4  Performance Metrics

4.1 Primary Performance Metrics

Resolution 24-09 (ICCAT 2024) describes the initial operational management objectives for Southern Atlantic Albacore:

  1. Stock Status. The stock should have a 60% or greater probability of occurring in the green quadrant of the Kobe matrix over a 30-year projection period: i.e. \(SB > SB_{MSY}\) and \(F < F_{MSY}\) simultaneously.

  2. Safety. There should be no greater than 15% probability of the stock falling below \(B_{LIM}\) at any point during the 30-year projection period, using an interim \(B_{LIM}\) of 40% of \(SB_{MSY}\). So that higher values are better for every PM, this is expressed as the probability of the stock remaining at or above \(B_{LIM}\) throughout the projection period, with a target of at least 85%.

  3. Yield. The objective is to maximise overall catch levels. As the Resolution does not specify a particular statistic, the mean annual catch is used.

  4. Stability. Any change in total allowable catch (TAC) between management periods should be 20% or less, noting that asymmetric stability limits (e.g. different thresholds for TAC increases versus decreases) may also be evaluated. This is expressed as the probability that the change in TAC between successive management cycles is less than 20%; i.e. calculated between the TAC values actually set every 3 years.

Table 4.1 summarises these objectives together with the corresponding performance metric and the associated target. The equation for each performance metric is given below the table.

Table 4.1: Summary of the Resolution 24-09 (ICCAT 2024) initial operational management objectives and the corresponding performance metrics used to evaluate CMP performance.
Objective Performance Metric Target
Stock Status Probability of occurring in the Kobe green quadrant ≥ 60%
Safety Probability of remaining at or above \(B_{LIM}\) (40% \(SB_{MSY}\)) throughout the projection ≥ 85%
Yield Mean annual catch Maximise
Stability Probability that the change in TAC between management periods is < 20% Ranked

Each PM can also be calculated for an individual OM or across a set of OMs (e.g. the Reference Set). In the latter case, the simulations from every OM in the set are first combined into a single pooled MSE object and the summary statistic (e.g. a probability or a mean) is then calculated over that combined set of simulations.

The performance metrics in Table 4.1 are calculated as follows:

Stock Status: \[ \text{Prob}\left(SB/SB_{MSY} > 1 \text{ and } F/F_{MSY} < 1\right) \]

Safety: \[ \text{Prob}\left(\min_y(SB_y/SB_{MSY}) \geq 0.4\right) \]

Yield: \[ \text{mean}_y(C_y) \]

Stability: \[ \text{Prob}\left(\lvert (TAC_c - TAC_{c-1})/TAC_{c-1}\rvert < 0.2\right) \]

4.2 Secondary Performance Metrics

Beyond the four primary metrics above, a wider set of performance metrics are reported for every CMP/OM combination (Table 4.2).

Every performance metric (PM) is calculated over the full 30-year projection period. Status, Yield, SB_SBMSY, and F_FMSY are also broken down into three time windows:

  1. Short: the first 10 years (2028 – 2037);
  2. Medium: the second 10 years (2038 – 2047);
  3. Long: the last 10 years (2048 – 2057).
Table 4.2: Secondary performance metrics computed for every CMP/OM combination, in addition to the four primary metrics above.
Code Metric Description
SB_SBMSY_All SB/SBMSY (all years) Mean annual SB/SBMSY ratio over all projection years.
F_FMSY_All F/FMSY (all years) Mean annual F/FMSY ratio over all projection years.
Depletion_Min Minimum depletion Lowest annual SB/SB0 (depletion) reached during the projection.
ATV Average TAC variability Mean yield variability between management cycles across the projection.
Status_Short Status (years 1-10) Probability that SB > SBMSY and F < FMSY simultaneously, over the first 10 projection years (short-term).
Status_Medium Status (years 11-20) Probability that SB > SBMSY and F < FMSY simultaneously, over the middle 10 projection years (medium-term).
Status_Long Status (years 21-30) Probability that SB > SBMSY and F < FMSY simultaneously, over the final 10 projection years (long-term).
Yield_Short Yield (years 1-10) Mean annual catch over the first 10 projection years (short-term).
Yield_Medium Yield (years 11-20) Mean annual catch over the middle 10 projection years (medium-term).
Yield_Long Yield (years 21-30) Mean annual catch over the final 10 projection years (long-term).
SB_SBMSY_Short SB/SBMSY (years 1-10) Mean annual SB/SBMSY ratio over the first 10 projection years (short-term).
SB_SBMSY_Medium SB/SBMSY (years 11-20) Mean annual SB/SBMSY ratio over the middle 10 projection years (medium-term).
SB_SBMSY_Long SB/SBMSY (years 21-30) Mean annual SB/SBMSY ratio over the final 10 projection years (long-term).
F_FMSY_Short F/FMSY (years 1-10) Mean annual F/FMSY ratio over the first 10 projection years (short-term).
F_FMSY_Medium F/FMSY (years 11-20) Mean annual F/FMSY ratio over the middle 10 projection years (medium-term).
F_FMSY_Long F/FMSY (years 21-30) Mean annual F/FMSY ratio over the final 10 projection years (long-term).