384 
20,000 
15,000 
10,000 
Year 
Fishery Bulletin 118(4) 
MMA (millions) 
MBaye=-45 
MMA (millions) 
Year 
HCR — HRO --- HR10 --- HR15 -- HR15U --- HR30 
Figure 2 
Median mature male biomass (MMB) and median mature male abundance (MMA) of golden king crab 
(Lithodes aequispinus) in the Aleutian Islands under 5 harvest control rules (HCRs), with the initial state of 
the stock set at (A and B) healthy or (C and D) overfished, for scenario 1 of the operating model in which a 
linear relationship between catch per unit of effort and selected abundance is assumed. Metric tons (t) is the 
unit for MMB, and number of crab is the unit for MMA. Values are based on a 30-year projection period that 
begins with 2018. The stock is projected from 2 initial levels of abundance: a healthy state (i.e., MMB.;¢/ 
MMB;;=1.55, where MMBoo 3 is MMB in 2018 and MMB,, is 35% of the unfished level of MMB) and an over- 
fished state (i.e., MMB..1:/MMB,;=0.50). Horizontal dashed lines indicate the MMB,, and average MMA 
(MMA,,,.) thresholds. The HCRs include HRO, the reference HCR with a zero exploitation rate; HR10, with a 
maximum 10% exploitation rate and a 0.25 catch proportion cap on legal-sized male abundance; HR15, with 
a maximum 15% exploitation rate and a 0.25 catch proportion cap on legal-sized male abundance; HR15U, 
with a maximum 15% exploitation rate and no cap on the proportion of legal-sized male abundance that can 
be caught; and HR30, with a maximum 30% exploitation rate and a 0.25 catch proportion cap on legal-sized 
male abundance. Data used in the model are for golden king crab in 1981-2018. 
Mature male abundance is determined from Equation 2 
without w;. 
Parameterization of the operating model 
The population dynamics model has seventeen 5-mm size 
classes over the size range of 101-185 mm CL. The last size 
class (181-185 mm CL) is a plus group that includes all golden 
king crab larger than 185 mm CL. The values for the param- 
eters of the model were estimated on the basis of fitting the 
model to available data (Siddeek et al., 2020; for some of the 
estimated parameters, see Supplementary Figure 3 [online 
only]). Although Bayesian or Monte Carlo methods could have 
been used to estimate distributions for the parameters of the 
operating model, these methods were not pursued because 
they were found to be computationally infeasible. The param- 
eters of the operating model differed depending on whether 
CPUE was assumed to be proportional to selected abundance 
or the square root of selected abundance because the oper- 
ating model was fitted to the available monitoring data for 
golden king crab in the Aleutian Islands (for the results for 
linear relationship [hereafter referred to as the linear choice], 
see Tables 2 and 3 and Supplementary Tables 1 and 2 [online 
only]; for the results for the nonlinear relationship [hereaf- 
ter referred to as the nonlinear choice], see Supplementary 
Tables 3-6 [online only]). Tables and figures for the linear 
choice are provided (selected tables and figures for the nonlin- 
ear choice are given in Supplementary Materials [online only]). 
