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Fishery Bulletin 115(3) 
time growth rate (simply calculated as L„ divided by 
the maximum age observed). Growth for each species 
was estimated by using the von Bertalanffy growth 
curve fitted to the mean age and length observations 
by using AD Model Builder (Fournier et ah, 2012). Esti- 
mates of the von Bertalanffy growth curve parameters 
for each of the species investigated when aging error 
is not included and when it is included (along with the 
maximum age observed in the bottom trawl surveys) 
are provided in Supplementary Table 1 (online only). Re- 
lationships between the distribution of age sample size 
and other life-history characteristics were also investi- 
gated (including the von Bertalanffy estimated growth 
coefficient, k), but for brevity we show these 4 statis- 
tics because they resulted in the strongest relationship 
with the distribution of age-composition sample sizes. 
Step 2: sample size for determining age composition and 
SCAA model uncertainty 
A simulation approach was used to evaluate the influ- 
ence of the magnitude of fishery-independent survey 
uncertainty (including both age composition and bio- 
mass) on resulting SCAA model uncertainty across spe- 
cies types. Operating models for the species types were 
constructed with simplified versions of the stock assess- 
ments for 3 species: GOA arrowtooth flounder ( Atheres - 
thes stomias [Turnock and Wilderbuer 4 ]) as an example 
for the flatfish species type, Pacific ocean perch ([Han- 
selman et al. 5 ]) as an example for the rockfish species 
type, and walleye pollock ( Gadus chalcogrammus [Dorn 
et al. 6 ]) as an example for the roundfish species type. 
The operating models for the 3 species types were 
constructed by fitting standard SCAA models to simi- 
lar data sources for each example species. Catch-at-age 
in year y (C a y ) was modeled with the Baranov (1918) 
catch equation and numbers-at-age in year y (iV ajy ) 
were estimated by following the theory of survival pre- 
sented by Ricker (1975), which are given by 
C a , y = N a:y ^-(1 - e“ Zaj ) and (8) 
Z a,y 
= (9) 
4 Turnock, B. J., and T. K. Wilderbuer. 2011. Assessment of 
the arrowtooth flounder stock in the Gulf of Alaska. In Stock 
assessment and fishery evaluation report for the groundfish 
resources of the Gulf of Alaska. North Pacific Management 
Council, Anchorage, AK. [Available from website.] 
5 Hanselman, D., S. K. Shotwell, P. J. F. Hulson, J. Heifetz, and 
J. N. Ianelli. 2011. Assessment of the Pacific ocean perch 
stock in the Gulf of Alaska. In Stock assessment and fishery 
evaluation report for the groundfish resources of the Gulf 
of Alaska. North Pacific Management Council, Anchorage, 
AK. [Available from website.] 
6 Dorn, M., K. Aydin, S. Barbeaux, M. Guttormsen, K. Spalin- 
ger, and W. Palsson. 2011. Assessment of the walleye pol- 
lock stock in the Gulf of Alaska. In Stock assessment and 
fishery evaluation report for the groundfish resources of the 
Gulf of Alaska, p. 51-146. North Pacific Management Coun- 
cil, Anchorage, AK. [Available from website.] 
where Z a y - the instantaneous total mortality, com- 
posed of natural mortality, M a >y> and fish- 
ing mortality, F a y . 
Fishing mortality was modeled as year-specific and 
age-specific factors (Doubleday, 1976), 
F a,y = S a f y , (10) 
where s a = age-specific selectivity (asymptotic); and 
f y = the annual fishing mortality rate for fully se- 
lected fish. 
Data that were fitted in the objective function to 
construct the operating models included total catch bio- 
mass (lognormal), commercial fishery age and length 
compositions (multinomial, effective sample size set 
at the square root of sample size), bottom trawl sur- 
vey biomass (lognormal), and bottom trawl survey age 
composition (multinomial, effective sample size set at 
square root of sample sizes). The primary differences 
between the actual stock assessment models and the 
simplified SCAA models used here included combined- 
sex rather than sex-specific models, time-invariant sur- 
vey catchability and selectivity, time-invariant fishing 
selectivity, and effective sample sizes used. The point 
of constructing the operating models was not to rep- 
licate the exact results of each assessment but to ob- 
tain reasonable parameter estimates indicative of the 
3 species type life histories. Parameter estimates from 
the final 30 years of the time series of the operating 
models for each species type were treated as ‘true’ val- 
ues from which process error in recruitment and obser- 
vation error in survey age compositions and biomass 
were generated. The parameter estimates used in the 
operating models for each of the 3 species types inves- 
tigated are provided in Supplementary Table 2 (online 
only). The same time scale and amount of data (annu- 
ally) were used for each species type so that resulting 
uncertainty in the estimation models was not sensitive 
to the length or quantity of the data time series. 
Process error in recruitment was generated from 
the operating models with the lognormal distribution. 
Recruitment deviation parameters were generated in- 
dependently following the estimation method used in 
the stock assessment SCAA models (as opposed to us- 
ing autocorrelation or a stock-recruitment model). The 
mean recruitment on the log-scale was 6.3 (SD 0.32) 
for arrowtooth flounder, which was comparable to the 
2011 assessment values with a log-scale mean of 6.3 
(SD 0.29) from 1980 to 2011 (Turnock and Wilder- 
buer 4 ). For Pacific ocean perch the log-scale mean re- 
cruitment used was 3.9 (SD 0.45), which was similar 
to the 2011 assessment mean from 1980 to 2011 of 3.9 
(SD 0.49) (Hanselman et al. 5 ). The log-scale mean re- 
cruitment was 6.23 (SD 0.70) for walleye pollock, the 
mean was slightly larger than the assessment mean of 
6.0, and the SD was smaller from the assessment value 
of 0.92 from 1980 to 2011 (Dorn et al. 6 ). 
For each process error replicate of recruitment, ob- 
servation error was then generated in age composition 
