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Fishery Bulletin 119(2-3) 
Table 2 
Comparison of features between the 4 age-structured estimation models (EMs) evaluated in this study: the Assessment Model for 
Alaska (AMAK), the Age Structured Assessment Program (ASAP), the Beaufort Assessment Model (BAM), and Stock Synthesis 
(SS). The letter Y indicates that the feature is implemented in the EM. F=fishing mortality rate. 
Feature AMAK 
Age modeled 1+ 
Timing of spawning Real month 
Timing of survey Real month 
Survey index unit Biomass/number 
Spawner-recruit model 
Standard Beverton—Holt Y 
Ricker Y 
Average recruitment YG 
Bias adjustment of recruitment 
Types of selectivity available 
Free parameter approach Bound 
Simple-logistic function Y 
Double-logistic function Y (3 parameters) 
Logistic-exponential function 
Joint-logistic function 
Double-Gaussian function 
F in terminal year 
Definition of F 
Likelihoods available 
Landings, lognormal Y 
Survey index, lognormal Y 
Age composition, standard multinomial Y 
Age composition, Dirichlet multinomial 
Priors 
None 
Lognormal 
Beta 
Normal 
Reference or website (see for details of 
other features) 
Last year 
Flexible 
website 
that is associated with median-unbiased spanwer-recruit 
parameters because of lognormal deviation in recruitment 
residuals (Methot and Taylor, 2011). 
Bias adjustment is handled differently in the 4 EMs. 
In the BAM, a bias adjustment is applied when median- 
unbiased parameters are used to compute equilibrium 
recruitment for the spawner-recruit model (Suppl. Table 3) 
(online only) (Williams and Shertzer, 2015). In contrast, in 
SS, mean-unbiased parameters are used for the spawner- 
recruit model, and then a bias adjustment is applied when 
computing annual recruitment (Suppl. Table 3) (online only) 
(Methot and Taylor, 2011). In the AMAK and ASAP, bias 
adjustment is not included as part of the internal machin- 
ery. Details of differences between the EMs are documented 
in the “Spawner-recruit parameters in bias adjustment 
of recruitment” subsection of the “Results” section and 
in Supplementary Table 3 (online only). For cases 10 and 
11, Op was set to 0.6 to make the differences in estimates 
noticeable, if any were present. We also adjusted the esti- 
mates of MSY-based reference points from the AMAK and 
ASAP with the BAM bias adjustment method in case 10 
ASAP BAM SS 
0+/1+ 
Real month 
Real month 
Biomass/number 
1+ 1+ 
Fraction Fraction 
Real month Fraction 
Biomass/number Biomass/number 
Y 
Y 
Random walk Random walk/logit 
Y Y 
Y (4 parameters) Y (4 parameters) 
Ye 
Y 
Last year 
Flexible 
Last year 
Apical F 
Y 
Y 
Y 
KK x 
KKK K 
Williams and 
Shertzer (2015) 
website 
to make estimates comparable among all 4 EMs (Suppl. 
Figs. 1 and 2) (online only). We adjusted the estimates of 
unfished recruitment (RO) and steepness (h) to mean- 
unbiased values and then adjusted MSY-based reference 
points from the AMAK and ASAP in case 11 (Suppl. Figs. 1 
and 2) (online only). The estimates from cases 10 and 11 
were compared with the estimates from case 2 to quantify 
the effect of bias adjustment methods on EM performance. 
Estimation models 
Four EMs were evaluated in this study. The AMAK was 
compiled with AD Model Builder, vers. 12.1, from source 
code available on GitHub (website, accessed November 
2019). We used the executable file of the ASAP, vers. 3.0.16, 
available on the National Marine Fisheries Service Inte- 
grated Toolbox website (accessed December 2019). For the 
BAM, the source code is available from the authors or in 
the appendix of a NOAA publication (Williams and 
Shertzer, 2015) and was compiled by using AD Model 
Builder. We used the executable file of SS, vers. 3.30.15, 
