164 
Fishery Bulletin 95(1), 1997 
where, P t = estimated population (millions) of fish 
in length group l; l u and l low = length (mm) at upper 
and lower limits of^ the mode, which are so defined 
that l u and l /ow are the length groups at which abun- 
dance fms declined to half that at the modal size (Fig. 
2). If length is normally distributed, l~N( l , s 2 ), the 
population within the upper and lower limits of the 
mode so defined would account for about 75% of the 
total population of that cohort (Shi, 1994). 
Date The dates used in growth and mortality esti- 
mation were also population-weighted means. The 
dates when the samples were taken cannot be used 
directly in growth and mortality estimation without 
being standardized. Estuarine samples had to be 
taken during low low tide (LLT) periods, and we were 
often forced to take estuarine samples at unequal 
time intervals. 
We made every effort to carry out the monthly 
nearshore surveys during the intervals between the 
Grays Harbor and Willapa Bay surveys, but they 
sometimes had to be done either before or after the 
estuarine trips owing to logistic difficulties. This 
made the time between the first and last surveys for 
a given month more than a half-month apart. The 
population-weighted mean date (PWMD) was cho- 
sen to standardize the “date” of monthly surveys and 
is the best estimate of the average sampling date for 
the total population in our study area. The PWMD 
was computed from 
3 
X P 'Jm d(lte ‘J 
PWMD jm = -^h-g , (2) 
y p 
;=i 
where, PWMD /m = population-weighted mean date 
in month j (May, June, July, August, and Septem- 
ber) for mode m (1 or 2); P = population of mode m 
in system i (GH, WB, NS), month j; dateij = mean 
date of a survey carried out in month j and system i, 
i.e. number of days from 1 May. 
Temperature A population-weighted mean bottom 
temperature (PWMBT) was developed in this study 
because of extensive seasonal ontogenetic migrations 
«/->0»o©‘r>0*no*nou-)©v>©»''}Ow">Qio©‘n©«o©*n©»/->© 
Length (mm) 
Figure 2 
A diagram illustrating how the upper (/ ) and lower (l low ) limits of a mode were determined. P m is the 
estimated modal population and P low , P up are the estimated population of the lower and upper limits of the 
mode. 
