| Category | Management Objective | Performance Metric |
|---|---|---|
| Safety | Maintain SSB above the LRP with at least 80% probability | Probability that SB > LRP (17% \(SB_0\)) in every year of the evaluation period |
| Status | Maintain fishing intensity (F) at the target value with at least 50% probability | Probability that F \(\leq\) F\(_{40\%}\) & median F\(_{40\%}\)/F |
| Stability | Change in TAC between years should be relatively gradual | Probability that the change in TAC between consecutive management periods is \(\leq\) 10% |
| Probability of no management change: probability that the change in TAC between consecutive management periods is \(\leq\) 1% | ||
| Yield | Maintain catches above average historical catch levels | Probability that the annual catch is \(\geq\) the mean 2008–2010 catch |
| Mean annual catch (maximized tuning objective) |
4 Performance Metrics
4.1 Management Objectives
The CMPs are evaluated against the following management objectives (Table 4.1):
Safety: Maintain spawning biomass above the limit reference point (LRP; 0.17\(SB_0\)) with at least 80% probability. A simulation in which spawning biomass falls below the LRP in any year of the evaluation period is considered a breach.
Status: Maintain fishing mortality at or below the target value (F\(_{40\%}\)) with at least 50% probability.
Stability: Changes in the TAC between management periods should be relatively gradual. This is measured by the probability that the TAC changes by no more than 10% between consecutive management periods, and by the probability of no management change (the TAC changes by no more than 1%; the CMPs leave the TAC unchanged when the change would be less than 1%).
Yield: Maintain catches above the average historical catch level, measured by the probability that the annual catch is at least the mean catch in 2008–2010. The mean annual catch is also reported.
The CMPs are tuned in the base case OM to maximise the mean annual catch subject to the Safety objective (probability of at least 0.8) and the Status objective (probability of at least 0.5; Section 5.7). The Stability and Yield metrics are not used in the tuning; the trade-off between TAC stability and catch is shown by the variants of each CMP type with different limits on the change in the TAC.
4.2 Primary Performance Metrics
All performance metrics are calculated over the 30 years in which the CMPs set the TAC (2028–2057), for each OM and CMP. The following notation is used:
- \(s = 1, \ldots, S\) indexes the simulations and \(y \in \mathcal{Y}\) the \(N_Y\) = 30 years;
- \(B_{s,y}\) is the annual spawning biomass relative to \(SB_0\);
- \(F_{s,y}\) is the annual apical fishing mortality;
- \(C_{s,y}\) is the annual catch (total removals of all fleets, in t);
- \(\text{TAC}_{s,c}\) is the TAC set in management cycle \(c = 1, \ldots, N_C\), and \(\Delta_{s,c} = \lvert \text{TAC}_{s,c} - \text{TAC}_{s,c-1} \rvert / \text{TAC}_{s,c-1}\) is the relative change in the TAC;
- \(\mathrm{I}(\cdot)\) is 1 if the condition is true and 0 otherwise.
Safety: the probability that spawning biomass remains above the LRP in every year:
\[ P_{\text{Safety}} = \frac{1}{S} \sum_{s} \mathrm{I}\left(\min_{y \in \mathcal{Y}} B_{s,y} > 0.17\right) \]
Status: the probability that fishing mortality is at or below the F target, and the median ratio of the F target to fishing mortality:
\[ P_{\text{Status}} = \frac{1}{S N_Y} \sum_{s} \sum_{y} \mathrm{I}\left(F_{s,y} \leq F_{\text{target}}\right) \]
\[ \frac{F_{\text{target}}}{F} = \frac{1}{S} \sum_{s} \operatorname*{median}_{y} \left(\frac{F_{\text{target}}}{F_{s,y}}\right) \]
where \(F_{\text{target}}\) is F\(_{40\%}\), the apical fishing mortality that reduces the female spawning potential ratio to 40%.
Stability: the probability that the TAC changes by no more than 10% between management cycles, and the probability of no management change, i.e. that the TAC changes by no more than 1%:
\[ P_{\text{Stability}} = \frac{1}{S N_C} \sum_{s} \sum_{c} \mathrm{I}\left(\Delta_{s,c} \leq 0.1\right) \]
\[ P_{\text{No change}} = \frac{1}{S N_C} \sum_{s} \sum_{c} \mathrm{I}\left(\Delta_{s,c} \leq 0.01\right) \]
Yield: the probability that the annual catch is at least the mean historical catch in 2008–2010 (\(\bar{C}_{\text{ref}}\), in the OM), and the mean annual catch:
\[ P_{\text{Yield}} = \frac{1}{S N_Y} \sum_{s} \sum_{y} \mathrm{I}\left(C_{s,y} \geq \bar{C}_{\text{ref}}\right) \]
\[ \bar{C} = \frac{1}{S N_Y} \sum_{s} \sum_{y} C_{s,y} \]
4.3 Secondary Performance Metrics
Average TAC variability: the mean absolute relative change in the TAC between management cycles:
\[ \text{AAVY} = \frac{1}{S N_C} \sum_{s} \sum_{c} \Delta_{s,c} \]
Kobe green quadrant: the probability that the stock is not overfished and overfishing is not occurring:
\[ P_{\text{Kobe}} = \frac{1}{S N_Y} \sum_{s} \sum_{y} \mathrm{I}\left(\frac{SB_{s,y}}{SB_{\text{MSY}}} > 1 \ \text{and} \ \frac{F_{s,y}}{F_{\text{MSY}}} < 1\right) \]
4.4 Summary of All Performance Metrics
Safety (no breach within the window), mean catch, and \(SB/SB_0\) are also calculated for three time windows:
- Short: the first 10 years (2028–2037);
- Medium: the second 10 years (2038–2047);
- Long: the last 10 years (2048–2057).
All the performance metrics reported for every CMP and OM combination are listed in Table 4.2.
| Metric | Description |
|---|---|
| Probability SB > LRP | Probability that spawning biomass remains above the limit reference point (LRP; 17% SB0) in every year of the projection period: a simulation that falls below the LRP in any year is a breach. |
| Probability F <= F target (F40%) | Probability that fishing mortality is at or below the F target (F40% of the HCR), over all projection years. |
| F target / F | Median ratio of the F target (F40%) to fishing mortality over the projection years; values above 1 mean F is below the target. |
| Catch stability (TAC change <= 10%) | Probability that the TAC changes by no more than 10% between consecutive management cycles. |
| Probability of no management change | Probability of no management change: the probability that the TAC changes by no more than 1% between consecutive management cycles. |
| Probability catch >= 2008-2010 catch | Probability that the annual catch is at least the mean historical catch in 2008-2010, over all projection years. |
| Mean catch (all years) | Mean annual catch (t) over all projection years. |
| Mean catch (years 1-10) | Mean annual catch (t) over the first 10 projection years (short-term). |
| Mean catch (years 11-20) | Mean annual catch (t) over the middle 10 projection years (medium-term). |
| Mean catch (years 21-30) | Mean annual catch (t) over the final 10 projection years (long-term). |
| Probability SB > LRP (years 1-10) | Probability that spawning biomass remains above the limit reference point (LRP; 17% SB0) in every year of the first 10 projection years (short-term). |
| Probability SB > LRP (years 11-20) | Probability that spawning biomass remains above the limit reference point (LRP; 17% SB0) in every year of the middle 10 projection years (medium-term). |
| Probability SB > LRP (years 21-30) | Probability that spawning biomass remains above the limit reference point (LRP; 17% SB0) in every year of the final 10 projection years (long-term). |
| SB/SB0 (all years) | Mean spawning biomass relative to the equilibrium unfished spawning biomass (SB/SB0) over all projection years. |
| SB/SB0 (years 1-10) | Mean SB/SB0 over the first 10 projection years (short-term). |
| SB/SB0 (years 11-20) | Mean SB/SB0 over the middle 10 projection years (medium-term). |
| SB/SB0 (years 21-30) | Mean SB/SB0 over the final 10 projection years (long-term). |
| Minimum SB/SB0 | Lowest annual SB/SB0 reached during the projection. |
| Probability Kobe green quadrant | Probability that SB > SBMSY and F < FMSY in the same year, over all projection years. |
| SB/SBMSY (all years) | Mean annual SB/SBMSY over all projection years. |
| F/FMSY (all years) | Mean annual F/FMSY over all projection years. |
| Average TAC variability | Mean absolute relative change in the TAC between management cycles. |