Siddeek et al.: Development of harvest control rules for hard-to-age crab stocks 
385 
The value of h was determined through the use of a 
2-step procedure. The first step was to calculate F;,, by using 
an analysis of spawning biomass per recruit (for a plot of 
spawning potential ratio [SPR] versus fishing mortality [F], 
where the SPR for a given level of fishing mortality is the 
ratio of the spawning biomass per recruit at that level of 
fishing mortality to the spawning biomass per recruit in an 
unfished state, see Supplementary Figure 4A [online only]). 
The value of F is related to the total fishing mortality for 
the directed pot fishery when computing SPR, with fishing 
Table 2 
The factors considered during the evaluation of the perfor- 
mance of harvest control rules for golden king crab (Lith- 
odes aequispinus) in the eastern portion of the Aleutian 
Islands. The 3 values are lower limits; the model estimates 
for 2018, indicated with asterisks (*); and upper limits con- 
sidered in the evaluation of the performance of harvest con- 
trol rules. The values are based on the operating model in 
which a linear relationship between catch per unit of effort 
and selected abundance is assumed. Data used in the model 
are for golden king crab in 1981-2018. MMB=mature male 
biomass; MMA=mature male abundance. 
Factors Values 
0.600, 0.729%, 1.200 
0.100, 0.274*, 0.800 
0.000, 0.455*, 0.900 
0.000, 0.039%, 0.100 
Steepness (h) 
Recruitment variation (Gp) 
Autocorrelation in recruitment (pp) 
Extent of annual catch 
implementation error (6) 
Extent of MMB estimation error (6g) 0.000, 0.214*, 0.300 
Autocorrelation in MMB estimation 0.000, 0.700, 0.900 
error (pp) 
Extent of MMA estimation error (6x) 0.000, 0.216*, 0.300 
Autocorrelation in MMA estimation 0.000, 0.700, 0.900 
error (Py) 
mortality attributable to bycatch in the groundfish fishery 
set to the estimated average during 1999-2018 (although 
this source of mortality is negligible). The second step was 
to calculate MMB for various h values by projecting the pop- 
ulation model forward deterministically given F=F, and to 
find h such that MMB=0.35xMMB, (where MMB, is the vir- 
gin mature male biomass; Suppl. Fig. 4B [online only]). 
The selected value of h ensures that fishing at F;,, pro- 
duces MMB,,, which is equivalent to 0.35xMMB, (a proxy 
for Bysy), and a proxy MSY (see Supplementary Figure 5 
[online only]). Figure 3 shows the fitted (deterministic) 
Ricker stock—recruitment relationship when h was set 
by using this procedure (h=0.729, Rj=2.528 million crab, 
MMB,=18,862 metric tons) along with the MMB,_, (MMB 
estimated 8 years prior to year ¢t) and recruit (R,) pairs 
of data points from the stock assessment model. Figure 4 
depicts the estimated number of recruits from the model, 
along with a 95% confidence interval, indicating that 
uncertainty in these estimates increased over time. 
Harvest control rules 
Federal harvest control rule The federal HCR is based on 
MMB and is needed to determine the OFL and the ABC for 
each year of the projection period. The OFL fishing mortal- 
ity (For) is determined by using this equation (NPFMC’): 
Fs, if MMB,>MMB,,, 
MMB, nee 
MMB;, 
l-a 
Fa =y Fa if 0.25MMB,.<MMB,<MMB,,, and (3) 
0 if MMB,«0.25MMBy,, 
where o = 0.1 (a preset value). 
The OFL of total catch is calculated by applying Foy, to 
male stock abundance through the use of Equations A1—A3 
in Supplementary Materials (online only) and by summing 
Table 3 
The reference points used in the evaluation of candidate harvest control rules for golden king crab 
(Lithodes aequispinus) from the eastern portion of the Aleutian Islands: a proxy for biomass corre- 
sponding to maximum sustainable yield (35% of the unfished level of mature male biomass [MMB,,]), 
the fishing mortality rate corresponding to 35% of the unfished spawning biomass per recruit (F';), 
mean catch, average mature male abundance (MMA 
ave 
), and mean catch per unit of effort (CPUE). 
The estimates are based on the operating model in which a linear relationship between CPUE and 
selected abundance is assumed. Data used in the model are for golden king crab in 1981-2018. 
Reference point Estimate 
MMB;; 
P55, 0.656/year 
6601.61 t 
Mean catch 1492.82 t 
Basis of estimation 
Assessment model 
Assessment model 
Period from the 2005-2006 fishing season through the 
2018-2019 fishing season (post-rationalization period) 
MMA 5.45 million crab 
ave 
Period from the 1985-1986 fishing season through the 
2018-2019 fishing season (estimation period) 
Mean CPUE 31.70 crab/pot lift 
Period from the 2005-2006 fishing season through the 
2018-2019 fishing season (post-rationalization period) 
