.
Quantity Region Mohn's rho
Recruitment 1 −0.221
Spawning biomass 1 −0.235

8.3 Model Configurations

The dev model configuration is read from config/base.yml. The vign column summarizes the specification reproduced by analysis/run_vignette_case.R from the SPoRC single-region EBS pollock vignette. The flattened and summarized settings in Table 9 document the model configurations used by the rendered assessment.

Show code
gt(config_table_wide) |>
  sub_missing(columns = c(dev, vign), missing_text = "") |>
  cols_label(
    section = "Section",
    setting = "Setting",
    dev = "dev",
    vign = "vign"
  )
Table 9: SPoRC dev and vign model configuration settings.
Section Setting dev vign
biology biology.fit_lengths 0
biology biology.fixed_M.age1 0.9
biology biology.fixed_M.age2 0.45
biology biology.fixed_M.age3plus 0.3
biology biology.M_spec fix
biology biology.M_spec.fixed_M
fix, age1 = 0.9, age2 = 0.45, age3plus = 0.3
catch catch.sigmaC 0.05
catch catch.sigmaC_spec fix
catch catch.sigmaC_spec.sigmaC
fix, 0.05
catch catch.Use_F_pen 1
data data.object
SPoRC::sgl_rg_ebswp_data
dimensions dimensions.n_fish_fleets 1
dimensions dimensions.n_regions 1
dimensions dimensions.n_regions.n_sexes.n_fish_fleets.n_srv_fleets
1, 1, 1, 3
dimensions dimensions.n_sexes 1
dimensions dimensions.n_srv_fleets 3
fishery fishery.fish_idx_type biom
fishery fishery.FishAgeComps_LikeType Multinomial
fishery fishery.FishAgeComps_Type agg_Year_1-terminal_Fleet_1
fishery fishery.FishLenComps_LikeType none
fishery fishery.FishLenComps_Type none_Year_1-terminal_Fleet_1
fishery_selectivity fishery_selectivity.fish_fixed_sel_pars_spec est_all
fishery_selectivity fishery_selectivity.fish_fixed_sel_pars_start -0.9163, -1.385, 1.6094, 1.9459, -2.9444, -0.4055
fishery_selectivity fishery_selectivity.fish_q_blocks none_Fleet_1
fishery_selectivity fishery_selectivity.fish_q_spec est_all est_all
fishery_selectivity fishery_selectivity.fish_sel_blocks none_Fleet_1
fishery_selectivity fishery_selectivity.fish_sel_model dbnrml_Fleet_1 logist1_Fleet_1
fishery_selectivity fishery_selectivity.fishsel_pe_pars_log_sigma
0.075
fit fit.base_only TRUE
fit fit.newton_loops 3
fit fit.newton_loops.random
3, NULL
fit fit.silent FALSE
movement movement.do_recruits_move 0
movement movement.Fixed_Movement
movement movement.use_fixed_movement 1
paths paths.admb_results_rds /Users/jim/_mymods/pollock/results/derived/admb_2024.rds
paths paths.admb_source_root /Users/jim/_mymods/pollock/admb
paths paths.comparison_dir analysis/comparisons
paths paths.data_rds data/ebs_pollock.rds
paths paths.outputs_dir analysis/outputs
recruitment recruitment.do_rec_bias_ramp 0
recruitment recruitment.equil_init_age_strc 2
recruitment recruitment.free_init_age_composition TRUE
recruitment recruitment.h_spec fix
recruitment recruitment.init_age_strc 1
recruitment recruitment.init_age_strc.equil_init_age_strc
1, 2
recruitment recruitment.ln_global_R0 10
recruitment recruitment.ln_sigmaR 0, 0
recruitment recruitment.rec_model bh_rec bh_rec
recruitment recruitment.sigmaR_spec fix
recruitment recruitment.sigmaR_switch 1
recruitment recruitment.steepness_h 0.623013
recruitment recruitment.steepness_h.sigmaR_spec
0.623013, fix
recruitment recruitment.steepness_is_h TRUE
recruitment recruitment.t_spawn 0.25
selectivity_random_effects selectivity_random_effects.cont_tv_fish_sel 2dar1_Fleet_1 2dar1_Fleet_1
selectivity_random_effects selectivity_random_effects.cont_tv_srv_sel iid_Fleet_1, 2dar1_Fleet_2, 2dar1_Fleet_3 iid_Fleet_1, 2dar1_Fleet_2, 2dar1_Fleet_3
selectivity_random_effects selectivity_random_effects.corr_opt_fish_semipar corr_zero_y_b
selectivity_random_effects selectivity_random_effects.fish_sel_devs_spec est_all
selectivity_random_effects selectivity_random_effects.fishsel_pe_pars_log_sigma 0.3
selectivity_random_effects selectivity_random_effects.fishsel_pe_pars_spec fix
selectivity_random_effects selectivity_random_effects.random_effects
selectivity_random_effects selectivity_random_effects.srv_sel_devs_spec est_all, est_all, est_shared_f_2
selectivity_random_effects selectivity_random_effects.srvsel_ats_avo_log_sigma 0.15
selectivity_random_effects selectivity_random_effects.srvsel_bts_logistic_log_sigma 0.075
selectivity_random_effects selectivity_random_effects.srvsel_pe_pars_spec fix, fix, fix
source source.url
https://chengmatt.github.io/SPoRC/articles/f_single_region_ebs_pollock_case_study.html
sporc sporc.ref main
survey survey.srv_fixed_sel_pars_spec fix, est_all, est_shared_f_2
survey survey.srv_fixed_sel_pars_start.BTS 3, 1
survey survey.srv_idx_type biom, biom, biom
survey survey.srv_q_blocks none_Fleet_1, none_Fleet_2, none_Fleet_3
survey survey.srv_q_spec est_all, est_all, est_all est_all, est_all, est_all
survey survey.srv_sel_blocks none_Fleet_1, none_Fleet_2, none_Fleet_3
survey survey.srv_sel_model logist1_Fleet_1, logist1_Fleet_2, logist1_Fleet_3 logist1_Fleet_1, logist1_Fleet_2, logist1_Fleet_3
survey survey.SrvAgeComps_LikeType Multinomial, Multinomial, none
survey survey.SrvAgeComps_Type agg_Year_1-terminal_Fleet_1, agg_Year_1-terminal_Fleet_2, none_Year_1-terminal_Fleet_3
survey survey.SrvLenComps_LikeType none, none, none
survey survey.SrvLenComps_Type none_Year_1-terminal_Fleet_1, none_Year_1-terminal_Fleet_2, none_Year_1-terminal_Fleet_3
tagging tagging.UseTagging 0
weights weights.Wt_Catch 1
weights weights.Wt_F 1
weights weights.Wt_FishAgeComps 1
weights weights.Wt_FishIdx 1
weights weights.Wt_FishLenComps 1
weights weights.Wt_Rec 1
weights weights.Wt_SrvAgeComps 1
weights weights.Wt_SrvIdx 1
weights weights.Wt_SrvLenComps 1
weights weights.Wt_Tagging 0

8.4 Input Sample Sizes

The age-composition sample sizes used in the multinomial likelihood calculations are year-specific and are read directly from the conditioned SPoRC input object. The values in Table 10 are the input sample sizes used for fishery, BTS, and ATS age-composition likelihoods.

Show code
gt(composition_sample_sizes, groupname_col = "fleet") |>
  fmt_number(columns = input_sample_size, decimals = 2) |>
  cols_label(
    likelihood = "Likelihood",
    year = "Year",
    input_sample_size = "Input sample size"
  )
Table 10: Input sample sizes used for multinomial age-composition likelihood calculations by fleet and year.
Likelihood Year Input sample size
Fishery
Multinomial 1964 10.00
Multinomial 1965 10.00
Multinomial 1966 10.00
Multinomial 1967 10.00
Multinomial 1968 10.00
Multinomial 1969 10.00
Multinomial 1970 10.00
Multinomial 1971 10.00
Multinomial 1972 10.00
Multinomial 1973 10.00
Multinomial 1974 10.00
Multinomial 1975 10.00
Multinomial 1976 10.00
Multinomial 1977 10.00
Multinomial 1978 39.00
Multinomial 1979 39.00
Multinomial 1980 39.00
Multinomial 1981 39.00
Multinomial 1982 39.00
Multinomial 1983 39.00
Multinomial 1984 39.00
Multinomial 1985 39.00
Multinomial 1986 39.00
Multinomial 1987 39.00
Multinomial 1988 39.00
Multinomial 1989 39.00
Multinomial 1990 39.00
Multinomial 1991 260.30
Multinomial 1992 228.05
Multinomial 1993 344.45
Multinomial 1994 286.36
Multinomial 1995 256.95
Multinomial 1996 189.08
Multinomial 1997 318.68
Multinomial 1998 354.57
Multinomial 1999 476.14
Multinomial 2000 482.43
Multinomial 2001 328.17
Multinomial 2002 486.56
Multinomial 2003 440.91
Multinomial 2004 390.52
Multinomial 2005 494.38
Multinomial 2006 506.21
Multinomial 2007 500.22
Multinomial 2008 523.65
Multinomial 2009 420.03
Multinomial 2010 549.41
Multinomial 2011 728.07
Multinomial 2012 607.46
Multinomial 2013 753.27
Multinomial 2014 606.34
Multinomial 2015 821.23
Multinomial 2016 704.11
Multinomial 2017 606.72
Multinomial 2018 667.84
Multinomial 2019 700.80
Multinomial 2020 565.24
Multinomial 2021 817.58
Multinomial 2022 641.24
Multinomial 2023 443.04
BTS
Multinomial 1982 162.04
Multinomial 1983 130.70
Multinomial 1984 63.27
Multinomial 1985 73.54
Multinomial 1986 151.95
Multinomial 1987 61.21
Multinomial 1988 82.23
Multinomial 1989 53.19
Multinomial 1990 48.27
Multinomial 1991 79.42
Multinomial 1992 85.22
Multinomial 1993 91.98
Multinomial 1994 86.85
Multinomial 1995 104.90
Multinomial 1996 226.47
Multinomial 1997 73.38
Multinomial 1998 65.19
Multinomial 1999 95.43
Multinomial 2000 90.69
Multinomial 2001 183.01
Multinomial 2002 186.33
Multinomial 2003 125.66
Multinomial 2004 188.66
Multinomial 2005 194.49
Multinomial 2006 329.61
Multinomial 2007 192.70
Multinomial 2008 235.41
Multinomial 2009 144.72
Multinomial 2010 107.89
Multinomial 2011 165.27
Multinomial 2012 107.12
Multinomial 2013 66.53
Multinomial 2014 117.66
Multinomial 2015 103.67
Multinomial 2016 122.84
Multinomial 2017 234.59
Multinomial 2018 158.32
Multinomial 2019 120.68
Multinomial 2021 149.48
Multinomial 2022 172.83
Multinomial 2023 126.78
Multinomial 2024 64.21
ATS
Multinomial 1994 43.00
Multinomial 1996 32.00
Multinomial 1997 49.00
Multinomial 1999 67.00
Multinomial 2000 70.00
Multinomial 2002 72.00
Multinomial 2004 51.00
Multinomial 2006 47.00
Multinomial 2007 39.00
Multinomial 2008 35.00
Multinomial 2009 26.00
Multinomial 2010 34.00
Multinomial 2012 44.00
Multinomial 2014 79.00
Multinomial 2016 61.00
Multinomial 2018 50.00
Multinomial 2020 1.00
Multinomial 2022 52.00
Multinomial 2024 79.00

8.5 Parameter Estimates

Estimated fixed-effect parameters and their standard errors from the SPoRC dev model are shown in Table 11. Repeated parameter names are distinguished by their instance number in the underlying parameter vector.

Show code
gt(parameter_summary) |>
  fmt_number(columns = c(Estimate, `Std. Error`), decimals = 4) |>
  cols_label(
    parameter = "Parameter",
    instance = "Instance",
    Estimate = "Estimate",
    `Std. Error` = "Standard error"
  )
Table 11: SPoRC dev-model fixed-effect parameter estimates and standard errors.
Parameter Instance Estimate Standard error
ln_global_R0 1 11.8034 NaN
ln_InitDevs 1 −2.7475 NaN
ln_InitDevs.1 1 −2.7671 NaN
ln_InitDevs.2 1 −4.0436 NaN
ln_InitDevs.3 1 −5.1608 NaN
ln_InitDevs.4 1 −3.6680 NaN
ln_InitDevs.5 1 −4.2403 NaN
ln_InitDevs.6 1 −6.0079 NaN
ln_InitDevs.7 1 −38.7926 NaN
ln_InitDevs.8 1 −36.0825 NaN
ln_InitDevs.9 1 −33.7880 NaN
ln_InitDevs.10 1 −33.7768 NaN
ln_InitDevs.11 1 −23.4553 NaN
ln_InitDevs.12 1 −21.6448 NaN
ln_InitDevs.13 1 −1.4677 NaN
ln_RecDevs 1 −2.4240 NaN
ln_RecDevs.1 1 1.1567 NaN
ln_RecDevs.2 1 0.5540 NaN
ln_RecDevs.3 1 1.4350 NaN
ln_RecDevs.4 1 1.0698 NaN
ln_RecDevs.5 1 1.1330 NaN
ln_RecDevs.6 1 0.7584 NaN
ln_RecDevs.7 1 −0.0062 NaN
ln_RecDevs.8 1 −0.2820 NaN
ln_RecDevs.9 1 0.7952 NaN
ln_RecDevs.10 1 0.4360 NaN
ln_RecDevs.11 1 0.7619 NaN
ln_RecDevs.12 1 0.9341 NaN
ln_RecDevs.13 1 1.2014 NaN
ln_RecDevs.14 1 1.7049 NaN
ln_RecDevs.15 1 2.8512 NaN
ln_RecDevs.16 1 1.7814 NaN
ln_RecDevs.17 1 1.5899 NaN
ln_RecDevs.18 1 0.0658 NaN
ln_RecDevs.19 1 1.2197 NaN
ln_RecDevs.20 1 −1.1084 NaN
ln_RecDevs.21 1 0.5754 NaN
ln_RecDevs.22 1 −0.4123 NaN
ln_RecDevs.23 1 −1.0987 NaN
ln_RecDevs.24 1 −1.2994 NaN
ln_RecDevs.25 1 −1.2084 NaN
ln_RecDevs.26 1 1.1836 NaN
ln_RecDevs.27 1 0.3814 NaN
ln_RecDevs.28 1 0.0540 NaN
ln_RecDevs.29 1 1.0768 NaN
ln_RecDevs.30 1 −0.5720 NaN
ln_RecDevs.31 1 −0.7830 NaN
ln_RecDevs.32 1 0.1501 NaN
ln_RecDevs.33 1 0.5407 NaN
ln_RecDevs.34 1 −0.3908 NaN
ln_RecDevs.35 1 −0.1092 NaN
ln_RecDevs.36 1 0.2849 NaN
ln_RecDevs.37 1 0.7746 NaN
ln_RecDevs.38 1 0.2492 NaN
ln_RecDevs.39 1 −0.0687 NaN
ln_RecDevs.40 1 −0.8978 NaN
ln_RecDevs.41 1 −1.3691 NaN
ln_RecDevs.42 1 −0.3065 NaN
ln_RecDevs.43 1 0.6995 NaN
ln_RecDevs.44 1 −0.9146 NaN
ln_RecDevs.45 1 1.4134 NaN
ln_RecDevs.46 1 0.3430 NaN
ln_RecDevs.47 1 0.2425 NaN
ln_RecDevs.48 1 −0.4873 NaN
ln_RecDevs.49 1 1.2119 NaN
ln_RecDevs.50 1 1.1273 NaN
ln_RecDevs.51 1 0.0792 NaN
ln_RecDevs.52 1 −0.9221 NaN
ln_RecDevs.53 1 −0.6188 NaN
ln_RecDevs.54 1 −0.3238 NaN
ln_RecDevs.55 1 1.6893 NaN
ln_RecDevs.56 1 −0.1832 NaN
ln_RecDevs.57 1 −0.0192 NaN
ln_RecDevs.58 1 −0.2866 NaN
ln_RecDevs.59 1 0.3107 NaN
ln_RecDevs.60 1 1.0637 NaN
ln_F_mean 1 −2.2069 NaN
ln_F_devs 1 0.8671 NaN
ln_F_devs.1 1 0.9502 NaN
ln_F_devs.2 1 0.8002 NaN
ln_F_devs.3 1 1.3466 NaN
ln_F_devs.4 1 1.3584 NaN
ln_F_devs.5 1 1.3650 NaN
ln_F_devs.6 1 1.5851 NaN
ln_F_devs.7 1 1.7964 NaN
ln_F_devs.8 1 1.8872 NaN
ln_F_devs.9 1 1.9520 NaN
ln_F_devs.10 1 2.1813 NaN
ln_F_devs.11 1 2.2894 NaN
ln_F_devs.12 1 2.0649 NaN
ln_F_devs.13 1 1.7255 NaN
ln_F_devs.14 1 1.6097 NaN
ln_F_devs.15 1 1.3456 NaN
ln_F_devs.16 1 0.9541 NaN
ln_F_devs.17 1 0.3385 NaN
ln_F_devs.18 1 −0.3374 NaN
ln_F_devs.19 1 −0.6896 NaN
ln_F_devs.20 1 −0.7453 NaN
ln_F_devs.21 1 −0.7283 NaN
ln_F_devs.22 1 −0.7378 NaN
ln_F_devs.23 1 −0.9949 NaN
ln_F_devs.24 1 −0.5629 NaN
ln_F_devs.25 1 −0.4959 NaN
ln_F_devs.26 1 −0.0951 NaN
ln_F_devs.27 1 −0.0021 NaN
ln_F_devs.28 1 0.1894 NaN
ln_F_devs.29 1 −0.3681 NaN
ln_F_devs.30 1 −0.6843 NaN
ln_F_devs.31 1 −0.8018 NaN
ln_F_devs.32 1 −0.8002 NaN
ln_F_devs.33 1 −0.6314 NaN
ln_F_devs.34 1 −0.6820 NaN
ln_F_devs.35 1 −0.6929 NaN
ln_F_devs.36 1 −0.5564 NaN
ln_F_devs.37 1 −0.4148 NaN
ln_F_devs.38 1 −0.2683 NaN
ln_F_devs.39 1 −0.1964 NaN
ln_F_devs.40 1 −0.3705 NaN
ln_F_devs.41 1 −0.4709 NaN
ln_F_devs.42 1 −0.2938 NaN
ln_F_devs.43 1 −0.3240 NaN
ln_F_devs.44 1 −0.4258 NaN
ln_F_devs.45 1 −0.5712 NaN
ln_F_devs.46 1 −0.7948 NaN
ln_F_devs.47 1 −0.5608 NaN
ln_F_devs.48 1 −0.5997 NaN
ln_F_devs.49 1 −0.7779 NaN
ln_F_devs.50 1 −0.8775 NaN
ln_F_devs.51 1 −0.7068 NaN
ln_F_devs.52 1 −1.0120 NaN
ln_F_devs.53 1 −1.0220 NaN
ln_F_devs.54 1 −1.1693 NaN
ln_F_devs.55 1 −1.1613 NaN
ln_F_devs.56 1 −0.6312 NaN
ln_F_devs.57 1 −0.6173 NaN
ln_F_devs.58 1 −0.8872 NaN
ln_F_devs.59 1 −0.9181 NaN
ln_F_devs.60 1 −0.9287 NaN
ln_fish_fixed_sel_pars 1 −0.7322 NaN
ln_fish_fixed_sel_pars.1 1 −99.3477 NaN
ln_fish_fixed_sel_pars.2 1 1.1542 NaN
ln_fish_fixed_sel_pars.3 1 2.4920 NaN
ln_fish_fixed_sel_pars.4 1 −6.0565 NaN
ln_fish_fixed_sel_pars.5 1 −1.6848 NaN
ln_fish_q 1 0.2388 NaN
ln_fishsel_devs 1 0.0134 NaN
ln_fishsel_devs.1 1 0.0233 NaN
ln_fishsel_devs.2 1 −0.0240 NaN
ln_fishsel_devs.3 1 0.0445 NaN
ln_fishsel_devs.4 1 0.0102 NaN
ln_fishsel_devs.5 1 0.0614 NaN
ln_fishsel_devs.6 1 0.0198 NaN
ln_fishsel_devs.7 1 −0.0008 NaN
ln_fishsel_devs.8 1 −0.0009 NaN
ln_fishsel_devs.9 1 −0.0003 NaN
ln_fishsel_devs.10 1 0.0005 NaN
ln_fishsel_devs.11 1 0.0012 NaN
ln_fishsel_devs.12 1 0.0012 NaN
ln_fishsel_devs.13 1 −0.0009 NaN
ln_fishsel_devs.14 1 −0.0707 NaN
ln_fishsel_devs.15 1 0.0474 NaN
ln_fishsel_devs.16 1 −0.0084 NaN
ln_fishsel_devs.17 1 0.0086 NaN
ln_fishsel_devs.18 1 0.0608 NaN
ln_fishsel_devs.19 1 0.0006 NaN
ln_fishsel_devs.20 1 0.0339 NaN
ln_fishsel_devs.21 1 −0.0036 NaN
ln_fishsel_devs.22 1 −0.0158 NaN
ln_fishsel_devs.23 1 −0.0100 NaN
ln_fishsel_devs.24 1 −0.0038 NaN
ln_fishsel_devs.25 1 0.0035 NaN
ln_fishsel_devs.26 1 0.0099 NaN
ln_fishsel_devs.27 1 0.0088 NaN
ln_fishsel_devs.28 1 −0.0038 NaN
ln_fishsel_devs.29 1 −0.0473 NaN
ln_fishsel_devs.30 1 0.0670 NaN
ln_fishsel_devs.31 1 0.0294 NaN
ln_fishsel_devs.32 1 0.0202 NaN
ln_fishsel_devs.33 1 0.0275 NaN
ln_fishsel_devs.34 1 −0.0297 NaN
ln_fishsel_devs.35 1 0.0141 NaN
ln_fishsel_devs.36 1 −0.0005 NaN
ln_fishsel_devs.37 1 −0.0161 NaN
ln_fishsel_devs.38 1 −0.0142 NaN
ln_fishsel_devs.39 1 −0.0058 NaN
ln_fishsel_devs.40 1 0.0040 NaN
ln_fishsel_devs.41 1 0.0117 NaN
ln_fishsel_devs.42 1 0.0100 NaN
ln_fishsel_devs.43 1 −0.0018 NaN
ln_fishsel_devs.44 1 −0.0317 NaN
ln_fishsel_devs.45 1 0.0606 NaN
ln_fishsel_devs.46 1 0.0534 NaN
ln_fishsel_devs.47 1 0.1069 NaN
ln_fishsel_devs.48 1 −0.0078 NaN
ln_fishsel_devs.49 1 −0.0599 NaN
ln_fishsel_devs.50 1 −0.0096 NaN
ln_fishsel_devs.51 1 −0.0050 NaN
ln_fishsel_devs.52 1 −0.0101 NaN
ln_fishsel_devs.53 1 −0.0122 NaN
ln_fishsel_devs.54 1 −0.0067 NaN
ln_fishsel_devs.55 1 0.0034 NaN
ln_fishsel_devs.56 1 0.0112 NaN
ln_fishsel_devs.57 1 0.0096 NaN
ln_fishsel_devs.58 1 0.0001 NaN
ln_fishsel_devs.59 1 −0.0224 NaN
ln_fishsel_devs.60 1 0.0718 NaN
ln_fishsel_devs.61 1 0.0583 NaN
ln_fishsel_devs.62 1 0.0584 NaN
ln_fishsel_devs.63 1 0.0218 NaN
ln_fishsel_devs.64 1 −0.0554 NaN
ln_fishsel_devs.65 1 −0.0075 NaN
ln_fishsel_devs.66 1 −0.0085 NaN
ln_fishsel_devs.67 1 −0.0101 NaN
ln_fishsel_devs.68 1 −0.0085 NaN
ln_fishsel_devs.69 1 −0.0056 NaN
ln_fishsel_devs.70 1 0.0029 NaN
ln_fishsel_devs.71 1 0.0106 NaN
ln_fishsel_devs.72 1 0.0092 NaN
ln_fishsel_devs.73 1 0.0012 NaN
ln_fishsel_devs.74 1 −0.0169 NaN
ln_fishsel_devs.75 1 0.0870 NaN
ln_fishsel_devs.76 1 0.0605 NaN
ln_fishsel_devs.77 1 0.1027 NaN
ln_fishsel_devs.78 1 0.0159 NaN
ln_fishsel_devs.79 1 −0.0948 NaN
ln_fishsel_devs.80 1 −0.0182 NaN
ln_fishsel_devs.81 1 −0.0113 NaN
ln_fishsel_devs.82 1 −0.0124 NaN
ln_fishsel_devs.83 1 −0.0084 NaN
ln_fishsel_devs.84 1 −0.0042 NaN
ln_fishsel_devs.85 1 0.0033 NaN
ln_fishsel_devs.86 1 0.0103 NaN
ln_fishsel_devs.87 1 0.0090 NaN
ln_fishsel_devs.88 1 0.0017 NaN
ln_fishsel_devs.89 1 −0.0138 NaN
ln_fishsel_devs.90 1 0.1498 NaN
ln_fishsel_devs.91 1 0.1058 NaN
ln_fishsel_devs.92 1 0.0927 NaN
ln_fishsel_devs.93 1 −0.0514 NaN
ln_fishsel_devs.94 1 −0.0986 NaN
ln_fishsel_devs.95 1 −0.0300 NaN
ln_fishsel_devs.96 1 −0.0129 NaN
ln_fishsel_devs.97 1 −0.0122 NaN
ln_fishsel_devs.98 1 −0.0092 NaN
ln_fishsel_devs.99 1 −0.0042 NaN
ln_fishsel_devs.100 1 0.0037 NaN
ln_fishsel_devs.101 1 0.0104 NaN
ln_fishsel_devs.102 1 0.0089 NaN
ln_fishsel_devs.103 1 0.0019 NaN
ln_fishsel_devs.104 1 −0.0122 NaN
ln_fishsel_devs.105 1 0.1465 NaN
ln_fishsel_devs.106 1 0.0638 NaN
ln_fishsel_devs.107 1 0.0679 NaN
ln_fishsel_devs.108 1 −0.0202 NaN
ln_fishsel_devs.109 1 −0.0586 NaN
ln_fishsel_devs.110 1 −0.0092 NaN
ln_fishsel_devs.111 1 −0.0167 NaN
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ln_srvsel_devs.1031 1 −0.0079 NaN
ln_srvsel_devs.1032 1 −0.0220 NaN
ln_srvsel_devs.1033 1 −0.0201 NaN
ln_srvsel_devs.1034 1 −0.0053 NaN
ln_srvsel_devs.1035 1 −0.0047 NaN
ln_srvsel_devs.1036 1 −0.0159 NaN

8.6 Gradient Diagnostics

The fixed-effect parameters with the largest absolute gradients are shown in Table 12. These entries identify the parameters that are furthest from satisfying first-order optimality in the current dev fit.

Show code
gt(gradient_summary) |>
  fmt_scientific(columns = c(gradient, absolute_gradient), decimals = 3) |>
  cols_label(
    parameter = "Parameter",
    instance = "Instance",
    gradient = "Gradient",
    absolute_gradient = "Absolute gradient"
  )
Table 12: Fixed-effect parameters with the largest absolute gradients in the SPoRC dev model.
Parameter Instance Gradient Absolute gradient
ln_global_R0 1 1.923 × 10−4 1.923 × 10−4
ln_F_mean 1 3.472 × 10−5 3.472 × 10−5
ln_InitDevs 14 2.851 × 10−5 2.851 × 10−5
ln_fish_fixed_sel_pars 1 2.368 × 10−5 2.368 × 10−5
ln_RecDevs 27 2.204 × 10−5 2.204 × 10−5
ln_RecDevs 16 2.164 × 10−5 2.164 × 10−5
ln_RecDevs 2 2.037 × 10−5 2.037 × 10−5
ln_RecDevs 10 2.005 × 10−5 2.005 × 10−5
ln_RecDevs 6 1.782 × 10−5 1.782 × 10−5
ln_RecDevs 4 1.690 × 10−5 1.690 × 10−5