Illustrative 2027 TAC calculation

How the Candidate Procedures Would Produce 2027 Advice

This is a calculation plan, not a 2027 TAC recommendation. None of the candidate management procedures (CMPs) has been adopted. A numerical recommendation cannot be produced until the complete annual index data, the previous catch-advice value, and the rules for data timing, missing values, rounding, and allocation have been confirmed.

This page shows how the data available for the 2027 decision would be passed through each CMP. It also identifies where the approximately 630 kt estimate from the 2026 northern Chile acoustic survey could, and could not, be used.

1 First settle which data year applies

The current MSE runs use a one-year data delay and a one-year management delay. Under that tested timing:

the CMP calculation made in 2026 produces catch advice for 2027;
the most recent observations used are from 2025;
all eight CMPs use 2023–2025 data; and
all eight use the same five-index calculation and three-year averaging window.

The 2026 northern Chile acoustic estimate therefore does not enter the 2027 calculation as it was tested in the MSE. It would first enter the following annual calculation, for 2028 advice.

Using observations from 2026 for the 2027 TAC would require a same-year data rule. That would change the timing assumed in the tested CMP and should be specified, coded, and checked before it is used. Under such a revised rule, the three-year window would be 2024–2026.

2 Data required

All eight CMPs in the named SC14 release use the same five indices.

CMPs	Annual series required	Is the northern Chile acoustic survey used?
MP29, MP43, MP45, MP47, MP32, MP44, MP46, MP48	Northern Chile acoustic survey (`Chile_AcousN`), Chile CPUE, Peru artisanal index, Peru industrial index, and offshore CPUE	Yes, when its data year falls within the approved window

For every series, retain the value, unit, survey or fleet coverage, source, revision status, and date received. Values must be comparable with those used in the 2019–2023 reference period.

3 Turn the observations into the CMP indicator

The raw indices are on different scales, so they cannot be averaged directly. The current procedure performs the following calculation.

3.1 Express each series relative to its reference-period average

For index $j$ in year $y$,

\[ R_{j,y} = \frac{\text{index }j\text{ in year }y} {\text{mean of index }j\text{ over 2019--2023}}. \]

A value of 1 means that the observation equals its own 2019–2023 average. A value of 1.25 means it is 25% above that average.

The reported acoustic estimate of about 630 kt cannot be entered directly into the harvest rule. If its year is eligible, it must first be checked against the same northern Chile acoustic series and converted to

\[ R_{\text{acoustic},2026} = \frac{630\text{ kt}} {\text{mean northern Chile acoustic biomass over 2019--2023}}. \]

The reference-period mean is not recorded on this site, so this contribution cannot yet be calculated here.

3.2 Combine the available series within each year

For each year, average the relative values for the indices required by the CMP. This gives one combined annual index $A_y$.

The analysis code averages the non-missing series. Before an operational calculation, the Scientific Committee should decide whether a missing required series may be omitted or whether it stops the calculation. A missing value should never be omitted without being reported.

3.3 Average across the recent years

The indicator supplied to the harvest rule is:

\[ I = \text{mean of the combined annual indices over the approved recent years}. \]

For the tested 2027 timing, use 2023–2025 for all eight CMPs. One common all-index value of $I$ is supplied to each rule.

4 Apply each harvest rule

The table gives the current settings. Catch quantities use the units of the jmMSE analysis; those units and the final rounding convention must be confirmed before providing formal advice.

Table 1: Settings for the eight CMPs in the named SC14 release.

CMP	Information	Rule	Minimum	Limit	Trigger	Target or breakpoint
MP29 (HS+20)	All five indices, 3 years	Hockey-stick	270	0.1	2.125000	2000
MP43 (HS-20)	All five indices, 3 years	Hockey-stick	270	0.1	1.937500	2000
MP45 (HSsym)	All five indices, 3 years	Hockey-stick	270	0.1	2.062500	2000
MP47 (HS-30)	All five indices, 3 years	Hockey-stick	270	0.1	2.000000	2000
MP32 (PR+20)	All five indices, 3 years	Power ramp	270	0.1	1.640625	1500
MP44 (PR-20)	All five indices, 3 years	Power ramp	270	0.1	1.601562	1500
MP46 (PRsym)	All five indices, 3 years	Power ramp	270	0.1	1.625000	1500
MP48 (PR-30)	All five indices, 3 years	Power ramp	270	0.1	1.578125	1500

In the new short-label convention, HS means hockeystick and PR means power ramp. +20 identifies a 20% maximum annual increase, while -20 identifies a 20% maximum annual decrease.

For a hockeystick CMP, the preliminary catch advice is the minimum at or below the limit, rises in a straight line between the limit and trigger, and equals the target at or above the trigger.

For each power-ramp CMP, let

\[ x = \frac{I-\text{limit}}{\text{trigger}-\text{limit}}. \]

The preliminary advice is the minimum when $I$ is at or below the limit. It is

\[ \text{minimum} + (\text{target}-\text{minimum})x^{2.5} \]

between the limit and trigger, and

\[ \text{target}(0.2+0.8x)^{0.6} \]

at or above the trigger. Unlike the hockeystick, the power-ramp advice can continue to rise above its stated target.

5 Apply the annual change limit

MP29 and MP32 limit the change from the previous year’s catch advice to a 15% decrease or a 20% increase. If $C^*$ is the preliminary advice and $C_{2026}$ is the agreed previous advice value, the 2027 value before rounding is

\[ C_{2027} = \max\left(0.85C_{2026}, \min\left(C^*,1.20C_{2026}\right)\right). \]

MP43 and MP44 instead allow a 20% decrease and a 15% increase:

\[ C_{2027} = \max\left(0.80C_{2026}, \min\left(C^*,1.15C_{2026}\right)\right). \]

MP45 and MP46 use symmetric 15% limits. MP47 and MP48 allow a 30% decrease and a 20% increase. The exact multipliers are read from the CMP registry in the worked calculation below. Under reference OM11, the realized mean probabilities of being in the dynamic Kobe green zone over 2041–2050 were 0.6098, 0.5918, 0.6042, 0.6038, 0.6026, 0.5984, 0.5954, and 0.6056 for MP29, MP43, MP45, MP47, MP32, MP44, MP46, and MP48, respectively.

The value 1385 appears as the initial value in the simulation controls. It should not automatically be treated as $C_{2026}$. The operational specification must say whether the annual limit is based on the previous TAC, the previous CMP recommendation, or another approved quantity.

6 Worked retrospective: 2025 advice using data through 2024

For this retrospective, the advice year is labelled as the year immediately after the last data year: 2024 observations produce illustrative 2025 advice. This simply backs the calendar labels up one year while retaining the candidate index calculations, harvest rules, and initial comparison value of 1385.

This remains an illustration rather than advice adopted by SPRFMO. The result is a total catch quantity in the analysis units, before an approved rounding rule or allocation among fisheries.

6.1 Historical inputs

The table contains the observations from the updated assessment data associated with input/0.15.dat. The two Peruvian series are retained separately as Peru_Artis and Peru_Ind. Each reference mean is calculated over the available observations in 2019–2023. The northern acoustic series has no 2022 value.

Table 2: Historical observations used for the retrospective calculation. A dash means that no value is stored.

	Series	2019–2023 mean	2022	2023	2024	2025
1	Chile_AcousN	1896.963	—	2502.157	2788.465	3058.843
2	Chile_CPUE	96.249	90.157	98.162	82.478	97.287
4	Peru_Artis	0.507	0.571	0.617	0.672	0.495
5	Peru_Ind	0.686	0.736	0.683	0.656	0.630
3	Offshore_CPUE	937.613	1339.693	1169.402	428.054	—

6.2 Indicators for the 2025 calculation

The all-index annual values are 1.141 for 2022, 1.159 for 2023, and 1.013 for 2024. Their three-year mean is 1.104. This same indicator is supplied to each of the eight rules.

Table 3: Relative-index values supplied to the candidate harvest rules for the retrospective 2025 calculation.

Used by	Index set	Years averaged	Indicator
All eight SC14 CMPs	All five indices	2022–2024	1.104

6.3 Turn the indicator into preliminary advice

The indicator is a relative measure, not a catch quantity. A value of 1 means that the recent indices are, on average, equal to their 2019–2023 reference levels. A value above 1 means they are higher; a value below 1 means they are lower.

Each candidate then puts its indicator into its own harvest-control rule. The rule converts the relative indicator into a catch quantity. Because the candidates have different limits, triggers, targets, and rule shapes, the same indicator can produce different preliminary advice.

We write this preliminary catch advice as $C^*$. Here, $C$ means catch advice and the star means provisional: it is the harvest-control-rule result before the annual change limit is applied. The star is not another calculation.

The table shows the substitution explicitly. Values displayed in the calculation are rounded to three decimal places; the code uses the unrounded values.

Table 4: How each candidate converts its indicator into preliminary catch advice (C*).

CMP	Indicator	Rule	Substitute the indicator in the rule	C* before annual limit
MP29	1.104	Hockeystick	270.000 + (1.104 − 0.100) × (2000.000 − 270.000) ÷ (2.125 − 0.100)	1128.100
MP43	1.104	Hockeystick	270.000 + (1.104 − 0.100) × (2000.000 − 270.000) ÷ (1.938 − 0.100)	1215.661
MP45	1.104	Hockeystick	270.000 + (1.104 − 0.100) × (2000.000 − 270.000) ÷ (2.062 − 0.100)	1155.428
MP47	1.104	Hockeystick	270.000 + (1.104 − 0.100) × (2000.000 − 270.000) ÷ (2.000 − 0.100)	1184.554
MP32	1.104	Power ramp	x = (1.104 − 0.100) ÷ (1.641 − 0.100) = 0.652; 270.000 + (1500.000 − 270.000) × x raised to 2.5	692.139
MP44	1.104	Power ramp	x = (1.104 − 0.100) ÷ (1.602 − 0.100) = 0.669; 270.000 + (1500.000 − 270.000) × x raised to 2.5	720.131
MP46	1.104	Power ramp	x = (1.104 − 0.100) ÷ (1.625 − 0.100) = 0.659; 270.000 + (1500.000 − 270.000) × x raised to 2.5	703.035
MP48	1.104	Power ramp	x = (1.104 − 0.100) ÷ (1.578 − 0.100) = 0.680; 270.000 + (1500.000 − 270.000) × x raised to 2.5	738.187

For example, MP29 uses the hockeystick rule:

\[ C^* = 270 + \frac{(1.104-0.100)(2000-270)} {(2.125-0.100)} = 1128.10. \]

The value 1128.10 is therefore MP29’s harvest-rule result. It is not yet the final value because the annual change limit must still be applied.

6.4 Apply the annual change limit

With 1385 as the initial comparison value, each CMP applies the decrease and increase multipliers recorded in the registry. The table reports the range that affects each result rather than applying one common limit to all CMPs.

Table 5: Illustrative 2025 total catch advice using observations through 2024 and an initial comparison value of 1385.

CMP	Index years	Indicator	C* before annual limit	Adjustment	Result after annual limit
MP29	2022–2024	1.104	1128.100	15% decrease floor	1177.250
MP43	2022–2024	1.104	1215.661	None	1215.661
MP45	2022–2024	1.104	1155.428	15% decrease floor	1177.250
MP47	2022–2024	1.104	1184.554	None	1184.554
MP32	2022–2024	1.104	692.139	15% decrease floor	1177.250
MP44	2022–2024	1.104	720.131	20% decrease floor	1108.000
MP46	2022–2024	1.104	703.035	15% decrease floor	1177.250
MP48	2022–2024	1.104	738.187	30% decrease floor	969.500

These values should not be interpreted as eight equally supported recommendations: MP43 and MP44 are the focal cases, MP29 and MP32 are sensitivity cases, and MP45–MP48 are comparison cases. The table checks that every rule can be reproduced from one shared set of observations and the settings in the named registry.

7 Why this example stops with 2024 observations

The updated data contain both Peruvian series through 2025, but the 2025 offshore CPUE is absent. Rather than silently omit that series or invent a replacement, the worked calculation backs off one year and uses the complete set available through 2024. Once the missing-data rule and 2025 offshore CPUE status are settled, the same calculation can be advanced one year to produce an illustrative 2026 result.

8 Complete and record the recommendation

For each CMP, save:

the original data files and their units;
the 2019–2023 average for each index;
every annual relative index $R_{j,y}$;
the combined annual indices $A_y$;
the recent-year indicator $I$;
the preliminary harvest-rule result $C^*$;
the previous-advice value and annual-change adjustment;
the unrounded and rounded total recommendation;
any allocation calculation; and
all missing-data, revision, or exceptional-circumstances warnings.

The current simulations divide the total catch among fisheries using average catch shares over the previous five years. The release check records this implemented method consistently. It is not treated here as a further analytical comparison; responses to review comments about allocation are handled separately.

9 What can be concluded from the currently reported value

The approximately 630 kt acoustic estimate alone is not sufficient to calculate a TAC:

it is outside the tested data window for a 2027 recommendation;
it must be expressed relative to the 2019–2023 average for the same survey;
the other four required indices are also needed.

Once the complete annual data table and the agreed previous-advice value are available, the calculations above can be run side by side to show the recommendation produced by every candidate.

10 Implementation basis

This calculation plan is part of SC14-MSE-2026-RC1. It reads the eight current settings directly from the CMP registry. The automatic agreement report compares that registry with the exact 500-draw simulation controls and records the analysis-code revision. The historical index extract used in the worked calculation is saved as cmp-historical-indices.csv. It was extracted from the updated h1_0.16 assessment output associated with input/0.15.dat, retaining both Peruvian index series. The main implementation sources are run_candidate_mps.R and tune_candidate_change_limits.R in the analysis revision named in that report. If the data delays, recent-year windows, combined-index calculation, or annual change rule are revised, this page and the MSE tests must be updated together.

--- title: "Illustrative 2027 TAC calculation" --- {{< include ../_includes/sprfmo-banner.qmd >}} <div class="paper-title">How the Candidate Procedures Would Produce 2027 Advice</div> ::: {.status-note} **This is a calculation plan, not a 2027 TAC recommendation.** None of the candidate management procedures (CMPs) has been adopted. A numerical recommendation cannot be produced until the complete annual index data, the previous catch-advice value, and the rules for data timing, missing values, rounding, and allocation have been confirmed. ::: This page shows how the data available for the 2027 decision would be passed through each CMP. It also identifies where the approximately 630 kt estimate from the 2026 northern Chile acoustic survey could, and could not, be used. ## First settle which data year applies The current MSE runs use a one-year data delay and a one-year management delay. Under that tested timing: 1. the CMP calculation made in 2026 produces catch advice for 2027; 2. the most recent observations used are from 2025; 3. all eight CMPs use 2023–2025 data; and 4. all eight use the same five-index calculation and three-year averaging window. The 2026 northern Chile acoustic estimate therefore **does not enter the 2027 calculation as it was tested in the MSE**. It would first enter the following annual calculation, for 2028 advice. Using observations from 2026 for the 2027 TAC would require a same-year data rule. That would change the timing assumed in the tested CMP and should be specified, coded, and checked before it is used. Under such a revised rule, the three-year window would be 2024–2026. ## Data required All eight CMPs in the named SC14 release use the same five indices. | CMPs | Annual series required | Is the northern Chile acoustic survey used? | |---|---|---| | MP29, MP43, MP45, MP47, MP32, MP44, MP46, MP48 | Northern Chile acoustic survey (`Chile_AcousN`), Chile CPUE, Peru artisanal index, Peru industrial index, and offshore CPUE | Yes, when its data year falls within the approved window | For every series, retain the value, unit, survey or fleet coverage, source, revision status, and date received. Values must be comparable with those used in the 2019–2023 reference period. ## Turn the observations into the CMP indicator The raw indices are on different scales, so they cannot be averaged directly. The current procedure performs the following calculation. ### Express each series relative to its reference-period average For index $j$ in year $y$, $$ R_{j,y} = \frac{\text{index }j\text{ in year }y} {\text{mean of index }j\text{ over 2019--2023}}. $$ A value of 1 means that the observation equals its own 2019–2023 average. A value of 1.25 means it is 25% above that average. The reported acoustic estimate of about 630 kt cannot be entered directly into the harvest rule. If its year is eligible, it must first be checked against the same northern Chile acoustic series and converted to $$ R_{\text{acoustic},2026} = \frac{630\text{ kt}} {\text{mean northern Chile acoustic biomass over 2019--2023}}. $$ The reference-period mean is not recorded on this site, so this contribution cannot yet be calculated here. ### Combine the available series within each year For each year, average the relative values for the indices required by the CMP. This gives one combined annual index $A_y$. The analysis code averages the non-missing series. Before an operational calculation, the Scientific Committee should decide whether a missing required series may be omitted or whether it stops the calculation. A missing value should never be omitted without being reported. ### Average across the recent years The indicator supplied to the harvest rule is: $$ I = \text{mean of the combined annual indices over the approved recent years}. $$ For the tested 2027 timing, use 2023–2025 for all eight CMPs. One common all-index value of $I$ is supplied to each rule. ## Apply each harvest rule The table gives the current settings. Catch quantities use the units of the `jmMSE` analysis; those units and the final rounding convention must be confirmed before providing formal advice. ```{r} #| label: tbl-annual-cmp-settings #| tbl-cap: "Settings for the eight CMPs in the named SC14 release." #| echo: false annual_registry <- read.csv("../data/cmp-registry.csv", stringsAsFactors = FALSE, check.names = FALSE) annual_registry <- annual_registry[ tolower(annual_registry$sc14_release) == "yes", ] annual_settings <- data.frame( CMP = paste0(annual_registry$cmp_id, " (", annual_registry$label, ")"), Information = "All five indices, 3 years", Rule = ifelse(grepl("hockeystick", annual_registry$hcr), "Hockey-stick", "Power ramp"), Minimum = annual_registry$min, Limit = annual_registry$lim, Trigger = annual_registry$trigger, `Target or breakpoint` = annual_registry$target, check.names = FALSE ) knitr::kable(annual_settings, digits = 8) ``` In the new short-label convention, **HS** means hockeystick and **PR** means power ramp. **+20** identifies a 20% maximum annual increase, while **-20** identifies a 20% maximum annual decrease. For a hockeystick CMP, the preliminary catch advice is the minimum at or below the limit, rises in a straight line between the limit and trigger, and equals the target at or above the trigger. For each power-ramp CMP, let $$ x = \frac{I-\text{limit}}{\text{trigger}-\text{limit}}. $$ The preliminary advice is the minimum when $I$ is at or below the limit. It is $$ \text{minimum} + (\text{target}-\text{minimum})x^{2.5} $$ between the limit and trigger, and $$ \text{target}(0.2+0.8x)^{0.6} $$ at or above the trigger. Unlike the hockeystick, the power-ramp advice can continue to rise above its stated target. ## Apply the annual change limit MP29 and MP32 limit the change from the previous year's catch advice to a 15% decrease or a 20% increase. If $C^*$ is the preliminary advice and $C_{2026}$ is the agreed previous advice value, the 2027 value before rounding is $$ C_{2027} = \max\left(0.85C_{2026}, \min\left(C^*,1.20C_{2026}\right)\right). $$ MP43 and MP44 instead allow a 20% decrease and a 15% increase: $$ C_{2027} = \max\left(0.80C_{2026}, \min\left(C^*,1.15C_{2026}\right)\right). $$ MP45 and MP46 use symmetric 15% limits. MP47 and MP48 allow a 30% decrease and a 20% increase. The exact multipliers are read from the CMP registry in the worked calculation below. Under reference OM11, the realized mean probabilities of being in the dynamic Kobe green zone over 2041–2050 were 0.6098, 0.5918, 0.6042, 0.6038, 0.6026, 0.5984, 0.5954, and 0.6056 for MP29, MP43, MP45, MP47, MP32, MP44, MP46, and MP48, respectively. The value 1385 appears as the initial value in the simulation controls. It should not automatically be treated as $C_{2026}$. The operational specification must say whether the annual limit is based on the previous TAC, the previous CMP recommendation, or another approved quantity. ## Worked retrospective: 2025 advice using data through 2024 For this retrospective, the advice year is labelled as the year immediately after the last data year: 2024 observations produce illustrative 2025 advice. This simply backs the calendar labels up one year while retaining the candidate index calculations, harvest rules, and initial comparison value of 1385. This remains an illustration rather than advice adopted by SPRFMO. The result is a total catch quantity in the analysis units, before an approved rounding rule or allocation among fisheries. ```{r} #| label: worked-calculation-setup #| include: false historical_indices <- read.csv( "../data/cmp-historical-indices.csv", na.strings = c("", "NA"), check.names = FALSE ) all_indices <- c( "Chile_AcousN", "Chile_CPUE", "Peru_Artis", "Peru_Ind", "Offshore_CPUE" ) reference_means <- aggregate( value ~ index, historical_indices[historical_indices$year %in% 2019:2023, ], function(x) mean(x, na.rm = TRUE) ) names(reference_means)[2] <- "reference_mean" relative_indices <- merge( historical_indices, reference_means, by = "index", all.x = TRUE ) relative_indices$relative <- relative_indices$value / relative_indices$reference_mean annual_relative <- function(indices) { selected <- relative_indices[relative_indices$index %in% indices, ] annual <- aggregate( relative ~ year, selected, function(x) mean(x, na.rm = TRUE) ) annual$n_available <- vapply(annual$year, function(y) { sum(selected$year == y & !is.na(selected$value)) }, integer(1)) annual } recent_indicator <- function(end_year, n_years, indices) { annual <- annual_relative(indices) years <- seq(end_year - n_years + 1, end_year) mean(annual$relative[annual$year %in% years]) } controls <- annual_registry controls$label <- controls$cmp_id controls$hcr <- sub("\\.hcr$", "", controls$hcr) selected_mps <- c( "MP29", "MP43", "MP45", "MP47", "MP32", "MP44", "MP46", "MP48" ) controls <- controls[match(selected_mps, controls$label), ] calculate_advice <- function(control_row, end_year, previous = 1385) { indices <- all_indices n_years <- control_row$window_years indicator <- recent_indicator(end_year, n_years, indices) if (control_row$hcr == "hockeystick") { preliminary <- if (indicator <= control_row$lim) { control_row$min } else if (indicator < control_row$trigger) { control_row$min + (indicator - control_row$lim) * (control_row$target - control_row$min) / (control_row$trigger - control_row$lim) } else { control_row$target } } else if (control_row$hcr == "powerramp") { x <- (indicator - control_row$lim) / (control_row$trigger - control_row$lim) preliminary <- if (indicator <= control_row$lim) { control_row$min } else if (indicator < control_row$trigger) { control_row$min + (control_row$target - control_row$min) * x^2.5 } else { control_row$target * (0.2 + 0.8 * x)^0.6 } } lower <- control_row$dlow * previous upper <- control_row$dupp * previous adjusted <- max(lower, min(preliminary, upper)) adjustment <- if (preliminary < lower) { paste0(round(100 * (1 - control_row$dlow)), "% decrease floor") } else if (preliminary > upper) { paste0(round(100 * (control_row$dupp - 1)), "% increase ceiling") } else { "None" } data.frame( CMP = control_row$label, `Index years` = paste0(end_year - n_years + 1, "–", end_year), Indicator = indicator, `C* before annual limit` = preliminary, Adjustment = adjustment, `Result after annual limit` = adjusted, check.names = FALSE ) } advice_for_year <- function(end_year) { do.call(rbind, lapply(seq_len(nrow(controls)), function(i) { calculate_advice(controls[i, ], end_year = end_year) })) } advice_2024 <- advice_for_year(2024) calculation_text <- function(control_row, indicator) { fmt <- function(x) formatC(x, digits = 3, format = "f") if (indicator <= control_row$lim) { return(paste0( "Indicator is at or below the limit; use minimum ", fmt(control_row$min) )) } if (control_row$hcr == "hockeystick") { if (indicator >= control_row$trigger) { return(paste0( "Indicator is at or above the trigger; use target ", fmt(control_row$target) )) } return(paste0( fmt(control_row$min), " + (", fmt(indicator), " − ", fmt(control_row$lim), ") × (", fmt(control_row$target), " − ", fmt(control_row$min), ") ÷ (", fmt(control_row$trigger), " − ", fmt(control_row$lim), ")" )) } x <- (indicator - control_row$lim) / (control_row$trigger - control_row$lim) if (indicator < control_row$trigger) { return(paste0( "x = (", fmt(indicator), " − ", fmt(control_row$lim), ") ÷ (", fmt(control_row$trigger), " − ", fmt(control_row$lim), ") = ", fmt(x), "; ", fmt(control_row$min), " + (", fmt(control_row$target), " − ", fmt(control_row$min), ") × x raised to 2.5" )) } paste0( "x = (", fmt(indicator), " − ", fmt(control_row$lim), ") ÷ (", fmt(control_row$trigger), " − ", fmt(control_row$lim), ") = ", fmt(x), "; ", fmt(control_row$target), " × (0.2 + 0.8 × x) raised to 0.6" ) } rule_names <- c( hockeystick = "Hockeystick", powerramp = "Power ramp" ) conversion_table <- do.call(rbind, lapply(seq_len(nrow(controls)), function(i) { data.frame( CMP = controls$label[i], Indicator = advice_2024$Indicator[i], Rule = unname(rule_names[controls$hcr[i]]), `Substitute the indicator in the rule` = calculation_text(controls[i, ], advice_2024$Indicator[i]), `C* before annual limit` = advice_2024$`C* before annual limit`[i], check.names = FALSE ) })) ``` ### Historical inputs The table contains the observations from the updated assessment data associated with `input/0.15.dat`. The two Peruvian series are retained separately as `Peru_Artis` and `Peru_Ind`. Each reference mean is calculated over the available observations in 2019–2023. The northern acoustic series has no 2022 value. ```{r} #| label: tbl-retrospective-inputs #| tbl-cap: "Historical observations used for the retrospective calculation. A dash means that no value is stored." #| echo: false recent_inputs <- historical_indices[ historical_indices$year %in% 2022:2025, ] wide_inputs <- reshape( recent_inputs, idvar = "index", timevar = "year", direction = "wide" ) names(wide_inputs) <- sub("^value\\.", "", names(wide_inputs)) input_table <- merge(reference_means, wide_inputs, by = "index", all.x = TRUE) input_table <- input_table[ match(all_indices, input_table$index), c("index", "reference_mean", "2022", "2023", "2024", "2025") ] names(input_table) <- c( "Series", "2019–2023 mean", "2022", "2023", "2024", "2025" ) old_na <- getOption("knitr.kable.NA") options(knitr.kable.NA = "—") knitr::kable(input_table, digits = 3) options(knitr.kable.NA = old_na) ``` ### Indicators for the 2025 calculation The all-index annual values are 1.141 for 2022, 1.159 for 2023, and 1.013 for 2024. Their three-year mean is 1.104. This same indicator is supplied to each of the eight rules. ```{r} #| label: tbl-retrospective-indicators #| tbl-cap: "Relative-index values supplied to the candidate harvest rules for the retrospective 2025 calculation." #| echo: false indicator_table <- data.frame( `Used by` = "All eight SC14 CMPs", `Index set` = "All five indices", `Years averaged` = "2022–2024", Indicator = recent_indicator(2024, 3, all_indices), check.names = FALSE ) knitr::kable(indicator_table, digits = 3) ``` ### Turn the indicator into preliminary advice The indicator is a relative measure, not a catch quantity. A value of 1 means that the recent indices are, on average, equal to their 2019–2023 reference levels. A value above 1 means they are higher; a value below 1 means they are lower. Each candidate then puts its indicator into its own harvest-control rule. The rule converts the relative indicator into a catch quantity. Because the candidates have different limits, triggers, targets, and rule shapes, the same indicator can produce different preliminary advice. We write this preliminary catch advice as $C^*$. Here, $C$ means catch advice and the star means **provisional**: it is the harvest-control-rule result before the annual change limit is applied. The star is not another calculation. The table shows the substitution explicitly. Values displayed in the calculation are rounded to three decimal places; the code uses the unrounded values. ```{r} #| label: tbl-indicator-to-advice #| tbl-cap: "How each candidate converts its indicator into preliminary catch advice (C*)." #| echo: false knitr::kable(conversion_table, digits = 3) ``` For example, MP29 uses the hockeystick rule: $$ C^* = 270 + \frac{(1.104-0.100)(2000-270)} {(2.125-0.100)} = 1128.10. $$ The value 1128.10 is therefore MP29's harvest-rule result. It is not yet the final value because the annual change limit must still be applied. ### Apply the annual change limit With 1385 as the initial comparison value, each CMP applies the decrease and increase multipliers recorded in the registry. The table reports the range that affects each result rather than applying one common limit to all CMPs. ```{r} #| label: tbl-retrospective-advice #| tbl-cap: "Illustrative 2025 total catch advice using observations through 2024 and an initial comparison value of 1385." #| echo: false knitr::kable(advice_2024, digits = 3) ``` These values should not be interpreted as eight equally supported recommendations: MP43 and MP44 are the focal cases, MP29 and MP32 are sensitivity cases, and MP45--MP48 are comparison cases. The table checks that every rule can be reproduced from one shared set of observations and the settings in the named registry. ## Why this example stops with 2024 observations The updated data contain both Peruvian series through 2025, but the 2025 offshore CPUE is absent. Rather than silently omit that series or invent a replacement, the worked calculation backs off one year and uses the complete set available through 2024. Once the missing-data rule and 2025 offshore CPUE status are settled, the same calculation can be advanced one year to produce an illustrative 2026 result. ## Complete and record the recommendation For each CMP, save: 1. the original data files and their units; 2. the 2019–2023 average for each index; 3. every annual relative index $R_{j,y}$; 4. the combined annual indices $A_y$; 5. the recent-year indicator $I$; 6. the preliminary harvest-rule result $C^*$; 7. the previous-advice value and annual-change adjustment; 8. the unrounded and rounded total recommendation; 9. any allocation calculation; and 10. all missing-data, revision, or exceptional-circumstances warnings. The current simulations divide the total catch among fisheries using average catch shares over the previous five years. The release check records this implemented method consistently. It is not treated here as a further analytical comparison; responses to review comments about allocation are handled separately. ## What can be concluded from the currently reported value The approximately 630 kt acoustic estimate alone is not sufficient to calculate a TAC: - it is outside the tested data window for a 2027 recommendation; - it must be expressed relative to the 2019–2023 average for the same survey; - the other four required indices are also needed. Once the complete annual data table and the agreed previous-advice value are available, the calculations above can be run side by side to show the recommendation produced by every candidate. ## Implementation basis This calculation plan is part of `SC14-MSE-2026-RC1`. It reads the eight current settings directly from the [CMP registry](../data/cmp-registry.csv). The [automatic agreement report](../governance/release-check.qmd) compares that registry with the exact 500-draw simulation controls and records the analysis-code revision. The historical index extract used in the worked calculation is saved as [`cmp-historical-indices.csv`](../data/cmp-historical-indices.csv). It was extracted from the updated `h1_0.16` assessment output associated with `input/0.15.dat`, retaining both Peruvian index series. The main implementation sources are `run_candidate_mps.R` and `tune_candidate_change_limits.R` in the analysis revision named in that report. If the data delays, recent-year windows, combined-index calculation, or annual change rule are revised, this page and the MSE tests must be updated together.