Clark’s Method for Estimating F% proxy for Fmsy Clark’s maximin method of estimating F% is determined by the intersection of the least productive and most productive sr curves used in the analysis Clark’s method of selecting the range of sr curves was somewhat subjective – He reasoned that the range of F that fish stocks can sustain before collapse was F=M up to F=5M However, Clark’s generalized groundfish stock used fishery selectivity equal to maturity For crab stocks fishery selectivity is at larger sizes than maturity and the majority of the catch is male crab

Snow crab yield, Beverton Holt SR F target pre-2000 was F=1.1. Tau 0.33=steepness 0.43, Tau 0.5 = steepness 0.33

Figure 1. Example of Clark minimax method to determine F% proxy for Fmsy. Numbers are for steepness parameter of the SR curve (steepness of 0.33 is tau 0.5, steepness of 0.71 is tau 0.1). Maximin F

Ricker curve steepness 0.7(tau = 0.12) fit to data for all years. A Beverton Holt curve that represents the most current period of low recruitment ( year classes) has a steepness of 0.45 (tau = 0.36). The steepness for the Beverton Holt curve was estimated from the slope of the line connecting (0,0) with the point for the lowest spawning biomass with the highest recruitment (280,784).

Figure 11. Spawner recruit estimates from the Tanner crab stock assessment model. Ricker curves are fit to all years (steepness 0.73, tau 0.09) and fit to the most recent low recruitments from the year classes (shown in red) (steepness 0.52, tau 0.24). A ricker curve with steepness = 0.65 (tau = 0.13) was used to develop the current harvest strategy for Tanner crab.

Red king crab recruitment and female effective spawning biomass. A Ricker curve was fit to all years estimated steepness at 0.47 (tau = 0.287). A Ricker curve fit to year classes after 1976 regime shift onward estimated steepness at 0.36 (tau=0.45). Clear squares – yr class solid – yr class

Meta- analysis Specify prior distribution for steepness of the spawner recruit curve that does not include SR data used in the analysis Assemble spawner recruit data for appropriate crab stocks – Red king, Tanner, Snow crab Estimate posterior distribution of steepness using sr data and prior Use estimated steepness to determine F% proxy for Fmsy in spawning biomass per recruit model

Management Strategy Evaluation Future work

Red king crab pre-crash F ranged from about 0.45 to 0.88 (discard included in M). Recent F(since 1996) ranged from 0.15 to F was 0.31