Solve for fishing mortality corresponding to a target TAC

`get.f()` finds the fishing mortality (FM) that produces a given total allowable catch (TAC) over a TAC period, accounting for seasonal structure, natural mortality, selectivity, and recruitment. Internally, it repeatedly calls the catch-prediction logic (e.g. [predCatch()]) and uses a numerical root-finding or optimisation routine to match predicted catch to the target `TAC`.

Usage

get.f(
  TAC,
  NAA,
  MAA,
  sel,
  weight,
  seasons,
  ns,
  y,
  h,
  asmax,
  mat,
  pzbm,
  spawning,
  R0,
  SR,
  bp,
  recBeta,
  recGamma,
  eR,
  indage0,
  lastFM = 0.01,
  upper = log(100)
)

Arguments

TAC: Numeric value giving the target total allowable catch for the TAC period (e.g. over the seasons specified in `seasons`).
NAA: Numbers-at-age at the start of the TAC period (typically a vector or matrix indexed by age and possibly season).
MAA: Natural mortality-at-age (and, if applicable, season) used in the projection.
sel: Selectivity-at-age (and possibly season) applied to fishing mortality when computing catch.
weight: Mean weight-at-age (and possibly season) used to convert numbers caught into catch biomass.
seasons: Integer vector with the season indices included in the TAC period (e.g. quarters or months within a year).
ns: Integer giving the total number of seasons per year.
y: Integer index of the current year in the projection.
h: Steepness (or related parameter) of the stock–recruitment relationship, used when updating recruitment along the projection.
asmax: Integer giving the maximum spawning age (or related age limit) used when computing spawning biomass and recruitment.
mat: Maturity-at-age (and possibly season), used to calculate spawning biomass.
pzbm: Additional parameter controlling the timing or proportion of biomass contributing to spawning (exact role depends on the internal implementation).
spawning: Indicator (e.g. logical or integer vector) identifying the spawning season(s) within the year.
R0: Unfished recruitment level used in the stock–recruitment relationship.
SR: Character string or code specifying the type of stock–recruitment function (e.g. Beverton–Holt, Ricker), as used in the operating model.
bp: Additional parameter (or vector of parameters) for the stock–recruitment relationship (e.g. breakpoints or shape parameters).
recBeta: Parameter (or vector) controlling the slope or shape of the recruitment function.
recGamma: Parameter (or vector) controlling the curvature or shape of the recruitment function.
eR: Stochastic recruitment deviation(s) applied to the expected recruitment (e.g. lognormal errors).
indage0: Integer index specifying the recruitment age (age at which new recruits enter the age structure).
lastFM: Numeric value giving the starting (or typical) fishing mortality used as an initial guess in the numerical search. Default is `0.01`.
upper: Numeric value giving the upper bound (on the log scale) for the search over fishing mortality. Default is `log(100)`, corresponding to a relatively high maximum F.

Value

A numeric value giving the fishing mortality (or F-multiplier) that produces a predicted catch matching `TAC` as closely as possible under the given biological and seasonal assumptions.

Details

This function is typically called internally by higher-level IAMSE functions when implementing HCRs that are specified in terms of TAC (rather than directly in terms of fishing mortality).

The function typically:

Defines an objective function measuring the difference between the predicted catch (for a given FM) and the target `TAC`.
Searches over FM (on a log scale) between a lower bound and `upper`, using `lastFM` as an initial value.
Returns the FM that minimises this difference (or sets the root to zero), within numerical tolerance.

The exact optimisation method depends on the internal implementation (e.g. use of [stats::optimize()] or [stats::uniroot()]).