Li et al.: A comparison of 4 age-structured stock assessment models 
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Table 1 (continued) 
Description 
Landings in year y (in metric tons) 
Case 0 value or 
expression Estimated 
Survey abundance at age a in year y (in number) 
Survey abundance (sum across ages) in year y (in number) 
Observed landings in year y (in metric tons) with noise 
Proportion at age a in year y for fishery landings 
Observed proportion at age a in year y for fishery landings 
Observed survey abundance in year y with noise (in number) 
Proportion at age a in year y for survey 
Observed proportion at age a in year y for survey 
Length at age a (in millimeters) 
Weight at age a (in metric tons) 
Proportion that reached maturity at age a 
Unfished spawning biomass per recruit (in metric tons) 
Total mortality rate at age a in year y 
Fully selected F in year y (year ') 
Fishery selectivity at age a 
Survey selectivity at age a 
Number of spawners per recruit at age 
Op Spawning biomass per recruit given F (in metric tons) 
Re Equilibrium recruitment (in number) 
qd Catchability coefficient for survey 
Stochastic deviation: process error 
Standard deviation of log recruitment 
Recruitment deviations in year y 
Standard deviation of log fully selected F 
Fully selected F deviations in year y 
Stochastic deviation: observation error 
CV, Coefficient of variation of fishery landings 
SL Landings deviations in year y 
CV, Coefficient of variation for survey 
oo Survey abundance deviations in year y 
Fishing mortality pattems In case 0, the fully selected F 
increased over time from a relatively low value (0.01) to a 
higher rate (Fi,i.,) (Fig. 2). Two additional trends in F were 
investigated on the basis of methods from Johnson et al. 
(2015) and Ono et al. (2015). In this study, the F either 
increased from a low value (0.01) to F},,1, during the first 24 
years and then decreased to a lower rate (F,,,,,; case 4; Fig. 
2) or that F remained constant over time across 3 levels: 
Fy, the F that corresponds to maximum sustainable yield 
(Fysy), or Fhigh (cases 5-7; Fig. 2). Values of F,,, and Fyich 
corresponded to 80% of maximum sustainable yield (MSY). 
Comparing cases 4—7 with case 0 allowed an evaluation of 
whether different fishing patterns affected the magnitude of 
error in estimating parameters of interest. 
Selectivity patterns A comparison between case 8 and 
case 0 was used to examine the influence on assessment 
3.46 x 1077 
0.2 
Rdev, ~ N(O, OR’) 
0.2 
fdev, ~ N(O, of”) 
0.05 
Be N(0,1og(1 + cv2)} 
0.2 
ep, ~N(0,log(1+ cv?)} 
performance of using double-logistic selectivity for the 
fishery and the survey instead of simple logistic selectiv- 
ity (case 0). 
Multiple surveys Comparing case 9 (which includes 2 
surveys with the same level of observation errors) with 
case 0 (which includes 1 survey) allowed an evaluation of 
whether use of an additional survey reduced error in esti- 
mating quantities of interest. 
Bias adjustment of recruitment For case 10, the median- 
unbiased spawner-recruit parameters were used, whereas 
for case 11 the mean-unbiased spawner-recruit param- 
eters were used to conduct a bias adjustment in the OM. 
The arithmetic mean curve of recruitment that is associ- 
ated with the mean-unbiased spawner-recruit parameters 
is higher than the geometric mean curve of recruitment 
