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Deterministic Recruitment

Get_Det_Recruitment.Rd

Computes deterministic recruitment by population and region using either a mean recruitment model or a Beverton–Holt stock–recruitment relationship.

Usage

Get_Det_Recruitment(
  recruitment_model,
  rec_dd,
  y,
  rec_lag,
  R0,
  rec_region_prop,
  rec_seas_prop,
  h,
  n_pop,
  n_regions,
  n_ages,
  n_fish_fleets,
  WAA,
  MatAA,
  natmort,
  SSB_vals,
  Movement,
  sgl_seas_spawning_movement,
  stray_rate,
  do_recruits_move,
  t_spawn,
  init_F,
  dmr,
  fish_sel,
  ret_sel,
  n_seas,
  spawn_seas,
  natal_region,
  seasdur,
  sexratio_f
)

Arguments

recruitment_model

Integer flag specifying the recruitment model:

  • 0 Mean recruitment

  • 1 Beverton–Holt recruitment with steepness

rec_dd

Integer flag specifying the density dependence structure:

  • 0 Local density dependence (population or region specific)

  • 1 Global density dependence (shared across regions; only valid when n_pop = 1)

y

Current model year index.

rec_lag

Recruitment lag (in seasons) between spawning and recruitment. 1 is the classic lagged case: recruitment uses SSB_vals from rec_lag seasons prior. 0 is age-0 recruitment: recruitment uses the SAME year's SSB (SSB_vals[,,y]). The caller is responsible for supplying that value already computed from survivors only (i.e. before this year's recruits exist) when rec_lag = 0 – see SPoRC_rtmb.R, Simulate_Population.R, and Do_Population_Projection.R for how each population-dynamics loop does this.

R0

Numeric vector (n_pop) of unfished recruitment by population.

rec_region_prop

Matrix (n_pop × n_regions) giving the proportion of recruitment allocated to each region.

rec_seas_prop

Matrix (n_pop × n_seas) giving seasonal recruitment proportions. When rec_lag = 0, must be zero for every season before spawn_seas (age-0 recruits can't predate the spawning event that produced them) – validated at setup by Setup_Mod_Rec/Setup_Sim_Rec.

h

Matrix (n_pop × n_regions) of Beverton–Holt steepness values.

n_pop

Number of populations.

n_regions

Number of spatial regions.

n_ages

Number of age classes (including the plus group).

n_fish_fleets

Integer. Number of fishery fleets.

WAA

Array (n_pop × n_regions × n_seas × n_ages) of weight-at-age.

MatAA

Array (n_pop × n_regions × n_seas × n_ages) of maturity-at-age.

natmort

Array (n_pop × n_regions × n_ages) of natural mortality.

SSB_vals

Array (n_pop × n_regions × n_years) of spawning biomass.

Movement

Array (n_pop × origin × destination × n_seas × n_ages) giving seasonal movement probabilities.

sgl_seas_spawning_movement

Array (n_pop × origin × destination × n_ages) describing spawning movement when a single season is used and n_pop > 1.

stray_rate

Numeric vector of stray rates by population.

do_recruits_move

Indicator for whether recruits move in their first year.

t_spawn

Fraction of the spawning season that occurs before spawning.

init_F

Array (n_regions × n_seas × n_fish_fleets) of initial fishing mortality.

dmr

Array (n_regions × n_seas × n_fish_fleets) of initial (first year) discard mortality.

fish_sel

Array (n_pop x n_regions × n_seas x n_ages x n_fish_fleets) of total fishery selectivity.

ret_sel

Array (n_pop x n_regions × n_seas x n_ages x n_fish_fleets) of retained fishery selectivity.

n_seas

Number of seasons per year.

spawn_seas

Season index in which spawning occurs.

natal_region

Integer vector (n_pop) mapping each population to its natal region.

seasdur

Numeric vector (n_seas) giving seasonal durations as fractions of a year.

sexratio_f

Matrix (n_pop × n_regions) giving female recruitment proportions.

Details

Recruitment is distributed spatially using regional recruitment proportions and seasonal recruitment timing. When Beverton–Holt recruitment is used, unfished spawning biomass per recruit (\(S_0\)) is calculated internally by projecting a single recruit through the full seasonal population dynamics, including movement and mortality.

Two recruitment formulations are supported.

**Mean recruitment**

When recruitment_model = 0, recruitment is constant:

$$R_{p,r} = R_{0,p} \times RecProp_{p,r}$$

where recruitment is distributed spatially according to rec_region_prop.

**Beverton–Holt recruitment**

When recruitment_model = 1, recruitment follows the Beverton–Holt relationship:

$$ R = \frac{4hR_0SSB}{(1-h)S_0 + (5h-1)SSB} $$

where:

  • \(SSB\) is spawning biomass lagged by rec_lag seasons (or, when rec_lag = 0, the current year's own spawning biomass – see the rec_lag parameter above)

  • \(S_0\) is unfished spawning biomass per recruit

  • \(h\) is steepness

\(S_0\) (and the age-composition of spawning biomass per recruit more generally) does not depend on rec_lag – it is a pure per-recruit, equilibrium quantity. The recruit age class (the first age) is always included in the sum; when rec_lag = 0, maturity at that age is required to be exactly zero (validated at setup by Setup_Mod_Biologicals/Setup_Sim_Biologicals), so it contributes nothing regardless.

Spawning biomass per recruit (\(S_0\)) is computed internally by projecting a single recruit through all ages and seasons under both unfished and fished conditions. The algorithm:

  1. Allocates a recruit across regions and seasons.

  2. Applies seasonal movement.

  3. Applies natural and fishing mortality, where fishing mortality is decomposed into retained (\(F \cdot sel \cdot ret\)) and dead discard (\(F \cdot sel \cdot (1 - ret) \cdot dmr\)) components.

  4. Computes spawning biomass during the spawning season.

  5. Solves the plus group analytically using annual transition matrices.

When multiple populations are modeled, recruitment for each population depends on spawning biomass in its natal region. Contributions from other populations are scaled by the specified stray rates.