FISHERY BULLETIN: VOL. 84, NO. 2 



schools off the transect plane Quinn (1979) and 

 Burnham et al. (1980) showed that this model is 

 robust and flexible and provides the best fit to the 

 detection function in most applications. This esti- 

 mator, at zero distance, is 



1(0) 



= ^ + £ 



w 



k=\ 



% 



where w* = truncation width, or the effective limit 

 of the range of detection, beyond 

 which all observations are discarded 

 and 



<*fc 



nw 



Z. COS 



1=1 



knX; 



w 



(Burnham et al. 1980) 



where n = number of schools observed 



x { = perpendicular distance off transect 



for the i th school 

 k = term number = 1,2,3,. . .m [The num- 

 ber of terms (m) is determined by a 

 stopping rule in the computer pro- 

 gram TRANSECT]. 



TRANSECT also computes the school abundance 

 estimate D and its variance which is estimated by 

 the equation: 



var 0) = (Df 



var (n) var [/"(0)] 



n c 



Lf(0)] 2 



Dimensions measured directly included depth of 

 school from the surface, distance off bottom, width, 

 thickness, radial distance from vessel, and bearing 

 to the right or left of a vertical line below the vessel 

 (Fig. 10). The perpendicular distance of the school 

 from the vertical plane of the vessel's path ("distance 

 off transect") was calculated from the radial distance 

 and bearing. All distances were measured or cal- 

 culated to the apparent geometric center of each 

 school (Burnham et al. 1980). The length of each 

 school was calculated from the product of vessel 

 speed and the duration that the school was being 

 detected by the sonar, and was corrected to account 

 for the variable sonar beam width parallel to the 

 vessel's path due to depth. 



The biomass of individual schools was estimated 

 by the formula 



h % = ti l { w % di 



where b t = estimated biomass of school i 



t { = average thickness of school i, top to 



bottom (echo sounder data) 

 l { = length of school i, parallel to transect 



(sonar data) 

 w { = average width of school i perpendicular 



to transect plane (sonar data) 

 d i = mean integration density for school i 

 (g/m 3 ) assuming a target strength of 

 -35 dB/kg (see footnote 9) (echo 

 sounder data). 



The mean school biomass (MSB) was estimated from 

 the individual school biomass estimates; its variance 

 was determined from 



Mean school biomass estimates were derived from 

 density information (from echo sounder data), school 

 dimension information (from sonar data), and an 

 assumed target strength of -35 dB/kg. These esti- 

 mates were used in the line transect and line inter- 

 cept analyses. All information on schools detected 

 by the hydroacoustic systems was edited to discrim- 

 inate widow rockfish from other species using judg- 

 ments based on school form, density, location, and 

 test trawl records. Data on each school identified as 

 widow rockfish were then integrated to obtain mean 

 within-school density. The CRT display of the sec- 

 tor scanning sonar provided representations of the 

 size, shape, and position of fish schools within its 

 range of detection. The dimensions of all schools 

 identified as widow rockfish were measured on the 

 screen of a video monitor using the slow motion and 

 freezeframe features of the video recorder-player. 



" (b, - MSB) 2 



var (MSB) = 2. — 



v ; i-i N(N-1) 



where N = number of schools averaged for MSB. 



Total biomass estimates from the line transect and 

 line intercept methods were calculated for each 

 survey area using the formula 



B = AD (MSB) 



where B = estimated total biomass for the survey 

 area, and 

 A = total area (km 2 ) of the survey area. 



The variance of these estimates was determined 

 from 



300 



