ESC31 diagnostic note
The assessment table shows median relative total reproductive output (TRO) increasing from 0.255 in 2023 to 0.281 in 2026, while median relative biomass of fish aged 10 years and older (B10+) rounds to 0.231 in both years. The issue raised in the email discussion is not why the two measures have different levels. It is why they move differently over the same three-year period under the same 2026 reference set.
Short answer. This is a genuine age-composition result, not a calculation error. Fewer fish aged 10–14 in 2026 are offset in B10+ by more fish at older, heavier ages, leaving total age-10+ biomass almost unchanged. TRO also counts reproductive contribution below age 10 and weights older fish much more strongly through maturity and length-based fecundity. Increases at ages 8–9 and 20–24 therefore raise TRO even though aggregate B10+ is flat.
cat(
'<div class="metric-grid">',
sprintf(
'<div class="metric-card"><span class="value">%s</span><span class="label">reference-set draws with TRO increasing</span></div>',
fmt_pct(p_tro_up)
),
sprintf(
'<div class="metric-card"><span class="value">%s</span><span class="label">reference-set draws with B10+ increasing</span></div>',
fmt_pct(p_b10_up)
),
sprintf(
'<div class="metric-card"><span class="value">+%s</span><span class="label">centre-fit TRO change</span></div>',
fmt_pct(centre$change_pct[centre$Metric == "Relative TRO"] / 100)
),
sprintf(
'<div class="metric-card"><span class="value">+%s</span><span class="label">centre-fit B10+ change</span></div>',
fmt_pct(centre$change_pct[centre$Metric == "Relative B10+"] / 100)
),
'</div>'
)The model calculates both quantities from season-1 numbers-at-age, but applies different age-specific weights:
There is no reproductive senescence term in this calculation. Per-fish TRO weight increases with age in the fitted model. Moreover, the 2023 and 2026 weight-at-age vectors are identical for both TRO and B10+, so the contrast is entirely caused by the fitted numbers-at-age and their distribution among ages—not by a change in the measurement rules between years.
The accepted balanced nine-cell MCMC-grid cache contains 2,000 draws for every model year. The table below gives the equal-tailed 95% interval across those draws.
draw_summary |>
mutate(
`Median (95% interval)` = sprintf(
"%.3f (%.3f–%.3f)", median, lower, upper
)
) |>
select(Metric, Year, `Median (95% interval)`) |>
knitr::kable(align = c("l", "r", "r"))| Metric | Year | Median (95% interval) |
|---|---|---|
| Relative B10+ | 2023 | 0.231 (0.171–0.310) |
| Relative B10+ | 2026 | 0.231 (0.171–0.313) |
| Relative TRO | 2023 | 0.255 (0.189–0.338) |
| Relative TRO | 2026 | 0.281 (0.209–0.373) |
The paired-draw median change is 0.026 for relative TRO, or 10.3%, compared with 0.0001 for relative B10+, or 0.0%. TRO increases in every draw; the sign of the small B10+ change is almost evenly divided.
ggplot(paired_draws, aes(x = B10_change, y = TRO_change)) +
geom_hline(yintercept = 0, color = "#707b84", linewidth = 0.4) +
geom_vline(xintercept = 0, color = "#707b84", linewidth = 0.4) +
geom_point(color = tro_colour, alpha = 0.28, size = 1.45) +
annotate(
"label",
x = quantile(paired_draws$B10_change, 0.03),
y = quantile(paired_draws$TRO_change, 0.95),
label = paste0("TRO increased in ", fmt_pct(p_tro_up), " of draws"),
hjust = 0, color = "#17212b", fill = "white", label.size = 0
) +
annotate(
"label",
x = quantile(paired_draws$B10_change, 0.03),
y = quantile(paired_draws$TRO_change, 0.83),
label = paste0("B10+ increased in ", fmt_pct(p_b10_up), " of draws"),
hjust = 0, color = "#17212b", fill = "white", label.size = 0
) +
scale_x_continuous(labels = scales::label_number(accuracy = 0.005)) +
scale_y_continuous(labels = scales::label_number(accuracy = 0.005)) +
labs(
x = "Change in relative B10+ (2026 − 2023)",
y = "Change in relative TRO (2026 − 2023)"
)
The trajectories show that the divergence is a recent feature of the fitted age structure rather than an isolated 2026 calculation.
metric_colours <- c("Relative TRO" = tro_colour, "Relative B10+" = b10_colour)
ggplot(trajectory_summary, aes(x = Year, y = median, color = Metric, fill = Metric)) +
geom_vline(xintercept = c(2023, 2026), linetype = "dashed", color = "#87929c", linewidth = 0.4) +
geom_ribbon(aes(ymin = lower, ymax = upper), alpha = 0.16, color = NA) +
geom_line(linewidth = 0.85) +
scale_color_manual(values = metric_colours) +
scale_fill_manual(values = metric_colours) +
scale_x_continuous(breaks = c(2000, 2005, 2010, 2015, 2020, 2023, 2026)) +
scale_y_continuous(labels = scales::label_number(accuracy = 0.05)) +
labs(x = NULL, y = "Relative status", color = NULL, fill = NULL) +
theme(legend.position = "bottom")
The centre-cell maximum-likelihood fit provides the age detail needed to interpret the reference-set result. Its aggregate changes are:
centre |>
mutate(
`2023` = case_when(
Metric %in% c("Relative TRO", "Relative B10+") ~ sprintf("%.3f", value_2023),
Metric == "Age-10+ numbers" ~ paste0(fmt1(value_2023 / 1e6), " million"),
TRUE ~ paste0(fmt1(value_2023 * 1000), " kg")
),
`2026` = case_when(
Metric %in% c("Relative TRO", "Relative B10+") ~ sprintf("%.3f", value_2026),
Metric == "Age-10+ numbers" ~ paste0(fmt1(value_2026 / 1e6), " million"),
TRUE ~ paste0(fmt1(value_2026 * 1000), " kg")
),
Change = sprintf("%+.1f%%", change_pct)
) |>
select(Metric, `2023`, `2026`, Change) |>
knitr::kable(align = c("l", "r", "r", "r"))| Metric | 2023 | 2026 | Change |
|---|---|---|---|
| Relative TRO | 0.242 | 0.267 | +10.4% |
| Relative B10+ | 0.220 | 0.220 | +0.3% |
| Age-10+ numbers | 2.2 million | 2.1 million | -3.5% |
| Mean weight of age-10+ fish | 96.6 kg | 100.5 kg | +4.0% |
Numbers aged 10+ fall by 3.5%, while their abundance-weighted mean body weight rises by 4.0%. Those opposing effects almost cancel in B10+.
age_state |>
select(Age, `2023` = N_2023, `2026` = N_2026) |>
pivot_longer(c(`2023`, `2026`), names_to = "Year", values_to = "Number") |>
ggplot(aes(x = Age, y = Number, color = Year)) +
geom_vline(xintercept = 9.5, linetype = "dashed", color = "#707b84", linewidth = 0.45) +
geom_line(linewidth = 0.8) +
geom_point(size = 1.7) +
annotate(
"text", x = 10.1, y = max(age_state$N_2023, age_state$N_2026) * 0.8,
label = "B10+ begins", hjust = 0, color = "#51606f", size = 3.3
) +
scale_color_manual(values = c("2023" = "#59636e", "2026" = tro_colour)) +
scale_y_log10(
labels = scales::label_number(scale_cut = scales::cut_short_scale())
) +
scale_x_continuous(breaks = seq(0, 30, 2)) +
labs(x = "Age", y = "Number of fish (log scale)", color = NULL)
The clearest shifts are a decline at ages 10–14, increases at ages 8–9, and an increase around ages 20–24. These shifts affect the two metrics differently.
age_contributions <- age_state |>
transmute(
Age,
`TRO contribution change` = delta_TRO,
`B10+ contribution change (t)` = delta_B10
) |>
pivot_longer(-Age, names_to = "Metric", values_to = "Change") |>
mutate(Direction = if_else(Change >= 0, "Increase", "Decrease"))
ggplot(age_contributions, aes(x = Age, y = Change, fill = Direction)) +
geom_hline(yintercept = 0, color = "#4f5963", linewidth = 0.4) +
geom_vline(xintercept = 9.5, linetype = "dashed", color = "#87929c", linewidth = 0.4) +
geom_col(width = 0.8) +
facet_wrap(~Metric, ncol = 1, scales = "free_y") +
scale_fill_manual(values = direction_colours) +
scale_x_continuous(breaks = seq(0, 30, 2)) +
scale_y_continuous(
labels = scales::label_number(scale_cut = scales::cut_short_scale())
) +
labs(x = "Age", y = "Change in contribution", fill = NULL)
The age-group totals make the offsets explicit:
age_group_summary |>
transmute(
`Age group` = Age_group,
`Numbers, 2023` = scales::comma(round(N_2023)),
`Numbers, 2026` = scales::comma(round(N_2026)),
`Numbers change` = sprintf("%+.1f%%", N_change_pct),
`TRO change` = scales::comma(round(TRO_change)),
`B10+ change (t)` = scales::comma(round(B10_change_t))
) |>
knitr::kable(align = c("l", rep("r", 5)))| Age group | Numbers, 2023 | Numbers, 2026 | Numbers change | TRO change | B10+ change (t) |
|---|---|---|---|---|---|
| 0–3 | 13,007,376 | 8,909,368 | -31.5% | -136 | 0 |
| 4–7 | 3,177,375 | 4,466,009 | +40.6% | 23,782 | 0 |
| 8–9 | 731,165 | 1,174,424 | +60.6% | 73,903 | 0 |
| 10–14 | 1,286,740 | 948,369 | -26.3% | -147,346 | -28,778 |
| 15–19 | 683,432 | 778,378 | +13.9% | 67,406 | 10,057 |
| 20–24 | 128,324 | 307,847 | +139.9% | 157,390 | 21,233 |
| 25–29 | 101,802 | 85,373 | -16.1% | -15,758 | -2,042 |
| 30+ | 16,958 | 18,910 | +11.5% | 1,953 | 248 |
Ages 8–9 contribute 45.8% of the net TRO increase but are excluded from B10+. Ages 20–24 contribute 97.6% of the net TRO increase. Their gain is partly offset by the decline at ages 10–14; in B10+, that age-10–14 biomass loss is almost completely balanced by biomass gains at ages 15–24.
This pattern is consistent with cohort progression. The relatively abundant 2018 cohort is age 8 in 2026, while stronger 2005–2006 cohorts contribute at ages 20–21. At the same time, the cohorts occupying ages 10–14 in 2026 are collectively weaker. The metrics therefore differ because of which cohorts they include and how strongly they weight older fish.
The email sequence indicates a verification and interpretability concern, rather than evidence that rebuilding has stopped:
The concern is reasonable because readers often use both metrics as broad indicators of the adult stock. A flat B10+ alongside a clearly increasing TRO looks surprising until the age structure is shown, and it could otherwise be mistaken for a table or calculation error.
Not in the published headline comparison. Table 4 of the 2023 assessment reported the following medians and 80% intervals:
tibble(
`Assessment year` = c(2020L, 2023L),
`Relative TRO, median (80% interval)` = c("0.20 (0.16–0.24)", "0.23 (0.21–0.29)"),
`Relative B10+, median (80% interval)` = c("0.17 (0.14–0.21)", "0.22 (0.19–0.26)")
) |>
knitr::kable(align = c("r", "r", "r"))| Assessment year | Relative TRO, median (80% interval) | Relative B10+, median (80% interval) |
|---|---|---|
| 2020 | 0.20 (0.16–0.24) | 0.17 (0.14–0.21) |
| 2023 | 0.23 (0.21–0.29) | 0.22 (0.19–0.26) |
Both published medians increased between those rows—about 15% for TRO and 29% for B10+—so the current “rising TRO, flat B10+” contrast was not present there. There is an important caveat: the 2020 row was carried from the 2020 assessment, rather than recalculated as a 2020 state under the 2023 model, and the 2023 paper did not publish a full B10+ trajectory. The table therefore does not prove that the two metrics never diverged internally. The 2026 table makes the issue more visible because it compares 2023 and 2026 states under the same current reference set.
Between 2023 and 2026, declines in the number of fish aged 10–14 were offset in B10+ by increased abundance at older ages and greater mean weight within the age-10+ group. TRO nevertheless increased because it includes reproductive contribution from fish younger than age 10 and weights older fish much more strongly according to maturity and length-based fecundity. Increases at ages 8–9 and 20–24 therefore produced a substantial increase in TRO while aggregate B10+ remained almost unchanged.
This note is generated directly from:
ESC31/runs/grid_mcmc/esc31_grid_dense_mixed_accepted_20260723_failed_cells_1500/grid_combined_state_2000_draws.rds;ESC31/runs/esc31_base.rds; andsbt package source used to rebuild and verify the saved objective before extracting the centre-fit report.No model was refitted and no assessment artifact was altered to produce this diagnostic.