Jacobson et al.: Depth distributions and time-varying selectivities for various bottom fishes 
313 
The marginal distribution pjd) gives the proportion of 
the surveyed population (all sizes and ages) in depth stra- 
tum d based on data from the bottom trawl survey: 
The length distribution of the surveyed population pjL) 
was calculated by summing the joint distribution for depth 
and length across depth strata: 
pSd) 
P 
s ( Zy ) - ^ p s (L,d). 
( 4 ) 
where W s _ rf = the average (weighted by area swept) catch 
rate in stratum d\ and 
A s :l = the total area (km 2 ) of the survey stratum. 
Data collected from the surveyed population on the 
right-hand side of Equation 1 can be used to estimate 
depth distributions for the total population because bot- 
