Jacobson et a! : Depth distributions and time-varying selectivities for various bottom fishes 
321 
Table 6 (continued) 
Total length (cm) 
Depth intervals (fin) 
100-199 
200-299 
300-399 
400-499 
500-599 
600-699 
Depth distributions (females) 
20 
0.5897 
0.4066 
0.0037 
0.0000 
0.0000 
0.0000 
22 
0.6982 
0.2988 
0.0030 
0.0000 
0.0000 
0.0000 
24 
0.5842 
0.4119 
0.0016 
0.0022 
0.0000 
0.0000 
26 
0.5609 
0.4304 
0.0068 
0.0019 
0.0000 
0.0000 
28 
0.5189 
0.4687 
0.0100 
0.0025 
0.0000 
0.0000 
30 
0.4331 
0.5347 
0.0248 
0.0075 
0.0000 
0.0000 
32 
0.4580 
0.4632 
0.0549 
0.0217 
0.0020 
0.0002 
34 
0.3635 
0.4930 
0.0967 
0.0375 
0.0079 
0.0015 
36 
0.3025 
0.4605 
0.1421 
0.0670 
0.0241 
0.0038 
38 
0.2540 
0.3860 
0.1811 
0.1006 
0.0550 
0.0235 
40 
0.1294 
0.2488 
0.2352 
0.1598 
0.1578 
0.0691 
42 
0.0800 
0.1455 
0.2052 
0.1784 
0.1934 
0.1975 
44 
0.0580 
0.1481 
0.1680 
0.1662 
0.2185 
0.2412 
CV (females) 
20 
0.27 
0.40 
0.74 
— 
— 
— 
22 
0.18 
0.41 
1.00 
— 
— 
— 
24 
0 17 
0.25 
0.65 
0.80 
— 
— 
26 
0.15 
0.19 
0.49 
0.64 
— 
— 
28 
0.13 
0.13 
0.71 
0.35 
— 
— 
30 
0.19 
0.16 
0.40 
0.32 
— 
— 
32 
0.15 
0.14 
0.25 
0.22 
0.60 
1.00 
34 
0.19 
0.16 
0.32 
0.26 
0.48 
0.73 
36 
0.19 
0.14 
0.27 
0.24 
0.37 
0.73 
38 
0.20 
0.17 
0.21 
0.19 
0.23 
0.32 
40 
0.31 
0.14 
0.15 
0.19 
0.39 
0.24 
42 
0.26 
0.13 
0.15 
0.14 
0.25 
0.20 
44 
0.30 
0.20 
0.10 
0.14 
0.20 
0.14 
sion (see below for a discussion of possible bias). A simple ap- 
proach to measuring precision would be to fit smooth lines to 
the estimates and calculate variation of the residuals. Vari- 
ances might also be computed analytically, on the variance 
of depth distributions, or by bootstrapping (Efron, 1982). 
Depth distributions and commercial bottom trawl se- 
lectivities could be estimated from surveys with different 
types of survey bottom trawls because the selectivity of 
the survey gear cancels out in estimation of depth distri- 
butions for the population. It is important, however, not 
to simply pool survey data collected with different types 
of trawls. Estimates of depth distribution from individual 
surveys s p(cl \ L) should be averaged or combined instead. 
Our methods could be used to calculate depth distribu- 
tions and commercial bottom trawl selectivities as a func- 
tion of age if sufficient age data from bottom trawl surveys 
were available. In fact, the approach could be extended to 
include both length and age simultaneously. This proce- 
dure might be useful for species such as sablefish, where 
the relationship between age, length, and depth is complex 
(Norris, 1997; Methot et al., 1998). In the absence of sur- 
vey age data, an inverted von Bertalanffy growth model 
could be used to convert selectivities for commercial fish- 
ing based on length to selectivities based on age. 
Our approach to estimating fishery selectivities com- 
plements traditional approaches using stock assessment 
models because our assumptions were different. In partic- 
ular, our approach did not involve assumptions about re- 
lationships between fish size and natural mortality that 
were made either implicitly (natural mortality assumed 
constant for all size groups) or explicitly (e.g. Tagart, et 
ah, 1997) in most stock assessment models. As described 
above, size-dependent natural mortality rates and size-de- 
pendent fishery selectivities tended to be confounded in 
fishery length-composition or age-composition data (e.g. 
Tagart et ah, 1997). It is possible that estimates of fishery 
selectivity for commercial bottom trawls might be useful in 
stock assessment models as a basis for estimating trends in 
length-specific natural mortality. Another approach would 
be to use estimates of fishery selectivity from our method 
