32  Implementing Advice: One Complex, Multiple Fleets

This chapter covers a single complex (one stock, or several pooled under one joint TAC/Effort) fished by more than one fleet, so a single TAC or Effort value must be allocated or jointly solved across fleets.

If your model has only one fleet, the simpler procedure in Chapter 31 applies instead. If it has more than one complex, see Chapter 33 for how effort is reconciled across complexes.

TAC and Effort values are first resolved and pre-processed as described in Section 30.4 (carry-forward, implementation error, the TAC/Effort ceiling interaction).

32.1 TAC Allocation Across Fleets

A scalar (stock/complex-total) TAC is allocated across fleets using OM@Allocation. An MP can instead set Advice@TAC as a length-nFleet vector to specify each fleet’s TAC directly, bypassing OM@Allocation entirely.

32.2 Solving for Effort

The model solves jointly for every active fleet’s effort (a fleet is “active” if its allocated TAC is positive) on the log scale:

  1. Diagonal Newton-Raphson: each fleet’s effort is updated using only its own diagonal sensitivity, \[\log E_f^{(k+1)} = \log E_f^{(k)} + \operatorname{clamp}\!\left(\frac{r_f^{(k)}}{J_{ff}^{(k)} \cdot E_f^{(k)}},\, \pm\log_{10}\right), \qquad r_f = \text{TAC}_f - C_f(E)\] with the diagonal Jacobian \(J_{ff}\) estimated by finite difference.
  2. Full-Jacobian fallback: whenever the diagonal step fails to reduce the total squared residual across active fleets, a full Newton step is taken instead, estimating the complete cross-fleet Jacobian (capturing how one fleet’s effort affects another’s realised catch through shared vulnerable biomass) and solving the resulting linear system jointly.
  3. BFGS fallback (stats::optim()): used only if neither Newton-Raphson variant converges or saturates within maxIter (default 100) iterations.

Saturation: a fleet is declared saturated (its TAC treated as unachievable) when its effort reaches 99% of the hard ceiling maxEffort with a persistently positive residual, or when neither the diagonal nor full-Jacobian step improves the fit. In this case the fleet with the largest unresolved residual is considered saturated. Saturated fleets are frozen at their current effort and excluded from further iterations, so one severely depleted stock/fleet combination cannot prevent convergence for the other fleets. Fleets with no TAC constraint at all keep their previous effort (subject to any Effort-advice ceiling from Section 30.4).