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Fishery Bulletin 99(2) 
aging depth distributions was reasonable because effects 
of survey bottom trawl selectivities (that may have dif- 
fered because of area or year) were removed. Uncertainty 
in depth distributions was measured with coefficients of 
variation (CV) for average depth distributions from stan- 
dard formulas for weighted means (see “Discussion” sec- 
tion for other approaches). 
Fishery selectivities for commercial bottom trawls 
The catch equation (C=FiV, Ricker, 1975) holds for each 
depth stratum. Consequently, total catch by the fishery is 
the sum of catches in all depth strata 
c,L (7) 
d 
where F vd = a year- and depth-specific instantaneous 
fishing mortality rate multiplier; 
V L = length-specific vulnerability to commercial 
bottom trawl gear (the probability that a fish 
in the path of the fishing gear is captured); 
and 
N , L = average abundance during year y. 
Vulnerabilities, like selectivities, were scaled to a maxi- 
mum of one. Thus, the fishing mortality rate in a depth 
stratum for length groups fully vulnerable to the gear 
( V f = 1 ) is F yd and the corresponding rate for other length 
groups is F y d V L . 
Depth-specific fishing mortality rates F yd are related to 
nominal fishing effort at depth divided by the area of the 
depth stratum: 
where E d = nominal effort (hours towed) for bottom 
trawls in depth stratum cl during year y; 
and 
c = a constant proportional to average area swept 
per unit time (Paloheimo and Dickie, 1964). 
Depth-specific fishing mortality {F v d ) is inversely propor- 
tional to stratum area (A (/ ) because the fraction of the 
stock harvested after an hour of fishing in a small area 
will be larger than the fraction harvested after an hour of 
fishing in a large area (Jacobson and Hunter, 1993). 
Vulnerabilities (V L ) measure the probability of capture 
for a fish of length L given that the fish is in the path of 
the trawl. For this study, we calculated vulnerabilities us- 
ing the logistic function based on length: 
( L \ (9) 
, 7 , =21og,.(3)[L--^j, 
so that 
e' h 
y = —1 , 
1 l +e », (10) 
and L 50 = the length at which vulnerability is 50%. R is the 
difference between the predicted lengths at V 7 =75% and 
Table 4 
Parameter estimates from Perez-Comas (1996) and Perez- 
Comas 7 for logistic vulnerability models. All estimates 
are from alternate haul experiments and for commercial 
bottom trawls with 4V2-inch diamond mesh codends fished 
from commercial trawlers in the west coast groundfish 
fishery off northern California, Oregon, and Washington 
(34°40'N-48°30'N and east of 126°W) during 1988-90. L 50 
is the length at which vulnerability is 50% and R is the 
difference between the predicted lengths at 75% and 25% 
vulnerability. SE is the estimated standard error for a 
statistic. Parameter estimates for shortspine thornyhead 
were also used for longspine thornyhead. 
^50 
(cm) 
SE 
(cm) 
R 
(cm) 
SE 
(cm) 
Dover sole 
33.8 
1.01 
3.96 
1.22 
Shortspine thornyhead 
30.1 
1.90 
9.81 
1.85 
Sablefish 
33.6 
2.43 
8.53 
2.36 
1 Perez-Comas, J. A. 1998. Personal commun. Columbia Basin 
Research, School of Fisheries, Univ. Washington, Puget Sound 
Building, 1325 Fourth Ave., Seattle, WA 98101. 
V l = 25% for commercial bottom trawls with 4V2-inch mesh 
codends (i.e. L 75 -L 25 in Perez-Comas, 1996). Four and one- 
half inch mesh is the current legal minimum in bottom 
trawls along the west coast. We rescaled values from Equa- 
tion 10 so that the largest value was one. 
For Dover sole and shortspine thornyhead, we used spe- 
cies-specific vulnerability parameter estimates (Table 4) 
from Perez-Comas (1996). For sablefish, we used unpub- 
lished estimates (Perez-Comas 2 * * ) estimated in the same 
manner. Perez-Comas’s estimates were from paired bottom 
trawl experiments. The experiments measured vulnerabil- 
ity of fish of different sizes in commercial bottom trawls in 
relation to vulnerability in bottom trawls with 3-inch (be- 
tween knots) mesh codends as a reference standard (see 
“Results” and “Discussion” sections for information about 
possible bias due to escapement of small fish from commer- 
cial bottom trawls with 3-inch mesh codends). 
We assumed that vulnerability estimates for longspine 
thornyhead were the same as for shortspine thornyhead 
because no other information was available for longspine 
thornyhead. The two species are similar in shape and their 
size ranges overlap (shortspine thornyhead grow larger), 
but their depth distributions differ (Jacobson and Vetter, 
1995). 
Given vulnerabilities at length for commercial bottom 
trawls, an expression for commercial fishery selectivities 
at length can be derived because p(d\L) N vL = N vd i, 
where p(d \L) is for the total population computed as the 
average of s p(d\L) from each of the surveys. Substituting 
2 Perez-Comas, J. A. 1998. Personal commun. Columbia Basin 
Research, School of Fisheries, Univ. Washington, Puget Sound 
Plaza Building, 1325 Fourth Ave., Seattle, WA, 98101. 
