328 
Fishery Bulletin 115(3) 
Table 1 
Total mean length and age-composition sample sizes per survey and total number of ages sampled combined across years 
from the NOAA Alaska Fisheries Science Center bottom trawl surveys for the Gulf of Alaska (GOA, 1984-2011), Aleutian 
Islands (AI, 1980-2010), and Bering Sea (BS, 1982-2011) for the species investigated for this study. The “T used between 
Rougheye and blackspotted rockfish denotes that these species are assessed as a complex rather than individual species. 
Species: common name (scientific name, acronym) 
Region 
Mean 
sample size 
for length 
Mean 
sample size 
M for ages 
Total 
sample size 
for ages 
Flatfish 
Alaska plaice ( Pleuronectes quadrituberculatus, AP) 
BS 
11,934 
347 
5800 
Flathead sole ( Hippoglossoides elassodon, FS) 
BS 
17,354 
458 
7997 
Northern rock sole ( Lepidopsetta polyxystra, NRS) 
BS 
34,045 
441 
6751 
Yellowfin sole ( Limanda aspera, YS) 
BS 
32,025 
707 
20,539 
Arrowtooth flounder ( Atheresthes stomias, AF) 
GOA 
61,142 
924 
9244 
Dover sole ( Microstomus pacificus, DS) 
GOA 
7064 
404 
4642 
Flathead sole ( H . elassodon, FS) 
GOA 
21,364 
572 
5723 
Northern rock sole ( Lepidopsetta polyxystra, NRS) 
GOA 
8337 
434 
3474 
Rex sole ( Glyptocephalus zachirus, RS) 
GOA 
15,687 
423 
4563 
Rock sole (L. bilineata, SRS) 
GOA 
10,136 
455 
3638 
Rockfish 
Northern rockfish (Sebastes polyspinis, NR) 
AI 
7405 
483 
4990 
Pacific ocean perch (S. alutus, POP) 
AI 
19,878 
1068 
10,876 
Rougheye/blackspotted rockfish (S. aleutianus / melanostictus, RB) 
AI 
1701 
428 
3611 
Light dusky rockfish ( S . variabilis, LDR) 
GOA 
1883 
385 
4191 
Northern rockfish (S. polyspinis, NR) 
GOA 
4195 
413 
4521 
Pacific ocean perch (S. alutus, POP) 
GOA 
19,658 
1119 
11,511 
Rougheye/blackspotted rockfish ( S . aleutianus / melanostictus, RB) 
GOA 
3950 
516 
5279 
Roundfish 
Atka mackerel ( Pleurogrammus monopterygius, AM) 
AI 
9187 
598 
6068 
Walleye pollock ( Gadus chalcogrammus, WP) 
AI 
16,087 
1280 
12,498 
Pacific cod ( Gadus macrocephalus, PC) 
BS 
12,241 
883 
21,731 
Walleye pollock (G. chalcogrammus, WP) 
BS 
106,317 
1455 
42,078 
Pacific cod (G. macrocephalus, PC) 
GOA 
12,138 
607 
6676 
Walleye pollock (G.s chalcogrammus, WP) 
GOA 
31,387 
1428 
17,139 
second stage sample and 2 are investigated here: pro- 
portional allocation (selecting samples proportional to 
the length distribution) and fixed allocation (a fixed 
number of samples from each length class). The method 
outlined in Quinn and Deriso (1999) allows estimation 
of minimum sample sizes necessary to achieve a target 
level of precision (on the basis of a specified coefficient 
of variation [CV]) for all ages in the age composition 
data. The primary components used to estimate sample 
size is the estimated proportion-at-age (0 a ), the within- 
length interval variance component of the estimated 
proportion-at-age ( F a for fixed allocation, V a for pro- 
portional allocation) and the between-length interval 
variance component of the estimated proportion-at-age 
( B a ). In simple terms, one can think of within-length 
interval variance as the variability of ages within a 
given length bin (or, the number of ages represented 
for a given length) and between-length interval vari- 
ance as the variability in length bins within a given 
age (or, the number of lengths represented for a given 
age). From Quinn and Deriso (1999) an unbiased esti- 
mator under 2-stage random sampling is represented 
by the following equation: 
6 a ,y — £z=l„ . .,J <\y ' 01, a, y > ( 1 ) 
where & ly = the observed proportion of fish at length 
l in year y (the number of observations 
at length l divided by the total number of 
length observations); and 
B, a y = the observed proportion of fish of length l 
and age a in year y (the number of age 
observations at length l and age a divid- 
ed by the number of age observations at 
length l ). 
The within-length interval variance for fixed allocation 
sampling (F a y ) is defined as 
^^S|=i,">fA a , y (l-Vy)- (2) 
where J = the total number of length intervals; and 
a l y and 0j a y are as defined above. 
For proportional allocation, the within-length interval 
variance (V ay ) is defined by Quinn and Deriso (1999) 
as: 
a 1)y 0 1)a>y (1 - 0 1>a , y )• (3) 
