Jacobson et al : Depth distributions and time-varying selectivity for various bottom fishes 
311 
Figure 1 
(A-C): study areas, 100-199, 200-299, 300-399, 400-499, 500-599, and 600-699 fm 
depth contours, and location of National Marine Fisheries Service bottom trawl survey 
tows used to estimate gear selectivities in the commercial bottom trawl fishery. Letters 
A-H are map symbols defined in Table 3 that identify locations of tows from different 
bottom trawl surveys. 
Depth distributions 
All calculations were based on fish length (two centimeter 
length groups), rather than fish age, because insufficient 
survey age data (see below ) were available. The smallest and 
largest length groups in our analysis were “plus” groups. For 
example, a plus group of 20 cm at the low end of length com- 
position would include fish 20 cm FL and smaller. We chose 
the largest and smallest length groups to use the widest pos- 
sible range in lengths and to achieve reasonable precision 
and smoothness in commercial bottom trawl selectivity and 
depth distribution estimates for large and small fish. 
For each species, depth distributions in the total popu- 
lation were estimated by conditional probabilities *p(cl \L) 
which gave the odds, based on data from bottom trawl sur- 
vey s, of finding a fish of length L at depth cl in the popula- 
tion (Jacobson and Hunter, 1993). Following Jacobson and 
Hunter (1993), we used Bayes’s theorem and data from a 
single bottom trawl survey in the estimator: 
^ i r > _ P s (L,d) _ p s (L | d) p s (d) 
pKCl Lj) — — 
where the joint probability distribution pjL,d) gives the 
probability that a randomly selected fish taken in bottom 
trawl survey s was length L and from depth stratum cl. 
PjL) is the probability that a randomly selected fish taken 
in the survey was length L. Other terms are defined below. 
It is important to note that s p(d\L) refers to an esti- 
mate for the total population based on data from survey 
s (leading superscript notation), and terms on the right- 
hand side of the equation refer to the portion of the popu- 
lation selected by the gear used for survey s (trailing sub- 
script notation). The total and surveyed populations differ 
because survey bottom trawls tend to select fish of cer- 
tain size or ages and, depending on a variety of conditions, 
length composition data from survey catches will differ 
