30  Implementing Management Advice

This chapter gives the mathematical and mechanical specification of how the Advice object returned by a management procedure (MP) is used to update the population dynamics during Project(). For the conceptual overview of Simulate()/Project() see Chapter 18; for Data and Advice object structure see Management Procedures.

Everything in this chapter applies regardless of how many stocks, complexes, or fleets an operating model has. How a TAC or Effort value is actually converted into simulated fishing effort, however, depends on that structure. Use the table below to go straight to the chapter relevant to your model.

30.1 Which Chapter Do I Need?

Your model Effort-solving mechanics Chapter
One complex (any number of stocks pooled under one joint TAC/Effort), one fleet Direct root-finding: solve for the single fleet’s effort that hits the TAC Chapter 31
One complex, multiple fleets sharing that complex’s TAC TAC allocation across fleets, then joint Newton-Raphson/BFGS solving Chapter 32
Multiple complexes sharing one or more fleets (a true multi-stock OM) Cross-complex reconciliation and fleet-specific stock-targeting weights Chapter 33

The rest of this chapter describes processes that are identical across all three cases.

30.2 Management Intervals and Interim Years

Interval(OM) sets how often an MP is run:

\[\text{ManagementYears} = \{ Y_1, Y_{1+\text{Interval}}, Y_{1+2\cdot\text{Interval}}, \ldots \}\]

In a non-management year, the previous year’s Advice is used.

30.3 Data Passed to the MP

The Data object an MP receives is not necessarily built from the most recently completed year.

\[\text{DataYear} = \text{YearsAll}\bigl[\,n_{\text{Years}} - \text{DataLag} \times \text{Seasons}\,\bigr]\]

where DataLag (OM@DataLag) is in whole years and Seasons is the number of within-year time steps. DataTrim() truncates the simulated Data object to this year before the MP sees it, reflecting reporting/processing delays between when data are collected and when they are available to inform management.

30.4 Resolving TAC and Effort Values Before Solving

TAC and Effort values are resolved and pre-processed the same way before any effort-solving takes place:

  • If an MP leaves TAC/Effort unset this year, the previous year’s resolved value is reused (Section 30.2).
  • Implementation error is applied multiplicatively.
  • If Effort advice was also set this year for the same complex, the resolved Effort value acts as a hard ceiling on the TAC-solving effort for that fleet.
  • A scalar (stock-total) TAC with more than one fleet is allocated across fleets using OM@Allocation (see Chapter 32).

When TAC is returned by Advice, the model must solve for the fishing effort that would result in catches matching this TAC. How that root-finding problem is solved depends on the OM structure — see Section 30.1.

30.5 Direct Effort Advice

When an MP sets Effort directly (rather than a TAC to be solved for), it is applied per complex, A scalar Effort is expanded to all fleets; EffType ("Rel", relative to the last historical year’s effort, or "Abs", absolute). Then implementation error is applied to the effort recommendation and the population dynamics calculated with the resulting effort values.

This is the effort-application procedure for an OM with a single complex. Where multiple complexes set Effort for the same fleet, an additional reconciliation step applies; see Chapter 33.

30.6 Bag-Limit Regulations

Bag limits (Advice@BagLimit, in fish per trip) are a management method distinct from TAC/Effort controls. Rather than a stock-wide catch or effort target, they cap what an individual angler or vessel may retain per trip. Two parameters govern enforcement:

1. LimitType:

  • "angler" (default): the limit applies per angler, so the effective vessel-level cap is \(\text{BagLimit} \times \text{AnglerPerTrip}\);
  • "boat", applied directly per vessel trip.

2. ClosureMode: "discard" (default) or "stop", described below.

Trip count for a fleet/stock is \(T_f = E_f\) if Fleet@Effort@Units == "trips", otherwise \(T_f = \text{TripsScalar} \times E_f\).

30.6.1 ClosureMode = "discard"

The regulation does not stop fishing. Excess catch above the limit is discarded (subject to the fleet’s DiscardMortality).

Per-trip retained catch is modelled as negative binomially distributed, \(X \sim \text{NegBin}(\mu, \theta)\), with mean \(\mu_f = C_f^{\text{ret}} / T_f\) (retained numbers per trip at the current effort) and dispersion \(\theta\) (Fleet@Effort@Theta).

The expected excess above the cap \(B_{\text{cap}} = \text{BagLimit} \times (\text{AnglerPerTrip if angler-based})\) is

\[ \mathbb{E}[\max(X - B_{\text{cap}}, 0)] = \sum_{x = \lceil B_{\text{cap}}\rceil + 1}^{x_{\max}} (x - B_{\text{cap}}) \cdot \Pr(X = x) \]

evaluated by truncated summation up to the \(99.99\)th percentile of the negative binomial. The realised fraction of unconstrained catch actually retained is then

\[\rho_f = \frac{\mathbb{E}[\min(X, B_{\text{cap}})]}{\mu_f} = \min\!\Bigl(\max\bigl(\tfrac{\mu_f - \mathbb{E}[\max(X-B_{\text{cap}},0)]}{\mu_f},\, 0\bigr),\, 1\Bigr)\]

The fleet/stock’s retention-at-age and retention-at-length arrays are then scaled by \(\rho_f\) for the current year, proportionally reducing landings while preserving the age/size shape of retention. \(\rho_f\) is recomputed every year the bag limit is active (even if the BagLimit value itself is unchanged), because \(\mu_f\) moves with current stock abundance under a fixed regulation.

30.6.2 ClosureMode = "stop"

Rather than discarding excess catch, effort is capped so that aggregate retained catch does not exceed the bag-limit-implied seasonal allowance. In this mode, the model finds effort \(E_f \leq E_f^{\text{curr}}\) (the effort already resolved by the TAC/Effort steps above) such that

\[\text{RetainedNumbers}_f(E_f) = B_{\text{cap}} \times T_f(E_f^{\text{curr}})\]

This covers a bag limit set on a single stock’s own Advice object. Pooling a bag limit across several stocks for one fleet (AggregateBagLimit(), mmp-class MPs only) is described in Chapter 33.