Siddeek et al.: Development of harvest control rules for hard-to-age crab stocks 
Table 5 
Economic performance metrics for golden king crab (Lithodes aequispinus) in the Aleutian Islands, with the initial 
state of the stock set at healthy or overfished, for scenario 1 (based on best parameter estimates) of the operating 
model in which a linear relationship between catch per unit of effort and selected abundance is assumed. Values 
for the 4 harvest control rules (HCRs) evaluated by economic criteria, HR10, HR15, HR15U, and HR30, are prob- 
abilities that the estimated quantity is above or below the associated reference point (e.g., MMA<0.25MMA,,,, 
indicates the probability that mature male abundance [MMA] is below 25% of average MMA [MMA,,,,]), calculated 
for the last 10 years of the 30-year projection period, which begins with 2018. The exceptions are for values of catch 
(mean in metric tons), CPUE, (given as the number of crab per pot lift), and effort (given as the number of pot 
lifts). Harvest control rules were ranked among each other for each performance metric (ranks are given in paren- 
theses; ranks are the same for HCRs if probabilities are the same for those HCRs). Catch is the catch retained in 
the directed pot fishery. The stock is projected from 2 initial levels of abundance, measured in mature male bio- 
mass (MMB): a healthy state (i.e., MMBoo19/MMB,;=1.55, where MMB, o;, is MMB in 2018 and MMB,, is 35% of 
the unfished level of MMB) and an overfished state (i.e., MMBo9)3/MMB,,=0.50). For details about the HCRs, see 
Table 1. Catcha,.7i,¢=historical average catch; CPUE,,,.4;,.=historical average CPUE; and MMA,,,4;,,=historical 
average MMA. 
Metric Description or unit 
HR10 HR15 HR15U HR30 
Healthy 
Fishery closure 
MMA<0.25MMA,,,. 
Catch Mean 
Catch variability 
Relative catch Catch<Catcha,.nist 
Mean number 
CPUE<CPUE gy crist 
Number of pot lifts 
Stock status MMA<MMA,, Hist 
Overfished 
Fishery closure MMA<0.25MMA,,,. 
Catch Mean 
Catch variability 
Relative catch 
CPUE, Mean number 
CPUE, CPUE<CPUE yerist 
Effort Number of pot lifts 
Stock status MMA<MMA yy crist 
Catch<Catcha, nist 
The alternative of HR30 was the most aggressive policy, 
but with only marginally higher catches than HR15 and 
HR15U, and HR15U had the most variable catches (see 
Table 5 for the linear choice and Supplementary Table 8 
[online only] for the nonlinear choice). 
Performance of harvest control rules (all scenarios) 
Catch variability was high for the highest value of op 
(scenarios 3, 20-21, and 27-29) and very high when op 
and pr were at their maxima (scenarios 35-37 and 52-53 
in Figure 6). In contrast, catch variability was insensi- 
tive to the other factors considered and to the choice of 
management strategy (Fig. 6). The probabilities of catch 
being less than mean catch and CPUE being less than 
mean CPUE were very high when op and pz were at their 
maxima (scenarios 35-37 and 52-53) (see Figure 7 for 
the linear choice and Supplementary Figure 6 [online only] 
for the nonlinear choice). The probability of not achieving 
mean CPUE was higher for HR30 (Fig. 7H, Suppl. Fig. 6H 
Annual proportional change in catch 
Annual proportional change in catch 
0.000 (1) 
1508 (4) 
0.049 (1) 
0.468 (4) 
47.4 (1) 
0.000 (1) 
16,315 (1) 
0.002 (1) 
0.000 (1) 
1732 (3) 
0.052 (3) 
0.140 (2) 
36.7 (2) 
0.153 (2) 
24,202 (2) 
0.075 (2) 
0.000 (1) 
1735 (2) 
0.055 (4) 
0.141 (3) 
36.4 (3) 
0.174 (3) 
24,444 (3) 
0.078 (3) 
0.000 (1) 
1770 (1) 
0.052 (2) 
0.101 (1) 
33.0 (4) 
0.408 (4) 
27,506 (4) 
0.196 (4) 
0.000 (1) 
1354 (4) 
0.048 (1) 
0.807 (4) 
139.6 (1) 
0.000 (1) 
4974 (1) 
0.037 (1) 
0.000 (1) 
1510 (2) 
0.050 (3) 
0.477 (2) 
103.8 (2) 
0.000 (1) 
7460 (2) 
0.396 (2) 
0.000 (1) 
1512 (1) 
0.052 (4) 
0.475 (1) 
103.5 (3) 
0.000 (1) 
7492 (3) 
0.398 (3) 
0.000 (1) 
1508 (3) 
0.049 (2) 
0.503 (3) 
96.7 (4) 
0.000 (1) 
7997 (4) 
0.535 (4) 
[online only]) than for HR10, HR15, and HR15U for all 
scenarios, with probability levels lower for the nonlinear 
choice than for the linear choice. 
Figure 8 and Supplementary Figure 7 (online only) show 
the probabilities of MMA being less than MMA,,,, and 
of MMB being less than MMB; for the linear and non- 
linear choices, respectively, when MMB.o;, was greater 
than MMB,, for the 5 HCRs. Spawning biomass and 
abundance declined even under HRO (i.e., F=0) for sce- 
narios 35-37 and 52-53 because of high recruitment 
variability for the base level of the steepness parame- 
ter (Fig. 8, A and F; Suppl. Fig. 7, A and F [online only]). 
The probabilities of MMB being less than MSST and of 
MMA being less than 0.25MMA,,,. were closer to zero for 
all scenarios and HCRs across simulations and for the 
entire projection period (results not shown). 
The median rebuilding time for all HCRs under the lin- 
ear choice increased for scenarios 35-37 and 52-53 
because of high recruitment variability (Fig. 9). As 
expected, HRO had the shortest rebuilding time. The 
