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Fishery Bulletin 118(4) 
MMA‘“™s'ed = the estimate of MMA for year f; 
MMB, and MMA, = the true MMB and MMA during 
year ¢ in the operating model; 
Pp and py = the extents of autocorrelation in 
stock status estimation error; and 
Op and On = the extents of estimation error. 
The values for 6g and oy are set to the standard devia- 
tions of the logarithms of the estimates of MMB and MMA 
for 2018 rather than those of MMB/MMB,, and MMA/ 
MMA,,,, because the estimates of average MMB and MMA 
are precise. The autocorrelation in estimation error cannot 
be obtained from the assessment model; therefore, a range 
of plausible values are considered in the analyses. 
Implementation error 
The fishery does not catch the TAC exactly; therefore, 
implementation error is introduced as follows: 
Crewe Caireaeyand (13) 
2 
Tt ot N(0, 06,5) 
where (Ofer = the true catch for animals in size class j 
during year f; 
C;,;= the expected catch of animals in size class 
j during year t based on the simulated fish- 
ing mortality from the HCR; and 
Oc ¢,; =the standard deviation of the differences 
between TACs and actual catches for size 
class 7 based on the standard deviation of 
the differences between the TAC and total 
landed catches, 6c, in other words, 
SOC ia aa ae (14) 
yee t,j 
where ye Ct,j =the sum of the expected retained catches 
a of all size classes during year t. 
9G; 
Simulation design 
The design of the simplified MSE involved combining 
levels for each of the uncertainties. In total, 53 scenarios 
based on the selected uncertainties were considered for 
each relationship between CPUE and selected abundance 
(Table 2; Suppl. Tables 1—5 [online only]). 
Scenario 1 was based on the best estimates of the param- 
eters, and the specifications of this scenario are indicated by 
asterisks in Table 2 and Supplementary Table 5 (online only). 
Scenario 1 was also based on the middle level of autocorrela- 
tion in error when MMB and MMA were estimated (for the 
full list of scenarios and specifications, see Supplementary 
Tables 1 and 2 [linear choice] [online only] and Supplementary 
Tables 3 and 4 [nonlinear choice] [online only]). Scenarios 
2-17 involved changing the value of one of the parameters 
of scenario 1, and scenarios 18-53 changed the value of more 
than one parameter. The scenarios did not explore all possible 
combinations of parameters owing to computational and pre- 
sentational limitations. 
Two options (applied separately for each of the linear and 
nonlinear choices) were considered for the size structure at 
the start of the projection period (1 July 2018): 1) estimate 
in the assessment model (i.e., MMB/MMB,5=1.55; Siddeek 
et al., 2020) and 2) the MSST (0.5MMB,,). The second option 
was implemented by increasing the fishing mortality rate 
on the size structure for 2018 such that MMB approached 
0.5MMB;3;. Performances of candidate HCRs were eval- 
uated by projecting the stock from the initial abundance 
levels from these 2 options, in other words, a healthy state 
(MMB>MMB;;) and an overfished state (MMB=0.5MMB,,;). 
Performance metrics 
We considered conservation and economic criteria when 
evaluating the candidate HCRs. The conservation criteria 
were 1) the probability (across simulations and the entire 30- 
year period) of the stock being below MSST (..e., a threshold 
for being overfished), 2) the probability of total catch being 
greater than OFL (i.e., a threshold for overfishing occur- 
ring), 3) the probability of total catch being greater than 
ABC, and 4) the probability that MMB is less than MMB,,. 
The economic criteria were 1) the probability of fishery clo- 
sure, 2) the average annual catch (across simulations) for 
the directed fishery, 3) the annual variability of catch in the 
directed fishery, 4) the probability of retained catch being 
less than mean retained catch during 2005-2018 (post- 
rationalization period), 5) the average CPUE, 6) the prob- 
ability of CPUE being less than mean CPUE for the period 
2005-2018, 7) fishing effort (number of pot lifts, as approx- 
imated by using Catch/[CPUEx0.00195], where mean crab 
weight is assumed to be 0.00195 metric tons on the basis 
of unpublished data [Ben®] on the retained catch in 2018), 
and 8) the probability of MMA being less than MMA,,, (an 
average value for the period 1985-2018), an indication of 
whether the exploitation rate for a given management 
strategy reaches the maximum allowable exploitation rate 
in expectation. The reference points for comparison with 
simulation results are listed in Table 3 (linear choice) and 
Supplementary Table 6 (nonlinear choice) (online only). 
In addition, the time series of MMB, MMA, catch, effort, 
and catch variation were summarized as follows: 
e Time trends in median (over simulations) MMB, 
MMA, catch, and effort over the projection period; 
e Rebuilding time from the _ overfished level 
(0.5MMB,,;) to MMB;, and the rebuilding time from 
the corresponding MMA to MMA,,,; and 
e Median (over simulations) annual catch variability 
(AAR) computed with this equation: 
WAR] lesen) (15) 
XC 
3 Ben, D. 2018. Unpubl. data. Div. Commer. Fish., Alaska Dep. 
Fish Game, 351 Research Ct., Kodiak, AK 99615. 
