Siddeek et al.: Development of harvest control rules for hard-to-age crab stocks 383 
Table 1 
Summary of the 5 harvest control rules (HCRs) of the U.S. government and state of Alaska evaluated for golden king crab (Lithodes 
aequispinus) in the eastern portion of the Aleutian Islands. The management strategy with zero exploitation rate (HRO) is the ref- 
erence HCR; HR10 has a maximum 10% exploitation rate with a 0.25 catch proportion cap on legal-sized male abundance, HR15 
has a maximum 15% exploitation rate with a 0.25 catch proportion cap on legal-sized male abundance, HR15U has a maximum 
15% exploitation rate without a cap on the proportion of legal-sized male abundance that can be caught, and HR30 has a maximum 
30% exploitation rate with a 0.25 catch proportion cap on legal-sized male abundance. Average mature male abundance (MMA,,,,) 
was estimated for the period from the 1985-1986 fishing season through the 2018-2019 fishing season. The HCR currently imple- 
mented by the state of Alaska for golden king crab in the eastern portion of the Aleutian Islands is HR15. F=fishing mortality rate; 
MMB=mature male biomass; OF L=overfishing level; and ABC=allowable biological catch. 
Minimum 
MMB for a 
fishery to take 
Harvest 
control 
rule 
Maximum 
Government F ABC 
Federal 
State 
Fis 0.25MMB,, 0.750FL 
e Non-stationarity: changes over time in the form and 
parameters of the stock—recruitment relationship 
and time-varying natural mortality, growth, and 
selectivity; and 
e Other factors: spatial and stock structure and time- 
varying movement. 
Key features of the operating model 
The basic dynamics are governed by this equation: 
M]y 
1,J 
Nes = De Lue ri (Cri aP Dei + Tr; ele) 
+R, (2018sts2047), (1) 
+1,j 
where N;,,; = the number of male golden king crab in 
size class at the start (1 July, the start of 
fishing year) of year t+1; 
Cti =the number of individuals retained in 
catch of the directed pot fishery for size 
class i during year tf; 
Di; =the number of individuals discarded or 
dead in the pot fishery catch for size class i 
> during year f; 
Tr,; =the number of individuals discarded or 
dead in the groundfish fishery catch for 
size class i during year f; 
X;; =the probability of animals in size class 7 
growing into size class j during the year; 
y, = the time from 1 July to the midpoint of the 
fishery period during year ¢; 
M = the instantaneous rate of natural mortality 
(assumed to be 0.21/year for all size classes 
and over time; Siddeek et al., 2020); and 
Maximum 
exploitation 
rate 
Minimum 
MMA for a 
fishery to take 
Catch proportion 
cap on legal-sized 
male abundance 
Catch 
limit 
0.25MMA,,,. 
0.25MMA,,,,. 
0.25MMA,,,,. 
0.25MMA,,. 
0.25MMA,,. 
Ri; =the recruitment to size class j during 
year t+1. 
The equations used to compute future retained and dis- 
carded catches are provided in Equations Al—A4 in 
Supplementary Materials (online only). 
Future recruitment is an essential part of the operating 
model. However, fitted stock—recruitment models often fail 
to show the link between spawning individuals and recruits 
for many species (Subbey et al., 2014), including for most 
commercially important crab stocks in the Bering Sea and 
Aleutian Islands. Biomass of mature females is a general 
choice for an index of egg production for finfish species (e.g., 
Martell et al., 2008; Punt et al., 2008; Subbey et al., 2014). 
However, MMB has been adopted as a proxy for reproduc- 
tive output for stocks of golden king crab in the Aleutian 
Islands, largely as a result of uncertainties related to iden- 
tifying the component of the mature population that par- 
ticipates in mating and to defining optimal sex ratios and 
because fisheries have a male-only retention requirement 
(NPFMC’). The MMB is computed by using this equation: 
MMB, = dete ore 
=(Cy,5+Dij+ Tr, pe hy, (2) 
where y’ = the time from 1 July to 15 February in the fol- 
lowing year (NPFMC’); 
w; = the weight for size class j (Siddeek et al., 2020); 
m=the lowest size class with mature animals 
(i.e., maturity is assumed to be a knife-edged 
function of size at the carapace length [CL] of 
111 mm; Daly et al., 2019); and 
n = number of size classes. 
