Approaches to estimate proxy BRP values  Estimate equilibrium yield by a deterministic method, identify F and related BRPs, perform sensitivity analysis of various input parameter values  Estimate equilibrium yield by a deterministic method, identify F x% and related BRPs, perform sensitivity analysis of various input parameter values  Estimate average yields from 100-year fishery by projection modeling with stochastic S-R, identify F and related BRPs  Estimate average yields from 100-year fishery by projection modeling with stochastic S-R, identify F x% and related BRPs  Perform various diagnostic tests on selected F by projection modeling with stochastic S-R: (a) rebuilding possibility of a severely depleted stock under the chosen F with a less productive S-R curve (B-H with Tau=0.3), (b) distribution of relative mean ESB for a range of F ( c) CV of yield for a range of F values, and (d) extinction probability of the stock for a range of F values  Perform various diagnostic tests on selected F x% by projection modeling with stochastic S-R: (a) rebuilding possibility of a severely depleted stock under the chosen F x% with a less productive S-R curve (B-H with Tau=0.3), (b) distribution of relative mean ESB for a range of F x% values, ( c) CV of yield for a range of F x% values, and (d) extinction probability of the stock for a range of F x% values

Equilibrium Approach – Deterministic Simulation

Stochastic Approach – Projection Modeling

What is F%? SSB/R 0 SSB/R F e.g. F 20% is an F which produces a SSB/R F equivalent to 20% SSB/R 0

Identification of F Identification of F X%  Red king crab example - EXCEL

Year Age 1R1,1R2,1R3,1R4,1R5,1R6,1R7,1R8,1R9,1 2R1,2R2,2R3,2R4,2R5,2R6,2R7,2R8,2 3R1,3R2,3R3,3R4,3R5,3R6,3R7,3 4R1,4R2,4R3,4R4,4R5,4R6,4 5R1,5R2,5R3,5R4,5R5,5 6R1,6R2,6R3,6R4,6 Year class development for stochastic simulation – stock projection modeling

Testing the Stochastic Program  Stochastic program produced results coinciding with the deterministic estimates. e.g., R and Y predictions

Rebuilding red king crab stock from a 20%ESB MSY to MSY level under proposed harvest control rule with F 50. The data points correspond to 100-year fishery simulation under stochastic Beverton-Holt S-R model with female ESB, overall recruitment variability,  =0.7, serial correlation,  =.5, M = 0.18, h = 0.2, mating ratio=1:3, and  =0.3

Proportion of years ESB has depleted to < 25%ESB vs. relative ESB/R from 100-year fishery for the red king crab stock. The estimates are made under stochastic Beverton and Holt and Ricker stock-recruitment models with female ESB, M = 0.18, h = 0.2, mating ratio = 1:3, overall recruitment variability,  = 0.7, serial correlation,  = 0.5, and τ = The proportion of years ESB has depleted below 25%ESB is < 0.02 at F for all τ values up to 0.3. Proportion of years ESB has depleted to < 25%ESB MSY vs. relative ESB/R from 100-year fishery for the red king crab stock. The estimates are made under stochastic Beverton and Holt and Ricker stock-recruitment models with female ESB, M = 0.18, h = 0.2, mating ratio = 1:3, overall recruitment variability,  = 0.7, serial correlation,  = 0.5, and τ = The proportion of years ESB has depleted below 25%ESB MSY is < 0.02 at F 50 for all τ values up to 0.3.