Siddeek et al.: Development of harvest control rules for hard-to-age crab stocks 
0 
3 1119 27 35 43 51 
Scenario 
F HRO G HR10 H 
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oOo On Oo 
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Scenario 
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395 
— 
So & ES& 
Time (years) 
st 
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J 
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Figure 9 
Median time, in years, for a stock of golden king crab (Lithodes aequispinus) in the Aleutian Islands (A—E) to rebuild from an 
initial overfished state of 0.5MMB;;, where MMB; is 35% of the unfished level of mature male biomass, to a full MMB,, and 
(F—J) to rebuild from the corresponding mature male abundance to average mature male abundance under harvest control 
rules (HCRs) HRO, HR10, HR15, HR15U, and HR30, for the 53 scenarios of the operating model in which a linear relation- 
ship between catch per unit of effort and selected abundance is assumed. Data used in the model are for golden king crab in 
1981-2018. For details about the HCRs, see Table 1. 
computationally prohibitive to address all uncertainties 
by using a projection model, we considered a small set of 
scenarios focused on those uncertainties most likely to 
affect the performance of HCRs under the linear and 
nonlinear choices. 
Our findings indicate how projection results respond 
to changes in steepness, variation, and autocorrelation of 
the stock—-recruitment relationship, error in estimating 
MMB and MMA, and catch implementation error (Table 2, 
Suppl. Tables 1—5 [online only]). Although the values of the 
performance metrics differ between the linear and nonlin- 
ear choices, trends in HCR ranks were largely unchanged 
between these choices, indicating that our analysis for 
these choices is robust for evaluating policy trade-offs. The 
results presented here are based on approximate closed- 
loop simulations because, although errors in estimating 
MMB and MMA are considered, the full stock assessment 
is not simulated because of computational limitations, 
and our analysis is not a full MSE. Comparison of the full 
suite of scenarios (i.e., a range of contrasting parameter 
values) reveals the level of risk related to each source of 
uncertainty when relying on best estimates of parameters 
for decision-making. 
The projections in our study identify recruitment vari- 
ability as the most important factor determining the per- 
formances of the HCRs, yet understanding causes of 
recruitment fluctuations is a fundamental challenge in 
modeling crab population dynamics. The results of our 
simulations may underestimate recruitment variability 
or fail to capture the non-stationarity of the nature of 
recruitment, and such underestimation or failure may 
bias estimates of HCR performance. Well-defined stock— 
recruitment relationships are rare for crab and lobster 
species because the underlying physical and biological 
processes that influence larval survival to the juvenile 
stages are difficult to define (Wahle, 2003). For red king 
crab in Bristol Bay, recruitment trends are consistent 
with decadal climate shifts (Zheng and Kruse, 2003), 
indicating the importance of environmental factors 
(Zheng and Kruse, 2006). Nevertheless, because of uncer- 
tainties in the stock—recruitment relationship (or lack 
thereof) for golden king crab in the Aleutian Islands, 
