Hulson et al. : Distribution of sampling effort for age composition of multiple species 
327 
on the uncertainty of estimates determined from SCAA 
models. This is, however, a different investigation than 
the application of sample size within an SCAA model, 
or, the idea of effective sample size. The topic of effec- 
tive sample size and the use of age or length composi- 
tion data within stock assessments has received exten- 
sive attention in recent years (Francis, 2011; Maunder, 
2011). This study is also a different investigation from 
that of optimizing the number of hauls from which 
age-composition samples are obtained (Pennington et 
al., 2002; Hulson et al., 2011). While effective sample 
size is certainly related to the precision and accuracy 
that results from an SCAA model (Hulson et al., 2012) 
and determining the number of tows to sample is an 
important practical consideration (Pennington and Vpl- 
stad, 1994), here we are interested in how to distribute 
age-composition sample sizes across species before the 
data are input in a stock assessment model and after 
decisions have been made on the number of samples 
within a tow. 
We followed a 2-step procedure to address the 2 
topics presented in the preceding paragraphs: 1) how 
to distribute age-composition sample sizes across spe- 
cies on a statistical or biological basis, and 2) what 
is the effect on SCAA model uncertainty for species 
with different life histories by increasing or decreas- 
ing age-composition sample size. In the first step we 
used methods derived from sampling theory to deter- 
mine the minimum sample sizes necessary to achieve 
certain sampling goals for multiple species (Quinn 
and Deriso, 1999). Using this statistical procedure, 
we then attempted to relate these sample sizes to 
life-history characteristics of the species investigated 
to explore whether there exists a biological basis for 
distribution of sample size across multiple species. 
In the second step we used simulation to isolate and 
evaluate the influence of sample sizes that determine 
age composition from fishery-independent sources on 
resulting uncertainty in estimates from SCAA mod- 
els. The simulation analysis was applied to 3 species 
types with different life-history and survey character- 
istics to evaluate how age-composition sample size, in 
combination with survey index uncertainty, influenced 
SCAA model results and if this influence is dispro- 
portionate among different species type life histories. 
In addition to exploring these 2 topics the underlying 
goal of the research of this study is to provide prelimi- 
nary guidance for prioritizing the distribution of sam- 
ple size for age composition across multiple species, 
which has not been previously attempted or provided 
in fisheries research. 
Materials and method 
Step 1 : distribution of sample sizes to determine age 
composition across multiple species 
Age and length observations from fishery-independent 
bottom trawl surveys conducted by the AFSC in the 
Gulf of Alaska (GOA), Aleutian Islands (Al), and Ber- 
ing Sea (BS) were used to evaluate the distribution 
of sample sizes needed to determine age composition 
(henceforth, the term “age sample sizes”). These sur- 
veys provided an excellent opportunity to evaluate 
sample sizes for age composition because of the longev- 
ity of the surveys and the number of different species 
sampled for ages. Data (AFSC bottom trawl surveys, 
website) were used from trawl surveys conducted in 
the GOA from 1984 to 2011 (triennially from 1984 to 
1999 then biennially from 2001 to 2011, e.g., Raring et 
al., 2011), in the Al from 1980 to 2010 (triennially from 
1980 to 1986 and from 1991 to 1997, then biennially 
from 2000 to 2006 and 2010 on, e.g., von Szalay et al., 
2011), and in the BS from 1982 to 2011 (annually; e.g., 
Lauth and Conner, 2014). In the interest of brevity we 
refer to von Szalay et al. (2011) for a detailed descrip- 
tion of how the survey index and age-length composi- 
tions are estimated from the surveys. Our interest was 
the distribution of age-composition sample sizes across 
species before indices are estimated; therefore the de- 
tails concerning the indices are not provided here. 
Species included were those for which the number of 
aged otoliths were greater than 3000 across the time 
series of the trawl surveys. Within a given haul, the 
majority of species are sampled for ages with 2-stage 
sampling: 1) with a fixed allocation method, and 2) 
the remainder of species sampled with simple ran- 
dom sampling (SRS). Species were categorized into 3 
types that included ‘flatfish,’ ‘rockfish,’ and ‘roundfish’ 
(Table 1). Including rougheye ( Sebastes aleutianus) and 
blackspotted ( Sebastes melanostictus ) rockfish, which 
are assessed as a complex and considered a ‘single spe- 
cies’ in the context of this study (Spencer and Rooper 2 ; 
Shotwell et al. 3 ), there were 15 species and 23 stocks 
investigated across all areas, including 10 flatfish, 7 
rockfish, and 6 roundfish stocks. Otoliths that were 
read by both a ‘reader’ and a ‘tester’ were also collected 
for each of these species to evaluate the influence of ag- 
ing error on estimates of age-composition sample size. 
We estimated sample sizes for age composition fol- 
lowing the method for 2-stage sampling outlined in 
Quinn and Deriso (1999, chapter 8). In the first stage 
of sampling a subsample of fish from the total catch 
is taken to obtain lengths (either total or fork length 
depending on the species) and in the second stage of 
sampling a subset of these fish are then sampled for 
age determination within each predetermined length 
bin. There are several methods proposed to obtain the 
2 Spencer, P. D., and C. N. Rooper. 2014. Assessment of the 
blackspotted and rougheye rockfish stock complex in the Ber- 
ing Sea/Aleutian Islands. In Stock assessment and fishery 
evaluation report for the groundfish resources of the Bering 
Sea/Aleutian Islands regions. North Pacific Management 
Council, Anchorage, AK. [Available from website.] 
3 Shotwell, S. K., D. H. Hanselman, J. Heifetz, and P.-J. F. Hul- 
son. 2015. Assessment of the rougheye and blackspotted 
rockfish stock complex in the Gulf of Alaska. In Stock As- 
sessment and fishery evaluation report for the groundfish 
resources of the Gulf of Alaska. North Pacific Management 
Council, Anchorage, AK. [Available from website.] 
