WILKINS: ABUNDANCE OF WIDOW ROCKFISH 



The same procedures were used as in 1980 except 

 that nearly all operations were conducted after dark 

 and no mapping runs were made to define the 

 bounds of school groups. A diel variability study was 

 conducted on 20 March 1981 between the hours of 

 0153 and 1037, consisting of 13 replicates of track- 

 line 21. 



The conventional analysis of echo sounder data (in- 

 tegration) is based on the principle that the acoustic 

 intensity of a signal reflected from fish targets is pro- 

 portional to the density of fish in the region irradi- 

 ated by the echo sounder. Detailed descriptions of 

 the technique can be found in Moose and Ehrenberg 

 (1971), Forbes and Naaken (1972), and Thorne 

 (1977). During the 1980 and 1981 surveys, density 

 estimates from this method were obtained by aver- 

 aging returning acoustic signals over a series of 

 transmissions (25 transmissions over 12.5 s during 

 the Muir Milach cruise and 40 transmissions over 

 50 s during the Alaska and Chapman cruises). These 

 averages were then converted from relative to ab- 

 solute densities (kg/m 2 ) for various depth intervals 

 using calibration data and a scaling factor based on 

 an average target strength of -35 dB/kg. 9 Absolute 

 abundance (biomass) was estimated by extrapolating 

 absolute density estimates to the survey area. 



Each survey area was systematically transected 

 using the echo sounder and sonar to search for fish 

 schools and, thereby, to derive line intercept and line 

 transect estimates of school abundance (schools/ 

 km 2 ). Data on school dimensions and density were 

 collected from those schools sighted. With the line 

 intercept method, only the presence of a school (as 

 detected by the echo sounder) and its width were 

 used to estimate school abundance. This technique 

 is based on the theory that, for systematically 

 located transects, the probability of intersecting 

 school i equals wJW, where w^ is the width of 

 school i and W is the distance between adjacent 

 transects. The number of schools per unit area {D) 

 can then be estimated by 



0-1 



y-i wjL 



(Seber 1980) 



where n 



Wi 



number of schools measured on a 



transect of length L 

 width of j th school. 



9 The target strength value used in these analyses (-35 db/kg) 

 was not derived during work on widow rockfish. Since accurate 

 target strength estimation was not necessary for evaluating the 

 utility of the methodology, we used a value which had been esti- 

 mated for Pacific whiting (Dark et al. 1980) which has a similar 

 scattering cross section. 



The line intercept method was applied only to data 

 collected from the nonrandom run made on the night 

 of 27-28 March 1980. The data from this line were 

 subdivided into two artificial transects of unequal 

 length and the jackknife method (Seber 1980) was 

 used to estimate D and its variance. This technique 

 is described fully by Gunderson et al. (fn. 8). 



Line transect theory is based on the premise that 

 the probability of sighting a given object (or school) 

 is a function of its perpendicular distance from the 

 transect. A "detection function" is derived from 

 school sighting data which relates the probability of 

 a school being sighted to its distance from the 

 transect. This function is used to expand the number 

 of schools actually sighted to obtain an estimate of 

 school abundance. The advantage of this method is 

 that not all schools within sighting range need to 

 be detected in order to estimate the number of 

 schools in the area. 



Using line transect estimation, the school abun- 

 dance (schools per unit area) was estimated by 



D = 



nf(0) 

 2L 



n 



L 



/(0) 



where D = estimated number of schools per unit 

 area 



number of schools sighted 



length of transect 



"detection function'— a parameter 

 estimated from probability function 

 for the perpendicular distances off 

 transect of schools sighted. 



The assumptions necessary for the use of this 

 method are 



1) Schools directly on the transect plane will always 

 be sighted. 



2) Schools are sighted in the position they occupied 

 prior to the approach of the vessel, i.e. there is 

 no avoidance of or attraction to the vessel. 



3) Perpendicular distances off transect are mea- 

 sured precisely, particularly near the transect 

 plane 



4) The detection function remains constant. 



The computer program TRANSECT (Laake et al. 

 1979) was used to estimate the probability density 

 function of the perpendicular distance of schools 

 from the transect. The estimator model used is based 

 on a nonparametric Fourier series expansion fit to 

 data sets of observed perpendicular distances of 



299 



