314 
Fishery Bulletin 99(2) 
Table 1 
Depth stratum area (in 1000 km 2 ), percentage of total area, and nominal fishing effort (h/yr) by depth stratum for bottom trawls 
in the northern subarea (43°00'N-48°30'N) during 1978-96. Nominal fishing effort was calculated from Oregon and Washington 
bottom trawl logbook data as total hours trawled for trips catching any thornyheads, Dover sole, or sablefish. 
Depth (fm) 
Year 
100-199 
Area 5.213 
% total area 24 
200-299 
4.159 
19 
300-399 
3.131 
15 
400-499 
2.970 
14 
500-599 
3.055 
14 
600-699 
2.925 
14 
1978 
4224 
1059 
269 
6 
0 
0 
1979 
4808 
2991 
1744 
117 
0 
0 
1980 
1910 
1277 
811 
46 
5 
0 
1981 
3669 
1725 
1215 
118 
0 
0 
1982 
6955 
5172 
2252 
263 
16 
0 
1983 
5942 
4211 
2089 
354 
23 
0 
1984 
4845 
4542 
2026 
235 
0 
0 
1985 
9086 
6568 
3017 
1224 
14 
0 
1986 
6541 
5680 
1934 
237 
0 
0 
1987 
9083 
7639 
2864 
425 
0 
0 
1988 
12,762 
12,874 
5293 
706 
31 
6 
1989 
15,125 
17,458 
7609 
1792 
1793 
45 
1990 
13,820 
14,070 
8571 
7020 
4674 
314 
1991 
19,346 
20,148 
13,346 
7547 
2976 
221 
1992 
15,063 
15,191 
12,977 
12,233 
5467 
595 
1993 
22,571 
20,027 
14,144 
13,202 
10,498 
2262 
1994 
13,531 
13,569 
10,239 
12,773 
10,531 
1634 
1995 
13,318 
10,225 
8502 
11,117 
15,580 
2578 
1996 
13,539 
10,867 
8745 
9831 
12,831 
1673 
tom trawl survey gear selectivity cancels out. To prove this 
important point algebraically, note that 
and 
p{L,d) 
Id (L,d)<J sL 
V V n (L,d)a s L 
p s (L) 
T1 ( L ) (7 L 
XX ]Uh - d)(y L 
(I L 
(5) 
( 6 ) 
where y ri(L,d) = the joint probability of depth and length 
in the total population when the bottom 
trawl survey was carried out; 
s n(L) = the marginal probability distribution for 
length in the total population; and 
a s ! = the length specific selectivity for the 
survey bottom trawl gear (assumed the 
same in all depth strata, see “Discus- 
sion" section). 
Use Equation 1, substitute terms from Equations 5 and 
6, and simplify to get S p(c/|L) = *n(L,d)/ s n(L) = d1(d\L), 
where fl(d \L) is for depth distributions in the total popu- 
lation. This proof shows that selectivities (Oj ) for bottom 
trawl survey gear cancel out, and that length-specific 
depth distributions s p(d\L) from Equation 1, based on 
bottom trawl survey data, are algebraically equivalent to 
length-specific depth distributions in the total population 
s ll(d | L). Of course, depth distributions are statistics that 
include uncertainty (measured by CVs in our analysis) 
due to survey data measurement errors and natural vari- 
ability in survey selectivities (particularly natural vari- 
ability that depends on depth). 
Effects of survey gear selectivity on depth distribution 
estimates can be understood intuitively. Consider a hypo- 
thetical bottom trawl survey in our study area designed to 
measure abundance of a fish stock that consists of a single, 
1-cm length group. As long as the selectivity of the survey 
bottom trawl was the same in each depth interval, the sur- 
vey would measure the relative abundance of the length 
group in each depth stratum (N d ) and the relative abun- 
dance in the whole study area N = X A ' ■ The depth distribu- 
tion for the hypothetical stock could be computed simply 
as s p(d | L)=N d /N and the selectivity of the survey bottom 
trawl would not matter. 
We averaged depth distributions estimated from differ- 
ent bottom trawl surveys s p(d \ L) to use all available infor- 
mation. Preliminary results showed that survey-specific 
depth distributions were similar but relatively noisy. Aver- 
