Convert a target catch to fishing mortality for a single fleet via bisection

Uses interval bisection to find the scalar fishing mortality \(F\) that produces a predicted catch (Baranov catch equation, summed over ages and sexes in biomass) equal to catch. Retained and discarded catch components are handled separately via retention selectivity and discard mortality. Intended for closed-loop MSE harvest control rules where a TAC must be translated into an \(F\) for the operating model.

Usage

catch_to_F_singlefleet(
  f_guess,
  catch,
  NAA,
  WAA,
  natmort,
  fish_sel,
  ret_sel = {
     tmp = fish_sel[]
tmp[] <- 1
     tmp
 },
  dmr = 0,
  n.iter = 20,
  lb = 0,
  ub = 2
)

Arguments

f_guess: Numeric. Initial \(F\) guess (not used directly by the bisection algorithm but retained for API consistency).
catch: Numeric. Target catch in biomass units.
NAA: Numeric matrix [n_ages x n_sexes]. Numbers-at-age at the start of the time step.
WAA: Numeric matrix [n_ages x n_sexes]. Weight-at-age.
natmort: Numeric matrix [n_ages x n_sexes]. Instantaneous natural mortality rate.
fish_sel: Numeric matrix [n_ages x n_sexes]. Fishery selectivity (scaled to a maximum of 1).
ret_sel: Numeric matrix [n_ages x n_sexes]. Retention selectivity, i.e. the proportion of selected catch that is retained (vs. discarded). Default is an array of 1s matching dim(fish_sel) (full retention).
dmr: Numeric scalar. Discard mortality rate, i.e. the fraction of discarded fish that die. Default 0 (all discards survive).
n.iter: Integer. Number of bisection iterations. Default 20; approximately \(\log_2((ub - lb) / \epsilon)\) iterations are required for tolerance \(\epsilon\).
lb: Numeric. Lower bound of the \(F\) search interval. Default 0.
ub: Numeric. Upper bound of the \(F\) search interval. Default 2.

Value

Scalar numeric. The \(F\) value at the final bisection midpoint that most closely produces catch.

Convert a target catch to fishing mortality for a single fleet via bisection

Usage

Arguments

Value

See also