Area-specific spawner-recruitment

[k-doering-NOAA]

Imported from redmine, Issue #18311 Opened by @RickMethot on 2016-04-28 Status when imported: New

5. Conceptual problem in equilibrium calcs if fish move between areas Equil_Calc takes some total recruitment (Equ_Recr) it distributes according to recr_dist, then calculates equilibrium numbers at age taking into account F and movement between areas if outputs a value for total SPR (spawners per recruit) then SPR is input to Equ_Spawn_Recr_Fxn to calculate the equilibrium total recruits and spawners from this SPR

but if recruitment to an area depends on that areas SPB, then SPR needs to be area-specific but with movement between areas, the SPB in an area depends on the movement so SPR cannot be calculated independently for each area if there is movement so equil_calc will need to output area-specific SPR; this seems feasible

but it is still somewhat circular because the distribution of recruits to areas in equil_calc will depend on the SPB by area calculated by equil_calc

6. Need to reconcile the area-aspect of recr_dist with the R=F(SPB_area) area-specific R0 global steepness movement mixes B between areas fishing reduces area-specific B reduced area-specific B reduces E(area-specific R)

does global R=E(sum B) equal R = sum (E(Ba)) ??

current approach:

1. Given some reference recruitment level - R
2. Call equil_calc a. distribute R to areas according to recr_dist b. loop areas within ages c. for each age,/area calc SPB, Yield, Survivors d. for each age mix survivors among areas according to movement specs e. accumulate total SPB and Yield and return from equil_calc
3. calc SPB/R and Yield/R
4. call Equ_Spawn_Recr_Fxn to get B_equil and R_equil from SPB/R and SR parms

Proposed two-stage iterative area-specific approach for equilibrium calcs: step A:

1. Given some reference recruitment level - R
2. Call equil_calc a. distribute R to areas according to unfished recr_dist (which needs to be defined here) b. loop areas within ages c. for each age,/area calc SPB, Yield, Survivors d. for each age mix survivors among areas according to movement specs e. accumulate total and area-specific total SPB and Yield and return from equil_calc
3. calc area-specific SPB/R and Yield/R, using area-specific R
4. call Equ_Spawn_Recr_Fxn for each area to get B_equil and R_equil from SPB/R and SR parms
5. sum across areas to get adjusted total B_equil and R_equil
6. use ratio of B_equils among areas to calculate adjustment to recr_dist step B:
7. call equil_calc again, using the adjusted recr_dist