Calculate reference levels separately in each region

Find the unconstrained maximum catch and a risk-constrained reference level for each region on its own, so every region gets its own multiplier on the terminal exploitation rate (or the terminal catch) rather than sharing one multiplier across the model.

Usage

get_reference_region(
  proj_inputs,
  min_increase = 0,
  search_type = 1,
  ssb_lim = 0.2,
  plim = 0.05,
  pcrash = 0.2,
  Fmult_start = 0.2,
  Fmult_step = 0.2,
  Fmult_max = 20,
  tiny = 0.05
)

Arguments

proj_inputs

list of inputs prepared for projection, including SSB0 as an [n_iter, n_region] matrix. A per-region SSB0 is required, since the risk constraint is applied within each region.

min_increase

in terms of tons, minimum increase in a region's median catch required to keep raising its multiplier

search_type

default = 1 for exploitation rate, 2 for catch

ssb_lim

soft-limit fraction of SSB0 (0.2), or 0 for the unconstrained search

plim

probability of falling below ssb_lim used for reference level, default = 0.05

pcrash

probability of U going too high to sustain population, default = 0.2

Fmult_start

Starting point for Fmult, default = 0.2

Fmult_step

Coarse step, default = 0.2

Fmult_max

Largest multiplier the coarse pass will try, default = 20

tiny

Fine step used to refine around each region's coarse optimum, default = 0.05

Value

a list with multipliers (the chosen multiplier per region, NA for a region that meets no constraint even unfished), save_df (median summary by region at every multiplier tried), unconstrained_region_df and ref_region_df (per-iteration values by region under the chosen per-region multipliers, with any NA region projected unfished), and unconstrained_df and ref_df (the same iterations summed to all-region totals).

Details

The population dynamics contain no movement between regions and no shared exploitation term, so region \(r\)'s response to its own multiplier does not depend on what the other regions are doing. Each multiplier tried is therefore projected once with every region scaled together, and each region reads its own yield curve off that shared set of evaluations. The cost is close to a single whole-model search rather than one search per region. The multipliers finally chosen are then applied simultaneously, one per region, in a confirmation projection.

Selection within a region: the unconstrained level is the multiplier giving the largest median catch among those where exploitation stays sustainable in that region – the maximum catch before the risk constraint is applied. If that point breaches the soft-limit risk constraint, the reference level falls back to the largest median catch