Li et al.: A comparison of 4 age-structured stock assessment models 155 
Table 3 
Settings for recruitment variability (op), deviations in fishing mortality rates (Ff), patterns of F, selectivity patterns, and 
recruitment bias adjustment in the operating model (OM) that was used to evaluate 4 age-structured stock assessment models 
under different cases. A dash denotes that the value or information is the same as that given for the null case (case 0). For 
case 0, the OM creates the same set of F deviations for a given iteration. For case 3, the OM randomly generates a unique 
set of F deviations per iteration. F\,,=low F value; Fysy=F that corresponds to maximum sustainable yield; F\,,,=high F 
value; dp=spawning biomass per recruit based on F; ¢)>=unfished spawning biomass per recruit; RO=unfished recruitment; and 
h=steepness. 
Details 
Fishery 
F F and survey No. of Bias Initial 
Setting deviations patterns selectivity surveys adjustment condition 
Null case i Same Increase Simple- 1 No Op#0 
iteration logistic 
Recruitment : - — 
variability 
Stochastic F Stochastic 
iteration 
F patterns Roller coaster 
Constant Fioy 
Constant Fyysy - 
Constant Fyicn - 
Double-logistic - Double- 
selectivity logistic 
Multiple surveys - - 
Recruitment bias I - Yes (median-unbiased 
adjustment RO and h) 
Yes (mean-unbiased 
RO and h) 
Initial condition = 
available from the NOAA Virtual Laboratory (website, 
accessed November 2019). 
The 4 EMs estimated time series of spawning stock 
biomass (SSB), recruitment, F, abundance, biomass, and 
landings in weight. Annual age composition of landings 
from the fleet and from surveys was also estimated. The 
annual F values used in the comparison were apical F val- 
ues. The common output of biological reference points used 
in the comparison project included MSY, Fysy, and SSB at 
MSY (SSBysy). The relative F (calculated as F/Fygy) and 
relative SSB (calculated as SSB/SSBysy) for MSY-based 
reference points were also examined. 
atom Fussy Frigh 
Performance measures 
Figure 2 
The curve of the relationship of yield and fishing mortal- 
F h of th fe f the EM lu- 
ity rate (F) and the definitions of the low F value (F,,,,) PUREE he ee cae saan 
and the high F value (Fyig,) used in creation of various ated by comparing estimated values against the true val- 
patterns of F in the operating model. The horizontal black ues from the OM. The quantities of interest included RO, 
line indicates maximum sustainable yield (MSY), and the F in the “terminal” year (Frerminat)» SSBtermina MSY, Fyusy, 
dashed gray lines indicate 0.8MSY, which corresponds to SSBysy, relative F, and relative SSB. To evaluate perfor- 
F\,, and F},;,4- The vertical black line indicates the F that mance related to a management application (e.g., stock 
corresponds to MSY (F'ysy). status determination), Fiji, was set to Fygy and SSByiimit 
was set to half of SSBycy (Federal Register, 1998; Restrepo 
