Initial numbers and Beverton-Holt parameters

Computes the initial equilibrium numbers-at-age, unfished recruitment (R0), and Beverton-Holt stock-recruitment parameters.

Usage

get_initial_numbers(
  B0,
  h,
  M_a,
  spawning_potential_a,
  init_F_f = NULL,
  sel_fa = NULL,
  n_season = 1L,
  init_rdev_a = NULL,
  sigma_r = 0.6,
  init_bias_adj_a = NULL
)

Arguments

B0

Unfished spawning biomass.

h

Beverton-Holt steepness parameter.

M_a

a vector of natural mortality at age.

spawning_potential_a

a vector of spawning potential at age (maturity x fecundity).

init_F_f

an optional vector of initial fishing mortality by fishery.

sel_fa

an optional matrix of selectivity-at-age with dimensions [n_fishery, n_age].

n_season

Number of seasons used to translate annual initial fishing mortality into seasonal harvest fractions.

init_rdev_a

an optional vector of initial age deviations.

sigma_r

recruitment standard deviation used in lognormal correction.

init_bias_adj_a

an optional vector of bias adjustment scalars for initial age deviations. Defaults to zero so fixed zero initial deviations do not alter the equilibrium initial age structure.

Value

A list containing:

Ninit

Initial numbers-at-age (vector).

Ninit0

Initial unfished numbers-at-age (vector).

R0

Unfished recruitment (scalar).

alpha

BH alpha parameter.

beta

BH beta parameter.

lp_penalty

Penalty for constrained initial survival or recruitment.

Details

Seasonal survival and equilibrium recruitment relative to \(R_0\) are continued smoothly below 0.001 to keep trial initial states positive. The continuation is eps / (2 - x / eps) and adds (eps - x)^2 / eps to the penalty when x < eps. Values at or above the threshold are unchanged. A positive penalty marks a constrained trial state, not a valid fished equilibrium, and must be included in the fitting objective (as it is in opal_model()).